Algebra Readiness (Pre-Algebra) Answer Key · Mathematics: Course 3 CC-2 Pythagorean Proofs (...

Textbook Answer Key

Algebra Readiness (Pre-Algebra)

Answer Key

Mathematics: Course 3 CC-1 Cube Roots (CC6-CC7) Quick Check

1. a. 5 b. 1 c. 8

2. a. x = 6

b. x = 13

c. x = 27

Homework Exercises

1. 10 m 2. 1 cm 3. 9 ft 4. 6 5. 2 6. 4 7. 3 8. 8 9. 7 10. x = 5 11. x = 9

12. x = 16

13. x = 35

14. x = 89

15. x = 710

16. 81000

; 0.2

17. 0.6 18. No; The cube of 0.3 is equal to 0.3 ∙ 0.3 ∙ 0.3 = 0.027. So, 0.3 is the

cube root of 0.027, not 0.27. 19. a. 𝑥2 row: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100; 𝑥3 row: 1, 8, 27, 64,

125, 216, 343, 512, 729, 1,000 b. yes, 1 and 64 c. If x is a perfect square, then 𝑥3 is both a perfect cube and a perfect square

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Mathematics: Course 3 CC-2 Pythagorean Proofs (CC8-CC9) Activity 1

1. yes; 62 + 82 = 102 2. yes 4. (3, 4, 5); (5, 12, 13); (9, 12, 15); (12, 16, 20); (15, 20, 25) 5. Each triangle’s three angle measures should total 180°. 6. If the sides of a triangle satisfy the Pythagorean equation, the

triangle is a right triangle.

Activity 2

1. 𝑐2 2.

The areas are equal.

3. a; b 4. 𝑎2 + 𝑏2 5. 𝑎2 + 𝑏2 = 𝑐2; it is the Pythagorean equation. 6. The area of a square with side length c is equal to the sum of the

area of a square with side length a plus the area of a square with side length b.

Activity 3

1. Since ∆DEF is a right triangle, 𝑎2 + 𝑏2 = 𝑥2 2. Since 𝑎2 + 𝑏2 = 𝑐2 and 𝑎2 + 𝑏2 = 𝑥2, 𝑐2 = 𝑥2. So, c = x. 3. A and D; B and E; C and F. 4. Since F is a right angle and C is congruent to F, C is a right angle.

So, ∆ABC is a right triangle. 5. If the sides a, b, and c of a triangle satisfy the equation

𝑎2 + 𝑏2 = 𝑐2, then the triangle is a right triangle.

Exercises

1. yes; 182 + 242 = 302 2. yes; 72 + 242 = 252 3. no; 132 + 142 ≠ 152 4. yes; 82 + 152 = 172 5. no; 102 + 242 ≠ 252 6. yes; 152 + 362 = 392


Mathematics: Course 3 CC-2 Pythagorean Proofs (CC8-CC9)

7. The angle measures are the same for the 3-4-5 and 6-8-10 triangles, but different for the 5-12-13. Angle measures are the same when side lengths are proportional.

8. The areas of both figures are the same. Subtract the areas of the triangles from both figures. In the first figure, the rest of the area is equal to the sum of the area 𝑎2 of the square whose side is the shorter leg of the triangle and the area 𝑏2 of the square whose side is the longer leg of the triangle. In the second figure, the rest of the area is equal to the area 𝑐2 of the square whose side is the hypotenuse.

9. No, because the Converse of the Pythagorean Theorem. 10. The Pythagorean equation is given as a true statement about

∆ABC. However, it is not given that ∆ABC is a right triangle. It has to be proven that if the sides of ∆ABC satisfy the Pythagorean equation, then ∆ABC is a right triangle.


Mathematics: Course 3 CC-3 Types of Solutions of Linear Equations (CC10-CC11) Quick Check

1. a. no solution; result is 8 = 15, of form a = b b. one solution; result is x = 2, of form x = a c. infinitely many solutions; result is 12 = 12, of form a = a

d. one solution; result is x = 117

, of form x = a

Homework Exercises

1. no solution; result is 8 = 16, of form a = b 2. one solution; result is x = 3, of form x = a 3. infinitely many solutions; result is 9 = 9, of form a = a 4. infinitely many solutions; result is 3 = 3, of form a = a 5. one solution; result is y = 3, of form y = a 6. no solution; result is 1 = 9, of form a = b 7. infinitely many solutions; result is –24 = –24, of form a = a 8. one solution; result is w = –15, of form w = a 9. no solution; result is –6.4 = 6.4, of form a = b 10. infinitely many solutions; result is 2.4 = 2.4, of form a = a 11. one solution; result is s = 28.5, of form x = a

12. no solution; result is – 2 27

= – 59, of form a = b

13. x + 6 = 2 �12𝑥 + 3�; result is 6 = 6, of form a = a; the equation has

infinitely many solutions, so the statement is true for all numbers.

14. 𝑥 + 2 = 3 �13𝑥 + 3�; result is 2 = 18, of form a =b; the equation

has no solution, so the statement is true for no numbers. 15. Sample: 20y + 4 = 4(5y + 1) because the result is 4 = 4 of form a =

a; 20y + 4 = 4(5y + 2) because the result is 4 = 8 of form a = b. 16. a. all values of d

b. d= 3.5 17. Marco could be solving an equation of the form a = a, which has

infinitely many solutions, or he could be solving an equation of the form a = b, which has no solution. The form x = a could not be a solutions because it still has variable.


Mathematics: Course 3 CC-4 Transformations and Congruency (CC12-CC13) Activity 1

1. Figure W’X’Y’Z’ is a reflection of figure WXYZ over the y-axis. Figure W”X”Y”Z” is a translation of figure W’X’Y’Z’ down 7 units.

2. 3 units; 𝑊′𝑋′ and 𝑊′′𝑋′′ 3. Yes; because corresponding line segments are equal: WX = W’X’ =

W”X” = 3; XY = X’Y’ = X”Y” = 4; YZ = Y’Z’ = Y”Z” = 5; ZW = Z’W’ = Z”W” = 2√5

4. Yes; corresponding angle measurements are equal: m∠WXY = m∠W’X’Y’ = m∠W”X”Y” = 90°; m∠XYZ = m∠X’Y’Z’ = m∠X”Y”Z” = 90°; m∠YZW = Y’Z’W’ = Y”Z”W” = 63°; m∠ZWK = Z’W’X’ = Z”W”X” = 117°.

5. Yes. 6. Corresponding sides and angles on the two figures have the same

measures. The reflection and translation that created W”X”Y”Z” did not change the shape or size of WXYZ.

7. a. yes b. yes

Activity 2

1. Reflection over y-axis: A(0, 3) ⟶ A’(0, 3); B(2, 4) ⟶ B’(—2, 4); C(3, 0) ⟶ C’(—3, 0); 90° counterclockwise rotation about the origin: A’(0, 3) ⟶ A”(—3, 0); B’(—2, 4) ⟶ B”(—4, —2); C’(—3, 0) ⟶ C”(0, —3) Translation one unit down: A”(—3, 0) ⟶ A”’(—3, —1) B”(—4, —2) ⟶ B”’(—4, —3) C”(0, —3) ⟶ C”’(0, —4)

2. 𝐴𝐵 ≅ 𝐴′𝐵′ ≅ 𝐴′′𝐵′′ ≅ 𝐴′′′𝐵′′′; 𝐵𝐶 ≅ 𝐵′𝐶′ ≅ 𝐵′′𝐶′′ ≅ 𝐵′′′𝐶′′′; 𝐶𝐴 ≅ 𝐶′𝐴′ ≅ 𝐶′′𝐴′′ ≅ 𝐶′′′𝐴′′′; ∠𝐴 ≅ ∠𝐴′ ≅ ∠𝐴′′ ≅ ∠𝐴′′′; ∠𝐵 ≅ ∠𝐵′ ≅ ∠𝐵′′ ≅ ∠𝐵′′′; ∠𝐶 ≅ ∠𝐶′ ≅∠𝐶′′ ≅ 𝐶′′′.

3. Corresponding sides and angles are congruent.


Mathematics: Course 3 CC-4 Transformations and Congruency (CC12-CC13) Exercises

1. a. Sample: 180° rotation around the origin, then translation 1 unit to the right.

b. 𝑃𝑄 ≅ 𝑃′𝑄′ ≅ 𝑅𝑆 ≅ 𝑅′𝑆′; 𝑃𝑆 ≅ 𝑃′𝑆′ ≅ 𝑅𝑄 ≅ 𝑅′𝑄′; all 8 angles are congruent to each other, since they are all right angles. c. No; all images will be congruent.

2. a. Sample: 270° counterclockwise rotation around the origin, then translation 4 units down. b. Answers will vary. Sample: Translation 4 units down, then 90° clockwise rotation around point L c. No; none of the transformations changed the size and shape of the triangle.


Mathematics: Course 3 CC-5 Transformations and Similarity (CC14-CC15) Activity 1

1. See figure QRST above; parallelogram. 2. See figure Q’R’S’T’ above; yes. 3. See figure Q’’R’’S’’T’’ above; all three figures are similar; the

corresponding angles are congruent. Figures QRST and Q’R’S’T’ are similar because a reflection maintains the size and shape of a figure. Both of these are similar to Q’’R’’S’’T’’ because a dilation changes only the shape of figures.

Activity 2

1. Sample drawing:

2. Sample drawing

∠𝐴 = 109°,∠𝐵 = 43°,∠𝐶 = 28°

3. straight angle or 180° 4. Sample answer: Because the angle measure of a straight line is

180° and the three interior angles of the triangle form a straight line, the sum of the interior angles of the triangle is 180°.

Activity 3

1. m∠B = 65° = m∠R 2. ∆ABC ~ ∆QRP


Mathematics: Course 3 CC-5 Transformations and Similarity (CC14-CC15)

3. No; since the sum of the interior angles is 180°, the third angles must be congruent if the other two angles are congruent.

4. two. 5. If two angles in one triangle are congruent to two angles of

another triangle, then the triangles are similar.

Exercises

1. yes; translation and dilation 2. yes; rotation and dilation 3. ABCD ~ A’’B’’C’’D’’

4. ∆𝐴𝐵𝐶 ~ ∆𝑅𝑆𝑇 5. ∆𝐷𝐸𝐹 ~ ∆𝐽𝐾𝐿 6. No; each figure is similar to all the other figures regardless of

order.


Mathematics: Course 3 CC-6 Using the Pythagorean Theorem with Three-Dimensional Figures (CC16-CC17) Quick Check

1. 1,200 𝑐𝑚2 2. No; the diagonal length is only 13 cm

Homework Exercises

1. 576 𝑐𝑚2 2. 800 𝑖𝑛2 3. about 703 𝑐𝑚2 4. 17 in. 5. ≈ 27 cm 6. ≈ 17 in. 7. 50 in.; surface area; 2,688 𝑖𝑛2; surface area in square feet: 182

3

𝑓𝑡2; cost: $29.68 8. The surface area is 3,480 𝑐𝑚2 or 0.348 𝑚2; the wood costs $1.09. 9. In each case, you’re finding the missing measurement of a right

triangle. 10. a. 21

b. 25


Mathematics: Course 3 CC-7 Exploring Bivariate Data (CC18-CC19) Activity 1

1. hours of practice and baskets scored. 2. Free Throw Contest

No; either variable can go on the horizontal scale as long as the data points are plotted accordingly.

3. The data is clustered between 1 and 4 hours of practice and between 3 and 6 baskets scored.

4. Sample: because the more time a person practices, the more baskets the person will make.

5. The pattern of association is linear; as the hours of practice increase, the number of baskets scored increases.

6. The point at (1, 9) is an outlier that suggests that one participant was good at free throws with very little practice.

Activity 2

1. Charity Game Revenues

The pattern of association is nonlinear.

2. As price increases, the number of tickets decreases.


Mathematics: Course 3 CC-7 Exploring Bivariate Data (CC18-CC19)

3. Yes; the pattern of association changes when the ticket price is $4 because fewer people buy tickets when the price is greater than $4.

Exercises

1. a.

There are two data clusters. b. The weight room; it is used for a greater number of hours overall.

2. a.

The pattern of association is linear.


Mathematics: Course 3 CC-7 Exploring Bivariate Data (CC18-CC19)

b.

Yes; the pattern increases, then decreases.

3. a. The data for Sheila is clustered except for an outlier of 10 points. The data for Vincenza has a strong linear association. b. Sample: Sheila varied in ability each time she played, but Vincenza’s skill did not vary much.


Mathematics: Course 3 CC-8 Modeling Data With Lines (CC20-CC21) Activity 1

1. No, the points are the same. 2. Nancy drew a line through two of the points. 3. Francesca drew a line so that half of the points were above and

half were below 4. Francesca’s; more of the points seem to be about the same

distance from the line. 5. Actual Rate: $7.50, $8.50, $8, $8.50, $10, $9, $10, $10.50;

Predicted Rate: $8, $8.50, $9, $10, $10, $10.50, $11, $11.50; Closeness: $0.50, $0, $1, $1.50, $0, $1.50, $1, $1;

6. $0.8125; the values are an average of about $0.80 away from the line.

7. Actual Rate: $7.50, $8.50, $8, $8.50, $10, $9, $10, $10.50; Predicted Rate: $8, $8.25, $8.50, $9, $9, $9.25, $9.50, $9.75; Closeness: $0.50, $0.25, $0.50, $0.50, $1, $0.25, $0.50, $0.75; The values are about $0.50 away from the line.

8. Francesca’s; it is a closer estimate of the known data points. 9. Sample:

10. Sample: The line has the same number of points above and

below. 11. Check students’ work

Exercises

1. a. Line A; visually it is closer to more of the data points. b. Check students’ work.

2. a. Sample: The fit is not good; there are 6 points above the line and only 1 point below . b. Sample:


Mathematics: Course 3 CC-8 Modeling Data With Lines (CC20-CC21)

With this line, an even number of points are above and below.

3. Sample: Except for the outlier, the association is strongly linear. If the outlier is included when the distances of points from the line are calculated, the resulting line is not a best fit for the rest of the data points.

4. a. Sample: The line of best fit can be drawn so that all data points are close to the line and evenly spaced around it. b. Sample: A set of sample points could be selected to assess the fit of the line. c. Sample: The intercept shows that no education after high school has a salary of about $25k. For every year of education after high school, salary increases about $15k.


Mathematics: Course 3 CC-9 Relative Frequency (CC22-CC23)

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Activity

1. Gender and Movie Type 2.

3. 21 4. Action movie is the most popular movie type because it received

the most votes from moviegoers. 5. 18% 6.

7. 100%; yes, because you will always divide the number in each

category by the total number in all categories. 8.

9. The row total for men represents 100% of the men; the row total

for women represents 100% of the women. 10. No, the relative frequency is the same. 11.

12. Sample: Action movies were much more popular among men

than women, while dramas were almost equally popular with men and women.

Exercises

1. Sample Table


Mathematics: Course 3 CC-9 Relative Frequency (CC22-CC23)

©Pearson Education, Inc.

Yes; 80% of the students who walked did not have music lessons that day.

2. a. Freshman agreed: 432; freshman total: 912; sophomore no opinion: 120; junior disagreed: 216; senior total: 384; total disagree: 768; total total: 2,400. b. Freshmen agreed with the statement. c.

Yes; the student center is slightly more popular among freshman than among seniors. d. Seniors have less interest than freshmen in a student center because they will not benefit from it.

3. Check students’ work.


Mathematics: Course 3 CC-10 Slope and Similar Triangles (CC24-CC25) Activity 1

1. Yes. 2. because they are corresponding angles 3. Yes, they are corresponding angles, which are congruent 4. Yes, the triangles are similar because corresponding angles are

congruent.

5. 68

; 34

; the ratios are equivalent.

6. The ratio of side lengths is equal to the slope. 7. The slopes of the two line segments are equal because the ratios

of the vertical to horizontal lengths are equal. 8. The rise-run ratio between any two points of the line can be

represented by a triangle. All such rise-run ratios will form similar triangles with a ratio of the side lengths equal to m.

Activity 2

1. Yes, all corresponding angles are congruent.

2. 42

= 21

3. The ratios and slope are all equal to 2 4. 2 5. y = mx; check students’ answers. 6. The second triangle is translated three units upward. 7. no 8. 2; 3 9. y = mx + b; the slope of a line is the rate of change of the y-

coordinate divided by the corresponding change in the x-coordinate. The number b represents the value of y when x = 0.


Mathematics: Course 3 CC-11 Graphing Proportional Relationships (CC26-CC27) Activity 1

1. yes, because the ratios of the weight to the cost are the same for all three pricing structures.

2.

3. (0, 0)

4. 32

5. $1.50 per pound; the same as the cost of 1 pound of tomatoes: $1.50 per pound.

6. Slope is equivalent to unit rate. 7. The ratio used to find rate is equivalent to the slope,

Change in 𝑦−coordinateschange in 𝑥−coordinates

, of the line containing the points.

Activity 2

1. 30 miles per hour 2. The speed of train A 3. 45 miles per hour 4. Train B is moving faster. The unit rate for train B (45 miles per

hour) is faster than the unit rate for train A (30 miles per hour). 5. 35 miles per hour 6. The speed of train C is 35 miles per hour, so it is faster than train

A and slower than train B.

Exercises

1. a. The January blizzard; the slope for December is 74 inches per

hour; and the slope for January is 158

inches per hour.

b. 74 inches per hour; 15

8 inches per hour.


Mathematics: Course 3 CC-11 Graphing Proportional Relationships (CC26-CC27)

2. The giant sea kelp plant had a faster growth rate. Compare the

slopes (unit rates) in inches per hour. bamboo: 12; bull kelp: 1

6;

kudzu: 38; giant sea kelp: 5

8

3. Basketball burns more calories per hour (750) than cross-country skiing (660) because 11 calories per minute equals a rate of 660 calories per hour.


Mathematics: Course 3 CC-12 Solving Systems of Equations (CC28-CC31) Quick Check

1. a. infinitely many solutions b. (2, 2) c. no solution

2. a. (0.2, 1.4) b. (2.5, 1.5) c. (1.4, —0.3)

3. a. (2, 4) b. (17, —7) c. (—3, 6)

4. a. no solution b. infinitely many solutions c. (4, 6)

5. 10; $44

Homework Exercises

1. no solution 2. infinitely many solutions 3. (—1, 0) 4. (1.3, 0.4) 5. (3.5, 0.5) 6. (0.7, —3.8) 7. (1, 3) 8. (5, 4) 9. (7, —2) 10. (5, 8) 11. infinitely many solutions 12. no solution 13. 5; $24 14. The lines intersect at (3, 3.5); y = 0.5x + 2 and y = —1.5x + 8. 15. Yes; the lines intersect (2.5, 2). 16. (4, 2); Sample: Multiply the first equation by 3 and the second

equation by 5, and then add to eliminate x. 17. Yes, the boats could meet at (2.4, 2.8). 18. (4, 1); Sample: Use substitution since x – 2y = 2 can be written as

x = 2y +2 in one step. 19. (1, 2); Sample: use elimination since 5x – 2y = 1 can be multiplied

by 2 and added to 2x + 4y = 10 to eliminate the y variable. 20. no solution; Sample: Solve by inspection since both equations are

the expressions 5x – 2y set equal to two different numbers.


Mathematics: Course 3 CC-12 Solving Systems of Equations (CC28-CC31)

21. (3, 3); Sample: Solve by elimination since x can be eliminated by multiplying the second equation by 3 and adding it to the first.

22. (1, —4); Sample answer: Solve by graphing since both lines can be easily graphed and the point of intersection can be easily determined.

23. Infinitely many solutions; Sample: Solve by inspection since the second equation is the first equation multiplied by 4.


Course 3 Solution Key • Chapter 1, page 1

Chapter

1Integers and Algebraic Expressions pages 2–49

CHECK YOUR READINESS page 2

1. 3 , 4, so 0.3 , 0.4; ,. 2. 10.01 5 10.010; 5

3. 0.529 , 0.540, so 0.529 , 0.54; ,. 4. 31 . 27, so 0.031 . 0.027; .. 5. 0.034 1 1.2 5 0.034 1 1.200 5 1.2346. 10.25 2 9.29 5 0.96 7. 8.1 2 0.81 5 8.10 2 0.81 57.29 8. 45.27 1 2.03 5 47.30 5 47.3 9. 4.55 2 2.67 51.88 10. 0.36 1 9.8 5 0.36 1 9.80 5 10.16 11. Theproduct has 2 decimal places, so, since 17 ? 4 5 68, theproduct of 0.17 and 4 is 0.68. 12. The product has 1 1 1,or 2 decimal places, so, since 35 ? 42 5 1470, the productof 3.5 and 4.2 is 14.70, or 14.7. 13. The product has 1 1 1, or 2, decimal places, so, since 16 ? 97 5 1,552, theproduct of 1.6 and 9.7 is 15.52. 14. The product has 2 1 2, or 4, decimal places, so, since 6 ? 23 5 138, theproduct of 0.06 and 0.23 is 0.0138. 15. The product has 1 1 3, or 4, decimal places, so, since 75 ? 3004 5 225,300,the product of 7.5 and 3.004 is 22.5300, or 22.53. 16. Theproduct has 0 1 3, or 3, decimal places, so, since 8 ? 1,064 5 8,512, the product of 8 and 1.064 is 8.512.17. 11.36 4 2 < 12 4 2 5 6, and 1136 4 2 5 568, so 11.36 4 2 5 5.68. 18. 125.3 4 14 < 140 4 14 5 10, and1,253 4 14 5 89.5, so 125.3 4 14 5 8.95. 19. 0.46 4 5 <0.5 4 5 5 0.1, and 46 4 5 5 9.2, so 0.46 4 5 5 0.092.

1-1 Algebraic Expressions and theOrder of Operations pages 4–8

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM 1. 2. 96 3. 10 4. 44.45. 3

Quick Check 1. 15 times the number of hats, 15n

2. 7 2 m 5 7 2 (2) 5 7 2 2 5 5 3. 3x 1 x 4 3 53(12) 1 (12) 4 3 5 36 1 4 5 40 4. Let m 5 months ofmembership; 100 1 35m; 100 1 35(12) 5 100 1 420 5520; $520

Exercises 1. Answers may vary. Sample: An algebraicexpression may use variables. A numerical expressiondoes not. 2. 4x; 4(12) 5 48 3. p 2 2; the correct choiceis C. 4. n ÷ 2; the correct choice is B. 5. m 1 2; thecorrect choice is A. 6. 13 less than a number q is q 2 137. The number of days in w weeks 5 7w 8. The numberof bunches that can be made with 60 roses 5 60 4 f or 9. For a 5 20, a 2 17 5 20 2 17 5 3. For a 5 22, a 2

17 5 22 2 17 5 5. For a 5 25, a 2 17 5 25 2 17 5 8. Themissing values are 3, 5, and 8. 10. For m 5 7, 9m 5

9(7) 5 63. For m 5 9, 9m 5 9(9) 5 81. For m 5 11, 9m 5

9(11) 5 99. The missing values are 63, 81, and 99.11. For d 5 0, 4d 1 7 5 4(0) 1 7 5 7. For d 5 2, 4d 1

7 5 4(2) 1 7 5 15. For d 5 4, 4d 1 7 5 4(4) 1 7 5 23.The missing values are 7, 15, and 23. 12. 2n 1 5 2 n 5

60f

34

2(3) 1 5 2 (3) 5 6 1 5 2 3 5 11 2 3 5 8 13. 5

5 5 5 3 14. ? n 5

? (3) 5 ? 3 5 24 ? 3 5 72 15. Let h represent the number of hiking trips, then 12h represents the costof all the hiking trips. With the initial fee of $60, theexpression is 60 1 12h. For h 5 6, 60 1 12h 5 60 1 12(6) 560 1 72 5 132; $132 16. For each minute m, the balloongoes down 150 ft, so that part of the expression is 150m.It starts at 2,250, so the entire expression is 2,250 2150m. For m 5 6; 2,250 2 150m 5 2,250 2 150(6) 52,250 2 900 5 1,350. For m 5 8; 2,250 2 150m 5

2,250 2 150(8) 5 2,250 2 1,200 5 1,050. For m 5 10;2,250 2 150m 5 2,250 2 150(10) 5 2,250 2 1,500 5 750;1,350 ft, 1,050 ft, 750 ft 17a. Without the admission fee,the cost for r rides is 2r. With the admission fee, the totalcost is 2r 1 5, or 5 1 2r. 17b. First, subtract $5 just forthe admission fee: 16 2 5 5 11. You have $11 for therides, so you can go on 5 5.5 rides. However, sinceyou cannot take half rides, you can go on 5 rides.18. Each peach is 35 Calories and each banana is 105Calories, so the number of Calories in p peaches and n bananas is 35p 1 105n. 19. Each slice of bread is 65Calories, each bacon slice is 37 Calories, and each egg is75 Calories, so the number of Calories in 2 slices ofbread, b slices of bacon, and 1 egg is 65(2) 1 37b 1 75(1) 5130 1 37b 1 75 5 37b 1 205. 20. For m 5 5.2 and n 5 4.1, m 1 n 5 5.2 1 4.1 5 9.3. 21. For m 5 5.2,n 5 4.1, and r 5 8.5, mn 1 3r 5 (5.2)(4.1) 1 3(8.5) 521.32 1 25.5 5 46.82. 22. For m 5 5.2 and n 5 4.1,5m 2 2n ? 3 5 5(5.2) 2 2(4.1) ? 3 5 26 2 24.6 5 1.4.23. Answers may vary. Sample: I would choose SupremeTaxi if I knew I would be going 2 mi or less becauseSupreme is less expensive for under 3 mi. For any trips 3 mi or over, I would choose Town Taxi, which is lessexpensive. 24. Answers may vary. Sample: You have apencils, and you buy 3 more. 25. 3x 5 x 1 x 1 x; thecorrect choice is B. 26. x 2 3 is less than x; the correctchoice is C. 27. 3 1 x is a sum that is greater than x; thecorrect choice is A. 28. Let n 5 nickels, d 5 dimes and q 5 quarters. q 5 2n because there are twice as manyquarters as nickels, thus, the total change in the jar is q 1 n 1 d 5 2n 1 n 1 d 5 3n 1 d 29. 2x 2 3; thecorrect choice is D. 30. According to the Order ofOperations, you should add what is in the parenthesesfirst; the correct choice is F. 31. 12.5 1 6.39 512.50 1 6.39 5 18.89 32. 4.7 2 0.85 5 4.70 2 0.85 53.85 33. 2.111 1 5.99 5 2.111 1 5.990 5 8.101

VOCABULARY BUILDER page 9

1–3. Check students’ work. 4. 5.25 4 1.25 5 4; 4notepads 5. 21.6 4 3 5 7.2, 25 4 5 5 5, $7.20 . $56. The order on a number line from left to right is 1.17,

112

241

244 2 (3)

244 2 n

279

9 1 189

3(3) 1 18

3(3)

3n 1 183n

phm07c3_sk_ch01_natl.qxd 8/22/06 10:01 AM Page 1


1.7, 1.71, 7.1, 7.11, so this is the order from least togreatest. 7a-c. Check students’ work.

1-2 Integers and Absolute Valuepages 10–13

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM 1. An algebraic expressionis a mathematical phrase that uses numbers, variables,and operation symbols. 2. 11 3. 15 4. 12

Quick Check 1. On the number line, 27 is 7 units from0. This means «27« 5 7. On the number line, 7 is 7 unitsfrom 0. This means «7« 5 7.

2.

The numbers from least to greatest are 25, 0, 4.

3. Asia’s lowest recorded temperature is 2908F; SouthAmerica’s lowest recorded temperature is 2278F. Since|290| 5 90 and |227| 5 27, 290 has a greater absolutevalue than 227, so the lower temperature is 2908F; Asia

4. For s 5 25, 3«s« 5 3«25« 5 3(5) 5 15.

Exercises 1. Answers may vary. Sample: Integers includewhole numbers and their opposites. 2. 232 is 2 units left of 230; E. 3. 251 is 1 unit left of 250; A. 4. 234 is 1 unit right of 235; D. 5. 242 is 2 units left of 240; B.6. On the number line, 252 is 52 units from 0. Thismeans «252« 5 52. 7. On the number line, 26 is 26 units from 0. This means «26« 5 26. 8. On thenumber line, 0 is 0 units from 0. This means «0« 5 0.9. On the number line, 2200 is 200 units from 0.This means «2200« 5 200.

10.

The order from least to greatest is 212, 29, 28, 0, 2,5, 10.

11.

The order from least to greatest is 216, 213, 26, 24, 2,7, 11.12.

The order on a number line from left to right is 215,212, 29, 26, 22, 21, so this is the order from least togreatest.

13.

The order from least to greatest is 233, 227, 219, 19,27, 33. 14. Since 364 is the only positive integer, it is thegreatest integer. For negative integers, as the absolutevalue of a number increases, the value of the numberdecreases: «229« 5 29; «2452« 5 452; «2411« 5 411;«2320« 5 320; «2297« 5 297; «279« 5 79. Since

403020100–10–40 –30 –20

–33 –27 –19 19 27 33

0–5–15 –10

–15 –12 –9 –6 –2 –1

10–20 –15 –10 –5 0 5

–16 –13 –6 –4 2 7 11

2 6 100–2–6–10

–12 –9 0 2 5 10–8

2 40–2–4–6

452 . 411 . 320 . 297 . 79 . 29, the order of theboiling points from least to greatest is 2452, 2411,2320, 2297, 279, 229, 364. The order of the elements ishelium, neon, nitrogen, oxygen, radon, chlorine, iodine.15. For w 5 26, 8«w« 5 8«26« 5 8(6) 5 48. 16. For t 5

28, 5 1 «t« 5 5 1 «28«5 5 1 8 5 13. 17. For a 5 27,

10«a« 5 10«27« 5 10(7) 5 70. 18. For z 5 62, «3z« 5

«3(62)« 5 «186« 5 186. 19. «21,312« 5 1,312 ft;1,312 , 19,340 ft; Mount Kilimanjaro 20a. «29« 5 9;«212 5 12; since 9 , 12 and the integers are bothnegative 29 . 212. The second golfer wins. 20b. 212 is3 units from 29 on the number line, so the second golferwon by 3 strokes. 21. Since absolute values are alwayspositive, a negative number multiplied by the absolutevalue of a number is negative and a positive numbermultiplied by the absolute value of a number is positive.5|2x| is greater. 22. The one with the shortest red line isColorado. 23. Yes; the coldest temperature in Kansaswas 2408C, which is colder than 2388C. 24. «212« 5 12and «12« 5 12, so «212« 5«12«; 5 25. «3« 5 3, «24« 5

4, and 3 , 4, so «3« , «24«; , 26. «219« 5 19, «27« 5

7, and 19 . 7, so «219« . «27«; . 27. |6| 56, «29« 5 9,and 6 , 9, so «6« , «29«; , 28. «215« 5 15; 10 , x ,

15, x 5 11, 12, 13, or 14 29. No; for example, «25« .

«1«, but 25 , 1. 30. Yes; 21.5 and 1.5 are the samedistance from 0 on a number line. 31. «x« 5 2x for allnon-positive values of x because when a negativenumber is multiplied by 21 is the positive value of thenumber and absolute value of any number is the positivevalue of the number. Thus for all non-positive values of xthe equation is true. 32. x must be a value between 26and 23. The integers between 26 and 23 are 24 and25. Both make 26 , x , 23 true: 26 , 24 , 23, 26 ,25 , 23. 24 is not a choice, so the correct choice is C.33. (40.8 1 5.2) 3 2 5 46 3 2 5 92; the correct choice isJ. 34. The values in the right column are 5.25 times thevalues in the left column. The cost corresponds to thenumber of tickets multiplied by 5.25; 5.25t. The correctchoice is B. 35. If m represents the number of months,then 34.95m represents the cost of m months. With thesetup fee of $25, the expression is 25 1 34.95m. For m 5

1 month, 25 1 34.95m 5 25 1 34.95(1) 5 25 1 34.95 559.95. For m 5 3 months, 25 1 34.95m 5 25 134.95(3) 5 25 1 104.85 5 129.85; For m 5 6 months,25 1 34.95m 5 25 1 34.95(6) 5 25 1 209.7 5 234.7;$59.95, $129.85, $234.70

ACTIVITY LAB page 14

1. The amount of money that the company made byOctober is $600 and the amount of money that thecompany made by August is $450. Subtracting 450 from600 gives the amount of money Chantal made fromAugust to October; 600 2 450. 2. Check students’ work;600 2 450 5 150. 3. The amount of money that thecompany made in the beginning of the year is 2$500and the amount of money the company made by the endof the year is $800. The money Chantal made during theyear is obtained from subtracting 2500 from 800;

u



800 2 (2500). 4. Add the absolute value of 2500 to 800because it is equivalent to 800 1 500. 5. Answers mayvary. Sample: Add the absolute value of 2225 to 315because it is equivalent to 225 1 315.

CHECKPOINT QUIZ 1 page 14

1. 23s 2. v 4 12 or 3. m 4 10 or 4. 4 1 f5. «2304« 5 304 6. «15« 5 15. 7. 2 ? «8« 5 2 ? 8 5 168. 6 2 «23« 5 6 2 3 5 3 9. For c 5 23.5, 3«c« 5

3«23.5« 5 3(3.5) 5 10.5 10. For f 5 4 and g 5 7,«f ? g« 5 «4 ? 7« 5 «28« 5 28 11. For x 5 24.2 and y 5

3, «x« 1 y 5 «24.2« 1 3 5 4.2 1 3 5 7.212. If h represents the numbers of hours the mechanicworks, then 35h represents the cost of the mechanic for hhours. With the charge of $168 for parts, the expression is 168 1 35h. For h 5 3 hours, 168 1 35h 5 168 1 35(3) 5168 1 105 5 273; $273


1a. 25 1 (26) 5 211 1b. 22 1 (23) 5 252. Answers may vary. Sample: The sign of the sum of twonegative integers is negative. 3a. 3 1 (25) 5 223b. 23 1 5 5 24a.

24 1 5 5 14b.

8 1 (24) 5 44c.

2 1 (26) 5 244d.

29 1 2 5 275. Answers may vary. Sample: When the absolute valueof the positive number is greater than the absolute valueof the negative number. For example, 24 1 5 5 1;

6. Answers may vary. Sample: When the absolute valueof the positive number is less than the absolute value ofthe negative number. For example, 29 1 2 5 27;

–6 –5 –4 –3 –2 –1 0 1 2–9 –8 –7

543210–4 –3 –2 –1

–6 –5 –4 –3 –2 –1 0 1 2–9 –8 –7

6420–2–6 –4

86420–4 –2

543210–4 –3 –2 –1

m10

v12

1-3 Adding and SubtractingIntegers pages 16–19

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM 1. Answers may vary.Sample: When you simplify an expression, you write itssimplest name. When you evaluate an expression, youreplace each variable with a number and then simplify.

2. 19 3. 2 4. 38 5. 3Quick Check 1a. The integers have opposite signs, sofind the absolute value of each integer: «212« 5 12 and«30« 5 30. Subtract: 30 2 12 5 18. Since |30| . «212«,the sum is positive. Thus, 212 1 30 5 18. 1b. Theintegers have negative signs, so find the absolute valueof each integer: «212« 5 12 and «23« 5 3. Add:12 1 3 5 15. Since both numbers are negative the sum isnegative. Thus, 212 1 (23) 5 215 2a. 8 2 (24) 58 1 4 5 12 2b. 223 2 (211) 5 223 1 11 5 2122c. 2140 2 60 5 2140 1 (260) 5 22003. 294 1 (287) 5 2181

Exercises 1. The additive inverse of 0 is 0 because 0 1 0 5 0. 2. The negative integer has a greater absolutevalue so the sum is negative. 3. The sum of two negativeintegers is negative. 4. The positive integer has a greaterabsolute value so the sum is positive. 5. The integers areboth positive, so their sum is positive: 6 1 2 5 8.6. The integers have opposite signs, so find the absolutevalue of each integer: «28« 5 8 and «3« 5 3. Subtract:8 2 3 5 5. Since «28« . «3«, the sum is negative. Thus,28 1 3 5 25. 7. The integers have opposite signs, sofind the absolute value of each integer: «27« 5 7 and«5« 5 5. Subtract: 7 2 5 5 2. Since «27« . «5«, the sumis negative. Thus, 27 1 5 5 22. 8. 4 2 1 5 4 1 (21); theintegers have opposite signs, so find the absolute valueof each integer: «4« 5 4 and «21« 5 1. Subtract: 4 2 1 53. Since «4« . «21«, the sum is positive. Thus, 4 1 (21) 53. 9. The integers have opposite signs, so find theabsolute value of each integer: «4« 5 4 and «23« 5 3.Subtract: 4 2 3 5 1. Since «4« . «23«, the sum ispositive. Thus, 4 1 (23) 5 1. 10. 24 2 4 524 1 (24); the integers are both negative, so their sumis negative: 24 1 (24) 5 28. 11. The integers are bothnegative, so their sum is negative: 23 1 (25) 5 28.12. The integers have opposite signs, so find the absolutevalue of each integer: «49« 5 49 and «213« 5 13.Subtract: 49 2 13 5 36. Since «49« . «213«, the sum ispositive. Thus, 49 1 (213) 5 36. 13. The integers haveopposite signs, so find the absolute value of each integer:«215« 5 15 and «14« 5 14. Subtract: 15 2 14 5 1. Since«215« . «14«, the sum is negative. Thus, 215 1 14 521. 14. The integers have opposite signs, so find theabsolute value of each integer:«3« 5 3 and «212« 5 12.Subtract: 12 2 3 5 9. Since «212« . «3«, the sum isnegative. Thus, 3 1 (212) 5 29. 15. The integers areboth negative, so their sum is negative: 225 1 (27) 5232 16. The integers have opposite signs, so find theabsolute value of each integer: «217« 5 17 and «18« 5

18. Subtract: 18 2 17 5 1. Since «18« . «217«, the sum



is positive. Thus, 217 1 18 5 1. 17. The integers haveopposite signs, so find the absolute value of each integer:«223« 5 23 and «35« 5 35. Subtract: 35 2 23 5 12. Since«35« . «223«, the sum is positive. Thus, 223 1 35 5 12.18. The integers have opposite signs, so find the absolutevalue of each integer: «215« 5 215 and «2117« 5 117.Subtract: 215 2 117 5 98. Since «215« . «2117«, thesum is positive. Thus, 215 1 (2117) 5 98. 19. Theintegers have opposite signs, so find the absolute valueof each integer: «2508« 5 508 and «507« 5 507.Subtract: 508 2 507 5 1. Since «2508« . «507«, the sumis negative. Thus, 2508 1 507 5 21. 20. 25 2 8 525 1 (28) 5 213 21. 23 2 (27) 5 23 1 7 5 422. 6 2 18 5 6 1 (218) 5 212 23. 21 2 (215) 5 21 115 5 36 24. 238 2 38 5 238 1 (238) 5 27625. 223 2 (223) 5 223 1 23 5 0 26. 2 2 7 5 2 1 (27) 525; 258F 27. At 4,000 m the temperature is 28C and at6,000 m the temperature is 2118C. Find the difference:2 2 (211) 5 2 1 11 5 13; 138C. 28. The integers haveopposite signs, so find the absolute value of each integer:|28| 5 8 and |5| 5 5. Subtract: 8 2 5 5 3. Since |28| . |5|,the answer is negative. Thus, 28 1 5 5 23. 29. Theamount in the bank is a positive amount and the amountof the check is negative, since it’s removing money; 151 1(2248) 5 297; you need to deposit $97. 30. 7 1 (27) 50 and 27 1 7 5 0, so, the sum of a number and itsopposite is 0; never. 31. 7 2 (27) 5 7 1 7 5 14 and 27 2 (7) 5 214, so, the difference of a number and itsopposite is positive if the number is positive andnegative if the number is negative; sometimes.32. 8 2 7 5 1, so 8 2 1 5 7; 8 2 1 5 8 1 (21); add 21.33. No; you can add a negative integer to a number andcome out with less than you started with. 34. For x 5 2,y 5 22, and z 5 23, x 1 y 2 z 5 2 1 (22) 2 (23) 50 1 3 5 335.

x equals all integers greater than 1 or less than 23.36. 43 1 3 2 5 2 1 1 2 1 4 5 46 2 5 2 1 1 2 1 4 5 412 1 1 2 1 4 5 40 1 2 14 5 42 1 4 5 46; the correctchoice is C. 37. 245 2 10; the correct choice is H.38. The total amount is $1.25 plus the number of copiesmade multiplied by $.15: 0.15(8) 1 1.25; the correctchoice is B. 39. 214 is to the left of 12 on a number line;214 , 12 40. 23 is to the right of 24 on a number line;23 . 24 41. 26 is to the right of 210 on a number line;26 . 210

1-4 Multiplying and DividingIntegers pages 20–23

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM 1. opposites 2. 26 3. 2154. 26

x , 23 x . 1

x 1 1 2 1 , 22 2 1 x 1 1 2 1 . 2 2 1

x 1 1 , 22 x 1 1 . 2

2(x 1 1) 3 21 , 2 3 (21) u x 1 1 u . 2

2(x 1 1) . 2 u x 1 1 u 2 2 1 2 . 0 1 2

u x 1 1 u 2 2 . 0

Quick Check 1. 29 ? 8 ? (22) 5 272 ? (22) 5 1442. The change in depth is equal to 290 4 5. Since thesigns are different, the quotient is negative: 290 4 5 5218; 218 ft/min 3. For x 5 29, y 5 25, and z 5 23,2x 1 xy 4 z 2 3 5 2(29) 1 (29)(25) 4 (23) 2 3 5218 1 45 4 (23) 2 3 5 218 1 (215) 2 3 5 233 2 3 5233 1 (23) 5 236.

Exercises 1. 25(3) means the opposite of five groups ofthree. 2. A negative times a negative; a negative times anegative is always positive, and a negative times apositive is always negative. 3. 23 ? 6 5 218 and 9 ? 5 545; , 4. 6(27) 5 2 42 and 22(28) 5 16; , 5. 12 ? 4 548 and 8(211) 5 288; . 6. The signs are the same, sothe product is positive: 8 ? 3 5 24 7. The signs aredifferent, so the product is negative: 7(25) 5 2358. The signs are the same, so the quotient is positive: 5

4 9. The signs are the same, so the quotient is positive:5 4. 10. The number of negative signs is odd, so the

product is negative: 3 ? (215) ? 2 5 2(3 ? 15 ? 2) 5 290.11. The number of negative signs is even, so the productis positive: 28 ? (25) ? 4 5 8 ? 4 ? 5 5 160 12. Thenumber of negative signs is odd, so the product isnegative: 27(22)(21) 5 2(7 ? 2 ? 1) 5 214. 13. Thenumber of negative signs is even, so the product ispositive: 21 ? 3 ? 2 ? (26) 5 1 ? 3 ? 2 ? 6 5 36. 14. Thenumber of negative signs is even, so the product ispositive: 23(21)(24)(27) 5 3 ? 1 ? 4 ? 7 5 84. 15. Thenumber of negative signs is odd, so the product isnegative: 2(24)(28)(26) 5 2(2 ? 4 ? 8 ? 6) 5 2384.16. The signs are different, so the quotient is negative:

5 25. 17. The signs are the same, so the quotient is

positive: 5 10 18. The signs are different, so the

quotient is negative: 5 28. 19. The signs are

different, so the quotient is negative: 5 25 20. The signs are different, so the quotient is negative:272 4 9 5 28 21. The signs are the same, so the quotient is positive: 5 8 22. 21,000 4 8 5 2125;2125 ft per s 23. For c5 22 and d 5 5, cd 2 5d 5

(22)(5) 2 5(5) 5 210 2 25 5 210 1 (225) 5 235.24. For c 5 22 and d 5 5, dc 1 (c 2 d) 5 5(22) 1(22 2 5) 5 5(22) 1 [22 1 (25)] 5 5(22) 1 [27] 5210 1 (27) 5 217. 25. For c 5 22 and d 5 5, d 1

3c 4 2 5 5 1 3(22) 4 2 5 5 1 (26) 4 2 5 5 1 (23) 5 2.26. For c 5 22 and d 5 5, (2d 2 c) 4 4(d 1 c) 5[2(5) 2 (22)] 4 4[5 1 (22)] 5 [10 2 (22)] 44[5 1 (22)] 5 [10 1 2] 4 4[3] 5 12 4 12 5 1. 27. For c 5 22 and d 5 5, 5 5

5 5 3. 28. For c 5 22 and d 5 5, 5

5 5 5 210. 29. 2260 4 5 5

252; 2$52 30. 260(4) 5 2240; 2240 ft31.

Each incorrect answer is worth 225 points. 32. Positive;the signs are the same. 33. Negative; there are three

x 5 225

3x3 5 275

3

3x 5 275

6026

12(5)

(22) 1 (24)

12(5)

(22) 2 4

12dc 2 4

155

5 1 2 1 85

5 2 (22) 1 8

5d 2 c 1 8

5

24826

3527

2648

505

2459

21223

246



negative factors. When there are an odd number ofnegative signs, the product is negative. 34. 24 4 3 5 8;8 groups 35. (25)(260) 5 300, so 300 4 (25) 5 260;300. 36. The signs are different, so the quotient isnegative; negative. 37. The signs are different, so thequotient is negative; negative. 38. The signs are thesame, so the quotient is positive; positive. 39. (x 1 y) ispositive, so the numerator is negative and thedenominator is positive. The signs are different, so thequotient is negative. 40. (b 1 a) is negative, so thenumerator is negative and the denominator is positive.The signs are different, so the quotient is negative.41a. Since they drill downward, the integer is negative:240,230. 41b. A mile is 5,280 ft. Answers may vary.Sample: 240,230 4 5,280 < 240,000 4 5,000 5240 4 5 5 28; 8 mi 42. You eat three times a day andyou are hiking for four days so you multiply 4 3 3 tofind the amount of food that you will need for four days.Since five more people are coming, you need tomultiply the amount of food you will need for four daysby the total number of people that are going: 4 3 3 3 65 12 3 6 5 72; 72 meals 43. 2(24) 5 28; the correctchoice is A. 44. On a number line, from left to right, thedigits are 213, 27, 22, 21, 1, 4 . Therefore, this is alsoarranged from the least to greatest; the correct choice isH. 45. 290; the correct choice is B. 46. 8 1 (25) 5 347. 213 1 7 5 26 48. 210 2 3 5 210 1 (23) 5 213

49. 2 2 (26) 5 2 1 6 5 8

GUIDED PROBLEM SOLVING pages 24–25

1. Answers may vary. Sample: Since Rex misspelledthree words 3 3 (3) 5 9 points should be deducted from100; 100 2 9. However Rex got two bonus points so twopoints should be added to the previous quantity;100 1 3 3 (23) 1 2. 2a. If Rex gets one wrong themaximum points he can get is 100 1 2 2 3 5 99, so hecould never get a total score of 100. 2b. Answers mayvary. Sample: 100 1 2 2 3 5 99, 100 1 2 2 4 5 98,100 1 2 2 5 5 97, 100 1 2 2 3 2 3 5 96, 100 1 2 2 3 2 4 595, 100 1 2 2 4 2 4 5 94, 100 1 2 2 4 2 5 5 93,100 1 2 2 5 2 5 5 92, 100 1 2 23 2 4 2 4 5 91,100 1 2 2 3 2 4 2 5 5 90 3. The scuba diver starts off68 ft deep or 268 ft at 3:14 P.M. and starts rising 12 ft per minute, so after 4 minutes the scuba diver is268 1 12 3 (4) 5 220 ft at 3:14 1 4 min 5 3:18 P.M.After 3:18 P.M. the scuba diver descends 20 ft per minutefor 2 minutes, so the scuba diver is 220 1 (220) 3 2 5260 ft at 3:18 1 2 min 5 3:20 P.M. After 3:20 P.M. thescuba diver starts rising 15 ft per minute for 60 ft. Ittakes the scuba diver 60 4 15 5 4 minutes to reach thetop or 60 ft. Thus the scuba diver reaches the top at 3:201 4 min 5 3:24 P.M. 4. First, find the number of years ofherd growth. 2045 2 2005 5 40. Then find how manytimes the herd size will double in that time period.40 4 5 5 8. Then find how much the herd will grow inthat time. 28 5 256, the herds will be 256 times larger in2045. Then multiply each state’s current herd size by 256.AZ: 230 3 256 5 58,880; NV: 13,251 3 256 5 3,392,256;

WY: 3,991 3 256 5 1,021,696; NM: 82 3 256 5 20,992;CO: 800 3 256 5 204,800 5. The negative quantities arethe amount of money the salesman paid for the scooterand the positive quantities are the amount the salesmansold the scooter for. By finding the sum, you cancalculate the total amount of money the salesman made:2100 1 120 2 140 1 160 5 20 1 20 5 40; He made $40.6. 100 1 2(3) 5 106; 106 2 90 5 16; 16 5 10 1 6 52(5) 1 2(3); 2; the highest possible test score was 106, 16points more than Sara received. Since 16 4 5 5 3 R1,Sara got two problems wrong and had 3 points taken offtwo times for not showing her work.

1-5 Properties of Numberspages 26–30

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM 1. To simplify an expressionmeans to replace it with its simplest name.2. 99 3. 100 4. 221 5. 32

Quick Check 1. 26 1 (212) 1 34 5 26 1 34 1(210 2 2) 5 60 1 (210) 1 (22) 5 50 2 2 5 482. 46 2 92 5 (4 1 42) 2 92 5 4 1 (42 2 92) 5 4 1(250) 5 246 3. 24 ? 121 ? (25) 5 24 ? (25) ? 121 520 ? 121 5 2,420 4. 6(m 1 3) 5 6m 1 6 ? 3 5 6m 1 185. 20(8.1) 5 20(8 1 0.1) 5 160 1 2 5 162; $162

Exercises 1. By the Identity Property of Multiplication,multiplying a number by 1 does not change the number’svalue. 2. Adding 0 to a number does not change its value: Ident. Prop. of Add. 3. Switching numbersdoes not change the product: Comm. Prop. of Mult.4. Regrouping numbers does not change the sum:Assoc. Prop. of Add. 5. Switching numbers does notchange the sum: Comm. Prop. of Add. 6. Regroupingnumbers does not change the product: Assoc. Prop. ofMult. 7. Multiplying a number by 1 does not change itsvalue: Ident. Prop. of Mult. 8. 3.5 1 9 1 6.5 53 1 9 1 6 1 0.5 1 0.5 5 12 1 6 1 1 5 19 9. 14 2 31 5217 10. 24 ? 6 ? (225) 5 100 ? 6 5 600 11. 27 ? 2 1 73 ?2 5 (27 1 73)2 12. 67 1 63 1 25 5 (60 1 7) 1(60 1 3) 1 25 5 (60 1 60) 1 (7 1 3) 1 25 5 120 1 10 125 5 130 1 25 5 155 13. 87 1 32 1 13 5 (87 1 13) 132 5 100 1 32 5 132 14. 178 1 288 1 22 5 178 1 22 1288 5 200 1 288 5 488 15. 13 2 67 5 (6 1 7) 2 67 56 1 (7 2 67) 5 6 1 (260) 5 254 16. 38 2 59 5(9 1 29) 2 59 5 9 1 (29 2 59) 5 9 1 (230) 5 22117. 24 2 46 5 (8 1 16) 2 46 5 8 1 (16 2 46) 58 1 (230) 5 222 18. 5 ? 245 ? 20 5 5 ? 20 ? 245 5100 ? 245 5 24,500 19. 22(43)(25) 5 22(25)(43) 510 ? 43 5 430 20. 20(34)(25) 5 20(25)(34) 52100(34) 5 23,400 21. 5(a 1 6) 5 5a 1 5 ? 6 55a 1 30 22. 7(b 2 9) 5 7b 2 7 ? 9 5 7b 2 6323. 24(t 1 3) 5 24t 1 (24) ? 3 5 24t 1 (212) 524t 2 12 24. (v 2 2)9 5 v ? 9 2 2 ? 9 5 9v 2 1825. (8 1 r)4 5 8 ? 4 1 r ? 4 5 32 1 4r26. (211 1 w)(22) 5 211 ? (22) 1 w ? (22) 522 1 (22)w 5 22 2 2w, or 22w 1 22 27. 6(2.5) 5



6 3 (2 1 0.5) 5 (6 3 2) 1 (6 3 0.5) 5 12 1 3 5 1528. 5(0.9) 5 5(1 2 0.1) 5 (5 3 1) 2 (5 3 0.1) 55 2 0.5 5 4.5 29. 4(1.98) 5 4(2 2 0.02) 5(4 3 2) 2 (4 3 0.02) 5 8 2 0.08 5 7.92 30. 3.49 3 4 5(3 1 0.4 1 0.09) 3 4 5 (3 3 4) 1 (0.4 3 4) 1 (0.09 3 4) 512 1 1.6 1 0.36 5 13.6 1 0.36 5 13.96; $13.9631. 3 3 1.99 5 3 3 (2 2 0.01) 5 (3 3 2) 2 (3 3 0.01) 56 2 0.03 5 5.97; 2 3 0.89 5 2 3 (1 2 0.11) 5(2 3 1) 2 (2 3 0.11) 5 2 2 0.22 5 1.78; 5.97 < 6, 1.78 <2, 6 1 2 5 8; 8 . 7; no, you do not have enough money.32. 4 3 38 5 4 3 (40 2 2) 5 (4 3 40) 2 (4 3 2) 5160 2 8 5 152; no 33. 4 3 2.97 5 4 3 (3 2 0.03) 5(4 3 3) 2 (4 3 0.03) 5 12 2 0.12 5 11.88; 3 3 1.99 53 3 (2 2 0.01) 5 (3 3 2) 2 (3 3 0.01) 5 6 2 0.03 5 5.97;5 3 0.99 5 5 3 (1 2 0.01) 5 (5 3 1) 2 (5 3 0.01) 55 2 0.05 5 4.95; 11.88 1 5.97 1 4.95 5 22.8; $22.8034a. 0.40 1 0.60 1 1.95 5 1 1 1.95 5 2.95; 2.95 , 3;yes 34b. 3 2 2.95 5 0.05; $0.05 change 35. Answersmay vary. Sample: mental math; 4(5.98) 5 4(6 2 0.02) 524 2 0.08 5 23.92 36. 250 1 2 1 108 1 (2450) 5250 1 (2 1 108) 1 (2450) 5 250 1 (110) 1 (2450) 5250 1 (2450) 1 (110) 5 2500 1 (110) 52500 1 100 1 10 5 2400 1 10 5 239037. (40)(22)(29)(210) 5 (40)(210)(22)(29) 5(2400)(22)(29) 5 (800)(29) 5 800(30 2 1) 5800 ? 30 2 800 ? 1 5 24,000 2 800 5 23,20038. 11.92 1 12.20 1 12.08 1 11.86 511.92 1 0.08 1 12 1 11 1 0.80 1 0.20 1 12 1 0.06 512 1 12 1 12 1 12 1 0.06 5 24 1 24 1 0.06 5 48.06;48.06 2 41.37 5 6.69; 6.69 s 39. Answers may vary.Sample: I would use the Comm. Prop. of Add. to get(268) 1 (232) 1 6(299). This simplifies to 2100 1 6(299). Then I would use the Dist. Prop.to get 2100 1 (2594). This simplifies to 2694.40. Answers may vary. Sample: The Comm. Prop. ofAdd. applies only if all the operations are addition.

41. 12 3 15 5 12(10 1 5) 5 120 1 60 5 180; 180 3 2 5360; 20 3 16 5 20(10 1 6) 5 200 1 120 5 320; No, 20 lbis 320 oz. Two dozen cans weigh 360 oz. 42. 3.49 < 3.50,1.19 < 1.20, 0.79 < 0.80, 3.50 1 1.20 1 2(0.80) 54.70 1 1.60 5 6.30; the correct choice is C. 43. Multiply4 by 5 and subtract the product from 100; the correctchoice is G. 44. 215, 27, 21, 1, 3, 7; all of these numbersare in order from least to greatest; the correct choice isD. 45. 26 ? (22) ? 3 5 12 ? 3 5 36 46. 3(24) ? 2 5212 ? 2 5 224 47. 22 ? 5 ? (21) ? 6 5(22 ? 5) ? [(21) ? 6] 5 (210) ? (26) 5 60


1. 279 1 15 5 264 2. 23 2 (214) 5 23 1 14 5 373. 232 2 11 5 232 1 (211) 5 243 4. 24 4 (21) 5 45. 230 4 (23)(2) 5 230 4 (26) 5 30 4 6 5 56. 7 2 (29) ? 2 5 7 2 (218) 5 7 1 18 5 257. 70 1 19 1 30 5 100 1 19 5 119 8. 540 1 160 2 2802 10 5 500 1 100 1 40 1 60 2 290 5 700 2 290 5 4109. 4 3 15.98 5 4 3 (16 2 0.02) 5 64 2 0.08 5 63.92;$63.92 10. 237 2 16.5 or 237 1 (216.5)


1a.

1b.

1c.

x 5 28

x 1 3 2 3 5 25 2 3

x 1 3 5 25

x 5 22

3x3 5 26

3

3x 5 26

x 5 22

x 1 5 2 5 5 3 2 5

x 1 5 5 3


1d.

2. Answers may vary. Sample: Add the same negativenumber to each side. For example, if x 1 5 5 1, add 25to each side to get x 5 24.

1-6 Solving Equations by Addingand Subtracting pages 33–36

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM 1. inverses 2. 211 3. 04. 27 5. 26

Quick Check1. Check:

✔2. Let x 5 the number of notices mailed yesterday.

Check:

✔

Exercises 1. Answers may vary. Sample: An equationhas an equal sign, but an expression does not.2. Since 8 1 9 5 17, 17 2 9 5 8; m 5 17 3. y 2 4 5 84. 23 1 4 5 1 ? 7; no 5. 23 2 7 5 210 5 210; yes6. 21 1 (23) 5 24 ? 4; no 7. 23 2 3 5 26 ? 0; no8. 7 1 (23) 5 4 5 4; yes 9. 23 1 3 5 0 5 0; yes10. 11.

Check: Check:

✔

12. 13.

Check: Check:

14. 15.

Check: Check:

1 5 1✔ 236 5 236✔ 46 2 45 0 1 236 0 222 2 14 m 2 45 5 1236 5 t 2 14

m 5 46 222 5 t m 2 45 1 45 5 1 1 45236 1 14 5 t 2 14 1 14

m 2 45 5 1 236 5 t 2 14 22 5 22✔ 237 5 237✔

0 2 2 0 22 237 0 235 2 2 b 2 2 5 22237 5 y 2 2

b 5 0 235 5 y

b 2 2 1 2 5 22 1 2237 1 2 5 y 2 2 1 2

b 2 2 5 22237 5 y 2 2

45 5 45✔ 212 5 212

54 2 9 0 45 211 2 1 0 212

a 2 9 5 45p 2 1 5 212

a 5 54 p 5 211 a 2 9 1 9 5 45 1 9 p 2 1 1 1 5 212 1 1

a 2 9 5 45 p 2 1 5 212

52 5 52 x 5 44 notices

44 1 8 0 52 x 1 8 2 8 5 52 2 8

x 1 8 5 52 x 1 8 5 52

210 5 210 x 5 23

23 2 7 0 210 x 2 7 1 7 5 210 1 7

x 2 7 5 210 x 2 7 5 210

x 5 2

5x5 5 10

5

5x 5 10 16. 17.

Check: Check:

18. 19.

Check: Check:

20. 21.

Check: Check:

22. 23.

Check: Check:

24.

Check:

25. 26.

Check: Check:

27.

Check:

28. Let x 5 original balance.Check:

512 5 512✔ x 5 $62

62 1 450 0 512 x 1 450 2 450 5 512 2 450

x 1 450 5 512 x 1 450 5 512

250 5 250✔

271 1 21 0 250

h 1 21 5 250

h 5 271

h 1 21 2 21 5 250 2 21

h 1 21 5 250

100 5 100✔ 32 5 32✔

53 1 47 0 100 19 1 13 0 32

f 1 47 5 100 19 1 g 5 32

f 5 53 g 5 13

f 1 47 2 47 5 100 2 47 19 1 g 2 19 5 32 2 19

f 1 47 5 10019 1 g 5 32

210 5 210✔ 210 0 3 1 213

210 5 3 1 c

213 5 c (210) 1 (23) 5 3 1 (23) 1 c

210 5 3 1 c

27 5 27✔ 252 5 252✔ 234 1 61 0 27 279 1 27 0 252

b 1 61 5 27 r 1 27 5 252

b 5 234 r 5 279

b 1 61 2 61 5 27 2 61 r 1 27 2 27 5 252 2 27

b 1 61 5 27r 1 27 5 252

22 5 22✔ 22 5 22✔

211 1 9 0 22 21 1 1 0 22

v 1 9 5 22 x 1 1 5 22

v 5 211 x 5 21

v 1 9 2 9 5 22 2 9 x 1 1 2 1 5 22 2 1

v 1 9 5 22 x 1 1 5 22

10 5 10✔ 25 5 25✔ 25 1 15 0 10 27 2 32 0 2 5

a 1 15 5 10 w 2 32 5 2 5

a 5 25 w 5 27

a 1 15 2 15 5 10 2 15 w 2 32 1 32 5 25 1 32

a 1 15 5 10w 2 32 5 2 5

231 5 231✔ 23 5 23✔ 216 2 15 0 2 31 23 0 35 2 12

d 2 15 5 2 31 23 5 q 2 12

d 5 216 35 5 q

d 2 15 1 15 5 231 1 15 23 1 12 5 q 2 12 1 12

d 2 15 5 23123 5 q 2 12



29. Let p 5 population (thousands) of Kansas in 1950.

The population of Kansas in 1950 was 1,905,000 people.

30. Let t 5 the temperature at 6:00 A.M.

Check:

31.

23, 3 are solutions

32.

21, 1 are solutions

33.

23, 1 are solutions

34. Let c 5 the amount the collector paid for the card.

The collector paid $5.55 for the card.35. Let p 5 the pounds of cans the student collected.

The student collected 13 lb of cans.

p 5 13

p 2 5.2 1 5.2 5 7.8 1 5.2

p 2 5.2 5 7.8

c 5 5.55

c 1 3.75 2 3.75 5 9.30 2 3.75

c 1 3.75 5 9.30

4 2 2

u 4 u 0 2

u 3 1 1 u 0 2

u n 1 1 u 5 2

3 2 2 2 5 2✔ 1 2 2

u 3 u 0 2 u 2 u 0 2 u 1 u 0 2

u 2 1 1 u 0 2 u 1 1 1 u 0 2 u 0 1 1 u 0 2

u n 1 1 u 5 2 u n 1 1 u 5 2 u n 1 1 u 5 2

0 2 2 1 2 2 2 5 2✔ u 0 u 0 2 u 21 u 0 2 u 22 u 0 2

u 21 1 1 u 0 2 u 22 1 1 u 0 2 u 23 1 1 u 0 2

u n 1 1 u 5 2 u n 1 1 u 5 2u n 1 1 u 5 2

4 2 2

3 1 1 0 2

u 3 u 1 1 0 2

u n u 1 1 5 2

3 2 2 2 5 2✔ 1 2 2

2 1 1 0 2 1 1 1 0 2 0 1 1 0 2

u 2 u 1 1 0 2 u 1 u 1 1 0 2 u 0 u 1 1 0 2

u n u 1 1 5 2 u n u 1 1 5 2 u n u 1 1 5 2

2 5 2✔ 3 2 2 4 2 2

1 1 1 5 2 2 1 1 0 2 3 1 1 0 2

u 21 u 1 1 0 2 u 22 u 1 1 0 2 u 23 u 1 1 0 2

u n u 1 1 5 2 u n u 1 1 5 2un u 1 1 5 2

23 5 23✔ 2u 3 u 0 23

2u n u 5 23

22 2 23 21 2 23 0 2 23

2u 2 u 5 23 2u 1 u 5 23 2u 0 u 0 23

2u n u 5 23 2u n u 5 23 2u n u 5 23

21 2 23 22 2 23 23 5 23✔ 2u 21 u 5 23 2u 22 u 0 23 2u 23 u 0 23

2u n u 5 23 2u n u 5 23 2u n u 5 23

12 5 12✔ t 5 238F

23 1 15 0 12 t 1 15 2 15 5 12 2 15

t 1 15 5 12 t 1 15 5 12

p 5 1,905

p 1 783 2 783 5 2,688 2 783

p 1 783 5 2,688

36. Check students’ work. Sample: You have an amountof money a. After you get another $8.40, you have a totalof $11.55. How much did you start with?37.

38.

39.

40. All values of x; by the Subtr. Prop. of Eq.,x 1 15 2 15 5 x 1 6 1 9 2 15. So x 5 x. This statementis true for all values of x. 41. x 1 96 5 102 representsthe sum of an unknown quantity and 96, which is equalto 102. In choice D, Joey and his cat weigh 102 lbstogether. Joey’s weight is 96 lbs and his cat weighs anunknown quantity, x. The correct choice is D.42. ; the correct choice is F.

43. 18 1 6(2) 1 2(3) 5 18 1 12 1 6 5 30 1 6 5 36; thecorrect choice is D. 44. 3 1 (212) 5 2945. 215 1 (26) 5 221 46. 221 2 37 5 25847. 224 2 (29) 5 224 1 9 5 215


1.

2. 17 1 22 1 27 5 66

y 5 2

222 1 22 1 y 5 222 1 24

22 1 y 5 24

242 1 42 1 22 1 y 5 242 1 66

42 1 22 1 y 5 66

x 5 42

x 1 7 2 7 5 49 2 7

x 1 7 5 49

217 1 17 1 x 1 7 5 217 1 66

17 1 x 1 7 5 66

w 5 37

212 1 12 1 w 5 212 1 49

12 1 w 5 49

217 1 17 1 12 1 w 5 217 1 66

17 1 12 1 w 5 66

c 5 3

c 2 4 1 4 5 21 1 4

c 2 4 5 21

2 2 2 1 c 2 4 5 2 2 3

22 1 c 1 (24) 5 23

b 5 23

b 2 2 1 2 5 25 1 2

b 2 2 5 25

22 1 2 1 b 2 2 5 22 2 3

2 1 b 1 (22) 5 23

a 5 25

22 1 2 1 a 1 0 5 22 2 3

2 1 a 1 0 5 23

2 1 (21) 1 (24) 5 23

81 1 4.05 1 153

25.6 5 m

212 1 6.4 5 26.4 1 m 1 6.4

212 5 26.4 1 m

h 5 22.7

h 2 (27) 1 (27) 5 4.3 1 (27)

h 2 (27) 5 4.3

w 5 5.55

w 2 2.45 1 2.45 5 3.1 1 2.45

w 2 2.45 5 3.1



3. 26 1 4 1 5 1 (29) 5 26

4. Yes; you just added 3(25) or 215 to each column,row, and diagonal. 5. 4; you need to have at least 3numbers in one row, column, or diagonal to figure outthe sum. You can complete the other rows, columns, anddiagonals by using the sum and one other number.

1-7 Solving Equations by Multiplying and Dividing pages 38–41

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM 1. undo 2. 24 3. 2214. 22 5. 3Quick Check

1. 2.

Check: Check:

✔ ✔ 212 5 212 25 5 25

3(24) 0 212 2408 0 25

3y 5 212 t8 5 25

y 5 24 t 5 240

3y3 5 212

3 8 ? A t8 B 5 8 ? (25)

3y 5 212 t8 5 25

z 5 6 3 2 3 1 0 1 z 5 3 1 3

23 1 0 1 z 5 3 9 2 9 2 3 1 0 1 z 5 9 2 6

29 1 (23) 1 0 1 z 5 26 p 5 3

5 2 5 1 p 5 5 2 2 25 1 p 5 22

22 1 2 2 5 1 p 5 22 1 0 2 2 5 1 p 5 0

6 2 6 1 2 2 5 1 p 5 6 2 6 26 1 2 1 (25) 1 p 5 26

n 5 22 n 2 8 1 8 5 210 1 8

n 2 8 5 210 1 2 1 1 n 2 8 5 1 2 11

21 1 n 2 8 5 211 25 1 5 2 1 1 n 2 8 5 25 2 6

5 1 (21) 1 n 1 (28) 5 26 m 5 24

m 1 1 2 1 5 23 2 1 m 1 1 5 23

m 1 1 2 7 1 7 5 210 1 7 m 1 1 2 7 5 210

24 1 4 1 m 1 1 1 (27) 5 24 2 6 4 1 m 1 1 1 (27) 5 26

z 5 32

z 1 27 2 27 5 59 2 27

z 1 27 5 59

27 1 7 1 z 1 27 5 27 1 66

7 1 z 1 27 5 66 More Than One Way Methods may vary. Sample: I canwrite an equation to solve this problem. Let s 5 thenumber of students in the school.

Exercises 1. A value is a solution if it makes theequation true. 2. Div. Prop. of Eq. 3. Add. Prop. of Eq.4. Mult. Prop. of Eq. 5. Subtr. Prop. of Eq.

6. 7.

no yes8. 9.

yes yes10. 11.

no no12. 13.

Check: Check:

14. 15.

Check: Check:

16. 17.

Check: Check:

18. 19.

Check: Check:

2.5 5 2.5✔21.4 5 21.4✔

2.5 0 6024 21.4 0 29.8

7

2.5 5 c24 21.4 5

g7

60 5 c 29.8 5 g

24 ? 2.5 5 24 ? A c24 B 7 ? (21.4) 5 7 ?

g7

2.5 5 c24 21.4 5

g7

5 5 5✔ 3 5 3✔

23527 0 5 227

29 0 3

k27 5 5h

29 5 3

k 5 235 h 5 227

27 ? A k27 B 5 27 ? 5 29 ? A h

29 B 5 29 ? 3

k27 5 5 h29 5 3

252 5 252✔217 5 217✔

252 0 572211217 0 2153

9

252 5 a211217 5 w

9

572 5 a 2153 5 w

211 ? 252 5 211 ? A a211 B 9 ? 217 5 9 ? Aw

9 B252 5 a

211 217 5 w9

21 5 21✔ 34 5 34✔

255 0 21 340

10 0 34

x5 5 21d10 5 34

x 5 25 d 5 340

5 ? x5 5 5 ? (21) 10 ? A d

10 B 5 10 ? 34

x5 5 21 d10 5 34

9 2 29 7 2 27

0 2924525

7 0 355

245z 5 29 7 5 35

w

25 5 25 10 5 10

2 5(25) 0 25 10 0 22(25)

25p 5 25 10 5 22t

23 5 23 2125 2 25

1525 0 23 25(25) 0 25

15m 5 23 25v 5 25

s 5 360 students

3 ? s3 5 3 ? 120

s3 5 120



20. 21.

Check: Check:

22. 23.

Check: Check:

24. 25.

Check: Check:

26. 27.

Check: Check:

28. 29. 5

Check: Check:

30. Let x 5 the number of students in the orchestra.

There are 31 students in the orchestra.31. Let g 5 the number of teeth on the rear gear.

There are 11 teeth on the rear gear.32.

5

Each tiger eats 47.6 kg of meat in a week.33. Division by zero is undefined. 34a. Check students’work 34b. Check students’ work

x 5 47.6

40.8 3 76

6x6

6x 5 40.8 3 7

g 5 11

4g4 5 44

4

4g 5 44

x 5 31

4x4 5 124

4

4x 5 124

285 5 285✔ 336 5 336✔ 285 0 17(25) 112(3) 0 336

285 5 17j 112h 5 336

25 5 j h 5 3

17j17

28517 112h

112 5 336112

285 5 17j 112h 5 336

216 5 216 2460 5 2460✔ 216 028(2) 20(223) 0 2460

216 5 28d20b 5 2460

2 5 d✔ b 5 223

21628 5 28d

8 20b20 5 2460

20

216 5 28d 20b 5 2460

144 5 144✔ 1 5 1✔

224(26) 0 144 22 A212 B 0 1

224k 5 144 22p 5 1

k 5 26 p 5 212

224k224 5 144

224 22p22 5 1

22

224k 5 144 22p 5 1

299 5 299✔ 432 5 432✔ 3(233) 0 299 4(108) 0 432

3w 5 299 4t 5 432

w 5 233 t 5 108

3w3 5 299

3 4t4 5 432

4

3w 5 299 4t 5 432

230 5 230✔ 28 5 28✔

26(5) 0 230 2623.25 0 28

26y 5 230 m23.25 5 28

y 5 5 m 5 26

26y26 5 230

2623.25 ? A m23.25 B 5 23.25 ? 28

26y 5 230m 23.25 5 28 35. 36.

; $5.34 ; 4 weeks37. 38.

39. 40.

41. 15 tickets must be sold for every winner,

; 360 tickets; check students’ work.42. Let x equals the number of students that go to themuseum.

; 3 students go to the museum.43.

; the correct choice is D.44. Multiply 1.5 and 224; the correct choice is J.45. 2c 2 4; the correct choice is A. 46. 5(0.98) 55 3 (1 2 0.02) 5 5(1) 2 5(0.02) 5 5 2 0.1 5 4.947. 7(1.2) 5 7 3 (1 1 0.2) 5 7(1) 1 7(0.2) 5 7 1 1.4 58.4 48. 3.1(9) 5 (3 1 0.1) 3 9 5 (3)9 1 (0.1)9 527 1 0.9 5 27.9


1–10. Explanations may vary.

1.

2.

3.

4. 5.

6.

y 5 51

y 2 1712 1 171

2 5 3312 1 171

2

y 2 1712 5 331

2

y 5 124 x 5 7

2 ?y2 5 2 ? 62 25x

25 5 17525

y2 5 62 25x 5 175

y 5 155

y 2 45 1 45 5 110 1 45

y 2 45 5 110

x 5 60

x 1 11 2 11 5 71 2 11

x 1 11 5 71

x 5 120

3 ? x3 5 3 ? 40

x3 5 40

h 5 37.5

0.08h0.08 5 3

0.08

0.08h 5 3

x 5 3

62 5 2x2

6 5 2x

16 2 10 5 2x 2 10

16 5 2x 1 10

16 5 2(x 1 5)

x 5 360

x15 3 15 5 24 3 15

x15 5 24

42.12 5 r f 5 750

25.2 ? (28.1) 5 25.2 ? A r25.2 B

0.4f0.4 5 300

0.4

28.1 5 r25.2 0.4f 5 300

7 5 b 2721 5 2b

21

p 5 229.16 27 5 2b 2p21 5 29.16

21 7 ? 21 5 7 ? A2b7 B

2p 5 29.16 21 5 2b7

x 5 4 x 5 5.33

12x12 5 48

12 9x9 5 48

9

12x 5 48 9x 5 48



7.

8.

9. 10.

11. Answers may vary. Sample: If x plus a positivenumber is 103, then x must be less than 103.

12. A 5 ( ) 3 ( ) 5 5 3 5 5 25; 25 ft2

TEST-TAKING STRATEGIES page 43

1. 90 1 15 5 105; 5 1 5 1 ; 1.75 h; grid 1.752. 3.2 1 1.3 1 2.7 1 3.6 5 6.8 1 4 5 10.8; 10.8 mi; grid10.8 3. For t 5 4, 9t 1 4 5 9(4) 1 4 5 36 1 4 5 40; $40;grid 40 4.

; $3.68; grid: 3.68

CHAPTER REVIEW pages 44–45

1. You simplify a numerical expression 2. The absolutevalue of a number is its distance from zero on a numberline. 3. The statement 5(a 1 6) 5 5a 1 30 shows theDistributive Property. 4. A value that makes anequation true is a solution. 5. Use inverse operations toisolate a variable in an equation. 6. A variable is asymbol that stands for one or more numbers. 7. Positiveand negative whole numbers are called integers. 8. Amathematical sentence with an equal sign is an equation.9. For x 5 2, 6(x 2 1) 5 6(2 2 1) 5 6(1) 5 6 10. For x 5 2, 242 4 x 1 5.5 5 242 4 2 1 5.5 5 221 1 5.5 5215.5. 11. For x 5 2, 242 4 (x 1 5.5) 5 242 4(2 1 5.5) 5 242 4 7.5 5 25.6.12. 27 1 g 13. 14. 500r15. Since 218 is farther to the left on the number linethan 211, 218 , 211; ,. 16. Since 237 is farther tothe left on the number line than 2, 237 , 2; ,.17. «234 5 34; since 34 is farther to the right on thenumber line than 21, «234« . 21; .. 18. «24« 5 4 and«4« 5 4, so «24« 5 «4«; 5. 19. 281 , 29; NorthAmerica 20. 29 1 (23) 5 212 21. 211 2 (25) 5211 1 5 5 26 22. 234 4 22 5 34 4 2 5 1723. 4(210) 5 240 24. 25 2 2 5 25 1 (22) 5 2725. 39 4 (23) 5 213 26. 315 2 65 2 13 1 26 5250 1 13 5 263; $263 27. (25)(168)(20) 5 (2100)(168) 5216,800 28. 125 1 394 1 575 5 700 1 394 5 1,09429. 4(218)(25) 5 100 3 (218) 5 21,80030. 3(p 2 7) 5 3p 2 21 31. (m 1 4)8 5 8m 1 3232. 25(22 2 k) 5 10 1 5k

33. 34.

Check: Check:

6 5 6✔ 23 5 23✔ 6 0 3 1 3 30 2 7 0 23

6 5 r 1 3 d 2 7 5 23

3 5 r d 5 30 6 2 3 5 r 1 3 2 3 d 2 7 1 7 5 23 1 7

6 5 r 1 3 d 2 7 5 23

u

y4

14.952 11.27

3.68

34

4560

10560

102

102

x 5 15 x 5 7

15x15 5 225

15 0.5x0.5 5 3.5

0.5

15x 5 225 0.5x 5 3.5

y 5 3

y 2 1.7 1 1.7 5 1.3 1 1.7

y 2 1.7 5 1.3

x 5 60

x 1 2912 2 291

2 5 8912 2 291

2

x 1 2912 5 891

235. 36.

Check: Check:

37. Check:

38. Check:

CHAPTER TEST page 46

1. The word ‘sum’ implies addition: v 1 18. 2. You get462 mi for g gallons and for 1 gallon: . 3. There are 365 days in a year, so there are years in d days; .4. One minute has 60 s, so the number of seconds in mminutes is 60m; 60m. 5. 6 1 3 ? 5 5 6 1 15 5 216. 18 4 (3 ? 2) 1 3 5 18 4 6 1 3 5 3 1 3 5 67. (10 1 14) 4 4 ? 2 5 24 4 4 ? 2 5 6 ? 2 5 128. 5 2 (8 1 6 4 2) 5 5 2 (8 1 3) 5 5 2 11 5 269. 9 2 5 1 2 ? 4 5 9 2 5 1 8 5 4 1 8 5 1210. 5 4 (1 1 4) ? 6 5 5 4 5 ? 6 5 1 ? 6 5 6 11. For b 5 8,b 1 7 5 8 1 7 5 15. For b 5 12, b 1 7 5 12 1 7 5 19.For b 5 20, b 1 7 5 20 1 7 5 27. The values are 15, 19,27. 12. For c 5 215, «c« 5 «215« 5 15. 13. For h 5 8,5 1 «h« 5 5 1 «8« 5 5 1 8 5 13 14. For v 5 27,2«3v« 5 2«3(27)« 5 2«221« 5 2(21) 5 221 15. Fort 5 9, 6 2 «2t« 5 6 2 «29« 5 6 2 9 5 23 16. For y 5

23, 4«y« 5 4«23« 5 4 ? 3 5 12 17. For f 5 16, «5f« 5

«5 ? 16« 5 «80« 5 80 18. Since 60 is farther from 0 than14 on the number line, the sum is positive: 60 2 14 5 4619. 7 2 24 5 7 1 (224); since 224 is farther from 0 than7 on the number line, the sum is negative: 217. 20. Thesigns are different, so the quotient is negative: 5 23.21. The signs are different so the product is negative:24 ? 3 5 212. 22. The signs are the same, so the productis positive: 29(28) 5 72. 23. There are an odd number ofnegative signs, so the product is negative: (22)(22)(22) 5(22)(4) 5 28 24. 6 1 (29) 5 23; 23 yd 25. Order thenumbers according to their relative position on thenumber line: 29, 24, 22, 0, 3. 26. Order the numbersaccording to their relative position on the number line:217, 214, 213, 8. 27. Order the numbers according totheir relative position on the number line: 210, 27, 23,21, 4. 28. Order the numbers according to their relativeposition on the number line: 221, 217, 2, 5, 22. 29. Form 5 24 and p 5 2, mp 2 5p 5 (24)(2) 2 5 ? 2 5 28 210 5 218. 30. For m 5 24 and p 5 2, (4p 2 m) 4 4 5(4 ? 2 2 (24)) 4 4 5 (8 1 4) 4 4 5 12 4 4 5 3. 31. For

m 5 24 and p 5 2, 5 5

5 5 1.8. 32. For m 5 24 and p 595

2 1 4 1 35

2 2 (24) 1 3

5p 2 m 1 3

5

2155

d365

d365

462g

462g

0.4 5 0.4✔ z 5 2

25 0 0.4 5 ?z5 5 5 ? 0.4

z5 5 0.4

z5 5 0.4

212 5 212✔ h 5 48

4824 0 212 24 ? h

24 5 (24) ? (212)

h24 5 212 h24 5 212

49 5 49✔8 5 8✔

7(7) 0 49 8 0 23 1 11

7p 5 49 8 5 23 1 a

p 5 7 11 5 a

7p7 5 49

7 8 1 3 5 23 1 a 1 3

7p 5 49 8 5 23 1 a



2, m 1 p ? (27) 5 24 1 2 ? (27) 5 24 1 (214) 5 218.33. Answers may vary. Sample: Positive integers canshow a change from deeper to less deep and negativeintegers show a change from deep to deeper.34. Regrouping does not change the product: Assoc.Prop. of Mult. 35. Multiplying a number by 1 does notchange the value: Ident. Prop. of Mult. 36. Switchingpositions of addends does not change the sum: Comm.Prop. of Add. 37. Distributing a common factor doesnot change the product: Dist. Prop. 38. 30(12) 530(10 1 2) 5 30 ? 10 1 30 ? 2 5 300 1 60 5 36039. 6 ? 32 5 6(30 1 2) 5 6 ? 30 1 6 ? 2 5 180 1 12 5192 40. 4(8.8) 5 4(9 2 0.2) 5 4 ? 9 2 4 ? 0.2 536 2 0.8 5 35.2

41. 42.

43. 44.

45. 46.

47.

The lowest point is 282 ft below sea level.

48.

The store sold 5 bicycles.

49. 4 1 (29)

TEST PREP page 47

1. According to Moore’s Law a computer of the sameprice will have twice the power after 18 months, so thecorrect choice is B. 2. After 3 years a computer of thesame price will have doubled in power twice so thecomputer will be 22, 2 ? 2, or 4 times as powerful; thecorrect choice is H. 3. After 4 years a computer of thesame price will have doubled in power three times so thecomputer will be 23, 2 ? 2 ? 2, or 8 times as powerful; thecorrect choice is C. 4. Let x 5 the number of 18 monthperiods it takes for computers to be 128 times aspowerful. 2x 5 128

x 5 77 ? 1.5 5 10.5 years; the correct choice is G.

5. The lesser divisors of 15 are 1, 3, and 5. 1 1 3 1 5 5 9;9 , 15; the correct choice is A. 6. The lesser divisors of18 are 1, 2, 3, 6, and 9. 1 1 2 1 3 1 6 1 9 5 21; 21 . 18;18 is abundant; the correct choice is F. 7. The lesserdivisors of 28 are 1, 2, 4, 7, and 14. 1 1 2 1 4 1 7 1 14 528; 28 5 28; 28 is a perfect number; the correct choice C.8. Check each answer to find which is an abundantnumber. A: the lesser divisors of 9 are 1 and 3. 1 1 3 5 4;

12

b 5 5

250b250 5

1,250250

250b 5 1,250

x 5 2282

x 1 11,331 2 11,331 5 11,049 2 11,331

x 1 11,331 5 11,049

y 5 29 w 5 11

2 1 y 2 2 5 27 2 2 w 1 7 2 7 5 18 2 7

2 1 y 5 27 w 1 7 5 18

x 5 25.2 h 5 26

x 1 4 2 4 5 21.2 2 4 3h3 5 218

3

x 1 4 5 21.2 3h 5 218

a 5 25 m 5 55

22 ? a22 5 22 ? 2.5 m 2 45 1 45 5 10 1 45

a22 5 2.5m 2 45 5 10

4 , 9, so 9 is deficient, not an abundant number. B: thelesser divisors of 16 are 1, 2, 4, and 8. 1 1 2 1 4 1 8 5 15;15 , 16, so 16 is deficient, not an abundant number. C:the lesser divisors of 32 are 1, 2, 4, 8, and 16. 1 1 2 1 4 18 1 16 5 31; 31 , 32, so 32 is deficient, not an abundantnumber. D: the lesser divisors of 40 are 1, 2, 4, 5, 8, 10,and 20. 1 1 2 1 4 1 5 1 8 1 10 1 20 5 50; 50 . 40, so 40is abundant; the correct choice is J.

DK PROBLEM SOLVING APPLICATIONpages 48–49

1a. The starting place is the origin, (0, 0). The sub startsat an elevation of 0 (on the surface) and at a horizontalposition of 0. 1b. The horizontal position increases (15)because the sub goes forward (to the right). The verticaldecreases as the sub dives below the surface.

2.

From point

Vertical

Horizontal

initial + change

To point

= end

E F

–20 0 –20

+50 +5 +55

From point

Vertical

Horizontal

initial + change

To point

= end

D E

–40 +20 –20

+35 +15 +50

From point

Vertical

Horizontal

initial + change

To point

= end

C D

–35 –5 –40

+25 +10 +35

From point

Vertical

Horizontal

initial + change

To point

= end

B C

–15 –20 –35

+5 +20 +25



From point

Vertical

Horizontal

initial + change

To point

= end

G H

–30 –10 –40

+60 0 +60

From point

Vertical

Horizontal

initial + change

To point

= end

F G

–20 –10 –30

+55 +5 +60

3a–c. Check students’ work.

From point

Vertical

Horizontal

initial + change

To point

= end

I X

–45 0 –45

+65 +5 +70

From point

Vertical

Horizontal

initial + change

To point

= end

H I

–40 –5 –45

+60 +5 +65




Chapter

2Rational Numbers pages 50–103


1. For n 5 4, 3(n 1 2) 2 n 5 3(4 1 2) 2 4 5 3(6) 2 4 518 2 4 5 14. 2. For n 5 4, 3n 1 2 ? 5 5 3(4) 1 2 ? 5 512 1 10 5 22. 3. For n 5 4, ? n 5 ? 4 5

? 4 5 ? 4 5 2. 4. For n 5 4, 5 5 5 2.5. The order from left to right on a number line is 211,24, 0, 3, so this is the order from least to greatest.6. The order from left to right on a number line is 29,26, 8, 13, so this is the order from least to greatest.7. The order from left to right on a number line is 221,28, 9, 16, so this is the order from least to greatest.8. The order from left to right on a number line is 235,217, 23, 22, so this is the order from least to greatest.9. 25 1 8 5 3 10. 16 2 29 5 16 1 (229) 5 213 11. 223 1 (214) 5 237 12. 236 2 (211) 5236 1 11 5 225 13. The signs are different, so theproduct is negative: 4 ? (212) 5 248 14. The signs are different, so the quotient is negative: 5 2615. There are an even number of negative factors, so theproduct is positive: 27 ? 2 ? (23) 5 21 ? 2 5 42 16. The signs are the same, so the quotient is positive:

5 5 9

2-1 Factors pages 52–56

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. product 2. 2100 3. 564. 40 5. 0

Quick Check 1. composite; divisible by 22a.

2b.

3a. Find the factors of 54: 1, 2, 3, 6, 9, 18, 27, 54; find thefactors of 63: 1, 3, 7, 9, 21, 63; the GCF is 9. 3b. Find the

240

1202

602

302

152

3 5

96

166

32 4 4

2 2 2 2

10812

2108212

2549

84

3 1 54

3 1 5n

12

36

34 1 2

3n 1 2

factors of 18: 1, 2, 3, 6, 9, 18; find the factors of 48: 1, 2, 3,4, 6, 8, 12, 16, 24, 48; the GCF is 6. 4. The factors of 63are 1, 3, 7, 9, 21, and 63. The factors of 84 are 1, 2, 3, 4, 6,7, 12, 14, 21, 28, 42, and 84. The common factors are 1, 3,7, and 21. The GCF is 21. The length of each pipe shouldbe 21 ft.

Exercises 1. The greatest number that is a factor of twoor more numbers is the GCF of the numbers. 2. Thefactors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. 3. No; the onesdigit is not 0, 2, 4, 6, or 8, therefore, 2 is not a factor of105, that means 105 is not divisible by 2. 4. No; the onesdigit is not 0 or 5, therefore, 5 is not a factor of 91, thatmeans 91 is not divisible by 5. 5. Yes; the sum of thedigits is 6, which is divisible by 3, therefore, 3 is a factorof 123, that means 123 is divisible by 3. 6. In Elliot’swork, all factors are prime; in Sophia’s work, the 4 canbe factored into 2 3 2. 7. composite; 48 is a wholenumber greater than 1 with more than 2 factors; 48 52 ? 2 ? 2 ? 2 ? 3 8. composite; 25 is a whole numbergreater than 1 with more than 2 factors; 25 5 5 ? 59. prime; 73 is a whole number greater than 1 withexactly 2 factors, 1 and itself 10. prime; 79 is a wholenumber greater than 1 with exactly 2 factors, 1 and itself11. composite; 99 is a whole number greater than 1 withmore than 2 factors; 99 5 3 ? 3 ? 11 12. composite; 250is a whole number greater than 1 with more than 2factors; 250 5 2 ? 5 ? 5 ? 5 13. prime; 101 is a wholenumber greater than 1 with exactly 2 factors, 1 and itself14. composite; 1,011 is a whole number greater than 1with more than 2 factors; 1,011 5 3 ? 33715. 16. 17.

18. 19.

33

3

27

9

55

2

100

50

2

2002

400

252

22

2

16

8

4232

2

12

6

52

2

20

10

phm07c3_sk_ch02 _natl.qxd 8/22/06 10:04 AM Page 14


20. 21. 22.

23. The factors of 6 are 1, 2, 3, and 6. The factors of 18are 1, 2, 3, 6, 9, and 18. The common factors are 1, 2, 3,and 6. The GCF is 6. 24. The factors of 15 are 1, 3, 5, and15. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. Thecommon factors are 1 and 3. The GCF is 3. 25. Thefactors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The factors of72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The commonfactors are 1, 2, 3, and 6. The GCF is 6. 26. The factorsof 21 are 1, 3, 7, and 21. The factors of 63 are 1, 3, 7, 9, 21,and 63. The common factors are 1, 3, 7, and 21. The GCFis 21. 27. The factors of 52 are 1, 2, 4, 13, 26, and 52. Thefactors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78. The commonfactors are 1, 2, 13, and 26. The GCF is 26. 28. Thefactors of 38 are 1, 2, 19, and 38. The factors of 82 are 1,2, 41, and 82. The common factors are 1 and 2. The GCFis 2. 29. The factors of 44 are 1, 2, 4, 11, 22, and 44. Thefactors of 68 are 1, 2, 4, 17, 34, and 68. The commonfactors are 1, 2 and 4. The GCF is 4. 30. The factors of30 are 1, 2, 3, 5, 6, 10, 15, and 30. The factors of 50 are 1,2, 5, 10, 25, and 50. The common factors are 1, 2, 5, and10. The GCF is 10. 31. The prime factorization of 14 is 2 ? 7. The prime factorization of 35 is 7 ? 5. The GCF is 7.32. The prime factorization of 27 is 3 ? 3 ? 3. The primefactorization of 36 is 2 ? 2 ? 3 ? 3. The GCF is 3 ? 3, or 9.33. The prime factorization of 30 is 2 ? 3 ? 5. The primefactorization of 45 is 3 ? 3 ? 5. The GCF is 3 ? 5, or 15.34. The prime factorization of 32 is 2 ? 2 ? 2 ? 2 ? 2. Theprime factorization of 48 is 2 ? 2 ? 2 ? 2 ? 3. The GCF is 2 ? 2 ? 2 ? 2, or 16. 35. The prime factorization of 44 is 2 ? 2 ? 11. The prime factorization of 66 is 2 ? 3 ? 11. TheGCF is 2 ? 11, or 22. 36. The prime factorization of 62 is2 ? 31. The prime factorization of 93 is 3 ? 31. The GCF is31. 37. The prime factorization of 86 is 2 ? 43. The primefactorization of 94 is 2 ? 47. The GCF is 2. 38. The primefactorization of 57 is 3 ? 19. The prime factorization of 76is 2 ? 2 ? 19. The GCF is 19. 39. Find the GCF of 50 and75. The factors of 50 are 1, 2, 5, 10, 25, and 50. The factorsof 75 are 1, 3, 5, 15, 25, and 75. The GCF is 25. Thegreatest number of groups that can be made is 25.40. Find the GCF of 35 and 15. The factors of 35 are 1, 5,7, and 35. The factors of 15 are 1, 3, 5, and 15. Thecommon factors are 1 and 5. The GCF is 5. The longestpossible side of each square is 5 m. The greatest possibledimension are 5 m by 5 m. 41. Find the GCF of 36, 72,and 144. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and72. The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24,36, 48, 72, and 144. The common factors are 1, 2, 3, 4, 6, 9,12, 18, and 36. The GCF is 36. The greatest number ofstudents who can receive fruit is 36.

133

39

72

2

56

28

142

132

26 42.

2 2 2 2 2 3 2 2 2 2 2 3Regardless of the method used, the prime factorizationof a number consists of only prime numbers. 43. Findthe GCF of 48 and 300. The factors of 48 are 1, 2, 3, 4, 6,8, 12, 16, 24, 48. The factors of 300 are 1, 2, 3, 4, 5, 6, 10,12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300. The commonfactors are 1, 2, 3, 4, 6, and 12. The GCF is 12. Each rowhas 12 chairs. 44. The prime factorization of 22 is 2 ? 11.The prime factorization of 33 is 3 ? 11. The primefactorization of 44 is 2 ? 2 ? 11. The GCF is 11. 45. Theprime factorization of 27 is 3 ? 3 ? 3. The primefactorization of 45 is 3 ? 3 ? 5. The prime factorization of281 is 23 ? 3 ? 3 ? 3. The GCF is 3 ? 3, or 9. 46. Theprime factorization of 12 is 2 ? 2 ? 3. The primefactorization of 224 is 22 ? 2 ? 2 ? 3. The primefactorization of 36 is 2 ? 2 ? 3 ? 3. The GCF is 2 ? 2 ? 3, or12. 47. Answers may vary. Samples are given. 7 1 53;13 1 47; 17 1 43; 19 1 41; 23 1 37; 29 1 31 48a. Findthe GCF of 120, 78, 24, and 54. The prime factorizationof 120 is 2 ? 2 ? 2 ? 3 ? 5. The prime factorization of 78 is 2 ? 3 ? 13. The prime factorization of 24 is 2 ? 2 ? 2 ? 3. Theprime factorization of 54 is 2 ? 3 ? 3 ? 3. The GCF is 2 ? 3,or 6. There are 6 classes. 48b. 120 4 6 5 20; 78 4 6 513; 24 4 6 5 4; 54 4 6 5 9; each class gets 20paintbrushes, 13 boxes of markers, 4 packs of paper, and9 sets of watercolors. 49. Since w is divisible by 2 and 2is divisible by 2, w 1 2 is also divisible by 2. 50. 1; thefactors of any prime number are 1 and the number.51. For x 5 0, 2x2 1 7x 1 7 5 2(0)2 1 7(0) 1 7 5 7.For x 5 2, 2x2 1 7x 1 7 5 2(2)2 1 7(2) 1 7 52(2)(2) 1 7(2) 1 7 5 24 1 14 1 7 5 17. For x 5 3,2x2 1 7x 1 7 5 2(3)2 1 7(3) 1 7 5 2(3)(3) 1 7(3) 1 7 529 1 21 1 7 5 19. Each result is divisible only by 1 anditself, so 7, 17, and 19 are all prime. 52. Two of thefactors are 1 and itself. The other factors must be powersof the least prime factor, which is 2. So, the factors are 1,2, 22, 23, and 24, or 1, 2, 4, 8, and 16. 53. 2 ft 5

2(12) 1 (12) 5 24 1 6, or 30 in.; 30 in. 2 18 in. 5 12 in. 5

1 ft 54. For x 5 3, 5(1.25) 1 x(1.45) 5 5(1.25) 1 3(1.45) 56.25 1 4.35 5 10.60; $10.60 55. 10 3 3 1 6 3 4 1 4 3 5 530 1 24 1 20 5 74 56. 3.4 1 5.6 1 8.3 5 9 1 8.3 5 17.357. 6 ? (27) ? 5 5 27 ? 30 5 2210 58. 12(8.1) 512(8 1 0.1) 5 96 1 1.2 5 97.2

2-2 Equivalent Forms of RationalNumbers pages 57–60

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. 2 ? 2 ? 5 ? 5 2. 6 3. 4

12

12

??????????

22 22

6

96

16

4432

22 22

8

96

12

4342



4. 25 5. 4Quick Check 1. The GCF of 12 and 20 is 4; 5

5 . 2. 5 5 3. 5 39 4 85 5 0.459

4. 1.42 5 5 5 5 1

Exercises 1. Since 123 is a rational number, it can be written in the form . 2. Yes; 5 0.441, 5 0.457, so

it increased from 0.441 to 0.457. 3. 5 0.25; the correct

choice is D. 4. 5 0.3; the correct choice is C. 5. 5

0.5; the correct choice is A. 6. 5 0.4; the correct choice

is B. 7. 5 5 8. 5 5 9. 2 5

2 5 2 10. 2 5 2 5 2 11. 5

5 12. 5 5 13. 2 5 2 5

2 14. 5 5 15. 5 2 4 3 < 0.667 16. 5

8 4 25 5 0.320 17. 5 17 4 16 < 1.063 18. 5

16 4 17 < 0.941 19. 2 5 213 4 7 < 21.857 20. 5

9 4 45 5 0.200 21. 5 5 4 13 < 0.385 22. 2 5

228 4 35 5 20.800 23. 34 hits in 102 times 5 5

34 4 102 < 0.333; 24 hits in 96 times 5 24 4 96 < 0.250;

0.333, 0.250 24. 1.4 5 5 5 5 1 25. 0.33 5 5

26. 0.24 5 5 5 27. 4.44 5 5 5

5 4 28. 2.8 5 5 5 5 2 29. 0.05 5 5

5 30. 0.005 5 5 5 31. 7.32 5 5

5 5 7 32. Restaurant A: 5 56 4 98 < 0.571;

Restaurant B: < 0.571; They have the same record.

33. 0.219 5 5 34. 5 1 4 4 5 0.25; 5

1 4 4 5 0.25; 5 1 4 3 5 0. ; 5 1 4 6 5 0.1 35. For

a 5 3 and b 5 25, 5 5 2 5 2 5 2 .

36. 5 24 4 25 5 0.960 37. 0.980 5 , he cannot

forget just of a birthday. 38. 5 5

39. 5 5 ; the correct choice is A. 40. 211 isless than 23, 1 and 5. 23 is more than 211 and is lessthan 1 and 5. 1 is more than 211 and 23 and is less than5. 5 is more than 211, 23, and 1. 211 , 23 , 1 , 5;211, 23, 1, 5; the correct choice is J. 41. By the Order ofOperations, Brandon should have divided 16 by 4 beforemultiplying 4 by 2; the correct choice is A.42. 219 1 (26) 5 225 43. 211 1 20 5 944. 225 2 25 5 225 1 (225) 5 250 45. 19 2 (215) 519 1 15 5 34


1. n 5 0. ; 10n 5 5. ; 10n 2 n 5 5. 2 0. ; 9n 5 5; n 5

2. n 5 0. ; 10n 5 7. ; 10n 2 n 5 7. 2 0. ; 9n 5 7; n 5

3. n 5 0. ; 100n 5 24. ; 100n 2 n 5 24. 2 0. ;99n 5 24; n 5 5 4. n 5 0. ; 100n 5 15. ;

100n 2 n 5 15. 2 0. ; 99n 5 15; n 5 5 5. n 5

0. ; 1,000n 5 135. ; 1,000n 2 n 5 135. 2 0. ;135135135135

533

15991515

1515833

2499

24242424

797777

595555

18

3 4 324 4 3

324

1101

77 4 777,777 4 77

777,777

12

24.525

2425

25

42(5)

1 1 32(5)

1 1 32(25)

1 1 a2b

61631

3

14

14

2191,000

0.2191

84147

5698

825

18325

732100

7.321

1200

51,000

0.0051

120

5100

0.051

45

145

2810

2.81

1125

11125

444100

4.441

625

24100

0.241

33100

0.331

25

75

1410

1.41

34102

2835

513

945

137

1617

1716

825

23

15

12 4 1260 4 12

1260

27

4 4 214 4 2

414

29

18 4 981 4 9

1881

15

20 4 20100 4 20

20100

29

12 4 654 4 6

1254

23

40 4 2060 4 20

4060

34

48 4 1664 4 16

4864

34

15 4 520 4 5

1520

25

12

310

14

1635

1534

1231

2150

7150

142100

1.421

3985

35

3 ? 3 ? 33 ? 3 ? 5

2745

35

12 4 420 4 4

1220

999n 5 135; n 5 5 6. n 5 0. ; 1,000n 5 282. ;

1,000n 2 n 5 282. 2 0. ; 999n 5 282; n 5 5

7. A repeating number is a rational number, because

it can be written in the form where b ? 0. For example,

0. 5 .

2-3 Comparing and OrderingRational Numbers pages 62–65

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. The numerator represents a part of the whole. 2. 3. 4. 5.

Quick Check 1. The multiples of 6 are 6, 12, 18, cThemultiples of 9 are 9, 18, c 5 5 ; 5 5 ;

since . , . ; , ; 2. Cats: 5 0.7; Dogs: 5

0.706; Dogs have the greater fraction of males because. . 3. 5 1.600; 1 5 1.500; 20.625 5 20.625; 2 5

20.875; 1.61 5 1.610; 20.875 , 20.625 , 1.500 , 1.600

, 1.610; 2 , 20.625, 1 , , 1.61

Exercises 1. The LCM is the smallest number that is a multiple of both numbers. 2. greater; 5 , .

3. 5 5 ; 5 5 ; since . , . ; .

4. 5 5 ; 5 5 ; since . , . ; .

5. 5 5 ; 5 5 ; since , , , ; .

6. 2 < 20.417; 20.4 5 20.400; 2 5 20.500; 2 <20.444; 20.4 is the largest. 7. The multiples of 15 are 15,30, 45, 60, 75, cThe multiples of 25 are 25, 50, 75, c

5 5 ; 5 5 ; since , , , ; .

8. 5 5 ; 5 5 ; since . , . ; .

9. The multiples of 21 are 21, 42, cThe multiples of 14

are 14, 28, 42, c2 5 2 5 2 ; 2 5 2 5

2 ; since 2 , 2 , 2 , 2 ; 2 . 10. 5 5 ;

5 5 ; since . , . ; . 11. The multiplesof 8 are 8, 16, 24, cThe multiples of 12 are 12, 24, c

5 5 ; 5 5 ; since , , , ; .

12. The multiples of 26 are 26, 52, 78,…The multiples of

39 are 39, 78,…2 5 2 5 2 ; 2 5 2 5

2 ; since 2 5 2 , 2 5 2 ; they are equal.13. The multiples of 22 are 22, 44, 66,…The multiples of33 are 33, 66,…2 5 2 5 2 ; 2 5 2 5

2 ; since 2 , 2 , 2 , 2 ; 2 14. The multiples of 20 are 20, 40, 60, cThe multiples of 15 are15, 30, 45, 60, c2 5 2 5 2 ; 2 5 2 5

2 ; since 2 . 2 , 2 . 2 ; 2 . 15. < 0.1204;

< 0.0987; since 0.1204 . 0.0987, the group having thegreater fraction of left-handed people was the men.16. < 0.692; < 0.679; since 0.692 . 0.679, . ; 9

131928

913

1928

913

23233

13108

920

715

920

2860

2760

2860

7 ? 415 ? 4

715

2760

9 ? 320 ? 3

920

1433

1433

1322

2866

3966

2866

14 ? 233 ? 2

1433

3966

13 ? 322 ? 3

1322

939

626

1878

1878

1878

9 ? 239 ? 2

939

1878

6 ? 326 ? 3

626

512

512

38

1024

924

1024

5 ? 212 ? 2

512

924

3 ? 38 ? 3

38

78

67

78

4856

4956

4856

6 ? 87 ? 8

67

4956

7 ? 78 ? 7

78

514

514

1021

1542

2042

1542

5 ? 314 ? 3

514

2042

10 ? 221 ? 2

1021

25

411

25

2055

2255

2055

4 ? 511 ? 5

411

2255

2 ? 115 ? 11

25

425

425

215

1275

1075

1275

4 ? 325 ? 3

425

1075

2 ? 515 ? 5

215

49

12

512

45

45

34

1620

1520

1620

4 ? 45 ? 4

45

1520

3 ? 54 ? 5

34

57

23

57

1421

1521

1421

2 ? 73 ? 7

23

1521

5 ? 37 ? 3

57

29

17

29

963

1463

963

1 ? 97 ? 9

17

1463

2 ? 79 ? 7

29

1428

1528

1428

12

85

12

78

78

12

85

710

1217

1217

710

16

218

318

19

16

218

318

218

1 ? 29 ? 2

19

318

1 ? 36 ? 3

16

111

14

311

35

191

ab

94333

282999282282

282282537

135999



17. < 1.706; < 1.727; since 1.727 . 1.706, . ; .

18. 2 5 21.375; 2 < 21.367;

since 21.367 . 21.375, 2 . 2 ; 2 . 19. 2 <20.632; 2 < 20.630; since 20.630 . 20.632,2 . 2 ; 2 . 20. < 0.769; < 0.789; 0.8 5 0.800;

23.13 5 23.130; 23.130 , 0.769 , 0.789 , 0.800; 23.13,

, , 0.8 21. < 0.333; 5 0.300; 0.03 5 0.030; 0.33 5

0.330; 0.030 , 0.300 , 0.330 , 0.333; 0.03, , 0.33,

22. 24 5 24.000; 23.9 5 23.900; 2 < 20.222; <0.182; 24.000 , 23.900 , 20.222 , 0.182; 24, 23.9, 2 ,

23. < 0.714; < 1.667; < 0.833; 5 2.5;

0.714 , 0.833 , 1.667 , 2.5; , , , 24. 5 0.500; 5

0.429; since 0.500 . 0.429, . ; lunch A 25. <

0.417; 5 < 0.462; since 0.417 , 0.462, , ;

greater. 26. 5 0.125; < 0.714; 0.125 , 0.714;

, ; , 27. 2 5 20.375; 5 28. 5 0.250;

0.250 . 0.025; . 0.025; . 29. 21 5 21.000; 2 <20.818; 21.000 , 20.818; 21 , 2 ; , 30. Answersmay vary. Sample: Change the fraction to a decimal andcompare it to 0.5; subtract the numerator from thedenominator and, if the result is less than the numerator,the fraction is greater than , and, if it is more, the

fraction is less than . 31. < 0.545; 5 <

0.848; since 0.848 . 0.545, . ; your friend 32. , , ,

; when the numerators are the same, the larger the denominator is, the smaller the value. 33. Erika worked5 min from 4:55 to 5:00 and 30 min from 5:00 to 5:30, for a total of 5 1 30, or 35 min. Maria worked h which is

the same as 5 , or 40 min. Erika worked 35 min and Maria worked 40 min; Maria. 34. The digits repeatin groups of 3, in the order of 3, 6, 5. Since 100 4 3 5 33R1, there are 33 complete groups of 3 with 1 digitremaining. The first digit in each group is 3, so the 100th digit is 3. 35. Mr. Alpert: < 0.167; Ms. Bee: 5 0.250;

Mr. Coe: 5 0.333; Ms. Drew: 50.500; the correct

choice is D. 36. Adrianna: < 0.429; Paul: < 0.444;

Jennifer: 5 0.500; Brian: < 0.455;0.429 , 0.444 , 0.455 , 0.500; 0.444: Paul; the correctchoice is J. 37. 58° 1 14° 2 4° 1 2° 1 1° 5 71°; thecorrect choice is C. 38. 9(r 2 7) 5 9r 2 6339. 28(26 1 b) 5 48 2 8b 40. (t 2 4)10 5 10t 2 40

2-4 Adding and SubtractingRational Numbers pages 66–69

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. 2, 0, 26 2. 210 3. 2904. 10

Quick Check 1. 1 5 1 5 1 515150

20150

1 ? 1510 ? 15

2 ? 1015 ? 10

110

215

511

24

49

37

3774

1236

2080

742

4060

2 ? 203 ? 20

23

53

54

57

58

3055

3946

3946

46 2 746

3055

12

12

911

911

14

14

38

57

18

57

18

613

512

613

5 1 112 1 1

512

2149

2652

2149

2652

52

53

56

57

52

56

53

57

211

29

211

29

13

310

310

13

1519

1013

1519

1013

1727

1219

1727

1727

1219

4130

118

4130

4130

118

1911

2917

1911

1911

2917 5 5 2. The LCD of 10 and 4 is 20: 2 5

2 5 5 2 . 3. 4 1 2 5 1 5 1 5

5 6 4. 17 1 x 5 20 ; 17 1 x 2 17 5

20 2 17 5 20 2 17 5 19 2 17 5 2 5 2 ; 2 in.

Exercises 1. The multiples of 2 are 2, 4, 6, 8, 10,…Themultiples of 10 are 10, 20,…The LCD is 10. 2. Themultiples of 3 are 3, 6, 9, 12, 15,…The multiples of 5 are5, 10, 15,…The LCD is 15. 3. The multiples of 4 are 4, 8,12, 16, 20, 24, 28,…The multiples of 14 are 14, 28,…The LCD is 28. 4. 1 A2 B 5 1 A B 5 5 5 2

5. 2 5 5 5 6. 3 1 2 5 3 1 2 5 5 5

5 1 1 5 6 7. Positive; 51 . 50, so , , and 2

is positive. 8. 1 5 1 5 1 5

9. 1 5 1 5 1 5 5 1

10. 2 1A2 B 5 1 A B 5 1 A B 5

1 A B 5 5 2 11. 1 5 1 5

1 5 5 1 12. 1 5 1 5

1 5 13. 2 1 A2 B 5 1 A B 5

1 A B 5 1 A B 5 5

2 14. 1 5 1 5 1 5 5

15. 2 5 2 5 2 5 . 16. 2 5

2 5 2 5 . 17. 2 5 2 5

2 5 . 18. 2 5 2 5 2 5

. 19. 2 5 2 5 2 5 5

5 2 . 20. 3 2(2 ) 5 3 1 5 3 1 5 3 5

3 1 1 5 4 5 4 21. 2 (22 ) 5 1 2 5 1 2 5

2 5 2 1 1 5 3 5 3 22. 1 2 (2 ) 5 1 1 5

1 1 5 1 5 1 23. 22 2 4 5 22 1 A24 B 5

22 1 A24 B 5 26 24. 24 2 6 5 24 1 A26 B 5

24 1 A26 B 5 210 25. 25 1 8 52A5 B 1 A8 B 5

2A5 1 B 1 A8 1 B 5 25 1 A2 B 1 8 1 5 3 1 5

3 26. 27 1 (2 ) 5 27 1 (2 ) 5 27 5

27 1 (21 ) 5 28 27. 7 1 11 5 7 1 11 5

18 5 18 1 1 5 19 28. 7 2 6 5 7 2 6 5

6 1 1 2 6 5 6 1 2 6 5 6 2 6 5 ; in.29. All of the students can be represented by 1, so,subtract the sum of and from 1 to find the remainder

of the students: 1 2 A 1 B 5 1 2 A 1 B 5 1 2 A B 5

2 5 5 . 30. 1 1 1 5 2 5 3; 3 in.

31. a 1 x 5 3; a 5 32. 2 1 x 5 2b; b 5

1 x 5 3 2 1 x 5 2

2 x 1 5 3 2 2 1 x 1 A22 B 5 2 1 (22 Bx 5 3 2 x 5 2 1 A22 Bx 5 2 2 x 5 2 1 A22 Bx 5 2 x 5 22

x 5 2212

36

12

16

26

12

22

16

13

12

16

13

16

16

12

12

12

13

16

12

13

16

12

22

12

12

25

410

610

1010

610

110

510

110

12

110

12

910

910

610

1510

610

1510

610

510

610

510

35

12

215

215

1715

515

1215

13

45

320

320

2320

1520

820

34

25

16

16

46

36

46

36

46

36

23

12

1112

312

812

14

23

14

23

38

28

18

14

18

14

18

320

960

560

460

560

115

560

115

16

212

212

1412

512

912

512

34

512

34

12

36

36

96

46

56

23

56

23

56

1330

21330

9 2 2230

2230

930

11 ? 215 ? 2

3 ? 310 ? 3

1115

310

130

330

430

1 ? 310 ? 3

2 ? 215 ? 2

110

215

110

810

910

4 ? 25 ? 2

910

45

910

421

221

621

221

2 ? 37 ? 3

221

27

49

29

69

29

2 ? 33 ? 3

29

23

1936

57108

12108

45108

1 ? 129 ? 12

5 ? 912 ? 9

19

512

1718

25154

24554

2654

25 ? 96 ? 9

21 ? 69 ? 6

256

219

56

19

1990

1090

990

1 ? 109 ? 10

1 ? 910 ? 9

19

110

115

1615

1015

615

2 ? 53 ? 5

2 ? 35 ? 3

23

25

2435

22435

21435

21035

22 ? 75 ? 7

22 ? 57 ? 5

225

227

25

27

340

4340

840

3540

1 ? 85 ? 8

7 ? 58 ? 5

15

78

1721

1421

321

2 ? 73 ? 7

1 ? 37 ? 3

23

17

151

150

150

151

215

215

1715

1215

515

45

13

12

36

5 2 26

26

56

14

228

5 2 78

278

58

78

58

12

12

510

810

1310

810

310

45

310

45

45

310

45

1920

13920

5520

8420

114

215

34

15

320

2 2 520

520

220

14

110

730

35 4 5150 4 5

35150



33. c 1 x 5 ; c 5 34. x 2 a 5 c; a 5 , c 5

1 x 5 x 2 5

1 x 2 5 2 x 2 1 5 1

x 5 2 x 5 1

x 5 2 x 5 1

x 5 2 x 5

35. 25 1 x 5 2 1 a; a 5 36. x 2 1 5 b; b 5

25 1 x 5 2 1 x 2 1 5

25 1x15 5 2 1 1 5 x 2 1 1 1 5 1 1

x 5 2 1 1 5 x 5 1 1

x 5 8 x 5 1 1

x 5 1

37. 2 5 2 5 38. 4 2 1 5 4 2 1 5

3 2 1 5 2 ; 2 in. 39. Answers may vary. Sample:

1 5 ; 5 , instead of finding the least common

denominator between the two fractions the student justadded the two denominators together. 40. You canrewrite all of the fractions using the LCD. Then add theintegers together and add the fractions together.Simplify. 41. When b 5 a 1 , b 2 1 5 a 1 2 1 5a 1 2 5 a 2 . 42. 1 1 2 1 1 3 1 1 5

1 1 2 1 1 3 1 1 5

1 1 2 1 3 1 1 1 1 1 1 1 5 7 1 5

7 1 2 5 9 ; the correct choice is C. 43. < 0.243;

< 4.111; 1, 2, 3, 4; the correct choice is H. 44. red: 5

0.500; blue: < 0.636; white: < 0.556; green: 5 0.800;

the correct choice is B. 45. 0.8 5 0.800; 5 0.008; 5

0.880; 0.008 , 0.800 , 0.808 , 0.880; , 0.8, 0.808,

46. 22 5 22.660; 22 5 22.060;

22.660 , 22.6 , 22.060 , 22.006; 22 , 22.6,22 , 22.006


1. 2 2 2 3 3 7

2. The factors of 99 are 1, 3, 9, 11, 33, and 99. The factorsof 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132. Thecommon factors are 1, 3, 11, and 33. The GCF is 33.3. 5 0.296 4. 0.56 5 5 5 5 5. 5

0.320; 2 < 22.143; 22.6 , 22.143 , 0.320 , 0.35 , 2;157

825

1425

2850

56100

0.561

827

?????

73

22

32

504

1264

216

350

3350

350

3350

2225

1125

2225

1125

45

59

711

12

379

937

720

720

4720

1620

420

1520

220

1020

1620

420

1520

220

1020

45

15

34

110

12

23

33

13

13

13

15

12 1 3

56

13

12

712

712

812

1512

812

312

23

14

821

621

1421

27

23

56

36

26

12

13

12

12

12

13

12

12

12

12

12

12

13

12

12

12

13

12

12

12

34

18

24

14

28

18

12

14

14

18

12

14

12

12

14

18

14

14

14

12

18

14

14

12

14

18 22.6, 2 , , 0.35, 2 6. 1 5 1 5 5

7. 5 2 5 4 1 1 2 5 4 1 2 5 4 1 5 4

8. 22 1 5 2 1 5 2 1 5 2 5 21

9. 2 2 5 5 2 5 2 5 2 5 22

10. 1 2 5 1 2 5 1 ; 1 c


1. ? 5

2. ? 5

3. ? 5 5

4. ? 5 5 215

1290

49

310

14

624

38

23

320

15

34

512

56

12

18

18

38

48

38

12

920

4920

10520

5620

214

145

14

45

2324

4724

524

5224

524

136

524

16

35

35

25

55

25

25

79

6 1 19

19

69

19

23

825

157



5. ? 5

6. ? 5 7. 3 ? 9 5 27 8. 4 ? 10 5 40

2-5 Multiplying and DividingRational Numbers pages 72–76

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies or Presentation Pro CD-ROM. 1. 2. 3. 4. 5.

Quick Check 1. Since the product of two negative numbers is positive, 2 ? A2 B 5 ? 5 5 5

2. 2 ? A21 B 5 ? A2 B 5 2 5 2 5 22

3. 13 4 2 5 4 5 ? 5 ? 5 5 5 ;

since you cannot make length, you can cut 5 lengths.

4. p 5 3 ; ? p 5 ? 3 ; p 5 ? 5 5 8

More Than One Way Use Eric’s method: 50 4 1 5

4 5 ? 5 5 33 ; I need 40 days worth of food and I have only 33 days worth of food. No, you only haveenough for 33 days; check students’ work.

Exercises 1. The reciprocal of a number is also called its multiplicative inverse. 2. x 5 2 ; < 1; 2 < 3; 1x 5

3; x 5 ; x < 3 3. ? 5 1; 1 4. 2 ? (2 ) 5 1; 2

5. 25 ? (2 ) 5 1; 25 6. 2 ? A2 B 5 ? 5 5 5

7. ? A2 B 5 2 ? 5 2 5 2 5 2

8. 2 ? A2 B 5 ? 5 5 5 5 3

9. 2 ? 5 2 5 2 10. 2 ? 5 2 5 2 5

2 11. ? A2 B 5 2 ? 5 2 5 2 5 2

12. 21 ? A24 B 5 1 ? 4 5 ? 5 5 6 13. 3 ? 2 5

? 5 5 5 5 8 14. 22 ? 4 5 2 ? 5

2 5 2 5 2 5 211 15. 4 A2 B 5 ? A2 B 5

2 ? 5 2 ? 5 2 16. 2 4 5 2 ? 5 2 ? 5

2 5 25 17. 8 4 5 4 5 ? 5 ? 5 17

18. 2 4 A2 B 5 4 5 ? 5 19. 4 100 5

4 5 ? 5 ? 5 20. 23 4 5

2 4 5 2 ? 5 2 ? 5 233 21. 4 A2 B 5

? A2 B 5 2 ? 5 2 22. 3 4 (29) 5 4 A2 B 5

? A2 B 5 2 ? 5 2 ? 5 2 23. 4 1 5 4 5

? 5 ? 5 24. m 5 5 ; m 5 ; ? m 5 ? ; m 5112

41

14

41

112

14

12

14

29

19

21

79

27

97

27

27

27

25

11

25

19

185

19

185

91

185

35

34

31

14

31

14

13

14

11

331

101

3310

110

3310

110

310

1101

11

1101

1100

100101

1001

100101

100101

4981

79

79

97

79

97

79

171

11

178

81

817

81

817

13

163

21

83

61

89

16

89

23

23

11

43

12

43

12

34

12

111

11 ? 11 ? 1

11 ? 44 ? 1

41

114

34

34

354

5 ? 74 ? 1

15 ? 74 ? 3

73

154

13

34

34

274

92

32

12

12

12

12

23

2 ? 13 ? 1

8 ? 39 ? 4

34

89

34

89

13

1 ? 11 ? 3

1 ? 22 ? 3

23

12

524

5 ? 16 ? 4

14

56

25

175

17 ? 15 ? 1

34 ? 735 ? 2

72

3435

72

3435

35

3 ? 15 ? 1

9 ? 210 ? 3

23

910

23

910

25

2 ? 15 ? 1

4 ? 15 ? 2

12

45

12

45

15

27

27

72

53

35

31

45

67

45

67

13

1003

23

501

32

501

12

16

496

72

73

12

73

37

73

12

37

12

12

112

11

112

25

554

52

554

12

34

4750

14750

21 ? 710 ? 5

75

2110

25

110

310

1 ? 35 ? 2

4 ? 35 ? 8

38

45

38

45

611

19

35

13

ab

635

37

25

116

14

14 ? 5 2 ? 11 5 22; 22 laps 25. 5b 5 6 ; 5b 5 ; ? 5b 5

? ; b 5 ? 5 5 1 ; 1 lb 26. j 5 12 ; j 5 ;

? j 5 ? ; j 5 ? 5 1 ? 25 5 25 27. y 5 ; ? y 5

? ; y 5 ? 5 28. m 5 1 ; m 5 ; ? m 5 ? ;

m 5 5 2 29. 2 b 5 1 ; 2 b 5 ; 2 ? (2 )b 5

2 ? ; b 5 2 ? 5 2 5 23 30. 1 p 5 24 ; p 5

2 ; ? p 5 ? (2 ); p 5 ? (2 ) 5 2 5 23

31. 2 u 5 6 ; 2 u 5 ; 2 ? (2 )u 5 2 ? ; u 5

2 ? 5 21 ? 19 5 219 32. 50 4 3 5 4 5

? 5 ? 5 < 16; 16 signs 33. 14 ? 5

? 5 5 10 ; 10 lb 34. 43 4 4 5 4 5

? 5 < 9; check students’ work. 35. For x 5 1,

(x 1 ) 4 5 (1 1 ) 4 ; 1 4 5 4 5 ? 5

? 5 5 6 36. For x 5 1, y 5 2, and z 5 3, ( 2 x) 5

( 2 1); ( 2 ) 5 (2 ) 5 2 ? 5 2 37. For x 5 1,

y 5 2, and z 5 3, 3 4 ( 2 ) 5 3 4 ( 2 );

3 4 ( 2 ) 5 3 4 ( 2 ) 5 3 4 5 3 4 5 3 ? 5

3 ? 2 5 6 38a. 4(11) ? 5 44 ? 5 22; 22 cups

38b. 22 4 3 5 22 4 5 22 ? 5 5 5 6 pies;6 pies 39. Dividing by a fraction is the same asmultiplying by its reciprocal. The reciprocal of a numberless than 1 is a number greater than 1, so the answer willbe greater. 40. Answers may vary. Sample: Dividing by 4 will give an answer that is less than 10. Dividing by will give an answer greater than 10 because it is the same as multiplying by 4. 41. 1 1 5 1 5 1 5 ;

3 5 5 5 10 ; 10 yd 42. Let n be the number of nickels and q be the number of quarters. The value of nnickels is 0.05n, and the value of q quarters is 0.25q. So,0.05n 5 ? 0.25q; 15 ? 0.05n 5 15 ? ? 0.25q;

0.75n 5 0.25q; 5 q; 3n 5 q. There are 36 coins in

all: n 1 q 5 36; n 1 3n 5 36; 4n 5 36; 5 ; n 5 9, or

9 nickels. 43. 10 4 1 5 4 5 ? 5 5

5 8 ; the correct choice is C. 44. 12 5 12.5;20 min 15 s 5 20 min min 5 20 5 20.25;3.2 1 12.5 1 20.25 5 35.95; the correct choice is J.45. Let Ben’s age 5 x; Donna’s age is x 1 6; Scott’s ageis 2x; the sum of their ages is x 1 2x 1 (x 1 6); thecorrect choice is D.46.

47.

48.

0 5 c

236 1 36 5 c 2 36 1 36

236 5 c 2 36

7 5 b

29 1 16 5 b 2 16 1 16

29 5 b 2 16

a 5 243

a 1 12 2 12 5 231 2 12

a 1 12 5 231

1560

1560

12

415

12415

31 ? 43 ? 5

45

313

54

313

14

13

364

4n4

0.250.25

0.75n0.25

115

115

58

58

858

178

178

38

148

38

74

38

34

14

78

558

11016

516

165

15

12

12

21

12

36

16

46

16

23

12 ? 3

23

xyz

yz

16

13

12

13

12

33

23

12

23

12

yz

xy

61

11

61

51

65

15

65

15

15

15

15

15

x5

78481

29

3929

92

3929

12

59

78

78

878

34

292

34

12

50831

231

2541

1031

2545

3110

2545

110

45

191

11

193

31

13

31

193

13

13

13

14

134

131

14

133

34

43

34

133

43

13

13

34

154

152

12

1514

72

27

72

1514

27

114

27

23

83

43

21

12

21

43

12

13

12

35

15

31

25

32

23

32

25

23

251

11

252

21

12

21

252

12

12

12

13

13

43

43

11

203

15

15

203

23

111

21




1. The multiplicative inverse is the number by which youmultiply a given number to get a product of 1. 2. Thefirst sentence is incorrect. The prime factorization canhave more than two factors. The second sentence is alsoincorrect. The number 1 is not a prime number. The thirdsentence is correct.


1–2. Answers may vary. Samples are given. 1. When you divide by 2, the result is 2 of the 6 pieces in the

whole, or half of the remaining pieces. 2. No; he will have the remaining left, is the amount that is not

shaded in the diagram. 3. Check students’ work.

Exercises 1. 6 ? 1 1 ? 1 5 6 ? 1 ? 5 1 ? 5

8 1 5 8 ; 8 cans 2. 2 4 5 4 5 ? 5

? 5 5 5 ; 5 meals 3. The mean is

5 5 83. If Max expects similar sales for rest of the year, the sales would beapproximately $83 per month for rest of the 7 months.Thus Max would earn about 415 1 (7)(83) 5415 1 581 5 $996 in royalties during the year, whichapproximately equals $1,000. 4. Let x represent the number of eggs. equals the remaining eggs after

giving some to Sam. equals the remaining

eggs after giving some to Sam and Alonzo.5 0 because after giving eggs to Sam,

Alonzo and Jacquelyn, Melita has no eggs left. The total number of eggs Melita had is 7 eggs.


1–6. Answers may vary. Samples are given. 1. yes, thesolution seems reasonable; 84 1 19 5 103 2. no, thesolution does not seem reasonable; (240)(5) ? 24003. yes, the solution seems reasonable; < 3 4. no, the solution does not seem reasonable; 256 2 35 ? 2215. 13 < 14; M 5 (220 2 A); M 5 (220 2 14) 5

(206) < 165; about 165 6. 13 < 14; F 5 (226 2 A);

F 5 (226 2 14) 5 (212) < 170; about 17045

45

45

1012

45

45

45

1012

14050

x 5 568 5 7

8 ? 18x 5 7

8 ? 8

18x 2 78 1 7

8 5 0 1 78

18x 2 78 5 0

12(14x 2 3

4) 5 0

12(14x 2 1

4) 2 12 5 0

12(12(1

2x 2 12) 2 1

2 5 0

212

12(1

2(12x 2 1

2)212)

12(1

2x 2 12) 2 1

2

12x 2 1

2

4155

85 1 95 1 70 1 85 1 805

12

12

112

11

112

21

114

12

114

12

34

23

23

23

23

11

2 ? 41

43

12

43

13

12

13

46

46

23

2-6 Formulas pages 81–84

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. add; subtract 2. 5 3. 244. 24 5. 10

Quick Check 1a. A 5 h(b1 1 b2) 5 (4.2)(1.4 1 4.6) 5

(4.2)(6.0) 5 2.1(6) 5 12.6; 12.6 cm2 1b. A 5 /w 5

? 3 5 ? 5 2; 2 yd2 2. d 5 rt; 870 5 r(550); 5 ;

5 r; 870 4 550 < 1.58; 1.58 mi/h 3. A 5 w 2 5;A 1 5 5 w 2 5 1 5; A 1 5 5 w; w 5 A 1 5

Exercises 1. / is the length; w is the width. 2. Solve theformula d 5 rt for r by dividing both sides of theequation by t. 3. A 5 /w 5 (1.75)(0.5) 5 0.875 5

5 ; cm2 4. 2 ft 5 ft 5 3 12 in. 5 28 in; A 5

/w 5 (28)( ) 5 7 ? 5 35; 35 in.2 5. Area of a trapezoid;h is the height; b1 and b2 are the bases. 6. Distanceformula; d is the distance, r is the rate, and t is the time.7. Perimeter of a square; s is the side length. 8. A 5

/w 5 (7.3)(4.1) 5 29.93; 29.93 m2 9. A 5 h(b1 1 b2) 5(4)(4 1 8) 5 (4)(12) 5 2 ? 12 5 24; 24 m2 10. A 5 s2 5

92 5 9 ? 9 5 81; 81 cm2 11. A 5 /w 5 (5)A2 B 5 A BA B 5

5 12 ; 12 in.2 12. A 5 s2 5 (0.5)2 5 (0.5)(0.5) 5

0.25; 0.25 cm2 13. d 5 rt; 3,610 5 r(33.5); 5 ;

5 r; 3,510 4 33.5 < 108; about 108 mi/h 14. V 5

/wh; 5 ; 5 h; h 5 15. d 5 rt; 5 ; 5 t; t 5

16. C 5 2pr; 5 ; 5 r; r 5 17. K 5 C 1 273;K 2 273 5 C 1 273 2 273; C 5 K 2 273 18. V 5 Bh;

5 ? ? h; 5 ? h; ? 5 ? ? h; 5 h; h 5

19. W 5 g 2 25; W 1 25 5 g 2 25 1 25; g 5 W 1 25

20. d 5 rt; 5 20t; ? 5 ? t; 5 t; h; there are

60 min/h and 60 s/min, so there are 60 ? 60, or 3,600 s/h.Find the number of seconds in h: ? 5 5

45; 45 s. 21. d 5 rt; 12 5 r(0.5); 5 ; 5 r;

12 4 0.5 5 24; 24 mi/h 22. d 5 rt; 120 5 45t; 5

; 5 t; t 5 2 ; 2 h 23. V 5 pr2h; h 5 5 5

5 5 ; ft 24. You use properties of equality;

instead of getting a number for an answer, you get anexpression. 25a. height 5 222(air temperature 2 dew-point temperature) 5 222(80 2 70) 5222(10) 52,220; 2,220 ft 25b. The difference between the dewpoint and air temperature will grow larger, and theheight of the base of the cloud will increase. Examples:

26. Find the area of the square: A 5 s2 5 42 5 4 ? 4 5 16;16 cm2. Use the formula A 5 /w to solve for w: w 5 .Solve for the width of the rectangle: w 5 5 5

3.2; 3.2 cm. 27. Divide C and 2pr by 2p to solve for the

165

A/

A/

H 5 222(80 2 60) 5 4,440 ft H 5 222(80 2 70) 5 2,220 ft

9p

9p

273p

2713p9

2713p32

V13pr2

13

23

23

83

45t45

12045

120.5

0.5r0.5

120.5

3,60080

3,6001

180

180

180

180

201

120

14

120

14

3VB

3VB

B3

3B

V1

3B

B3

V1

B1

13

V1

13

C2p

C2p

2pr2p

C2p

dr

dr

rtr

dr

V/w

V/w

/wh/w

V/w

3,61033.5

33.5r33.5

3,61033.5

12

12

252

52

51

12

12

12

12

51

54

73

73

13

78

78

8751,000

870550

550r550

870550

31

23

23

12

12

12



radius; the correct choice is C. 28. ? because there is

of a pizza split between 3 people; the correct choice is G.

29. 1 1 c 5 1; 1 1 c 5 ; 1 c 5 ;

2 1 c 5 2 ; c 5 ; the correct choice is B.30. The prime factorization of 32 is 2 ? 2 ? 2 ? 2 ? 2. The prime factorization of 48 is 2 ? 2 ? 2 ? 2 ? 3. The GCF is 2 ? 2 ? 2 ? 2, or 16. 31. The prime factorization of 51 is 17 ? 3. The prime factorization of 68 is 2 ? 2 ? 17. TheGCF is 17. 32. The prime factorization of 84 is 2 ? 2 ? 3 ? 7.The prime factorization of 90 is 2 ? 3 ? 3 ? 5. The GCF is 2 ? 3, or 6.


1. When P is in L3, a is in L1, and b is in L2, then L3 5

L1 1 L2. 2. When X is in L3, a is in L1, and b is in L2,then L3 5 3 3 L1 1 5 3 L2. 3. When A is in L3, a is inL1, and b is in L2, then L3 5 0.5 3 L1 3 L2. 4. When T isin L3 and a is in L1, then L3 5 L1

2. 5a. For A 5 bhwhen b 5 8 and h 5 10, 11, 12, 13, 14, and 15, then A 5

40, 44, 48, 52, 56, 60. 5b. For A 5 bh when b 5 8, 9, 10,11, 12, and h 5 10, then A 5 40, 45, 50, 55, 60. 6. 0. , 0. ,0. , 0. , 0. , 0. , 0. 7. The numbers in L2 are 41, 43, 47,53, 61, 71, 83. They are all prime; yes.

2-7 Powers and Exponentspages 86–89

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. factor 2. 4 3. 6 4. 165. 24 6. 16

Quick Check 1. 6 ? 6 ? 7 ? 7 ? 7 ? 7 ? 7 ? 7 has 2 sixes and 6 sevens: 62 ? 76. 2. (27)3 5 (27)(27)(27) 5 49(27) 52343 3. 273 5 2(7 ? 7 ? 7) 5 2343 4. 24 1 6 ? 32 5

24 1 6 ? 9 5 24 1 54 5 50 5. For s 5 5 and h 5 3, r 5

5 5 5 5 5 5 ; 5 m

Exercises 1. 3x; the correct choice is C. 2. m5; thecorrect choice is A. 3. yz; the correct choice is B. 4. Yes;x2 ? x3 5 x ? x ? x ? x ? x, which is x5. 5. 9 ? 9 ? 9 ? x has 3nines and 1 x: 93 ? x1, or 93 ? x 6. 4 ? 4 ? 4 ? 4 ? 4 has 5fours: 45. 7. z ? z ? z ? z ? z ? z has 6 z’s, or z6 8. 282 5

2(8 ? 8) 5 264 9. (28)2 5 (28)(28) 5 64 10. (21)2 2

2 ? 4 5 (21)(21) 2 8 5 1 2 8 5 27 11. 4 ? 4 ? 8 ? 8 ? 8 ? 8has 2 fours and 4 eights: 42 ? 84 12. 6 ? 6 ? 6 ? 11 has 3sixes and 1 eleven: 63 ? 111, or 63 ? 11. 13. 5 ? 5 ? x ? x ? x ? yhas 2 fives, 3 x’s, and 1 y: 52x3y1 or 52x3y 14. 9 ? a ? a ? b ? c ? c ? c has 1 nine, 2 a’s, 1 b, and 3 c’s:91a2b1c3 or 9a2bc3. 15. m ? p ? m ? p ? p has 2 m’s and 3 p’s: m2p3. 16. 7 ? w ? t ? 7 ? t has 2 sevens, 2 t’s, and 1 w:72t2w1 or 72t2w. 17. (22)5 5 (22)(22)(22)(22)(22) 5232 18. 225 5 2(2 ? 2 ? 2 ? 2 ? 2) 5 232 19. (26)3 5

(26)(26)(26) 5 2216 20. 263 5 2(6 ? 6 ? 6) 5 221621. 2152 5 2(15 ? 15) 5 2225 22. (215)2 5

(215)(215) 5 225 23. (23)4 5 (23)(23)(23)(23) 581 24. 234 5 2(3 ? 3 ? 3 ? 3) 5 281 25. (23)2 1 12 ? 4 5

23

23

173

346

25 1 92 ? 3

52 1 32

2 ? 3s2 1 h2

2h

76543

21

12

12

215

1315

1515

1315

1315

1515

1315

1515

1015

315

23

15

12

13

12 (23)(23) 1 12 ? 4 5 9 1 48 5 57 26. 232 1 12 ? 5 5

2(3 ? 3) 1 12 ? 5 5 29 1 60 5 51 27. (3 ? 2)2 1 5 5(6)2 1 5 5 6 ? 6 1 5 5 36 1 5 5 41 28. 32 ? 2 1 5 53 ? 3 ? 2 1 5 5 18 1 5 5 23 29. 4 1 (8 2 6)2 5 4 1 22 5

4 1 2 ? 2 5 4 1 4 5 8 30. 4 1 8 2 62 5 4 1 8 2 6 ? 6 54 1 8 2 36 5 12 2 36 5 224 31. For r 5 6 and h 5 30,V 5 pr2h < 3.14 ? 62 ? 30 5 3.14 ? 36 ? 30 5 3,391.2;3,391.2 cm3. 32. A 5 s2 5 102 5 100, area of the square 5100 square units; A 5 pr2 5 (3.14)(102) 5 314, area ofthe circle 5 314 square units; difference in areas:314 2 100 5 214; 214 square units. 33. For n 5 23,5n2 2 5(2n 2 3)2 5 5(23)2 2 5(2(23) 2 3)2 5

5(9) 2 5(26 2 3)2 5 45 2 5(29)2 5 45 2 5(81) 545 2 405 5 2360 34. For n 5 23, (4n)2 1 48 4 (24n) 5(4(23))2 1 48 4 (24)(23) 5 (212)2 1 48 4 (12) 5[(212)(212)] 1 4 5 144 1 4 5 148. 35. For n 5 23,

5 5 5 5 5 2.

36. For n 5 23, 5(2n 2 3)2 5 5(2(23) 2 3)2 5

5(26 2 3)2 5 5(29)2 5 5(29)(29) 5 405. 37. d 5

16t2 5 16 ? 32 5 16(3 ? 3) 5 16(9) 5 144; d 5 16t2 5

16 ? 42 5 16(4 ? 4) 5 16(16) 5 256; to find how far askydiver falls between the third and fourth secondssubtract the distance at 3 seconds from the distance at 4seconds: 256 2 144 5 112; 112 ft 38. h 5 160t 2 16t2 5

160(2) 2 16(22) 5 320 2 16(4) 5 320 2 64 5 256; 256 ft39. No; the product of any number and itself is alwayspositive. For example, 32 5 3 ? 3 5 9, and (23)2 5

23 ? 23 5 9. 40. V 5 pr3 5 (3.14)(33) 5 113.04; V 5

pr2h 5 (3.14)(62)(9) 5 339.12; to find how many fewercubic inches the sphere has than the cone find thedifference between their volumes: 339.12 2 113.04 5226.08 cubic units 41. Yes; when a 5 0 or b 5 0, andwhen a 5 1 or b 5 1. When a 5 0, (ab)2 5 (0 ? b)2 5

02 5 0 and ab2 5 0 ? b2 5 0; 0 5 0. When b 5 0, (ab)2 5

(a ? 0)2 5 02 5 0 and ab2 5 a ? 02 5 a ? 0 5 0; 0 5 0.When a 5 1 and b 5 1, (ab)2 5 (1 ? 1)2 5 12 5 1 and ab2 5 1 ? 12 5 1 ? 1 5 1; 1 5 1. 42. Try, check, and revise.Try addition: 5 1 5 1 5 1 5 1 5 5 25. Try multiplication:5 ? 5 ? 5 ? 5 ? 5 5 3,125. The solution requires bothmultiplication and either addition or subtraction. Try 5 ? 5 ? 5 ? 5 2 5: 625 2 5 5 620; too high. Try 5 ? 5 ? 5 2 5 2 5: 125 2 5 2 5 5 115; too high. The answer is 5 ? 5 ? 5 2 5 ? 5. 43. Let A 5 area, s 5 side length, and P 5 perimeter. P 5 4s; A 5 s ? s; A 5 2P 5

2(4s) 5 8s.Try each choice.A: A 5 4; 4 5 8s; 5 ; 5 s;

A 5 s ? s; 4 ? ? ; A does not work. B: A 5 16; 16 5 8s;

5 ; 2 5 s; A 5 s ? s; 16 ? 2 ? 2; B does not work. C: A 5

36; 36 5 8s; 5 ; 5 s; A 5 s ? s; 36 ? ? ; C does

not work. D: A 5 64; 64 5 8s; 5 ; 8 5 s; A 5 s ? s; 64 58 ? 8; P 5 4s; P 5 32; A 5 2P; 64 5 2(32); 64 5 64; the

correct choice is D. 44. C 5 (F 2 32) 5 (95 2 32) 5

(63) 5 (7) 5 35; the correct choice is F. 45. 1 5

1 5 ; 2 5 ; the correct choice is C.

46. 0.3 5 5 47. 6.36 5 5 5 5 6 925

15925

636100

6.361

310

0.31

715

815

1515

815

315

515

15

13

51

59

59

59

8s8

648

41241

2412

8s8

368

8s8

168

12

12

12

8s8

48

13

13

43

43

189

9 1 99

(23)(23) 1 9

(23)(23)

(23)2 1 9

(23)2

n2 1 9

n2

0014_3PHM07_sk_ch02.qxd 8/22/08 3:44 PM Page 21


48. 0.003 5 5 49. 0.45 5 5 5


1. x2 2 2x 1 5 for x 5 10: 10 ;

2 5 125; 125 2. (x 2 32)

for x 5 98.6: 98.6 ; 5

9 32 37; 37 3. 24x2 1 34x 2 6

for x 5 25: 25 ; 4

34 6 21,656; 21,656

4. Press and, next to Y1, enter the expression

4x2 27x 1 19. Press and set TblStart 5 1

and Tbl 5 1. Press to view the table. The table shows the values are 16, 21, 34, 55, 84, 121, 166.


1. ? (27) 5 ? (2 ) 5 2 5 22 2. 1 ? 1 5 ? 5

5 1 3. 1 4 3 5 4 5 ? 5 ? 5

4. 2 4 4 5 2 4 5 2 ? 5 2 ? 5 2

5. 10 2 24 ? 3 5 10 2 16 ? 3 5 10 2 48 5 2386. (25)2 2 6 ? 42 5 25 2 6 ? 16 5 25 2 96 5 2717. (32 1 1)2 5 (9 1 1)2 5 102 5 1008. (3 1 2)3 2 8 ? 4 5 53 2 32 5 125 2 32 5 939. ab

3 ? T 5 3 ? ab

10. A 5 h(b1 1 b2); h 5 2 , b1 5 4 , b2 5 3

A 5 (2 )(4 1 3 )

A 5 (2 )(4 1 3 )

A 5 (2 )(7 )

A 5 ? ?

A 5

A 5 10 ; 10 cm2

11.


A number is in scientific notation if the First Factor isgreater than or equal to 1 and less than 10.

4p cm 5 h

4812p 5 12ph

12p

48 5 12ph

48 5 13p36h

48 5 13p(6)2h

V 5 13pr2h

172

172

72172

10312

73

12

1912

13

12

1012

912

13

12

56

34

13

12

56

34

13

12

3Ta 5 b

3Ta 5 ab

a

13

T 5 13

257

219

13

419

16

194

16

34

16

715

75

13

725

53

257

53

47

23

79

169

43

43

13

13

45

145

71

25

25

Table2nd

TblSet2nd

Y5

52x31x2x

3(2)ENTERxSTO.

5)2x(

4ENTERxSTO.

5951x32x2x

ENTERxSTO.(2)

920

45100

0.451

31,000

0.0031

1.

2. The exponent of 10 is equal to the number of zeros inthe number being multiplied by 6.71. 3. Answers mayvary. Sample: The exponent is the number of places thedecimal point moves to the right. 4. When you multiplyby a positive power of 10, move the decimal point to theright the number of places equal to the exponent.

2-8 Scientific Notation pages 92–95

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. power 2. 20 3. 4514. 1,500 5. 18,030 6. 2,390,000

Quick Check 1. 7,660,000 km2 2. 3.476 3 106 m3. 0.00025 in. 4. 3.5 3 1026

Exercises 1. 1 2. When you move the decimal point 6places to the right, it takes 2 moves to get to the right of0.55. 3. greater than 0, because the number remainspositive even though the decimal point moves 5 placesto the left 4. Yes; the decimal point in each numberneeds to move 2 places to the left. 5. 3,200 6. 50,8007. 410,000,000 8. 7,145,000,000 9. 260,000 lb10. 4.8 3 103 11. 1.72 3 104 12. 1.8 3 105

13. 3.43502 3 105 14. 25 billion 5 25,000,000,000 52.5 3 1010 15. 0.0025 16. 0.0000512 17. 0.010518. 0.000000314 19. 0.00935 cm 20. 5.81 3 1023

21. 1.05 3 1023 22. 7.8 3 1026 23. 2.7 3 1025

24. 1.32 3 1027 25. 9 3 1029 26. 130 million 5130,000,000 5 1.3 3 108 27. 8 28. 5.6194 29. 2630. 4.802 31. 3.92 3 108 32. 492 is not between 1 and10. 33. 30 min 5 0.5 h, so the blast wave will travel 0.5 3 3 3 106 5 1.5 3 106 km. 34. 3 3 10100 is greaterbecause 10 to the power of 100 is ten times greater than10 to the power of 99 in scientific notation.35a. 5,500 ? 5 2,750 3 1,000 5 2,750,000 calories

35b. 2.75 3 106 calories 36. It increases by two becausean increase of one in the exponent stands for a increaseof 10 times. 37. 1029 2 1028 5 10 3 1028 2 1 3 1028 5

(10 2 1) 3 1028 5 9 3 1028 38. 380,000 5 3.8 3 105; thecorrect choice is C. 39. Let v 5 the number of peoplewho do not eat meat. 2 times as many people eat meat than don’t. 10 people eat meat. Since 2 times thenumber of people who do not eat meat equals 10, 10divided by 2 equals the number of people who do not eatmeat. v 5 10 4 2 ; the correct choice is G. 40. For V 5

24, l 5 4 and h 5 2, V 5 lwh is 24 5 4 ? w ? 2, or 24 5 8w.

12

12

12

12

12



To solve for w, divide both sides by 8; the correct choiceis D. 41. For x 5 3, y 5 x3 1 x4 2 x5 5 33 1 34 2 35 5

27 1 81 2 243 5 108 2 243 5 2135 42. For x 5 3, y 5

3x3 2 2x2 5 3(3)3 2 2(3)2 5 3(27) 2 2(9) 5 81 2 18 5 6343. For x 5 3, y 5 x2 2 x3 5 32 2 33 5 9 2 27 5 218


1. 3,100 4 1,000 5 3.1; 3.1 kg 2. 0.0052 ? 1,000 5 5.2;5.2 mm 3. 64,200,000 4 1,000,000 5 64.2; 64.2 Mb4.

5. Check students’ work. 6. The human’s hair is thicker;8 3 1025 m . 5 3 1025 m; check students’ work.7. Check students’ work.


1. Scientific notation is used when writing very large orvery small numbers. 2. Two numbers whose product isone are called reciprocals or multiplicative inverses.3. The LCM of 15 and 25 is 75. 4. The expression 32 ? 7 isthe prime factorization of 63. 5. An expression like 128

is a power. 6. A formula shows the relationshipbetween two or more quantities. 7. The numbers 8 and9 are relatively prime because 1 is their only commonfactor. 8. The number 0.3589402 is a terminatingdecimal. 9. The GCF of 15 and 25 is 5. 10. Theexpression 53 has an exponent of 3 and a base of 5.

11. 22 ? 5 ? 13

135

2

260

130

652

21,500 g

0.63 m

0.00005 m

16,000 m

Measure

2.15 � 103 g

Scientific Notation

21.5 kg

63 cm

50 µm

16 km

Metric Prefix

6.3 � 10�1 m

5 � 10�5 m

1.6 � 104 m

12. 22 ? 52 ? 7

13. 2 ? 33 ? 7

14. 1 ? 139

15. 22 ? 33 ? 5 ? 13

16. 0.16 5 5 5 17. 5 and 5 ; since

27 , 35, , ; , 18. 24 5 24.000; 2 < 24.667;

24.000 . 24.667; . 19. 5 0.625; 5 20. 2 1 5

2 1 5 1 5 5 5 2

21. 22 2 A21 B 5 22 1 1 5 22 1 1 5 21 5

21 22. 23 1 2 5 23 1 2 5 2A3 B 1 A2 B 5

2A3 1 B 1 A2 1 B 5 23 1 A2 B 1 2 1 5 21 1 5

2 1 5 2 5 2 23. 2 ? A2 B 5 ? 5 ? 5

24. 2 4 5 ? 5 ? 5 5 3 25.24 4 2 5

2 4 5 2 ? 5 2 ? 5 2 ? 5 2 5

22 26. 7 ft 4 2 ft 5 4 5 ? 5 ? 5 3

27. d 5 rt; 270 5 r(6); 5 ; 45 5 r; 45 mi/h

28. Solve for b: A 5 bh; 2A 5 2 ? bh; 2A 5 bh; 5 ;

b 5 . 29. y 5 mx 1 b; y 2 mx 5 mx 1 b 2 mx; b 5

y 2 mx 30. ; ; 31. (4 ? 2)2 2 3 582 1 3 5 8 ? 8 2 3 5 64 2 3 5 61 32. 52 ? 2 1 4 55 ? 5 ? 2 1 4 5 50 1 4 5 54 33. 28 1 2 ? 42 5

28 1 2 ? 4 ? 4 5 28 1 32 5 24 34. 3.5 3 103

35. 8.01 3 105 36. 2.05 3 1024 37. 8.1 3 1028

38. 380,000,000

r 5 dt dt 5 rt

t d 5 rt

2Ah

bhh

2Ah

12

12

6r6

2706

11

31

25

152

52

152

12

12

110

2110

310

71

320

141

920

143

209

143

29

23

14

134

132

12

1310

52

1013

12

116

18

12

38

16

38

16

23

46

26

66

26

36

16

36

16

36

16

36

16

12

16

12

510

310

810

310

45

310

45

18

218

27 1 68

68

278

68

78

34

78

58

143

79

35

3545

79

2745

35

425

16100

0.161

133

109

5233

7,020

7890

392

139

1391

33

32

378

636

97

52

52

700

7010

107




1. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of16 are 1, 2, 4, 8, and 16. The common factors are 1, 2, and4. The greatest common factor is 4. 2. The factors of 32are 1, 2, 4, 8, 16, and 32. The factors of 48 are 1, 2, 3, 4, 6,8, 12, 16, 24, and 48. The common factors are 1, 2, 4, 8,and 16. The greatest common factor is 16. 3. The factorsof 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 36, 48, 72, and 144.The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64,96, and 192. The common factors are 1, 2, 3, 4, 6, 8, 12, 16,and 48. The greatest common factor is 48.

4. 2 ? 32 ? 5

5. 24 ? 33

6. 1 ? 47

7. 23 ? 5 ? 7

8. 5 0.375; since 0.375 , 0.4, , 0.4; ,. 9. 2 5 2 ;

since 26 , 25, 2 , 2 ; ,. 10. 2 5 20.9 5 20.90;

20.89 . 20.90, so 20.89 . 2 ; .. 11. 5 0. ; 5

12. 5 2 4 5 5 0.400 13. 2 5 227 4 8 5 23.375

14. 5 19 4 15 < 1.267 15. 5 7 4 11 < 0.636

16. 0.64 5 5 17. Let 10n 5 6. and n 5 0. .

Then 10n 2 n 5 6. 2 0. ; 9n 5 6; n 5 5 . 18. 0.471 5

19. Let 1,000x 5 282. and x 5 0. . Then

1,000x 2 x 5 282. 2 0. ; 999x 5 282; x 5 5 .

20. 12 in. is the height after the first bounce, which was

12 4 5 12 ? 5 18. 18 in. is the height of the starting

point, which was 18 4 5 18 ? 5 27. The starting point

was 27 in. 21. 18 ? 5 ? 5 ? 5 5 4 ; 4 mi

22. 2 2 5 2 1 2 5 2 1 2 5 21415)5

15(915)1

3(35

13

35

12

12

92

12

91

14

181

14

32

23

23

32

23

23

94333

282999282282

2822824711,000

23

6966

661625

64100

711

1915

278

25

449

910

910

512

12

612

12

38

38

52

22

280

704

107

47

471

22

32

96

33

432

1084

542

5233

90

109

23. 2 5 1 2 5 2 5 2 24. 1 5

1 5 5 25. 3 2 2 5 3 2 2 5

3 1 2 2 1 5 3 1 1 (22) 1 A2 B 5

3 1 (22) 1 1 A2 B 5 1 1 A2 B 5 1 A2 B 5

26. 2 5 2 5 5 27. 2 2 3 5 2 2 A3 B 5

2 1 2 A3 1 B 5 2 1 1 (23) 1 A2 B 5

2 1 (23) 1 1 A2 B 5 2 1 (23) 1 1 A2 B 5

21 1 A2 B 5 2A1 1 B 5 21 28. 22 ? 5

2 ? 5 2 ? 5 2 5 22 29. 4 A2 B 5 2 4 5

2 ? 5 2 ? 5 2 5 21 30. 2 ? 5 2 ? 5 2

31. 21 4 5 2 4 5 2 ? 5 2 ? 5 2 5 23

32. 1 ? 2 5 2 ? 5 2 33. 4 5 ? 5

? 5 5 1 34. Answers may vary. Sample: The exponent 2 only applies to the number 4, not 24.35. (22)4 5 (22)(22)(22)(22) 5 16 36. 224 5

2(2)(2)(2)(2) 5 216 37. 33 1 52 5 27 1 25 5 52 38. 42 ? 2 1 8 5 4 ? 4 ? 2 1 8 5 32 1 8 5 4039. (9 2 3)2 5 62 5 6 ? 6 5 36 40. 22 2 72 5

22 2 7 ? 7 5 22 2 49 5 22 1 (249) 5 227 41. For m 5

24 and p 5 2, m2 2 p 1 12 5 (24)2 2 2 1 12 5(24)(24) 2 2 1 12 5 16 2 2 1 12 5 14 1 12 5 26.42. For m 5 24 and p 5 2, 2p2 2 (m 2 1)2 5

2 ? 22 2 (24 2 1)2 5 2 ? 4 2 (25)2 5 8 2 25 5 217.43. For m 5 24, 3(5m 2 1)2 5 3(5(24) 2 1)2 5

3(220 2 1)2 5 3(221)2 5 3(221)(221) 5 3(441) 5

1,323. 44. For m 5 24, 5 5

5 5 2. 45. 2.3 3 107 46. 1.5 3 106

47. 4.5 3 108 48. 7.0 3 1025 49. 8.9 3 1023

50 4.01 3 1022 51. 410,000 52. 80,200 53. 0.00554. 0.0000088 55. The number in scientific notation isgreater if the exponent of 10 is greater.6 3 1025 . 5 3 1026 56. d 5 rt; r 5 5 < 212;

about 212 mi/h. 57. A 5 <w 5 (2 )( ) 5 ? 5 5 1 ;

1 in.2 58. L 5 2prh; 5 ; r 5

59. V 5 Bh; B 5 5 60. S 5 a 1 2b; S 2 2b 5

a 1 2b 2 2b; a 5 S 2 2b 61. C 5 25d 1 p; C 1 5d 5

25d 1 p 1 5d; p 5 C 1 5d

TEST PREP page 101

1. The area of the paper is 2 ? 3 5 ? 5 , or 8 ; the correct choice is C. 2. 6(x 2 2) 5 6x 2 12; the correctchoice is H. 3. The area of the rectangle is 2.5 ? 6.5, or16.25 m2; the correct choice is C. 4. Find a quotientbetween 24 and 25. F: 2 4 (2 ) 5 ? (22) 5 2 5

25 5 25 , which is not between 24 and 25.

G: 25 4 (21 ) 5 2 ? (2 ) 5 5 3 , which is not

between 24 and 25. H: 29 4 2 5 2 ? 5 2 ? 5

2 5 24 , which is between 24 and 25; the correct

choice is H. 5. When m 5 3, 3 2 6m 5 3 2 6(3) 5

23

143

11

143

12

283

13

23

226

23

112

12

12

23

46

346

176

12

56

34

354

72

52

12

12

Bhh

Vh

L2ph

2prh2ph

L2ph

3132

3132

6332

78

94

78

14

3,75617.7

dt

16 1 1616

(24)(24) 1 16

(24)(24)

(24)2 1 16

(24)2

m2 1 16

m2

5050

501

150

5021

2150

2150

2150

2536

59

54

59

14

35

185

65

31

125

32

512

32

512

12

720

74

15

78

25

14

54

11

54

21

58

12

58

12

58

49

229

29

111

89

114

89

34

215

215

215

515

315

13

15

13

15

13

15

13

15

13

15

16

212

912

1112

34

1112

712

512

1212

512

812

312

23

14)2

3(14

)23(1

423

14

3536

105108

60108

45108

59

512

13

412)5

12(112

512

112



3 2 18 5 215; the correct choice is A. 6. F: Add thedigits of 66, 510: 6 1 6 1 5 1 1 1 0 5 18, 18 is divisibleby 3 so 66, 510 is divisible by 3; G: Test the last two digitsof 65, 510 for divisibility by 4; 10 is not divisible by 4. H:66, 510 has a zero in the ones place, so it is divisible by 5;J: The sum of the digits of 66, 510 is 18, so it is divisibleby 9. The correct choice is G. 7. Find the multiples of 24:24, 48, 72 . . . Find the multiples of 36: 36, 72 . . . The LCMis 72; the correct choice is D.8. a 1 y 5 18

a 2 a 1 y 5 18 2 ay 5 18 2 a; the correct choice is H.

9. The canoeist can paddle t a rate of , or

feet per second; the correct choice is D. 10. There are 3times as many birds b as there are trees t, so b 5 3 t;

the correct choice is F. 11. 1 5 1 5 ;

grid or 0.9 12. Find the factors of 24: 1, 2, 3, 4,6, 8, 12, 24; find the factors of 40: 1, 2, 4, 5, 8, 10, 20, 40;the GCF is 8. 13a–b. [2] Let x 5 the money she earnedbaby-sitting. 78 1 x 5 116

78 1 x 5 11678 2 78 1 x 5 116 2 78

x 5 38She earned $38 baby-sitting.[1] one part correct 14a–b. [4] The figure is a trapezoid so the equation for its area is

A 5 (b1 1 b2)h;

The length of x is 400 yards. x 5 400

325x325 5

130,000325

325x 5 130,000.

6502 ? x 5 130,000.

400 1 2502 ? x 5 130,000.

400 1 2502 ? x 5 130,000.1

2

910

910

510

410

12

25

23

23

50041

250 feet

2012 seconds

[3] correct equation and minor error in solving for x; [2]correct equation with incorrect value for x OR incorrectequation but value for x follows correctly from equation;[1] correct value for x without work shown and noequation


1a. frequency 5 number of vibrations, or cycles, persecond; 50 cycles per second 1b. period 5 duration ofone vibration, or cycle, in seconds; s

2.

3. Answers may vary. Sample: The period scorresponds to a frequency of 10 cycles per second,which is below the range of human hearing. Peoplecould not hear these elephant communications.4. Answers may vary. Samples are given. a. ultrasonic: afrequency of vibration above the range of humanhearing b. A frequency of 40,000 cycles per second has a period of 0.000025 s. 5. Check students’ work.

110

ApproximateFrequency (cycles Period

Sound per second) (seconds)

Lowest sound 20 0.05

Lowest note 82 0.012

Highest note 1,568 0.00064

Highest sound 20,000 0.00005

150

phm07c3_sk_ch02 _natl.qxd 8/23/06 2:49 PM Page 25


Chapter

3Real Numbers and the Coordinate Plane pages 104–157


1. For s 5 4 and t 5 23, 5s 1 16t 5 5(4) 1 16(23) 520 1 (248) 5 228 2. For s 5 4 and t 5 23, 44 2 2st 5

44 2 2(4)(23) 5 44 2 (224) 5 44 1 24 5 68 3. 211 1 2 5 29 4. 15 1 (22) 5 13 5. 5 2 (25) 55 1 5 5 10

6. 7. 8. 9.

0.833 1.615 0.864

10. c 5 a 1 b; c 2 a 5 a 1 b 2 a; b 5 c 2 a 11. d 5 16t;5 ; t 5 12. s 5 200 1 T; s 2 200 5 200 1 T 2 200;

T 5 s 2 200 13. 32 1 42 5 9 1 16 5 25 14. 52 2 22 5

25 2 4 5 21 15. 92 1 102 5 81 1 100 5 181

3-1 Exploring Square Roots andIrrational Numbers pages 106–110

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. exponent 2. 4 3. 44. 36 5. 100

Quick Check 1a. 6 ? 6 5 36 and 26 ? (26) 5 36; 6, 261b. 1 ? 1 5 1 and 21 ? (21) 5 1; 1, 21 1c. ? 5 and

2 ? 2 5 ; , 2 2a. 36 , 38 , 49, so 6 , , 7.Since 38 is closer to 36 than to 49, < 6. 3a. d 5

16t2; 480 5 16t2; 5 t2; 30 5 t2; 5 t; t < 5.5; 5.5 s

3b. d 5 16t2; 625 5 16t2; 5 t2; t 5 ; t 5 ;t 5 6.25; 6.3 s 4. Rational; the decimal repeats.

Exercises 1. Since 6 is not a perfect square, isirrational. All irrational numbers are real. 2. Since thedecimal repeats, it is rational. All rational numbers arereal. 3. Since the number is a ratio, it is rational. Allrational numbers are real. 4. Since 5 ? 5 5 25, it is aperfect square and therefore rational and real.5. 2 ? 2 5 4 and 22 ? (22) 5 4; 2, 22 6. ? 5 and

2 ? 2 5 ; , 2 7. 10 ? 10 5 100 and 210 ? (210) 5

100; 10, 210 8. ? 5 and 2 ? A2 B 5 ;

, 2 9. 7 ? 7 5 49 and 27 ? (27) 5 49; 7, 27110

110

1100

110

110

1100

110

110

12

12

14)1

2(12

14

12

12

!6

254#

62516

62516

!3048016

!38

!3814

14

116)1

4(14

116

14

14

d16

16t16

d16

0.863622q19.0

2176

140

2132 80

266 140

21320

1.615313q21.0

213 80 278

20 213

70 265

50

0.4

40q16.02160

0

0.83336q5.0 248

20

218 20

218 20

2182

10. 30 ? 30 5 900 and 230 ? (230) 5 900; 30, 230

11. ? 5 and 2 ? (2 ) 5 ; , 2 12. ? 5

and 2 ? A2 B 5 ; , 2 13. ? 5 and

2 ? A2 B 5 ; , 2 14. 1 , 3 , 4, so 1 , , 2.

Since 3 is closer to 4 than to 1, < 2.15. 9 , 10 , 16, so 3 , , 4. Since 10 is closer to 9

than to 16, < 3. 16. 225 , 222 , 216,

so 25 , 2 , 24. Since 222 is closer to 225 than to

216, 2 < 25. 17. 81 , 88 , 100, so 9 , , 10.

Since 88 is closer to 81 than to 100, < 9.

18. 264 , 254 , 249, so 28 , 2 , 27. Since

254 is closer to 249 than to 264, 2 < 27.

19. 2121 , 2105 , 2100, so 211 , 2 , 210.Since 2105 is closer to 2100 than to 2121, 2 <

210. 20. 144 , 150 , 169, so 12 , , 13. Since

150 is closer to 144 than to 169, < 12.

21. 2121 , 2120 , 2100, so 211 , 2 , 210.

Since 2120 is closer to 2121 than to 2100, 2 <

211. 22. s 5 20 5 20 5

20 < 330; 330 m/s 23. s 5 20 5

20 5 20 < 342; 342 m/s 24. s 5

20 5 20 5 20 <

324; 324 m/s 25. s 5 20 5 20 5

20 < 370; 370 m/s 26. Since the decimalterminates, it is rational. 27. Since 40 is not a perfectsquare, it is irrational. 28. Since the decimal does notrepeat, it is irrational. 29. Since 144 is a perfect square,it is rational. 30. Since 12 is not a perfect square, it isirrational. 31. Since the decimal does not repeat, it is irrational. 32. The formula for the area of a square is

A 5 s2; 5 s2; s 5 5 5 ; in.

33. The formula for the area of a square is A 5 s2; 484 5

s2; s 5 5 22; P 5 4s 5 4(22) 5 88; 88 ft 34. Find

the length of the side of the larger square: A 5 s2; 49 5 s2;

s 5 5 5 7, or 7 in. The length of each side

of the smaller square is 7 2 (2 1 2), or 3 in., so its area

is 32, or 9 in.2. 35. Answers may vary. Sample: 1.52 5

2.25 and 22 5 4; 2.25 , 3 , 4 so is an irrationalnumber that is less than 2 but greater than 1.5. 36. Findthe closest perfect square to 30, which is 25. Then takethe square root of 25, which is 5. 37a. Yes; the sum ofeven numbers is an even number. 37b. Yes; the sum oftwo irrational numbers is an irrational number becausethe sum cannot be written in the form , where a is anya

b

"3

"7 ? 7"49

"484

910

910" 9

10? 9

10# 81100

81100

"343

"273 1 70"273 1 T

"263"273 1 (210)"273 1 T

"293"273 1 20

"273 1 T"273

"273 1 0"273 1 T

"120

"120

"150

"150

"105

"105

"54

"54

"88

"88"22

"22

"10

"10

"3

"325

25

425

25

25

425

25

25

111

111

1121

111

111

1121

111

111

16

16

136

16

16

136

16

16



integer and b is any nonzero integer. 37c. No; the sumof two odd prime numbers is an even number which isdivisible by 2, so the sum of two prime numbers

can be a composite number. 38. 2 5

5 36 39. 5 5 5

10 40. 5 5 5 3.2

41. 2 5 5

42. 43.

Since 3 ? 3 ? 3 5 27, Since 4 ? 4 ? 4 5 64,33 5 27, so n 5 3. 43 5 64, so n 5 4.

44. 45.

Since 5 ? 5 ? 5 5 125, Since 22 ? 22 ? 22 5 28;53 5 125, so n 5 5. 223 5 28; n 5 22.

46. A 5 s2; 5 s2; s 5 5 5 ; in. 47. d 5

1.23 5 1.23 < 26.1; about 26.1 mi 48. when nis a perfect square, including 0 49. The student took thesquare root of 4 and added it to the square root of 9. Youmust add 4 1 9 first and then take the square root.50. 1 ? 1 5 1, 2 ? 2 5 4, 3 ? 3 5 9, 4 ? 4 5 16, 5 ? 5 525, 6 ? 6 5 36, 7 ? 7 5 49, 8 ? 8 5 64, 9 ? 9 5 81, and10 ? 10 5 100, so the only possible units digits for aperfect square are 1, 4, 9, 6, 5, and 0. No integermultiplied by itself ends in 2. 51. A 5 s2; 150 5 s2; s 5

; 144 , 150 , 169; , , ;12 , , 13; the side length of the square isbetween 12 and 13 cm; the correct choice is B. 52. Sincethere is an exponent of 25, the decimal in 1.7 must movefive places to the left so 1.7 3 1025 5 0.000017; thecorrect choice is F. 53. If x 5 the number of minutesJoel was on the phone, then the cost for a phone call toSpain will equal 2x 1 5, for the cost per minute plus the5 dollar connection fee. If the total cost of the call is 20dollars, then the equation for this situation is 2x 1 5 520; the correct choice is C. 54. In order to express18,000 in scientific notation, the first factor must begreater than or equal to 1 and less than ten, so thedecimal point in 18,000 must be moved 4 places to theleft to get 1.8. Since the decimal point moved 4 places,the second factor is 10 to the fourth power; 18,000 51.8 3 104 55. In order to express 6,038,000 in scientificnotation, the first factor must be greater than or equal to1 and less than ten, so the decimal point in 6,038,000must be moved 6 places to the left to get 6.038. Since thedecimal point moved 6 places, the second factor is 10 tothe sixth power; 6,038,000 5 6.038 3 106 56. In orderto express 49,700 in scientific notation, the first factormust be greater than or equal to 1 and less than ten, so

!150

!169!150!144!150

"450"h

56

56"5

6? 5

6"2536

2536

�8

4�2

�2�2

125

255

55

64

164

44

27

93

33

ua uA"a B A"a BA"a B"10.24"3.2 ? 3.2"(3.2)2

"100"10 ? 10"(10)2A"36 B A"36 BA"36 B

the decimal point in 49,700 must be moved 4 places tothe left to get 4.97. Since the decimal point moved 4places, the second factor is 10 to the fourth power;49,700 5 4.97 3 104


1a.

1b. The sum of the areas of the two smaller squares(A and B) is equal to the area of the largest square (C).2. a2 1 b2 5 c2, where a and b are the lengths of theshorter sides, and c is the length of the longest side.

3-2 The Pythagorean Theorempages 112–115

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. a number that whenmultiplied by itself is equal to the given number 2. 83. 11 4. 9 5. 5

Quick Check 1. a2 1 b2 5 c2; 122 1 162 5 c2;

144 1 256 5 c2; 400 5 c2; c 5 5 20; 20 cm

2. a2 1 b2 5 c2; 222 1 252 5 c2; 484 1 625 5 c2; 1,109 5

c2; c 5 < 33.3; 33 ft

Exercises 1. The hypotenuse is the longest side.

2a. 122 1 162 5 c2; 16 2b. 144 1 256 5 c2; 144

2c. 400 5 c2; 400 2d. 20 5 c; 20 3. a2 1 b2 5 c2;

82 1 152 5 c2; 64 1 225 5 c2; 289 5 c2; c 5 5 17;

17 cm 4. a2 1 b2 5 c2; 42 1 62 5 c2; 16 1 36 5 c2; 52 5

c2;c 5 < 7.2; 7.2 in. 5. a2 1 b2 5 c2; 52 1 52 5 c2;

25 1 25 5 c2; 50 5 c2; c 5 7.1; 7.1 cm.

6. a2 1 b2 5 c2; 42 1 72 5 c2; 16 1 49 5 c2; 65 5 c2;

c 5 < 8.1; 8.1 in. 7. a2 1 b2 5 c2; 32 1 42 5 c2;

9 1 16 5 c2; 25 5 c2;c 5 5 5 8. a2 1 b2 5 c2;

92 1 122 5 c2; 81 1 144 5 c2; 225 5 c2; c 5 5 15

9. a2 1 b2 5 c2; 72 1 242 5 c2; 49 1 576 5 c2; 625 5 c2; c 5

5 25 10. a2 1 b2 5 c2; 62 1 52 5 c2; 36 1 25 5

c2; 61 5 c2; c 5 < 7.8 11. a2 1 b2 5 c2;

112 1 142 5 c2; 121 1 196 5 c2; 317 5 c2; c 5 <17.8 12. a2 1 b2 5 c2; 182 1 222 5 c2; 324 1 484 5 c2;

808 5 c2; c 5 < 28.4 13. a2 1 b2 5 c2; 12 1 142 5

c2; 1 1 196 5 c2; 197 5 c2; c 5 < 14.04; 14.04 ft

14. a2 1 b2 5 c2; 62 1 82 5 c2; 36 1 64 5 c2; 100 5 c2;

"197

"808

"317

"61

"625

"225

"25

"65

<"50

"52

"289

"1,109

"400

Sides ofTriangle

3, 4, 5

5, 12, 13

6, 8, 10

9, 12, 15

Area ofSquare A

9

25

36

81

Area ofSquare B

16

144

64

144

Area ofSquare C

25

169

100

225



c 5 5 10. P 5 a 1 b 1 c 5 6 1 8 1 10 5 24; 24 cm

15a. a2 1 b2 5 c2; 162 1 222 5 c2; 256 1 484 5 c2; 740 5

c2; c 5 < 27.2; 27 in. 15b. Answers may vary.

Sample: a2 1 b2 5 c2; 202 1 182 5 c2; 400 1 324 5 c2;

724 5 c2; c 5 < 26.91< 27 in.; 20 in. by 18 in.16. a 5 b 5 5; a2 1 b2 5 c2; (5)2 1 (5)2 5 c2;

25 1 25 5 c2; 50 5 c2; c 5 < 7.1; 7.1 cm 17. a 5

b 5 2; a2 1 b2 5 c2; (2)2 1 (2)2 5 c2; 4 1 4 5 c2; 8 5 c2;

c 5 < 2.8; 2.8 cm 18. a 5 b 5 10; a2 1 b2 5 c2;

(10)2 1 (10)2 5 c2; 100 1 100 5 c2; 200 5 c2; c 5

< 14.1; 14.1 in. 19. a 5 b 5 12; a2 1 b2 5 c2;

(12)2 1 (12)2 5 c2; 144 1 144 5 c2; 288 5 c2; c 5

< 17.0; 17.0 m 20. 1.52 1 1.72 5 c2;

2.25 1 2.89 5 c2; 5.14 5 c2; c 5 < 2.3; 2.3 km

21. When you draw a right triangle with hypotenuse , the lengths of the legs are 100 ft and 200 2 50 5 150 ft. Using the Pythagorean theorem,

The distance across the lake is about 180.3 ft.22. 5 5, 5 6, 5 7, 5 8, 5

9, 5 10; 6 values 23. m2 1 (m 1 1)2 5 (m 1 2)2;

32 1 (3 1 1)2 0 (3 1 2)2; 32 1 (4)2 0 (5)2; 9 1 16 0 25;

25 5 25; the equation is true for m 5 3 because

32 1 42 5 52. 24. a2 1 b2 5 c2; (a2 1 b2) 1 c2 5 200;c2 1 c2 5 200; 2c2 5 200; c2 5 100; c 5 5 10; the

hypotenuse is 10. 25. 302 1 402 5 c2; 900 1 1,600 5 c2;

2,500 5 c2; c 5 5 50; 50 26. b 5 a 5 (24);

b 5 ? 3 5 15; 15 27. 20 ? 35 5 700; 700 ? 3 5 2,100;

5 35; 35 28. 2.97 3 103; because the exponent of10 is 3, the decimal point in 2.97 must be moved 3 places to the right, so 2.97 3 103 5 2,970. 29. 1.02 3 105;because the exponent of 10 is 5, the decimal point in 1.02must be moved 5 places to the right, so 1.02 3 105 5

102,000. 30. 8.11 3 104; because the exponent of 10 is 4,the decimal point in 8.11 must be moved 4 places to theright, so 8.11 3 104 5 81,100.


1. Answers may vary. Sample: Multiplying by 1.1 is thesame as multiplying by 1 1 0.1. By the DistributiveProperty, a number multiplied by 1 1 0.1 equals that

number plus of that number. 2. Answers may vary.Sample: Rounding 47 and 78 up increases the weight,

while ignoring “adding ” decreases the weight. 3. Thejogger runs around the perimeter of a rectangular park.

110

110

2,10060

51

58

58"2,500

"100

"100

"81"64"49"36"25

180.3 < BA "32,500 5 BA

32,500 5 BA2 10,000 1 22,500 5 BA2

1002 1 1502 5 BA2

AB

"5.14

"288

"200

"8

"50

"724

"740

"100 Her friend cuts through on a diagonal so that she runsaround the perimeter of a triangular area. Each onedoes 5 laps. The park is 1,000 ft long and 500 ft wide.First find the distance around the entire park using theformula for the perimeter of a rectangle: P 5

2(1,000 1 500) 5 2(1,500) 5 3,000. Then multiply by 5 tofind how far the jogger runs: 3,000 ft 3 5 5 15,000 ft.Convert this answer into miles: 15,000 4 5,280 < 2.84mi. Now find the length of the diagonal that the jogger’sfriend ran along using the Pythagorean theorem:a2 1 b2 5 c2; 1,0002 1 5002 5 c2; 1,000,000 1 250,000 5

c2; 1,250,000 5 c2; c 5 < 1,118. Then addthe length of all three sides together to find thedistance around the perimeter of the triangle:1,000 1 500 1 1,118 5 2,618. Now multiply by 5 to findhow far the friend runs: 2,618 ft 3 5 5 13,090 ft. Convertinto miles: 13,090 4 5,280 5 2.48 mi 4. The formula fordistance is d 5 16t2. The Sears Tower is 1,450 ft tall, sothe distance d is known, and the formula can be solvedfor t to find the time it takes the squeegee to fall fromthe top of the building to the sidewalk: d 5 16t2; 1,450 5

16t2; 1,450 4 16 < 90; 5 t2; t < 9.5; 9.5 s5a.

To complete the table, use the equation m 5 24p2 1 40p,and plug in the values provided for p to solve for m:m 5 24p2 1 40p; 24(2)2 1 40(2) 5 24(4) 1 80 5216 1 80 5 64; 24(3)2 1 40(3) 5 24(9) 1 120 5236 1 120 5 84; 24(4)2 1 40(4) 5 24(16) 1 160 5264 1 160 5 96; 24(5)2 1 40(5) 5 24(25) 1 200 52100 1 200 5 100; 24(6)2 1 40(6) 5 24(36) 1 240 52144 1 240 5 96; 24(7)2 1 40(7) 5 24(49) 1 280 52196 1 280 5 84; 5b. According to the table, thebusiness makes the most money at the price of $5. Thebusiness makes the least amount of money when itcharges $1. 6. If the wall forms a right angle, thedistance from the point on the wall to the point on thefloor can be found using the Pythagorean theorem:

a2 1 b2 5 c2; 32 1 42 5 c2; 9 1 16 5 c2; c2 5 25; c 5

; c 5 5; 5 ft. The distance from the point on the wallto the point on the floor is the hypotenuse of a righttriangle with legs of lengths 3 ft and 4 ft.

3-3 Using the PythagoreanTheorem pages 118–121

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. The PythagoreanTheorem states that in any right triangle, the sum of thesquares of the lengths of the legs (a and b) is equal tothe square of the length of the hypotenuse: a2 1 b2 5 c2.2. 5 3. 8.6

Quick Check 1. a2 1 b2 5 c2; 12.62 1 b2 5 20.22;

"25

p (dollars)

m (dollars)

1

36

2

64

3

84

4

96

5

100

6

96

7

84

Car Wash Business

"90

"1,250,000



158.76 1 b2 5 408.04; b2 5 249.28; b 5 <15.8; 15.8 ft 2. a2 1 b2 5 c2; 52 1 b2 5 182; 25 1 b2 5

324; b2 5 299; b 5 < 17.3; 17.3 ft

Exercises 1. The shorter sides are the legs: and .The longest side is the hypotenuse: . 2a. 62 1 b2 5

102; 10 2b. 36 1 b2 5 100; 36 2c. b2 5 64; 64 2d. b 5 8; 8 3. a2 1 b2 5 c2; a2 1 122 5 202; a2 1 144 5

400; 256 5 c2; c 5 5 16; 16 in. 4. a2 1 b2 5 c2;a2 1 6.12 5 8.12; a2 1 37.21 5 65.61; 28.4 5 c2; c 5

< 5.3; 5.3 m 5. a2 1 b2 5 c2; a2 1 62 5 92;

a2 1 36 5 81; a2 5 45; a 5 < 6.7; 6.7 ft 6. a2 1 b2 5

c2; a2 1 52 5 102; a2 1 25 5 100; a2 5 75; a 5 < 8.7;8.7 in. 7. a2 1 b2 5 c2; 52 1 b2 5 122; 25 1 b2 5 144;

b2 5 119; b 5 < 10.9 8. a2 1 b2 5 c2; 72 1 b2 5

252; 49 1 b2 5 625; b2 5 576; b 5 5 249. a2 1 b2 5 c2; a2 1 10.52 5 20.12; a2 1 110.25 5404.01; a2 5293.76 < 17.1 10. a2 1 b2 5 c2; 3.42 1 b2 5

6.72; 11.56 1 b2 5 44.89; b2 5 33.33; b 5 < 5.8 11. a2 1 b2 5 c2; a2 1 8.32 5 16.92; a2 1 68.89 5 285.61;

a2 5 < 14.7 12. a2 1 b2 5 c2; a2 1 112 5 152;

a2 1 121 5 225; a2 5 104; a 5 < 10.2 13. a2 1 b2 5 c2; 52 1 b2 5 102; 25 1 b2 5 100; b2 5 75;

b 5 < 8.7; 8.7 ft 14. Use the Pythagorean theoremto find the width of the screen to the nearest tenth:

a2 1 b2 5 c2; 92 1 b2 5 172; 81 1 b2 5 289; b2 5 208;

b 5 < 14.4, or 14.4 in. The formula for the area ofa rectangle is A 5 Ow. Use the provided length, 9 in., andthe discovered width, 14.4 in., to find the area of thewhole screen: A 5 Ow 5 9(14.4) 5 129.6, or 129.6 in.2.15. Find the length of the other leg: a2 1 b2 5 c2;

42 1 b2 5 52; 16 1 b2 5 25; b2 5 9; b 5 5 3. Find

the area of the triangle: A 5 bh 5 (3)(4) 5 6; 6 units2.

16. Find the length of the other leg: a2 1 b2 5

c2; 8.62 1 b2 5 102; 73.96 1 b2 5 100; b2 5 26.04; b 5

< 5.1. Find the area of the triangle: A 5 bh 5

(8.6)(5.1) < 21.9; 21.9 units2. 17. Find the length

of the other leg: a2 1 b2 5 c2; 7.32 1 b2 5 9.12;53.29 1 b2 5 82.81; b2 5 29.52; b 5 < 5.43. Findthe area of the triangle: A 5 bh 5 (7.3)(5.43) < 19.8;

19.8 units2 18. x2 1 102 5 202; x2 1 100 5 400; x2 5

300; x 5 < 17; 17 m 19. The student added 32 to

42 instead of subtracting it from 42. You must find

. 20a. The distance d between the bases isthe same, and the angles in a baseball diamond are rightangles. You can use the Pythagorean Theorem:d2 1 d2 5 127.32. Then solve for d. 20b. d2 1 d2 5

127.32; d2 1 d2 5 16,205.29; 2d2 5 16,205.29; 5

; d2 5 8,102.645; d 5 5

90.015,rounded to 90 ft 20c. The baseball diamond has

"8,102.64516,205.29

2

2d2

2

"(42 2 32)

"300

12

12

"29.52

12

12"26.04

12

12

"9

"208

"75

"104

"216.72

"33.33

"576

"119

"75

"45

"28.4

"256

PQ

RQPR

"299

"249.28 4 sides, each about 90 ft long. P 5 90(4) 5 360, or 360 ft 21. No; (a 1 b)2 5 a2 1 b2 1 2ab, so (a 1 b)2

2

a2 1 b2. 22. a2 1 b2 5 c2; 52 1 b2 5 8.52; 25 1 b2 5

72.25; b2 5 47.25; b 5 < 7; the correct choice

is B. 23. Since , , , 3 , , 4. Since

is closer than , is closer to 3; thecorrect choice is G. 24. 4.95 1 6.99 1 1.05 5 12.99;20.00 2 12.99 5 7.01; the correct choice is B. 25. TheLCD of 6 and 11 is 66, so write equivalent fractions with

66 as the denominator: 5 , 5 . Since . ,

. . 26. Since 0.1 expressed as a fraction is , and

the LCD of 8 and 10 is 40, write equivalent fractions

with 40 as the denominator: 5 , 5 . Since . ,

. 0.1. 27. Since 0.2 expressed as a fraction is , andthe LCD of 20 and 10 is 20, write equivalent fractions

with 20 as the denominator: 5 , 5 . Since 5 ,

5 0.2. 28. The LCD of 7 and 10 is 70, so write equivalent fractions with 70 as the denominator: 5

, 5 . Since . , . .

EXTENSION page 122

1. yes; 15 1 35 . 40; 50 . 40 2. no; 7 1 6 , 15; 13 , 15

3. yes; 1 1 2 . 3 ; 4 . 3 4. Check students’ work.5. The hypotenuse is the longest side, 10 cm. Use the Pythagorean theorem: a2 1 b2 5 c2; 62 1 82 0 102;36 1 64 5 100. yes; 62 1 82 5 102 6. The hypotenuse isthe longest side, 26 in. Use the Pythagorean theorem:a2 1 b2 5 c2; 102 1 242 0 262; 100 1 576 5 676. yes;102 1 242 5 262 7. The hypotenuse is the longest side,65 km. Use the Pythagorean theorem: a2 1 b2 5 c2;162 1 632 5 652; 256 1 3,969 5 4,225. yes; 162 1 632 5 652

8. ( )2 1 ( )2 5 ( )2

1 1 2 5 3

3 5 3

The equation a2 1 b2 5 c2 is true, so the triangle is aright triangle.


1. . . ; 10 . . 9. Since 85 iscloser to 81 than to 100, < 9

2. Irrational; 13 is not a perfect square. 3. Rational; thenumber is a ratio of two integers. 4. Irrational; thedecimal does not terminate or repeat. 5. 122 1 92 5 c2;144 1 81 5 c2; 225 5 c2; c 5 5 15; 15 cm

6. 82 1 212 5 c2; 64 1 441 5 c2; 505 5 c2; c 5 <

22.5; 22.5 ft 7. 72 1 b2 5 252; 49 1 b2 5 625; b2 5 576;

b 5 5 24; 24 in. 8. 152 1 192 5 c2; 225 1 361 5

c2; 586 5 c2; c 5 < 24.2; 24.2 m 9. 42 1 82 5 d2;16 1 64 5 d2; 80 5 d2; d 5 < 8.9; 8.9 m "80

"586

"576

"505

"225

"85

"85"81"85"100

"3"2"1

12

12

12

12

410

37

2870

3070

2870

410

3070

37

420

420

420

420

210

420

420

210

18

440

540

440

110

540

18

110

911

56

5466

5566

5466

911

5566

56

"10"16"9"10

"10"16"10"9

"47.25



3-4 Graphing in the CoordinatePlane pages 124–127

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. They are the samedistance from zero on a number line but on oppositesides of zero. 2. 25, 23, 21, 3 3. 26, 24, 2, 9 4. 210,28, 0, 6 5. 25, 22, 4, 7

Quick Check

1.

2. The three points form a right triangle. Use thePythagorean theorem: a2 1 b2 5 c2; 32 1 52 5 c2;9 125 5 c2; 34 5 c2; c 5 < 6; 6 mi

Exercises 1. Quadrant II; the correct choice is B.2. Quadrant I; the correct choice is A. 3. Quadrant IV;the correct choice is D. 4. Quadrant III; the correctchoice is C. 5. (24, 3) 6. (4, 2) 7. (23, 0) 8. (25, 22)9. (0, 21) 10. (3, 22)

11–18.

19. C 20. M 21. P 22. A 23. The distance d betweenthe bases is the same, and the angles in the softballdiamond are right angles. Use the Pythagorean theorem:

d2 1 d2 5 852; 2d2 5 7,225; 5 ; d2 5 3612.5;

d 5 < 60; about 60 ft 24. The length of is5 units. The length of is 5 units. Using the Pythagorean Theorem, the length of is the squareroot of 52 1 52; 52 1 52 5 c2; 25 1 25 5 c2; 50 5 c2; c 5

< 7.1; 7.1 units "50

AB

BC

AC"3,612.5

7,2252

2d2

2

2 4 6Ox

y4

2

E G

A

C

H

B

DF

"34

2Ox

y

2

�2

S

R

�2

25a.

25b. The points form the letter Y. 26. Draw two parallel lines to create two triangles and one rectangle within thetrapezoid. The dimensions of the triangles are the same.Find the length of the hypotenuse: 22 1 32 5 c2; 4 1 9 5c2; 13 5 c2; c 5 < 3.6. The bottom of the trapezoidis 7 units across, and the top is 3 units across. Perimeter:3 1 3.6 1 7 1 3.6 5 17.2, or 17.2 units.

27. 938 W 458 N; 978 W 418 N 28. Quadrant IV29. Quadrant I 30. Start at (25, 23). Then move to(24, 23), (24, 1), (23, 1), (23, 22), (22, 22), (22, 23),(4, 23), (4, 3), (1, 3), (1, 1), (3, 1), and (3, 2) in that order.31. The square is reflected over the x-axis.

2 4Ox

y

2 4

(3, 7)

(3, 2)

Ox

y

6

4

3

!3313

32 2

Ox

y

!3313

"13

2 4Ox

y

2



32. (22, 1.5); the correct choice is C.

33. Oscar grew 3 inches a year for 5 years, until he was18. So between ages 13 and 18, Oscar grew 15 inches. Tofind his height at age 18, 15 in. must be added to theheight he was at age 13. In order to do this, it isnecessary to know how tall Oscar was when he was 13;the correct choice is H.34. 402 1 602 5 c2; 1,600 1 3,600 5 c2; 5,200 5 c2; c 5

< 72; the correct choice is C. 35. < 7.1

36. 2 < 2 < 20.4 37. < 2.6

38. < 0.4


Activity 1. Answers may vary. Sample: Add the valuesof points A and C, then divide by 2. 2. The distancebetween points C and E is 27 2 7 5 20, or 20 units. Themidpoint is half the distance between the two points, so20 4 2 5 10. Therefore the midpoint D is ten units afterpoint C: 7 1 10 5 17.Exercises 1a. Point F is located at (24, 4) and point Gis located at (2, 4). The midpoint of this segment movesonly along the x-axis, so the y-axis coordinates stay thesame. Since point F is 4 units to the left of 0 and point Gis 2 units to the right of 0, the distance between the twopoints is 4 1 2 5 6, or 6 units. The midpoint is half thedistance, so 6 4 2 5 3, or 3 units. 3 units from point F is24 1 3 5 21, so the midpoint’s coordinates are (21, 4).1b. Point F is located at (24, 4) and point J is located at(24, 26). The midpoint of this segment moves onlyalong the y-axis, so the x-axis coordinates remain thesame. Since point F is 4 units above 0 and point J is 6units below 0, the distance between the two points is4 1 6 5 10, or 10 units. The midpoint is half the distance,so 10 4 2 5 5, or 5 units. 5 units above point J is26 1 5 5 21, so the midpoint’s coordinates are

(24, 21). 2. : 5 5 3; 5 5 1;

(3, 1); : 5 5 0; 5 5 24;

(0, 24) 3. Side (0,8), (8,12): 5 5 4; 5 5

10; (4, 10). Side (8, 12), (12, 4): 5 5 10;

5 5 8; (10, 8). Side (12,4), (4, 0):

5 5 8; 5 5 2; (8, 2). Side (4, 0), (0, 8):

5 5 2; 5 5 4; (2, 4). 4a. Los Angeles is

1,139 mi from Adrian, Texas. If you are 150 mi from LosAngeles, you are 1,139 2 150 5 989 mi from Adrian.4b. If Chicago is also 1,139 mi from Adrian, and you are989 mi from Adrian, you are 1,139 1 989 5 2,128 mifrom Chicago. 5. Add x1 and x2 and divide by 2. This isthe x-coordinate of the midpoint. Add y1 and y2 anddivide by 2. This is the y-coordinate of the midpoint.

82

0 1 82

42

4 1 02

42

4 1 02

162

12 1 42

162

12 1 42

202

8 1 122

202

8 1 122

82

0 1 82

282

22 1 (26)2

02

4 1 (24)2HJ

22

4 1 (22)2

62

4 1 22GH

"0.18

"7"0.16"16

"50"5,200


1. Pattern: Answers may vary. Earnings increase by $10as the number of hours worked increases by 4. Table:

2. Pattern: Answers may vary. Sample: Total costincreases by $10 as the number of guests increases by 3.Table:

3a.

3b.

4. Answers may vary. Sample: y 5 180 2 9x

3-5 Equations, Tables, and Graphspages 130–134

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. variable 2. 3 3. 21 4. 28

Quick Check

1.

t 5 15c, where t represents total cost andc represents number of CDs.

ExpressionTotal Cost(dollars)

15(0)

15(1)

15(2)

15(3)

15(c)

0

15

30

45

Numberof CDs

0

1

2

3

c t

Tickets Remaining

0

180 171 162 153

21 3 20

0

Number of Days



2.

More Than One Way 80 2 2(10) 5 80 2 20 5 60;60 oz; check students’ methods.

Exercises 1. A point that lies on the graph of a linearequation is a solution of the equation; so the correctchoice is C.

2.

3. Every minute you lose 0.75 gallons of water so theamount you have after t minutes is g 5 0.75t. 4. Labelthe x-axis “Number of Minutes (t)” and the y-axis“Gallons of Water Lost (g).” Four points that lie on thegraph: (1, 0.75), (2, 1.5), (3, 2.25), (4, 3)

5.

b 5 4s

6.

t 5 22h

ExpressionTemperature

Drop (°F)Time

(hours)

0

1

2

3

h

0

�2

�4

�6

�2(0)

�2(1)

�2(2)

�2(3)

�2(h) t

ExpressionTotal Number

of BabiesTime

(seconds)

0

1

2

3

s

0

4

8

12

4(0)

4(1)

4(2)

4(3)

4(s) b

Number of Minutes (t) 1 2 3 4

Gallons of Water Lost (g) 0.75 1.5 2.25 3

Water Loss

Temperature of aChemical Solution

80

60

40

20

20

0

Tem

per

atur

e (°

F)

4 6Time (min)

y

x

7.

8.

9.

It would take 26 squares.10. 11.

2 4Oxy

2O x

y

2

1 2 3 4 5 6 7 8 9 10O

x

y262422201816141210

8642

Nu

mb

er o

f S

qu

ares

Number of Circles

Number of Circles (x)

Number of Squares (y)

1

8

2

10

3

12

4

14

5

16

6

18

Test Score

2

80

100

60

40

20

0S

core

4 6Number of Incorrect

Answers

y

x0

Auto Repair Cost

160

120

80

40

200

Tota

l Co

st (d

olla

rs)

4Hours of Labor

y

x



12. 13. By graphing all of thesepoints on the coordinate plane,you can see that only point Adoes not lie on the same line asthe other points.

14. Let m 5 the number of mugs. Let t 5 the total cost.t 5 8m 1 515.

c 5 1.50/ 1 10; 20 5 1.50/ 1 10; 10 5 1.50/; ;/ 5 ; you can’t have of a letter so the maximum

number of letters you can engrave is 6. 16. Let m 5 thenumber of months. Let p 5 the weight you will be ableto lift. p 5 3 1 (2m); p 5 3 1 (2 3 5); p 5 3 1 10; p 5

13; 13 lb; check students’ methods. 17. Gina; the graphdrawn by Gina’s father shows the amount owed afterGina gives him $40 each week, not $20. 18. Let y 5

income or expenses. Let x 5 the number of calendarssold.

Income: y 5 4xExpenses: y 5 2x 1 20

The graphs intersect at (10, 40), which represents 10calendars costing $40 to make or sell. It is the breakeven point.

19. The ordered pairs of table B show points that lie onthe graph; the correct choice is B. 20. $4.69 2 $3.99 50.70. Let b 5 the number of pounds of bananas: 0.28b 5

0.70; 5 b 5 2.5; the correct choice is H.

21. Divide 23 by 20; the correct choice is B. 22. b 1 6 510; b 1 6 2 6 5 10 2 6; b 5 4 23. k 2 1 5 24;k 2 1 1 1 5 24 1 1; k 5 25 24. 24 1 n 5 40;24 1 n 1 4 5 40 1 4; n 5 44

0.700.28;0.28b

0.28

y

x5

60

80

40

20

0

Number Sold10 2520 300 15

Do

llars

Calendar Fundraiser

y = 2x + 20

y = 4x

(10, 40)

2362

3

101.50 5 1.50/

1.50

Numberof Letters

0

1

2

3

Expression

1.50(0) � 10

1.50(1) � 10

1.50(2) � 10

1.50(3) � 10

1.50( ) � 10

Total Cost(dollars)

10.00

11.50

13.00

14.50

c� �

Ox

y

4

2


1–4. Check students’ work.

3-6 Translations pages 136–139

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Quadrant II 2. (4, 2)3. (2, 1) 4. (5, 22) 5. (1, 21)

Quick Check

1.

J’(24, 7)

2. (x, y) S (x 1 6, y 1 2)

Exercises 1. A transformation is a change in theposition, shape, or size of a figure.

2. 6 units right. 3. 4.

5. 6.

7. 8.

2 4x

y

2

B

AC

O�3 2

x

y3

�2

B �

D �

B

D

A�

A

C �

C

2 4 6Oxy

X2 4Ox

yS

Ox

y

2

V

1Ox

y

2

TT

2 4O�2�4x

y

4

J

K

L

J�

K�

L�



9. 10.

11. (x, y) S (x 1 4, y 1 3) 12. (x, y) S (x 2 5, y)13. (x, y) S (x 1 3, y 2 4) 14. (x, y) S (x, y 2 4)

15. The original coordinates of the vertices are A(25, 0),B(23, 3), C(22, 4), D(0, 1), E(21, 0). To translate to theright, you add to the x-coordinate. To translate down,you subtract from the y-coordinate. A: 25 1 6 5 1;0 2 5 5 25. B: 23 1 6 5 3; 3 2 5 5 22. C: 22 1 6 5 4;4 2 5 5 21. D: 0 1 6 5 6; 1 2 5 5 24. E: 21 1 6 5 5;0 2 5 5 25. Ar(1, 25), Br(3, 22), Cr(4, 21), Dr(6, 24),Er(5, 25). 16. Q(3, 0) S Qr(23, 2); the correct choiceis B 17. R(22, 4) S Rr(1, 4); the correct choice is C.18. P(4, 21) S Pr(3, 26); the correct choice is A.

19. Answers may vary. Sample:

20a. (x, y) S (x 1 1, y 1 2)20b. (x, y) S (x 2 2, y 1 1)20c. (x, y) S (x 2 2, y 2 1)20d. (x, y) S (x 2 1, y 2 2)21. Subtract 1 from the x-coordinateand add 3 to the y-coordinate.

22.

23. A(2, 3): 2 1 2 5 4; 3 1 (24) 5 21; A’(4, 21); thecorrect choice is D. 24. First find the length of thehypotenuse, which is also a side of the square.92 1 122 5 c2; 81 1 144 5 c2; 225 5 c2; c 5 5 15.

The area of the square is 15 ? 15 5 225, or 225 unit2;the correct choice is J.

25. 26.

2Ox

y

22 4O x

y3

"225

y 5 12x 1 3

2 4Ox

y6

2

3x

y

B

CD

A

BA

C

EF

D2 4 xO

y

4


1–5.

6.

Jr(23, 6), Kr(0, 8), Lr(2, 5)7. (x, y) S (x 2 3, y 1 4)

8.

w 5 3x 1 5


1–3. Check students’ work. 4. D and Dr are the same distance from the fold; the same is true for theother vertices.

3-7 Reflections and Symmetrypages 141–144

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. distance

2. 3.

4Ox

y8

4 A

2Ox

y

2

A

Number ofExercises

0

1

2

3

x

Expression

3(0) + 5

3(1) + 5

3(2) + 5

3(3) + 5

3(x) + 5

WorkoutTime (min)

5

8

11

14

w

O 2 4 6

4

J�

K�

L� K

L

J

y

x�2

O 2 4 6

2

2A

B

C

D

E

24

y

x



4. 5.

Quick Check

1. D9(2, 1)

2. E9(4, 23), F9(3, 21), G9(1, 22)

3. yes; 1 line

Exercises 1. Line a is a line of symmetry if one half ofthe figure matches the other half exactly when the figureis reflected over line a. 2. Point A is positioned at(24, 2). If it is reflected over the y-axis, the x-axiscoordinate will be its opposite and the y-axis coordinatewill remain the same, so it will be positioned at (4, 2); thecorrect choice is D. 3. Point B is positioned at (22, 1).If it is reflected over the x-axis, the x-axis coordinate willremain the same and the y-axis coordinate will be itsopposite, so it will be positioned at (22, 21); the correctchoice is G. 4. Point H is positioned at (24, 22). If it isreflected over the y-axis, the x-axis coordinate will be itsopposite and the y-axis coordinate will remain the same,so it will be positioned at (4, 22); the correct choice is E.5. Point F is positioned at (2, 21). If it is reflected overthe y-axis, the x-axis coordinate will be its opposite andthe y-axis coordinate will remain the same, so it will bepositioned at (22, 21); the correct choice is G. 6. PointE is positioned at (4, 22). If it is reflected over the x-axis, the x-axis coordinate will remain the same andthe y-axis coordinate will be its opposite, so it will bepositioned at (4, 2); the correct choice is D. 7. Point C ispositioned at (2, 1). If it is reflected over the x-axis, the x-axis coordinate will remain the same and the y-axiscoordinate will be its opposite, so it will be positioned at(2, 21); the correct choice is F.

2 4Ox

y4

2

F

EG

F

D

2Ox

y2

2 4O x

y6

4

2

A

2Ox

y4

2

AExercises8–13. 8. H9(23, 22)

9. G9(22, 4)10. B9(3, 24)11. D9(0, 2)12. C9(4, 3)13. M9(25, 0)

14. M9(4, 25), P9(1, 22),S9(5, 21)

15. M9(24, 5),P9(21, 2),S9(25, 1)

16. M9(4, 29),P9(1, 26),S9(5, 25)

2 4 6Ox

y

4

2

M

P S

2 4O x

y

4

2

M

PS

2 4Ox

y

4

2

M

PS

2 4O x

y

4

2

G

M

CD

H

B



17.

18. no reflectional symmetry19.

20. The flag can be folded in half horizontally. Yes; 1line. 21. The following capital letters from the alphabethave reflection symmetry; A, B, C, D, E, H, I, K, M, O, T,U, V, W, X, Y 22a.

J9(0, 3), K9(23, 1), L9(21, 23); the y-coordinate didnot change

22b. J9(23, 3), K9(26, 1), L9(24, 23)

23. E9(22, 5),F9(24, 5),G9(26, 1),H9(23, 1)

24. E9(2, 25), F9(4, 25),G9(6, 21), H9(3, 21)

62O x

y

4

2

H

E F

G

4 62O x

y

4

2

H

E F

G

3 7O

x

y4 J

K

L

25. E9(2, 21),F9(4, 21),G9(6, 3),H9(3, 3)

26. 27. An infinite number;any line passing throughthe center of a circle is aline of symmetry.

28.

29. Point C is positioned at (4, 2). If it is reflected overthe x-axis, the x-axis coordinate will remain the sameand the y-axis coordinate will be its opposite, so it will bepositioned at (4, 22); the correct choice is B. 30. Inorder to express 93,000,000 in scientific notation, thefirst factor must be a value greater than or equal to 1and less than 10, so the decimal point in 93,000,000 mustbe moved 7 places to the left to get 9.3. Since thedecimal point moved 7 places to the left, the secondfactor is 10 to the power of 7: 93,000,000 5 9.3 3 107;the correct choice is J. 31. Evaluate the values of the numbers as decimals: 2.4, < 2.3, < 1.4, < 2.2.Then put these in order from least to greatest: 1.4, 2.2,2.3, 2.4, so , , , 2.4; the correct choice is B.

32. a2 1 b2 5 c2; 62 1 82 5 c2; 36 1 64 5 c2; 100 5

c2; c 5 5 10 33. a2 1 b2 5 c2; 52 1 122 5 c2;

25 1 144 5 c2; 169 5 c2; c 5 5 13 34. a2 1 b2 5

c2; 72 1 242 5 c2; 49 1 576 5 c2; 625 5 c2; c 5 5 25


1. Rotating an object around a triangle will rotate it 120°because a triangle has 360°. 120° 1 120° 1 120° 5 360°;120º 2. Rotating an object around a square will rotate it90° because a square has 360°. 90° 1 90° 1 90° 1 90° 5

360°; check students’ work; the angle of rotation is 90º.

"625

"169

"100

73"5"2

"5"273

4Ox

y

4

8

8

6O x

y

4

H

E F

G



3. 4. Rotate the originalfigure 120º about thecenter point.

3-8 Rotations pages 146–149

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM 1. matches 2. straight3. obtuse 4. obtuse 5. acute 6. acute 7. right

Quick Check

1. ? 360 5 72; 72º

2a.

2b.

Exercises1. A figure has rotational symmetry if it can be rotated180 degrees or less and exactly match its original figure.

2–4.

2. (23, 3) 3. (22, 4) 4. (23, 5) 5. The image matchesthe original after of a complete rotation. ? 3608 5 458.

6. The image matches the original after of a completerotation. ? 3608 5 728. 7. no rotational symmetry1

5

15

18

18

2 4Ox

y

4

2

M

L

N

B

AD

D 2Ox

y

2

3

B D

AD

1 5Ox

y3

7 3 7

15

8.

9.

10.

11. ? 360 5 180; 180º

12.

13. A complete rotation has 3608. A square can berotated 3608 4 4 or 908.

14.

x

y

O

2 4 6O

y

J

L

K

6

4

2

12

O 2 6xy

QR

P

O2 6

x

y

2

QR

P

2 6Ox

y

4

2

QR

P



15. 16.

17. Answers may vary. Sample: The repeating figure is rotated 908 and translated. It is then rotated 2708

and translated.

18. 19.

20.

Rotate the triangle 180º about the origin.21. Notice the rotation of the shapes in the squares. The

correct choice is D. 22. 5

5 5 8.90; the correct choice is G.

23. 124 2 2 32.74 5124 2 41.33 2 32.74 5 49.93;

the correct choice is B. 24. 0 1 2 5 2; 23 2 1 5 24;Mr(2, 24) 25. 0 2 3 5 23; 23 1 3 5 0; Mr(23, 0)

EXTENSION page 150

1. 2.

3. 4.



1243

17.802

(9 1 4.30 1 4.50)2

f2(4.50) 1 4.30 1 2(2.25)g2

4Ox

y2

Q

P

R

Ox

y

O x

y

x

y

OO x

y


1. The x-axis and the y-axis intersect at the origin anddivide a coordinate plane into quadrants. 2. Threetypes of transformations that change the position of afigure are translations, reflections, and rotations. 3. If afigure has an angle of rotation of 180º or less for whichits image matches the original figure, then the figure hasrotational symmetry. 4. A number such as 25, which isthe square of a whole number, is a perfect square.5. The hypotenuse is the longest side of a right triangle.

6. 21 5 3r2; 5 ; 7 5 r2; r 5 < 2.6; 2.6 ft

7. 240 5 3r2; 5 ; 80 5 r2; r 5 < 8.9; 8.9 ft

8. 570 5 3r2; 5 ; 190 5 r2; r 5 < 13.8;

9. 196 is a perfect square, so the number is rational.10. Both 25 and 36 are perfect squares, so the number isrational. 11. 57 is not a perfect square, so the number isirrational. 12. 1.6 is not a perfect square, so the numberis irrational. 13. 225 is a perfect square, so the numberis rational. 14. a2 1 b2 5 c2; 62 1 82 5 c2; 36 1 64 5 c2;

100 5 c2; c 5 5 10 15. a2 1 b2 5 c2; 122 1 62 5

c2; 144 1 36 5 c2; 180 5 c2; c 5 < 13.4

16. a2 1 b2 5 c2; 242 1 402 5 c2; 576 1 1,600 5 c2;

2,176 5 c2; c 5 < 46.6 17. The ladder, thehouse and the ground between the house and the ladderform a right triangle with the ladder as the hypotenuse.

a2 1 b2 5 c2; a2 1 62 5 242; a2 1 36 5 576; a2 5 540;

a 5 < 23.2; about 23.2 ft 18. (23, 22)19. (22, 3) 20. (1, 23) 21. Quadrant IV 22. y-axis23. Quadrant II

24. 25.

26. 27.

2Ox

y2

2Ox

y

1

4O xy

2Ox

y4

2

"540

"2,176

"180

"100

"1903r2

35703

"803r2

32403

"73r2

3213


sworthington

Typewritten Text

1.

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Answers may vary. Sample:

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x = minutes

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y = words

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Tim: y = 40x + 30

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Bo: y = 50x

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Answer: 30 min

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Minutes

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0

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0

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2

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4

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40

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80

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120

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160

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y

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x

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Number of Words

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Graph:

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28.

29. 30.


1. 12 ? 12 5 144 and 212 ? 212 5 144, so the two squareroots are 12 and 212. 2. 16 ? 16 5 256 and 216 ? 216 5256, so the two square roots are 16 and 216.3. 20 ? 20 5 400 and 220 ? 220 5 400, so the two square

roots are 20 and 220. 4. 5 5 10

5. 5 5 0 6. 2 5 2 5 217. Since 2. is a repeating decimal and can be written asthe ratio , it is rational. 8. Since 10 is not a perfectsquare, the number is irrational. 9. Since 21 can be

written as the ratio 2 , it is rational. 10. Since thedecimal is nonrepeating and non-terminating, it isirrational. 11. Since 49 is a perfect square, the number isrational. 12. A rational number can be expressed as where a and b are non-zero integers. An irrationalnumber cannot be expressed in that way. Rationalnumbers are terminating or repeating decimals.Irrational numbers are nonterminating,nonrepeating decimals. 13. a2 1 b2 5 c2; 32 1 b2 5 52;9 1 b2 5 25; 9 2 9 1 b2 5 25 2 9; b2 5 16; b 5 5 414. a2 1 b2 5 c2; a2 1 302 5 342; a2 1 900 5 1,156;a2 1 900 2 900 5 1,156 2 900; a2 5 256; a 5 5 1615. a2 1 b2 5 c2; 52 1 122 5 c2; 25 1 144 5 c2; 169 5 c2;c 5 5 13 16. a2 1 b2 5 c2; 482 1 b2 5 602;2,304 1 b2 5 3,600; 2,304 2 2,304 1 b2 5 3,600 2 2,304;b2 5 1,296; b 5 5 36 17. a2 1 b2 5 c2;

172 1 102 5 c2; 289 1 100 5 c2; 389 5 c2;c 5 < 20; 20 ft 18. Test two coordinate pairs online v with the equation y 5 3x 1 2: 2 5 3(0) 1 2, 2 5 2;(0, 2); 21 5 3(21) 1 2, 21 5 21; (21, 21). The correctchoice is v. 19. Test two coordinate pairs on line t withthe equation y 5 23x 2 2: 22 5 23(0) 2 2, 22 5 22;(0, 22); 1 5 23(21) 2 2, 1 5 1; (21, 1). The correctchoice is t. 20. Test two coordinate pairs on line s withthe equation y 5 x 2 3: 23 5 (0) 2 3, 23 5 23;(0, 23); 22 5 (2) 2 3, 22 5 22; (2, 22). The correct choice is s.

12

12

12

"389

"1,296

"169

"256

"16

ab

116

56

27799

79

"1 ? 1"1"0 ? 0"0

"10 ? 10"100

x

y3

A

C

B

x

y3

A

C

B

O x

y

A

C

B

21–23.

24. Quadrant III 25. Quadrant IV 26. x-axis

27. y 5 4x 1 2

28. c 5 5g 1 20

29.

30.

2 4 6Ox

y

4

2 L

J

K

2 4 6Ox

y

4

L

J

K

Number ofGames

1

2

3

4

g

Expression

5(1) + 20

5(2) + 20

5(3) + 20

5(4) + 20

5(g) + 20

Total Cost(dollars)

25

30

35

40

c

20

16

12

8

4

0x

y

2 40Number

of Games

Tota

l Co

st (d

olla

rs)

2 4Ox

y

4

2C

B

A



31.

32.

33.

34.

35. (x, y) S (x 1 4, y 2 4) 36. Check students’ work.37. Q9(24, 4)

2 4 6Ox

y

4

2 L

J

K

2 4 6Ox

y6

4

2 L

J

K

2 4 6Ox

y

4

L

J

K

2 4 6Ox

y

4

2 L

J

K

TEST PREP page 155

1. (25, 212) is in Quadrant III; it has negative x-coordinates and negative y–coordinates; the correctchoice is C. 2. The meat is at (3, 3), so dessert is at (3 1 2, 3 2 5) 5 (5, 22); the correct choice is G.3. The vegetables and beverages are on the samey–coordinate. The distance between them is 5 2 (25), or10 fathoms; the correct choice is A. 4. Reflecting a pointover the y–axis gives the opposite sign for the x–coordinate. The coordinates of the potatoes are (23, 3);the correct choice is F. 5. From (28, 3) to (28, 23)there are 3 2 (23), or 6 feet of space; the correct choiceD. 6. The point (0, 3) will be pushed up to (0, 10) so itwill be moved 7 feet back. (0, 0 1 7) 5 (0, 7); the correctchoice is G. 7. The piano is 5 feet long and 3 feet wide.If there were a corner at the origin and at the point (3, 3)the piano would be 3 feet long and 3 feet wide. Thecorrect choice is D. 8. The other 3 coordinates of thepiano’s corners in Exercise 6 were in Quadrant I. Thepiano is now turned to face the opposite direction so itsnew coordinates will be in Quadrant III. (0, 3) is inquadrant 1, so the correct choice is J.


1a. Different trails may start at a different number offeet above sea level. 1b. Some trails wind around moreand are longer. Some trails may be slower because theyhave particularly steep or difficult sections. 1c. Anelevation gain of 0 means that the starting elevation andending elevation are the same. The trail between thestart and the finish may have hills and valleys.

2.

3a. Check students’ work. 3b. Answers may vary.Sample: about 1.5 ft/s 3c. Answers may vary. Sample:about 44 min 3d. Check students’ work. 3e. Checkstudents’ work.

x

y

Time (h)

Ele

vati

on

Gai

n (

ft)

1 20 3 4

4,000

3,000

2,000

1,000

0

TABG



1. 5 5 2. 5 5 3. 5

5 4. 5 5 5. 5 17 4 27 < 0.630

6. 5 49 4 12 < 4.083 7. 5 10 4 31 < 0.323

8. 5 19 4 7 < 2.714 9. 5 18 4 35 < 0.514

10. 11.

12. 13.

14. 15.

16.

36.1 in.18.

28.8 cm

4-1 Ratios and Rates pages 160–163

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. The least commondenominator is the smallest multiple the denominatorshave in common. 2. 3. 4. 5.

Quick Check 1. 5 5 5

2. 5 5 , or 6.5 deliveries per hour

3. 5 $0.22/oz; 5 $0.30/oz. The 20-oz box has

the lower unit price, so it is the better buy.

$3.5912 oz

$4.2920

6.51

528

deliveriesnumber of hours

16

13 ? 2

30 s3 ? 60 s

30 s3 min

712

4554

45

39

c 5 "832 < 28.8

832 5 c2 256 1 576 5 c2 162 1 242 5 c2

a2 1 b2 5 c2

c < 36.1

"1,300 5 c 1,300 5 c2

400 1 900 5 c2 202 1 302 5 c2

a2 1 b2 5 c2

r 5 215 , or 41

5

x 5 30 r 5 35 ? 7

1

31 ? 13x 5 3 ? 10 65 ? 5

6r 5 65 ? 7

2

13x 5 10 56r 5 72

t 5 56

y 5 916 t 5 1

3 ? 52

12 ? 21y 5 1

2 ? 98 43 ? 3

4t 5 43 ? 5

8

2y 5 98 34t 5 5

8

b 5 14

13 ? 31b 5 1

3 ? 34 k 5 56

31b 5 34 2 ? 1

2k 5 2 ? 28

3b 5 34 12k 5 28

1835

197

1031

4912

1727

1120

66 4 6120 4 6

66120

57

45 4 963 4 9

4563

27

32 4 16112 4 16

32112

12

34 4 3468 4 34

3468

Exercises 1. The rate is a ratio that compares quantitiesmeasured in different units. The quantities 6 and 23 havethe same unit of students. 2. There are 8 ants and 6ladybugs for a total of 8 1 6, or 14 insects. So, ants : allinsects 5 8 : 14, or 4 : 7. 3. There are 6 ladybugs and 8ants, so, ladybugs : ants 5 6 : 8, or 3 : 4. 4. There are 6ladybugs and 14 insects, so, ladybugs : all insects 5

6 : 14,or 3 : 7. 5. 16 cm : 8 cm 5 5 6. 10 s to 2 min 5

10 s : 2 min 5 10 s : 2 ? 60 s 5 5 5 7. 5

5 5 5 8. 50 m : 30 m 5 5

9. 5 5 5 10. 5 5

5 11. 22 in. to 3 ft 5 22 in. : 3 ft 5 22 in. : 3 ? 12 in. 5

5 5 12. 6 ft to 6 yd 5 5

13. 36 cm : 132 cm 5 5 14. 36 gal in 12 min 5 5 ;

3 gal/min 15. $42 for 3 books 5 5 ; $14/book

16. 300 ft in 48 s 5 5 6.25; 6.25 ft/s 17. $21.60 for 12

roses 5 5 $1.80/rose 18. 200 m in 16 s 5 5 12.5;

12.5 m/s 19. 676 mi in 13 h 5 5 52; 52 mi/h 20. 330

gal in 22 min 5 5 15; 15 gal/min 21. < $.08/oz

and < $.09/oz; since $.08 , $.09, the better buy is the 32-oz container. 22. Apollo 11: 237,000 mi in 103 hr 5

< 2,301; Apollo 12: 237,000 mi in 123 hr 5

< 1,927; 2,301 – 1,927 5 374; 374 mi/hr 23. <

20.007; 20.0078C/m

24.

26.

27. 18,980 – 18,560 5 420; 420 mi in 7.5 hr 5 5 56;

56 mi/hr 28a. 8,750 : 250 5 35 : 1 28b. 410,000 gal/1,200grower 5 342 gal/grower 28c. 4.50 3 2 3 8 5 72; $72 29. The ratio will change from to , which is not the

same. 30. ? (60) 5 ? 5 ? 5 35; 35 red marbles;60 2 35 5 25; 25 black marbles. 31. 4,000 ft2 in 30 min 5

5 133 ft2; the correct choice is A. 32. Point C

(4, 1), (4 2 3, 1 2 2) 5 (1, 21); the correct choice is G.

13

4,00030

51

71

601

712

712

1915

1612

4207.5

5 114121

5 114 : 121

5 41 ? 57

2 : 41 ? 1214

2812 : 301

4 5 572 : 121

4

5 1776

5 34152

5 34 : 152

5 3 ? 343 : 3 ? 152

3

1113 : 502

3 5 3 ? 1113 : 3 ? 502

3

26.51,000

237,000123

237,000103

$.758

$2.6932

33022

67613

20016

21.6012

30048

141

423

31

3612

311

36132

13

6 ft6 ? 3 ft

1118

113 ? 6

223 ? 12

21

8040

80 yd120 4 3 yd

80 yd120 ft

730

28120

28 s2 ? 60 s

28 s2 min

53

5030

23

812

81 ? 12

32 in.4 ? 12 in.

32 in.4 ft

112

12 ? 6

102 ? 60

21

168

Applications of Proportions pages 158–207


Chapter

4

17.a2 1 72 5 12.32

a2 1 49 5 151.29a2 1 49 2 49 5 151.29 2 49

a2 5 102.29a 5

10.1 m"102.29 < 10.1

a2 1 b2 5 c2

25.

5 2183

5 21 : 83

514 : 203

4 5 214 : 83

4



33.

34. 15 ? 15 5 225; ;15 35. ? 5 ;

; 36. ? 5 ; ; 5

37. ? 5 ; ;


1. 5 15,000 4 24 5 625; 625 gallons 2–3. Check

students’ work. 4. 5 60,000 4 15,000 5 4; 5

350 4 4 5 87.5; 4 years; $87.50/yr 5–8. Check students’work.


1. A pencil is not very long, so use a small unit ofmeasure; inch. 2. A plum is smaller than an apple, so usea small unit of measure; ounce. 3. A car’s gas tank ismeasured in gallons; gallon. 4. The distance from Dallasto Reno is far; kilometers. 5. A small glass only holds agulp or two of liquid; milliliters. 6. The mass of an adultis too much to be measured in grams; kilogram.

4-2 Converting Units pages 166–170

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. 1 2. 3. 4. 5. 2

Quick Check 1. 2 mi 5 2.25 mi 5 ? 5

5 11,880 ft

2.

3a. The conversion factor is and 14,120 lb < 14,000 lb:

? 5 7 t; 7. 3b. The conversion factor is

and 9.8 c < 10 c: ? 5 5 pt; 5 4. 15 L 5

? 5 < 16.0 qt

Exercises 1. 2. ; the correct choice is E.

3. ; the correct choice is A. 4. ; the correct

choice is D. 5. ; the correct choice is B. 6. ; the correct choice is C.

7. 8.

5 25 m 5 2.7 ft

52,500 m

100 5 32 ft12

2,500 cm 52,500 cm

1 ? 1 m100 cm32 in. 5 32 in.

1 ? 1 ft12 in.

1 lb16 oz

12 in.1 ft

1,000 m1 km

16 oz1 lb

1 ft12 in.

12 in.1 ft

(15)(1)qt0.94

1 qt0.94 L

15 L1

1 pt2 c

10 c1

1 pt2 c

1 t2,000 lb

14,000 lb1

1 t2,000 lb

5 13.2 ft>s 5 792 ft

60 s

0.15 mi1 min 5 0.15 mi

1 min ? 1 min60 s ?

5,280 ft1 mi

(2.25)(5,280)ft1

5,280 ft1 mi

2.25 mi1

14

27

23

59

56

3504

60,00015,000

15,00024

1114"121

196 5 1114

121196

1114

1114

14

520" 25

400 5 520

25400

520

520

125" 1

625 5 125

1625

125

125"225 5 15

c 5 5.3; the correct choice is B.

"27.7 5 c

27.7 5 c2

10.89 1 16.81 5 c2

3.32 1 4.12 5 c2

a2 1 b2 5 c29.

10. 5 ? 11.

12. 13.

14.

15. The conversion factor is and 148 in. < 144 in.:

? 5 12 ft. 16. The conversion factor is and

82 oz < 80 oz: ? 5 5 lb. 17. The conversion

factor is and 500 min < 480 min: ? 5

8 h. 18. The conversion factor is and

3,980 mm < 4,000 mm: ? 5 4 m.

19. 25 cm 5 ? 5 5 9.8 in.

20. 18 qt 5 ? 5 5 16.9 L

21. 55 lb 5 5 5 24.8 kg

22. 23 in. 5 ? 5 5 58.4 cm

23. 10 kg 5 5 5 22.2 lb

24. 16 L 5 5

25. ? ? ; ? 5 217 m

26. 14 in. 5 5 < 35 cm

27.

28. Round to the nearest tenth.

29. F 5 C 1 32 30. F 5 C 1 32

F 5 ? 28 1 32 F 5 ? 14 1 32F 5 50.4 1 32 F 5 25.2 1 32F 5 82.4°F F 5 57.2°F

95

95

95

95

< 0.647 in.>s < 0.6 in.>s

5 194 ? 12 min60 ? 60 s

6423 yd>h 5

194 yd3 h ? 36 in.

1 yd ? 1 h60 min ? 1 min

60 s

5 190,080 ft>d 5

3 ? 5,280 ? 12 ft1d

112 mi>h 5 3 mi

2 h ?5,280 ft

1 mi ? 24 h1 d

(14)(2.54) cm1

14 in1 ? 2.54 cm

1 in.

7 s1

31 m1 s

7 s1

1 m3 ft

93 ft1 s

(16)(1) qt0.94 5 17.0 qt16 L

1 ?1 qt

0.94 L

(10)(1) lb

0.4510 kg

1 ? 1 lb0.45 kg

(23)(2.54) cm1 in.

2.54 cm1 in.

23 in.1

(55)(0.45) kg1

55 lb1 ?

0.45 kg1 lb

(18)(0.94)L1

0.94 L1 qt

18 qt1

(25)(1) in.

2.541 in.

2.54 cm25 cm

1

1 m1,000 mm

4,000 mm1

1 m1,000 mm

1 h60 min

480 min1

1 h60 min

1 lb16 oz

80 oz1

1 lb16 oz

1 ft12 in.

144 in.1

1 ft12 in.

5 440 ft3 s < 146.67 ft>s

5100 ? 5,280 ft

60 ? 60 s

100 mih 5 100 mi

h ?5,280 ft

mi ? 1 h60 min ? 1 min

60 s

5 3 gal>min 5 0.5 cm>h 5

12 gal4 min 5 12 cm

24 h

12 qtmin 5

12 qtmin ?

1 gal4 qt 12 cm

d 5 12 cmd ? 1 d

24 h

5 $.45>min 5 7.5 ft>min

5$27

60 min 5 90 ft12 min

$27h 5

$27h ? 1 h

60 min1 ft

12 in.90 in.min

90 in.min

5 15 kg

515,000 kg

1,000

15,000 g 515,000 g

1 ?1 kg

1,000 g


31. C 5 (F 2 32) 32. C 5 (F 2 32)

C 5 (32 2 32) C 5 (0 2 32)

C 5 (0) C 5 (232)

C 5 0°C C 5 217.8°C

33. 3.8 Cal/min 5 ? 5 5

228 Cal/hr; swimming 34. 4.4 Cal/min 5 ? 5

5 264 Cal/h; cycling 35. 2.9 Cal/min 5

? 5 5 174 Cal/h; dancing

36. 6.2 Cal/min 5 ? 5 5

372 Cal/hr; aerobics 37. Answers may vary. Sample:Count the number of times you blink in a minute, then

multiply by 3 . To find the number of times in

a week, multiply the result by . 38a. The conversion

factor is : ? 5 354,534 births/day.

38b. The conversion factor is : ? 5

14,772, or 14,772 births/h. 39. 4 ft 7 in. 2 3 ft 9 in. 5 3 ft19 in. 2 3 ft 9 in. 5 10 in.; 2 ft 5 in. 1 10 in. 5 2 ft 15 in. 5

3 ft 3 in. 40. 10 ft/s 5 ? ? ? 5

5 6.8 mi/h 41. 22 ? (21) 5 2

42. 5 5 $0.52/mi

43. 44.

45.


1. 5 5 5 2. 81 in. to

27 ft 5 5 5 5 3. 90 m : 15 m 5

5 5 ; 6 : 1 4. 5 5 5

5 5. $84 for 7 books 5 5 84 4 7 5

12; $12/book 6. 96 m in 8 s 5 5 96 4 8 5 12; 12 m/s968

847

34

54 4 1872 4 18

5472

18 ? 372

18 yd72 ft

61

90 4 1515 4 15

9015

14

81 4 81324 4 81

81324

8127 ? 12

115

48 4 48720 4 48

48720

48 s12 min 5 48

12 ? 60

x

y

O 2 4

xO 2

yy

O 2

2

x

$22.1042.5 mi

$22.1012,424.9 2 12,382.4 mi

(10)(60)(60) mi

5,280 hr

60 min1 hr

60 s1 min

1 mi5,280 ft

10 ft1 s

1 day24 h

354,534 births1 day

1 day24 h

1 yr365 d

129,405,000 births1 yr

1 yr365 d

7 days1 week

24 h1d

60 min1 h

(6.2)(60) Cal1 h

60 min1 h

6.2 Cal1 min

(2.9)(60) Cal1 h

60 min1 h

2.9 Cal1 min

(4.4)(60) Cal1 h

60 min1 h

4.4 Cal1 min

(3.8)(60) Cal1 h

60 min1 h

3.8 Cal1 min

59

59

59

59

59

59 7. 57 gal in 19 min 5 5 57 4 19 5 3; 3 gal/min

8. 232 mi in 29 h 5 5 232 4 29 5 8; 8 mi/h 9. $12/h 5

5 5 $0.20/min 10. 9 kg 5

5 5 20 lb 11. 16 L 5 5

5 17.0 qt 12. 20 cm 5 5

5 7.9 in. 13. 65 mi/h 5 ? 5

5 104.7 km/h 14. 5 5 38 4 8 5

4.75; $4.75/page 15. 5 ? ? 5

5 12.2 km/min

ACTIVITY LAB page 172–173

Activity1.

2.

3. Yes; all ratios equal .4.

5. The shape of the graph is a line. It intersects the y-axisat (0, 0). 6. 64 ? 4 5 256; 256 total blocks

0 10 20

Tota

l Blo

cks

30 40

144

120

96

72

48

24

0

y

x

14

1 4 9 16 25 36

4 16 36 64 100 144TotalBlocks

ShadedBlocks

14

14

14

14

14

14

Ratio shaded total

(455)(1.61) km60 min

1 h60 min

1.61 km1 mi

455 mi1 h

455 mih

388

$388 pages

(65)(1.61) km1 h

1.61 km1 mi

65 mih

(20)(1) in.

2.54

20 cm1 ? 1 in.

2.54 cm

(16)(1) qt0.94

16 L1 ?

1 qt0.94 L

(9)(1) lb

0.459kg

1 ? 1 lb0.45 kg

$(12)(1)60 min

$121 h ? 1 h

60 min

23229

5719




7. 8.

9. No; the ratios are not equivalent.10.

The graph is a line. It intersects the y-axis at (0, 2).11. Answers may vary. Sample: In both graphs, thenumber of shaded blocks increases as the total numberof blocks increases. However, the x- and y- values in thefirst graph are proportional, while in the second graphthey are not. 12. Check students’ work.

Exercises 1. Yes; all ratios equal . 2. No; the ratios arenot equivalent.

4-3 Solving Proportionspages 174–178

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Yes; there is no commonfactor between the numerator and the denominator.2. 3. 3 4. 5. 2

Quick Check1. 2.

More Than One Way Methods may vary. Sample: Theratio of defense players to total players is about 9 : 30, or

. So, of the 890 players are defense players: ? 890 53 ? 89 5 267, or 267 players. Reasons for choosing a method may vary. Sample: I chose Michelle’s method because it has fewer steps.

930

930

930

d 5 $240.96

1.245d1.245 5 300

1.245 168 2 161; no

1.245d 5 300 6 ? 28 0 7 ? 23

1.24501 5 300

d 67 0 2328

45

66301

12

1033

15

0 2 4Shaded Blocks

Tota

l Blo

cks

6 8 10

24

20

16

12

8

4

0

y

x

0

2TotalBlocks

ShadedBlocks

Ratio shaded total

37

49

511

25

130

2

6

4

10

6

14

8

18

10

22

Exercises

1. You can find the cross products of two ratios bymultiplying the denominator for each ratio by thenumerator of the other ratio.

2.

4.

6.

8.

10.

12.

14.

16.

18.

20.

22. The ratio of oranges to apples is : 1, so the

proportion is 5 . Use cross products to solve: ? 2 5

x; ? 5 x; x 5 . The manager needs crate.

23.

y 5 48,387 yen

0.0093y0.0093 5 450

0.0093

0.0093y 5 450

0.00931 5 450

y

34

34

94

13

14

13

x

214

13

1

13

5.4 5 c 275 5 5c

5

27 5 5c 3 ? 9 5 5c

3c 5 59

16 5 w 144

9 5 9w9

144 5 9w 12 ? 12 5 9w

129 5 w

12

9 5 t 728 5 8t

8

72 5 8t 12 ? 6 5 8t

12t 5 8

6

k 5 7

12k12 5 84

12

12k 5 84

12k 5 4 ? 21

k4 5 2112

200 5 200; yes

2 ? 100 0 5 ? 40

25 0 40100

200 5 200; yes

25 ? 8 0 40 ? 5

2540 0 5

8

30 2 32; no

3 ? 10 0 8 ? 4

38 0 410

60 5 60; yes

30 ? 2 0 4 ? 15

304 0 15

2

42 2 52; no

3 ? 14 0 13 ? 4

313 0 414

90 5 90; yes

5 ? 18 0 6 ? 15

56 0 1518 3.

5.

7.

9.

11.

13.

15.

17.

19.

21.

k 5 6,340 kroons

k 5 12.68 ? 500

12.681 5 k

500

x 5 40.5

14x14 5 567

14

14x 5 567

14x 5 63 ? 9

x63 5 914

12 5 b 18015 5 15b

15

180 5 15b 20 ? 9 5 15b

20b 5 15

9

3 5 y 4515 5

15y15

45 5 15y 45 ? 1 5 15y

4515 5

y1

a 5 45

2a2 5 90

2

2a 5 90

2a 5 9 ? 10

29 5 10a

135 5 135; yes

15 ? 9 0 27 ? 5

1527 0 5

9

352 2 396; no

11 ? 32 0 18 ? 22

1118 0 22

32

168 5 168; yes

7 ? 24 0 6 ? 28

76 0 2824

10 2 8; no

1 ? 10 0 4 ? 2

14 0 210

54 5 54; yes

6 ? 9 0 27 ? 2

627 0 29

24.

y 5 4,301 yen

0.0093y0.0093 5 40

0.0093

0.0093y 5 40

0.00931 5 40

y


25.

27.Write the cross products.Simplify.Use the Subtraction Property ofEquality to subtract 12 from eachside.Use the Division Property ofEquality.Simplify.

28.Write the cross products.Simplify.Use the Subtraction Property ofEquality to subtract 36 fromeach side.Use the Division Property ofEquality to divide each side by 9.Simplify.

29. The first ratio, , is and the second ratio, ,

is . h and 25 are reversed. 30. The circle on the

left has 15 out of 20 shaded wedges, so the ratio is . The circle on the right has 9 out of 12 shaded wedges, so the ratio is . Check the cross products. 0 ; 15 ? 12 0

20 ? 9; 180 5 180; yes.

31.

;methods may vary.

33.

Since ,multiply 1 by 2 to find h.

35. Find the amount you’ll get fromthe first bank: the second bank:

5 5

0.7975a 5 1,500 0.8352b 5 1,500a < 1,880.88 b < 1,795.98The difference is 1,880.88 2 1,795.98, or about 85Canadian dollars.

1,500b

0.83531

1,500a

0.79751

h < 2

h < 1 3 2

11 3 2 5 22

h22 < 111

455 < 111

h22.3 < h

22

h22.3 5 4

55

f < 3, or about 3 grams

354f 5 1,100

354f 5 20 ? 55

35420 5 55

f

912

1520

912

1520

distancehours

25h

hoursdistance

314

4 5 x

369 5 9x

9

36 5 9x 72 5 9x 1 36

6 ? 12 5 9(x 1 4)

69 5 x 1 412

x 5 212

4x4 5 22

4

4x 5 22

4x 1 12 5 10

(x 1 3)4 5 5 ? 2

x 1 32 5 5

4

y 5 22,581 yen

0.0093y0.0093 5 210

0.0093

0.0093y 5 210

0.00931 5 210

y 36. 5

38. 5

39. Answers may vary. Sample: x will only equal x 1 zwhen z is 0.40.

41. 5 5 0.09; the correct choice is C.42. Quadrant IV has positive x-coordinates and negativey-coordinates; the correct choice is J. 43. The number ofpoints Kiana’s team scored; the correct choice is A.44. 211 1 (25) 5 216 45. 225 1 6 5 21946. 213 2 14 5 213 1 (214) 5 227

GUIDED PROBLEM SOLVING page 179–180

1. Answers may vary. Sample: The unit rate is about0.029 min/page, which is about . Since of 1,000 isabout 30, 29 minutes is reasonable.2. No, 5 .

3.

4a. Complaints per Week

4b.

5a. No; saying only 5 students participated in the studymakes the sample size appear invalid.

5b.

6.

7. According to the study, your community would needto spend $30.32 3 25,000, or $785,000. The annualbudget of $437,500 is below the average.

x 5 14.12; about 14 times greater 4,304x 5 60,781

4.3041 5

60,781x

x 5 120; 120 students voted no 5x 5 600

600x 5 5

1

x 5 480; 480 students voted yes 5x 5 600 ? 4

600x 5 5

4

x 5 538.5; about 538 complaints per week

52x 5 28,000

28,000

52 5 x1

t 5 58 min

t 5 2,000 ? 0.029

2,000

t 5 10.029

ct 5 10.029

t 5 21.75 < 22 min

t 5 750 ? 0.029

750t 5 1

0.029

ct 5 10.029

10.029

ct

133

133

7.2080

$7.2016 ? 5

d < 48.3; 48.3 in. 1,450 5 30d

50 ? 29 5 30d

50d 5 30

29

x 5 25

5x 5 2

5x 5 13 ? 6

6x

513

x 5 69 5 2

3

9x 5 6

9x 5 12 ? 12

129

x12

26.

y 5 18,817 yen

0.0093y0.0093 5 175

0.0093

0.0093y 5 175

0.00931 5 175

y

32.

34.

Since ,divide 5 by 2 to find r.

r < 2.5

r < 5 4 2

3 4 2 5 1.5

1.5r < 3

5

34.97 < 3

5

1.5r 5 3

4.97

k < 5

4k < 20

k20 < 14

1247 < 1

4

k20 5 1247

37.

15 5 x 16 5 x 1 1

2 ? 8 5 x 1 1

8x 1 1 5 1

2




4-4 Similar Figures and Proportionspages 181–184

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. 10 ? 3 5 15 ? 2 2. 393. 110 4. 506

Quick Check 1. Yes; the corresponding angles arecongruent and the corresponding lengths areproportional.2.

3. 5 ; 5 ; 16x 5 14 ? 24; 16x 5 336; x 5 21; 21 ft

Exercises 1. No; similar figures must have the sameshape. 2. /P > /A, /R > /C; C 3. /Q > /B, /S >/D; D 4. 5 ; 5. Yes; the angles are all right angles, so they are congruent to each other, and the sides are proportional. 6. No; the angles are all right angles, so they are congruent to each other, but, 2 ,so 2 .

7.

9.

11.

13. Solve for x: 5 ; 120 5 15x; x 5 8. Solve for y: 5

; 216 5 15y; y 5 14.4. So, x 5 8 and y 5 14.4. 14. Solve for g: Since opposite sides are > in one figure and thefigures are similar, then opposite sides in the other figure are also >; so g 5 3 and h and f are also >. Solve for h: 5

; 24 5 5h; h 5 4.8 ; f 5 4.8. So, g 5 3, f 5 4.8, and h 5 4.8.

15.

/ 5 19.1 < 19 in.

21.5/21.5 5 410.75

21.5

21.5/ 5 26.5 ? 15.5

21.526.5 5 15.5

/

h8

35

y18

1215

x10

1215

y 5 48 y 5 2 ? 24

42 ? 2421 5 y

42 ? 24 5 21y (21 1 21)24 5 21y

21 1 2121 5

y24

ABDB 5 AC

DE

nABC , nDBE

6 5 h; 6 m 210 5 35h

26.25 ? 8 5 35h heightwidth : 26.25

35 5 h8

x 5 5 4x 5 20 4x 5 10 ? 2

x10 5 24

ACWY 5 AB

WX

MNTS

ONQT

69

47

QR QR

BC

PQ

AB

2416

x14

BCEC

ACDC

w 5 11.2 in.

5w5 5 56

5

5w 5 56

5w 5 4 ? 14

54 5 14w

14

16. Yes; the angles are always 908 and the lengths of thesides will always be proportional. 17. Not all rectangles are similar; the correct choice is D. 18. 5 ; 40c 5

57 ? 30; 40c 5 1,710; c 5 42.75 19. The ratio of the

corresponding sides is 5 1. . The ratio of the

perimeters is 5 1. . The ratios are the same.

20.

21. 5 ; the correct choice is F. 22. 2x 1 3 5 4; the

correct choice is D. 23. 5 16 4 20 5 0.8; 5 0.8

24. 5 7 4 8 2 0.875; 0.875 . 0.85; . 0.85 25. Since is

positive and 21.5 is negative, . 21.5. 26. <

5 4 14 2 0.357; 0.357 . 0. ; .


1.

2–3.

4. They are the same. 5. The ratio of the areas is thesame as the ratio of the lengths squared. 6. 30 units and50 units2; the perimeter would be 5 times the perimeterof rectangle A and the area would be 52, or 25, times thearea of rectangle A. 7. Explanation may vary. Sample:They are the same because perimeter varies directlywith length. 8. Explanations may vary. Sample: The ratioof the areas is the same as the ratio of the sides squared;if you double the length, the area quadruples.


1.

3.

w 5 8

16 ? 612 5 w

16 ? 6 5 12w 1612 5 w

6

k 5 38

k 5 6 ? 193

3k 5 6 ? 19

k6 5 193

Length/Length

Perimeter/Perimeter

Area/Area

1 : 2

1 : 2

1 : 4

1 : 4

1 : 4

1 : 16

1 : 2

1 : 2

1 : 4

A : B A : C B : CRatio

Area

A

B

C

2

4

8

6 units

12 units

24 units

2 units2

8 units2

32 units2

Rectangle Length Perimeter

0.35143

514

1812

1812

78

78

1620

1620

920c

3825

w 5 4.4; the correct choice is B.

10022.5 5 22.5w

22.5

100 5 22.5w 10 ? 10 5 22.5w

1022.5 5 w

10

33137102.75

334030

3040

c57

8.

10.

12.

w 5 12 in.

5w5 5 60

5

5w 5 60

5w 5 4 ? 15

54 5 15w

108 5 15

w

20 5 x 1,800 5 90x

30 ? 60 5 x(30 1 60)

30x 5 30 1 60

60

RSMN 5 ST

NT

nRST , nMNT x 5 32

9d 5 288 9d 5 18 ? 16

d18 5 169

JMDG 5 JK

DE

2.

4.

a 5 52

a 5 20 ? 135

5a 5 20 ? 13

513 5 20a

t 5 21

15 ? 75 5 t

15 ? 7 5 5t

15t 5 5

7


5.

7.

9.


1. Check students’ work. 2. Explanation may vary.Sample: nArBrCr is twice as big as nABC; all the newcoordinates are double the original coordinates.

4-5 Similarity Transformationspages 187–190

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. x2–5. y

O 2�2 4

2

4

6

xD

B

A

C

y 5 12

y 5 21618

18y 5 216

18y 1 432 5 648

18y 1 18 ? 24 5 24 ? 27

18(y 1 24) 5 24 ? 27

y 1 24

24 5 2718

y 1 24

24 5 9 1 1818

n 5 30

27n27 5 45 ? 18

27

27n 5 45 ? 18

n45 5 1827

n45 5 1818 1 9

d 5 19.80; about $19.80

43.43d43.43 5 860

43.43

43.43d 5 860

43.431 5 860

d

n 5 6

305 5 n

2 ? 155 5 5n

5

2 ? 15 5 5n

25 5 n

15Quick Check1.

2. Ar(0 ? , 0 ? ) 5 Ar(0, 0); Br(0 ? , 3 ? ) 5Br(0, 4); Cr(3 ? , 3 ? ) 5 (4, 4); Dr(3 ? , 0 ? ) 5

Dr(4, 0) 3. 5 5 5 3; enlargement

Exercises 1. Reduction; the dilation has a scale factor less than 1. 2. enlargement 3. 5 5 3

4.

5.

6. The vertices are A(2, 0), B(2, 2), C(5, 2), and D(5, 0).So, the vertices of the image are Ar(2 ? 2, 2 ? 0),Br(2 ? 2, 2 ? 2), Cr(2 ? 5, 2 ? 2), and Dr(2 ? 5, 2 ? 0), or Ar(4, 0), Br(4, 4), Cr(10, 4), and Dr(10, 0).

7. The vertices of the image are ArA ? 2, ? 0B,BrA ? 2, ? 2B, CrA ? 5, ? 2B, and Dr ? 5, ? 0B, or

Ar(1, 0), Br(1, 1), Cr(2.5, 1), and Dr(2.5, 0).

8. scale factor: 5 5 3; enlargement 9. scale

factor: 5 5 ; reduction 10. scale factor:

5 5 5 2; enlargement42

2 1 22

blueoriginal

12

24

blueoriginal

62

blueoriginal

4O x

y

2

12

12A

12

12

12

12

12

12

2 6 8Ox

y

4

2

C

A

BA

31

93

31

93

3 1 63

43

43

43

43

43

43

43

43

y

O4�4

�2

2

xF

D = D�

F� E�

E

6.

8.

10.

h 5 51 ft

h 5 3 ? 17

13 5 17h

2575 5 17

h

x 5 49.5 40x40 5

1,98040

40x 5 1,980 40x 5 30 ? 66

x30 5 6640

m 5 2.8

m 5 0.1 ? 28

0.7 ? 287 5 7m

7

0.7 ? 28 5 7m 0.7m 5 7

28




11. 5

12. Er 5 (22 ? 2, 21 ? 2) 5 (24, 22); Fr 5 (2 ? 2, 0 ? 2) 5(4, 0); Gr 5 (2 ? 2, 2 ? 2) 5 (4, 4); Hr 5 (21 ? 2, 2 ? 2) 5(22, 4)

13. Er 5 A23 ? , 0 ? B 5 A2 , 0B; F r 5 A1 ? , 24 ? B 5

A , 22B; Gr 5 A5 ? , 0 ? B 5 A , 0B; Hr 5 A1 ? , 4 ? B 5 A , 2B

14. Er 5 (3 ? 1.5, 0 ? 1.5) 5 (4.5, 0); F r 5

(0 ? 1.5, 22 ? 1.5) 5 (0, 23); Gr 5 (23 ? 1.5, 1 ? 1.5) 5(24.5, 1.5); Hr 5 (2 ? 1.5, 3 ? 1.5) 5 (3, 4.5)

15. Find the ratio of the shorter sides: 1 : 1 5 : 5

9 : 12 5 3 : 4. Find the ratio of the longer sides: 1 : 2 5

3 : 4. The scale factor is . 16. Find BC. ;

; ; 4x 5 24; x 5 6; Find ArCr. ;

; ; x = 40; Find the two perimeters.10x 5 1

410x 5 7

28

ACArCr 5 AB

ArBr14 5 x

24728 5 x

24

ABArBr 5 BC

BrCr34

12

32

98

12

18

O x

y

4

G

H

E

F

O x

y4

G

H

E

F

12

12

12

52

12

12

12

12

12

32

12

12

O x

y5

GH

EF

w 5 178; 17

8 in.

w 5 158

12 ? 2w 5 12 ? A 5

4 ? 31 B

2w 5 54 ? 3

1

2w 5 114 ? 3

3w

2

114

photo

reduction: nArBrCr 5 28 1 24 1 40, or 92; ^ABC 5 7 1 10 1 6, or 23. Find the ratio of the perimeters. 17. Answers may vary. Sample: To dilate a figure on a coordinate plane, find the coordinates of each vertex and multiply each coordinate by the scale factor. Then plot each of these points on the coordinate plane. 18. 5 5 0.35 19. 5 ; the correct choice is A. 20. The height of the restaurant; the correct choice is H.21.

12(5.6 3 2) 5 134.4; the correct choice is C.22.

23.


Activity 1. Check students’ work. 2. Ar 5

(0 ? 2.5, 0 ? 2.5) 5 (0, 0); Br 5 (5 ? 2.5, 4 ? 2.5) 5(12.5, 10); Cr 5 (6 ? 2.5, 1 ? 2.5) 5 (15, 2.5); Ar(0, 0),Br(12.5, 10), Cr(15, 2.5)

Exercises 1–2. Check students’ work. 3. It is the same as the scale factor; , or . 4a. 65, 16.25, 5

4b. The ratio of the areas is 0.25, or

4-6 Scale Models and Mapspages 192–195

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. multiplication 2. 12.83. 44.84 4. 39.6 5. 84.5

Quick Check

1. 5

2. The map distance is about 1 in.

< 140; about 140 mi

51,125

8

5 751 ? 15

8

d 5 75 ? 178

178

d

mapactual:

175 5

78

5 21316; 213

16 in.

5 9032

w 5 932 ? 10

10w

19

32

feetinches:

14

14

16.2565

12

1836

c 5 "9,025 5 95 in.

c2 5 9,025

c2 5 3,249 1 5,776

572 1 762 5 c2 a2 1 b2 5 c2

c 5 "400 5 20 cm

c2 5 400

256 1 144 5 c2 162 1 122 5 c2

a2 1 b2 5 c2

c 5 "31.36 5 5.6

20.25 1 11.11 5 c2

A412 B 2 1 A31

3 B 2 5 c2

A 5412 B 2 1 A 40

12 B 2 5 c2

14

312

720

2160

2392 5 1

4


Exercises 1. The scale is the ratio of map distance toactual distance. 2. 75 3 2 5 150; 150 mi 3. 1 : 2; themodel is half as large as the object, compared to a thirdas large.

4. 5 5. 5

x 5 2.5 ? 6 5 15 ft y 5 2.5 ? 2.3 5 5.75 ft

6. The actual height is 75 ft, so solve the

proportion 5

The actual diameter is 15 ft, so solve the proportion5

7. Find the height: Find the diameter:

The height and diameter of the models are, respectively,15 in. and 3 in.8. Find the height: Find the diameter:

The height and diameter of the models are, respectively,22.5 in. and 4.5 in.9. Find the height: Find the diameter:

The height and diameter of the models are, respectively,

12.5 in. and 2.5 in. 10. : 5 ; a 5 10 ? 3 5

? 5 32.5; 32.5 mi 11. : 5 ; a 5 10 ? 2 5

? 5 25; 25 mi 12. : 5 ; a 5 10 ? 4.4 5 44;

44 mi 13. : 5 ; a 5 10 ? 5.3 5 53; 53 mi 14. :

5 ; 22 5 4x; x 5 5.5; 5.5 in. 15. : 5 ; 86 5 4x;

x 5 21.5; 21.5 in. 16. : 5 ; 92 5 4x; x 5 23; 23 in.

17. : 5 ; 39 5 4x; x 5 9.75; 9.75 in. 18a. about

2 in. 18b. The key gives a scale of 1 in. to 150 mi: 5

; m 5 150 ? 2 5 318.75; 318.75 mi. 19. The map

distance is about 2 in.: 5 ; m 5 150 ? 2 5 300; 300 mi.2m

1150

18

218

m

1150

18

x39

14

inchmile

x92

14

inchmile

x86

14

inchmile

x22

14

inchmile

5.3a

110

inchmile

4.4a

110

inchmile

52

101

12

212

a1

10inchmile

134

101

14

314

a1

10inchmile

d 5 2.5 h 5 12.5

15 5 6d 75 5 6h 16 5 d

15 16 5 h75

d 5 4.5 h 5 22.5

103 d 5 15 10

3 h 5 75

1103

5d15

1103

5h75

d 5 3 h 5 15

15 5 5d 75 5 5h

15 5 d15 15 5 h

75

d 5 6; 6 in.

2 ? 3 5 d 25 ? 15

1 5 25 ? 5

2d

15 5 212d

d15

1

212

h 5 30; 30 in.

2 ? 15 5 h 25 ? 75

1 5 25 ? 5

2h

75 5 52h

75 5 212h

h75

1

212

2.3 in.y ft

1 in.

212 ft

6 in.x ft

1 in.

212 ft

20. From Exercise 19, 300 mi is 2 in. on the map, so findtwo cities that are about 2 in. from Fort Worth: Midland

and Galveston. 21. 5 ? 5 ; N scale 22. Check

students’ work. 23. The doors are each in. on the plan.

The scale is , so solve a proportion: 5 ; f 5

10 ? 5 2.5; 2.5 ft. 24. On the plan, the longest unbroken

wall of the bedroom is 1 in. The scale is , so solve a

proportion: 5 ; w 5 10 ? 1 5 17.5; 17.5 ft. 25. The

narrow section of the bedroom measures in. by in., so the actual dimensions are about 7.5 ft by 5 ft. Yes; thenarrow section of the bedroom is about 5 ft wide by 7.5 ft long. 26. 5 5 and 5 ; 1 in. : 50 ft

27. Check students’ work. 28. 5 3.5; 5 ; x 5

3.5 ? 40 5 140; the correct choice is D. 29. 2 5 20.25;the correct choice is H. 30. A 180º rotation of the 14thfigure in the pattern is the second option; the correctchoice is B. 31. (21)2 2 10(21 2 (1)3) 5 1 2 10(22) 51 1 20 5 21 32. ((21)5 1 (21)8)(17 2 15) 5(211 1)(1 2 1) 5 (0)(0) 5 0 33. 21 1 1 2 (21)2 2 12 5 0 21 2 1 5 22


Activity 1. ^PAD 2. Answers may vary. Sample: 5

; , , and are known.

3. 5

5

Exercises 1. ^EXY , ^EFG. 2. Answers may vary.

Sample 5 .

3.

4. No, only the corresponding sides must have the same units.

4-7 Similar and IndirectMeasurements pages 197–200

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. shape 2. /Y

FG 5 603.43 in. or 603.4312 5 50.3 ft

FG 3 14 4 14 5 8448 4 14

FG 3 14 5 1056 3 8

8FG 5 14

1,056

8FG 5 14

(88 3 12)

d2

d1

XYFG

1.5 3 AB 4 1.5 5 82.5 4 1.5 5 55 ft

1.5 3 AB 5 0.75 3 110

1.5110

0.75

AB

PR

PA

RS

AB

PAPRRS PR

PA

RS

AB

14

3.5x

14031

2

150

8400

150

6300

inchesfeet

12

68

34

134

w110

1 in.10 ft

34

14

14

f1

101 in.10 ft

14

1160

22

12

80

12

80




Quick Check 1.

Exercises 1. indirect 2. direct 3. indirect 4. direct5.

7.

9.

11.

13.

15.

16. Answers may vary. Sample: Measure the height of atower by measuring its shadow and the shadow of anobject of known height.17.

18.

x < 1,027; about 1,027 ft

647 ? 502194 2 647 5 647 2 647 1 x

647 ? 502194 5 647 1 x

647 ? 502 5 (647 1 x)194

647647 1 x 5 194

502

647647 1 x 5 194

194 1 308

< 34; 34 ft

t 5 221 ? 29189

189t 5 221 ? 29

treemonument:

t221 5 29

189

5 168; 168 m

w 5 200 ? 2.12.5

200 ? 2.1 5 2.5w monument

van : 2002.5 5 w

2.1

h < 27.1; 27.1 ft

14h 5 380

h10 5 3814

h10 5 24 1 1414

< 1,269.7; 1,269.7 m

d 5 725 ? 845482.5

482.5d 5 725 ? 845

d725 5 845

482.5

DEBA 5 CD

CB

5 360; 360 m

d 5 240 ? 225150

150d 5 240 ? 225

d240 5 225

150

PQTS 5

QRSR

5 8; 8 m

h 5 15 ? 1630

30h 5 15 ? 16

pole

tower: h15 5 16

30

b 5 8

3b3 5 4 ? 6

3

3b 5 4 ? 6

b4 5 6

3

x 5 52.5

8,400160 5 160x

160

8,400 5 160x

40 3 210 5 160x

40160 5 x

210

19.

20.

21. Answers may vary. Sample: Stand where you can see the basketball hoop in the mirror.22.

23. 5(3.25) 1 2(5.50) 1 2.25; the correct choice is G.24. The exponent of the base 10 indicates how manyplaces to move the decimal point. The exponent is 5, sothe decimal moves 5 places to the right: 202,000 25. Theexponent of the base 10 indicates how many places tomove the decimal point. The exponent is -2, so thedecimal moves 2 places to the left: 0.05 26. Theexponent of the base 10 indicates how many places tomove the decimal point. The exponent is -6, so thedecimal moves 6 places to the left: 0.000009606


1.

2. 5 ; the correct choice is G. 3. ; t 5 5

6 ? 5; the correct choice is D.

CHAPTER REVIEW pages 202-203

1. A speed of 30 mi/h is an example of a unit rate.2. A proportion is an equation stating that two ratios areequal. 3. A model of an office building may have a scalefactor of 1 : 200. 4. Indirect measurement helps you tomeasure the height of very tall objects. 5. A reduction isa dilation with a scale factor less than one. 6. You canuse a conversion factor to convert 3.4 miles to feet.7. 6 s out of 48 s 5 6 : 48 5 5

8. 5 ? 5 , or 3 9. 1 ft : 1 yd 5 ?

5 10. $42 for 1.5 h 5 5 5 , or $28/h

11. 826 mi in 14 h 5 5 5 59, or 59 mi/h

12. 150 km per 24 L 5 5 5 6.25, or

6.25 km/L 13. 5 $0.07/oz

5 $0.07/oz

Neither; the unit rate for each container is about $0.07.14. 33 m/h 5 ? 5 3,300 cm/h 15. 16 lb/ft 5100 cm

1 m33 m1 h

$1.6924 oz

$2.5236 oz

150 4 2424 4 24

150 km24 L

826 4 1414 4 14

826 mi14 h

281

843

421.5

13

1 yd3 ft

1 ft1 yd

13

103

100 cm1 m

10 m300 cm

10 m300 cm

18

648

18 ? 53

35 5 18

t2032

15.5x

h 5 7.27; the correct choice is C.

220h 5 1,600

2204 5 400

h

d 5 6; the correct choice is D.

1.44d 5 8.64

1.44d 5 3.60 ? 2.40

d3.60 5 2.40

1.44

z < 1,597; about 1,597 ft

"380,973 ?z

"380,9735 "380,973 ? 502

194

z

"380,9735 502

194

zy 5 308 1 194

194

< 617; about 617 ft

y 5 "380,973

y2 5 380,973

y2 5 418,609 2 37,636

y2 1 37,636 5 418,609

y2 1 1942 5 6472

6.

8.

2.8 ft10.

12.

14.

5 12; 12 m

h 5 2 ? 183

3h 5 2 ? 18

h2 5 183

h2 5 3 1 153

< 1,523.6; 1,523.6 m

r 5 870 ? 845482.5

482.5r 5 870 ? 845

r870 5 845

482.5

CECA 5 CD

CB

5 170; 170 m

e 5 255 ? 150225

225e 5 255 ? 150

e255 5 150

225

RTRP 5 SR

QR

7 ? 820 5 2.8;

7 ? 8 5 20h

telephone booth

fire hydrant : 7h 5 208

a 5 10

5 ? a5 5 5 ? 6

3

a5 5 6

3

2.

< 460.7; 460.7 m

5 691 ? 23

5 691 ? 23

w 5 691 ? 300450

691 ? 300 5 450w 691w 5 450

300

NLLJ 5 ML

KL


? 5 256 oz/ft 16. 1 L/min 5 ? ?

5 , or 16 mL/s 17. 3 mi/h 5 ? ?

5 380,160 ft/d 18. 30 m/h 5 ? ?

5 50, or 50 cm/min 19. $.30/min 5 ? 5

18, or $18/h

20.

22.

24.

26.

28. The sides of the blue figure are 4 times thecorresponding sides of the original figure, so the scalefactor is 4 : 1, or 4. Since 4 $ 1, it is an enlargement: 4;enlargement.29. 1 in. : 7 mi

5

x 5 6.2 ? 7 5 43.4 mi

31. 1 in. : 7 mi

5

x 5 4 3 7 5 32.7 mi

33. Find the length: Find the width:

The dimensions are 2 in. by 1 in.

34.

35.

AS 5 30.6 2 17 5 13.6

c 5 "936.36 5 30.6

729 1 207.36 5 c2 272 1 14.42 5 c2

a2 1 b2 5 c2 x 5 14.4

x 5 8 ? 2715

15x 5 8 ? 27

8x 5 1527

34

14

w 5 134 / 5 21

4

14 5 8w 18 5 8/ inches

feet S 18 5 w14 inches

feet S 18 5 /18

23

423 in.x

1 in.7 mi

6.2 in.x

1 in.7 mi

CE 5 7.5; 7.5 cm

2CE 5 15

2CE 5 3 ? 5

CE3 5 5

2

CE3 5 2 1 3

2

e 5 810 euros

e 5 0.81 ? 1,000

0.811 5 e

1,000

5 12

t 5 6 ? 2814

14t 5 6 ? 28

146 5 28

t

x 5 16

80 5 5x 4 ? 20 5 5x

45 5 x20

60 min1 h

$.301 min

1 h60 min

100 cm1 m

30 m1 h

24 h1 d

5,280 ft1 mi

3 mi1 h

23

1,00060

1,000 mL1 L

1 min60 s

1 L1 min

16 oz1 lb

16 lb1 ft

36. 5 ft 6 in. 5 5.5 ft

( )(12 in.) 9 in.; 11 ft 9 in.

CHAPTER TEST pages 204

1. 16 cm : 60 cm 5 5 2. 3 ft to 9 in. 5 ? 5

5 4 3. 5 ? 5 5 4. 6 yd to

36 ft 5 ? 5 5 5. 500 m : 2 km 5 ?

5 5 6. 5 ? 5 9 ? 8 5 72

7. 200 yd in 5 min 5 5 5 , or 40 yd/min

8. 700 L in 24 h 5 5 5 29 , or 29 L/h

9. 30 gal in 5 min 5 5 5 , or 6 gal/min

10. $2.50 for 10 oz 5 5 $.25/oz 11. $33/h 5

? 5 $.55/min 12. 3 ft/s 5 ? ? 5

60 yd/min

13.

15.

17. Multiply each of the coordinates by 3. Find the imageof A: Ar 5 (1 ? 3, 2 ? 3) 5 (3, 6). Find the image of B: Br 5

(4 ? 3, 3 ? 3) 5 (12, 9). Find the image of C: Cr 5 (22 ? 3, 5? 3) 5 (26, 15). The coordinates are Ar(3, 6), Br(12, 9), andCr(26, 15).18. 19.

20. 21.

22. 23.

24. 1 in. : 6 mi 25. 1 in : 6 mi

5 5

6x 5 23 6x 5 10

x 5 5 3.8 in. x 5 5 1.7 in.106

236

x10

16

x23

16

5 63.5 cm 5 12.6 kg

5(25)(2.54) cm

1 5(28)(0.45) kg

1

25 in. 5 25 in.1 5 2.54 cm

1 in. 28 lb 5 28 lb1 ?

0.45 kg1 lb

5 8.9 lb 5 9.6 qt

5(4)(1) lb

0.45 5(9)(1) qt

0.94

4 kg 54 kg

1 ? 1 lb0.45 kg 9 L 5 9 L

1 ?1 qt

0.94 L

y 5 22x 5 6

y 5 11 ? 189 x 5 12 ? 9

18

9y 5 11 ? 18 18x 5 12 ? 9

y11 5 18

9 x12 5 918

y11 5 9 1 9

9 x12 5 99 1 9

w 5 11 713

w 5 5 ? 3013

13w 5 5 ? 30

w5 5 3013

n 5 14

n 5 7 ? 63

3n 5 7 ? 6

37 5 6n

60 s1 min

1 yd3 ft

3 ft1 s

1 h60 min

$331 h

$2.5010 oz

61

30 4 55 4 5

30 gal5 min

16

16

700 4 2424 4 24

700 L24 h

401

200 4 55 4 5

200 yd5 min

8 oz1 c

54 c6 oz

54 c6 oz

14

5002,000

1 km1,000 m

500 m2 km

12

1836

3 ft1 yd

6 yd36 ft

524

100480

1 h60 min

100 min8 h

100 min8 h

369

12 in.1 ft

3 ft9 in.

415

1660

<1114

5 111114

b 5 5.5 ? 4521

5.5 ? 45 5 21b actualshadow :

5.521 5 b

45

21.

a 5 1

6 5 6a 6a 5 6

1

6a 5 183

23.

25. 5

27. 5

DE 5 4.5; 4.5 cm

2DE 5 9

2(DE 1 3) 5 3 ? 5

2DE 1 6 5 15

DE 1 33 5 5

2

2 1 32

DE 1 33

5 10; 10 cm

AE 5 4 ? 52

2AE 5 4 ? 5

AE4 5 5

2

2 1 32

AE4

5 72

b 5 16 ? 92

2b 5 16 ? 9

b16 5 92

30. 1 in. : 7 mi

5

x 5 9.5 ? 7 5 66.5 mi

32. 1 in. : 7 mi

5

x 5 8 ? 7 5 57.4 mi15

815 in.x

1 in.7 mi

9.5 in.x

1 in.7 mi

14.

16.

p 5 985.5, or $985.50

p 5 584 ? 270160

160p 5 584 ? 270

sharesdividend: 160

584 5 270p

a 5 1

100 5 100a 25 ? 4 5 100a

25a 5 100

4




26. 1 in. : 6 min 27. 1 in. : 6 mi

5 5

6x 5 45 6x 5 16

x 5 5 7.5 in. x 5 5 2.7 in.28. 1 in. : 15 mi 29. 1 in. : 15 mi

5 5

x 5 15 ? 8.6 5 129 mi x 5 15 ? (10 ) 5 155 mi

30. 1 in. : 15 mi 31. 1 in. : 15 mi

5 5

x 5 15 ? (7 ) 5 114 mi x 5 15 ? 11.2 5 168 mi

32. Answers may vary. Sample: Multiply the x- and y-coordinates by r. So, if a vertex’s coordinates were (x, y),the image coordinates would be (r ? x, r ? y).33. Ar 5 (22 ? 2, 21 ? 2) 5 (24, 22), Br 5 (0 ? 2, 2 ? 2) 5(0, 4), and Cr 5 (3 ? 2, 21 ? 2) 5 (6, 22)

34.

35. BY 5 4 and BC 5 6, so the scale factor is , or .

TEST PREP page 205

1. Use the Pythagorean theorem. c2 5 a2 1 b2 5

2.612 1 6.142 < 6.81 1 37.70 5 44.51; < 6.67;the correct choice is C. 2. The width of the copy is

, or about 0.77. 0.77 . 0.75 5 , so the copy is too wide; the correct choice is G. 3. Let x 5 the length of the poster bill.

34

22.61

"44.51

23

46

5 30; 30 ft

c 5 5 ? 9015

5 ? 90 5 15c studentcrane : 5c 5 15

90

6O x

y

4

B

CA

35

11.2x

115

735

x115

13

1013

x115

8.6x

115

166

456

x16

16

x45

16

; the correct choice is D.

4. The width can’t be less than 2.61 ? 1.5, or about 3.92in. The length can’t be less than 6.14 ? 1.5, or about 9.21

in.; the correct choice is G. 5. 5 5 13.7 : 9.6;the correct choice is A. 6. The total amount of food will be 50 ? 9.6 1 70 ? 13.7, so the ratio of the total food supplies that would belong to the female is

; the correct choice is J.


1a. 250 food Calories 5 ? ?

5 290.5; 290.5 watt-hours 1b. 1 2 5

; ? 290.5 5 72.625; about 72.6 watt-hours 2a. energy 575 3 10 5 750; 750 watt-hours 2b. From Exercise 1b,the energy left over from 1 sandwich is 72.625 watt-hours.Use the Energy Formula:

You could light the bulb for 58 minutes, or about 1 hour.2c.

3a. 2,500 ? 5 625; 625 Calories 5 625 C ? ?

5 726.25; about 726 watt-hours3b. Substitute the watts needed to run the appliance forx in the formula, 726 5 x ? t, and solve for t. Answersmay vary. Sample:

The dryer will run about 36 min. 5 0.605; 0.605 h, or 36.3 min

t 5 7261,200

726 5 1,200 ? t

0.001162 watt-hour1 g-cal

1,000 g-cal1 f. Cal.

14

5 2 h 1 (0.42083 ? 60 min) < 2 h 25 min

5 2.42083 h

t 5 72.62530

72.6 5 30 3 t

5 0.968 h ? 60 min1 h 5 58.08 min

5 0.968 h

t 5 72.675

72.6 5 75 3 t

14

14

34

0.001162 watt-hour1 g-cal

1,000 g-cal1 f. Cal.

250 f. Cal.1

50 ? 9.650 ? 9.6 1 70 ? 13.7

13.79.6

13.7 3 w9.6 3 w

x 5 12.28 ft

2.61x2.61 5 5.22 ? 6.14

2.61

2.61x 5 5.22 ? 6.14

2.615.22 5 6.14

x


Chapter

5Applications of Percent pages 208–257


1. 2. 2m 5 31.82

5

m 5 15.91

3. 4.

5. 5 6. 5 7. 5 8. 5 9. ? 100 5 30

10. 15 ? 5 8 11. 160 ? 5 100

12. 13.

14. 15.

16. 17.

5-1 Fractions, Decimals, andPercents pages 210–213

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. , b ? 0 2. 3. 4. 5.

Quick Check 1. 5 55% 2. 0.08 5 5 8%3. 150% 5 5 4. Convert each number to a decimal.76% 5 0.76; 5 0.75. Compare decimals:0.73 , 0.75 , 0.76, so the order from least to greatest is0.73 , , 76%; 0.73, , 76%.

Exercises 1. A percent compares a number to 100.2. 1.0 5 100%; the correct choice is D. 3. 5 6%; thecorrect choice is B. 4. 0.06 5 6%; the correct choice is B. 5. 5 14%; the correct choice is A. 6. 5 40%;

the correct choice is C. 7. 5 40% 8. 5 75% 9. 5

96% 10. 5 35% 11. 5 84% 12. 0.36 5 5 36%

13. 0.003 5 5 5 0.3% 14. 5.2 5 5 5

520% 15. 0.9 5 5 5 90% 16. 0.00007 5 5

5 0.007% 17. 105% 5 5 18. 220% 5 5

19. 22 % 5 22 4 100 5 ? 5 5

20. 66 % 5 66 4 100 5 ? 5 5 21. 5135150

23

200300

1100

2003

23

23

29

200900

1100

2009

29

29

115

220100

2120

105100

0.007100

7100,000

90100

910

520100

5210

0.3100

31,000

36100

4250

720

2425

34

25

1025

14100

12200

34

34

34

32

150100

8100

1120

14

720

45

910

ab

h 5 85.5 z 5 19

8h8 5 684

8 3z3 5 57

3

8h 5 684 3z 5 57

h76 5 98 53 5

z11.4

t 5 32

27t27 5 864

27

y 5 100 27t 5 864

14 5 25y 18

t 5 2748

k 5 2 n 5 36

225k225 5 450

225 7n7 5 252

7

225k 5 450 7n 5 252

k45 5 10225 712 5 21

n

58

12

1730

310

916

3664

112

672

58

2540

12

50100

v 5 1.75 x 5 237.5

95v95 5 166.25

95 0.32x0.32 5 76

0.32

95v 5 166.25 0.32x 5 76

20 5 p

31.822

2m2 16

0.8 50.8p0.8

16 5 0.8p

0.9 5 0.9 3 100% 5 90% 22. Convert each number to adecimal: 5 0.33 ; 36% 5 0.36; 5 0.375. Comparedecimals: 0.3 , 0.33 , 0.36 , 0.375, so 0.3 , , 36% , ;0.3, , 36%, 23. Convert each number to a decimal:

0.09% 5 0.0009; 5 0. ; 1.01% 5 0.0101. Compare decimals: 0.0009 , 0.01 , 0.0101 , 0. , so

0.09% , 0.01 , 1.01% , ; 0.09%, 0. , 1.01%,

24. Convert each number to a decimal: 5 0.22 ; 5

0.25; 20.9% 5 0.209. Compare decimals:

0.2 , 0.209 , 0.22 , 0.25, so 0.2 , 20.9% , , ; 0.2,

20.9%, , 25. Convert each number to a decimal:

150% 5 1.5; 5 1.8; 1.5% 5 0.015. Compare decimals:

0.015 , 1.5 , 1.8 , 150, so 1.5% , 150% , , 150;

1.5%, 150%, , 150 26. 5 5 0.933 5

93.3% < 93% 27. 5 0.8 5 83 ; , 0.8 , 83 28. 5

0.0524 5 5.24% 29. 75% 5 5 ; 58% 5 5

; , 30. 5 0.16 5 16% 31. 5 0.84 5 84%

32. 5 0.52 5 52% 33. 0.09% is equal to 0.0009, whichis not the same as 0.09. 34. 60% ? 135 5 0.6 ? 135 5 81,so of a 135-lb person; about 81 lb are water. 35. 5 0.5;

5 0.595; 62 % 5 0.625; 0.5 , 0.595 , 0.6 , 0.625 , 0.63,

so , , 0.6 , 62 % , 0.63; the correct choice is D.

36. 5

2x 5 7 ? 95

x 5 31.5 ft; the correct choice is J.

37. 15 5 3 ? 5; 39 5 13 ? 3; GCF 5 3 38. 75 5 3 ? 52; 100 5

22 ? 52; GCF 5 25 39. 18 5 2 ? 32; 54 5 2 ? 33; GCF 5 18

5-2 Estimating With Percentspages 214–217

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. 2. 27 3. 8 4. 54 5. 45Quick Check 1. 18% of 107 < 0.2 ? 100, or about 202. 35% of 24 < ? 24; or about 8 students 3. 10% of$72.10 < 0.1 ? 72 5 7.2; 5% of $72.10 < ? 7.2 5 3.6; 7.21 3.6 5 10.8; about $10.80

Exercises 1. 15% 5 0.15 and $38.90 < $40, so 15% of$40 5 0.15 ? 40 5 (0.10 1 0.05) ? 40 50.10(40) 1 0.05(40) 5 4 1 2 5 $6; the correct choice is B.2. 15% 5 0.15 and $20.79 < $20, so 15% of $20 50.15 ? 20 5 (0.10 1 0.05) ? 20 5 0.10(20) 1 0.05(20) 52 1 1 5 $3; the correct choice is A. 3. 15% 5 0.15 and$398 < $400, so 15% of $400 5 0.15 ? 400 5(0.10 1 0.05) ? 400 5 0.10(400) 1 0.05(400) 5 40 1 20 5$60; the correct choice is C. 4. 20% of $28; 10% of $28 is

12

13

73

7 ? 92

2x2

7x

29

12

2542

12

12

2542

12

1325

2125

425

2950

34

2950

58100

34

75100

13248

1335

61335

6

98105

45 1 19 1 34105

95

95

95

14

29

14

292

1422

9

199011

99

01

01199

38

13

38

133

3831

3


phm07c3_sk_ch05 national.qxd 8/22/06 10:13 AM Page 53


$2.80, so 20% of $28 is $2.80 ? 2 5 $5.60 5. Answers mayvary. Sample: 0.28 is close to 0.25, which is easy to workwith because it contains a multiple of 5. 191 <200. 0.25 3 200 5 50 6. 9% of 9 < 0.1 ? 10; or about 17. 63% of 62 < 0.6 ? 60; or about 36 8. 15% of 78 < 0.15? 80; or about 12 9. 52% of 492 < 0.5 ? 500; or about 25010. 38% of 81 < 0.4 ? 80, or about 32 11. 68% of 222 <0.7 ? 200, or about 140 12. 27% of 39 < ? 40; or about 10 13. 49.8% of 177 < ? 180, or about 90 14. 74.5% of

31 < ? 32; or about 24 15. 66% of 310 < ? 300; orabout 200 students 16. 10% of $9.85 < 0.1 ? 10 5 1; 5%of $9.85 5 ? 1 5 0.5; 1 1 0.5 5 1.5; about $1.5017. 10% of $12.63 < 0.1 ? 12 5 1.2; 5% of $12.63 5

? 1.2 5 0.6; 1.2 1 0.6 5 1.8; about $1.80 18. 10% of

$18.20 < 0.1 ? 20 5 2; 5% of $18.20 5 ? 2 5 1; 2 1 1 53; about $3 19. 10% of $27.55 < 0.1 ? 30 5 3; 5% of $27.55 5 ? 3 5 1.5; 3 1 1.5 5 4.5; about $4.50 20. 10%

of $31.49 < 0.1 ? 30 5 3; 5% of $31.49 5 ? 3 5

1.5; 3 1 1.5 5 4.5; about $4.50 21. 10% of $86.96 <

0.1 ? 90 5 9; 5% of $86.96 5 ? 9 5 4.5; 9 1 4.5 5 13.5;

about $13.50 22. 20% of 47.51 < 0.2 ? 50 5 10; about $10

23. 34% of 91% of 115,904,640 5 0.34 ? 0.91 ?115,904,640 < ? 0.9 ? 120,000,000; or about 36,000,000housing units. 24. 41% of 13,000,000 < 0.5 ? 10,000,000,or about 5 million people 25. 70% of $32.99 < 0.7 ? 33;or about $23 26. 70% of $29.99 < 0.7 ? 30; or about $2127. 70% of $32.49 < 0.7 ? 32; or about $22.40 28. No;15% of 41.28 is about $4 1 $2 5 $629. 30.

31.

32.

33. 40% of 301,421,900 is 0.40 3 302,000,000 <121,000,000; about 121,000,000 Americans 34. Answersmay vary. Sample: An estimate is a good way to check ananswer. 35. 24% of 2,000 5 0.24 ? 2,000 5 480;480 2 135 2 105 5 240; about 240 calories 36. 66.7% of717,449 < 478,538; the correct choice is C. 37. Thisgraph shows a line with a rise of 1 and a run of 23, sothe slope is 2 . The line crosses the y-axis at 1, so 1 is they-intercept. This graph can be represented by theequation y 5 2 x 1 1; the correct choice is H.

38. 8.2 3 10–4 5 0.00082; the correct choice is B.39. (x, y) S (x 1 4, y 1 5) 40. (x, y) S (x 2 13, y 1 5)

5-3 Percents and Proportionspages 218–222

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. proportion 2. 20 3. 664. 100 5. 3 6. 25

23

13

13

5.13 . 2.35

9% of 57 j 5% of 47

15.6 . 10.25

10% of 156 j 1% of 1,025

3.6 5 3.6 85% . 56

15% of 24 j 20% of 18 85% j 56

13

12

12

12

12

12

12

23

34

12

14

Quick Check

1. 2.

3. 4.

Exercises 1.

2. 5 ; the correct choice is B. 3. 5 ; the

correct choice is C. 4. 5 ; the correct choice is A.

5. 6.

7. 8.

9. 10.

11. 12.

13. 14.

11. 16.

17. 5 18.

100n 5 14,355

5

n 5 143.55; $143.55

19. 20.

21. 22.

w 5 250 w 5 950

48w48 5

12,00048 4w

4 53,800

4

48w 5 12,000 4w 5 3,800

120w 5 48

100 38w 5 4

100

w 5 231.25 w 5 5

32w32 5

7,40032 60w

60 5 30060

32w 5 7,400 60w 5 300

74w 5 32

100 3w 5 60100

w 5 7.5

80w80 5 600

8014,355

100100n100

80w 5 600

6w 5 80100

165100

n87

n 5 128.7 n 5 550.5

100n100 5

12,870100 100n

100 555,050

100

100n 5 12,870 100n 5 55,050

n66 5 195100 n75 5 734

100

n 5 165 n 5 4.5

100n100 5

16,500100 100n

100 5 450100

100n 5 16,500 100n 5 450

n60 5 275100 n3 5 150

100

n 5 48 n 5 82.8

100n100 5

4,800100 100n

100 58,280100

100n 5 4,800 100n 5 8,280

n24 5 200100 n24 5 345

100

n 5 16.9 n 5 5.52

100n100 5

1,690100 100n

100 5 552100

100n 5 1,690 100n 5 552

n65 5 26100 n46 5 12

100

n 5 19 n 5 33

100n100 5

1,900100 100n

100 53,300100

100n 5 1,900 100n 5 3,300

n50 5 38100 n55 5 60

100

n 5 1.44 n 5 57.6

100n100 5 144

100 100n100 5

5,760100

100n 5 144 100n 5 5,760

n48 5 3100 n72 5 80

100

x100

542

5100

z42

42100

5y

0 1.251

0% 100%80%

p 5 20% w 5 275 students

180p180 5

3,600180 40w

40 511,000

40

180p 5 3,600 40w 5 11,000

36180 5

p100 110

w 5 40100

n 5 199.75 n 5 70.3

100n100 5

19,975100 100n

100 57,030100

100n 5 19,975 100n 5 7,030

n85 5 235100 n95 5 74

100


23. 24.56x 5 100 ? 140

5

x 5 250; 250 students

25. 26.

27. 28.

29. 30.

31. Set a proportion: the percentage of the winner’svotes to the total percentage of votes will equal the number of votes cast for the winning candidate to the total number of votes cast. So, 5 ; 100x <

15,456,720; 5 ; x < 154,567. About 154,567 votes made up 72.2% of the total votes. The winningcandidate received those 154,567 votes. To find howmany votes he won by, first find the number of votes thatmake up the remaining part: 100% 2 72.2% 5

27.8%. 5 ; 100x < 5,951,479; 5 ;

x < 59,515. So the 27.8% of votes that did not go to thewinning candidate totaled about 59,515. To find howmany votes the winning candidate won by, subtract thatnumber of votes that made up the 27.8% from thenumber of votes he received: 154,567 2 59,515 5 95,052,or about 95,052 votes. 32. 3.75% of x is 5,000,000;

5 ; 3.75x 5 500,000,000; 5 ; <133 million items. 33. Answers may vary. Sample: A “whole” is an arbitrary number, and you can have a“part” that is more than that arbitrary number.

34. ? x 5 ? y; 2 y 5 15, so 2 x 5 15

35. Answers may vary. Sample: Percents let youcompare relative sizes.

36. 37.

38. 39. 5

30x 5 180;

5 ;x 5 6

40. 41.

n 5 1,095.12 1.485 5 x

100n100 5

109,512100 148.5

100 5 100x100

100n 5 109,512 0.108 ? 1,375 5 100x

n468 5 234

100 0.108100 5 x

1,375

w 5 49.8

18030

30x30 200w

200 59,960200

200w 5 9,960

30100

1.8x 99.6

w 5 200100

n 5 76,198.76 n 5 0.03

100n100 5

7,619,876100 100n

100 5 3100

100n 5 7,619,876 100n 5 3

n5,678 5

1,342100 n

120 5 0.025100

y100

x100

x100

y100

500,000,0003.75

3.75x3.75

3.75100

5,000,000x

5,951,479100

100x100

x214,082

27.8100

15,456,720100

100x100

x214,082

72.2100

p 5 800% p 5 37.5%

12p12 5

9,60012

64p64 5

2,40064

12p 5 9,600 64p 5 2,400

9612 5

p100 24

64 5p

100

p 5 40% p 5 4%

45p45 5

1,80045

300p300 5

1,200300

45p 5 1,800 300p 5 1,200

1845 5

p100 12

300 5p

100

p 5 12.5% p 5 64%

160p160 5

2,000160

25p25 5

1,60025

160p 5 2,000 25p 5 1,600

20160 5

p100 16

25 5p

100

w 5 600

100 ? 14056

56x56 25w

25 515,000

25

25w 5 15,000

140x 5 56

100 150w 5 25

10042. Find the area of Indiana:

Find the area of the United States:

43. No; for example, if the two numbers are 100 and 200,then (40% of 100) 1 (30% of 200) 5 40 1 60 5 100, but70% of 300 5 210.44. There were 27 2 2 5 25 students in the new class.100% 2 44% 5 56% of the students were female.

The original class had 14 females out of 27 students. 5

0.519 5 51.9% 45. 5 100 5 100 3 100% 5 10,000%

46. 21% of 500 is 3 500 5 105; 13% of 500 is 3 500 5 65; 105 2 65 5 40; the correct choice is B.

47. < 0.07; 1 2 0.07 5 0.93 5 93%; the correct choice is H. 48. 5 ; 2.99 ? 5; the correct choice is A.49. 10 cm : 25 m 5 10 cm : 2500 cm 5 1 cm : 250 cm50. 5 5 51. 5 5


1. 2. Answers may vary.Sample: The originalgraph made it appearthat there were largedifferences in thedata; the new graphshows that they’remuch closer.

3.

Per

cent

Barbecue SurveyResults

Yes Maybe No

100

80

60

40

20

0

Per

cen

t

Roc

kC

ount

ry

Rap

Hea

vyM

etal

Music Preferences100

80

60

40

20

0

7 oz16 oz

35 oz80 oz

35 oz5 lb

2 in.3 in.

16 in.24 in.

16 in.2 ft

x2.99

6012

345

13100

21100

1001

1427

n 5 14 females

100n100 5

1,400100

100n 5 1,400

n25 5 56100

w < 3,716,363.9 mi2 0.98w0.98 5

3,642,036.60.98

0.98w 5 3,642,036.6

36,420.366

w 5 0.98100

n 5 36,420.366

100n100 5

3,642,036.6100

100n 5 3,642,036.6

n1,231 5

2,958.6100




4. 5. Answers may vary.Sample: Withoutknowing that 200students did notrespond, it seemedthat most of thestudents said yes.Knowing that 200students did notrespond, you can seethat very few of thestudents said yes.

6. 7. In the bar graph,the highest bar,reaching 80%,represents Nikki’sfree throwpercentage, so shehas the bestpercentage.

8. No; she only shot 5times, so there is notenough data tosupport the statementthat she is the best.

5-4 Percents and Equationspages 224–227

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Equation; it contains an5 sign. 2. 40 3. 1.25 4. 15 5. 0.03125

Quick Check 1. Let t 5 the amount of sales tax.t 5 0.06 ? 195.99 5 $11.762.

More Than One Way Answers may vary. Sample: Let

p 5 the population of Texas that year. 5 ; 12p

5 267,500,000; 5 ; p < 22,291,667;

22,291,667 people. I chose the method of using a

proportion because I did not have to convert the

percentage to a decimal.

Exercises 1. 12 is 50% of 24. 2. n 5 0.31 ? 82 5 25.423. n 5 0.05 ? 28 5 1.4 4. n 5 0.27 ? 16 5 4.32 5. 5

6% 6. Greater; since 36 represents 20% of the whole,the whole must be greater. 7. Let t 5 the amount of salestax. t 5 0.06 ? 39.99 5 $2.40 8. Let t 5 the amount ofsales tax. t 5 0.0475 ? 19.95 5 $0.95

9. 10.

6.52 5 w 70 5 w 60.92 5 0.92w

0.92 2.80.04 5 0.04w

0.04

6 5 0.92w 2.8 5 0.04w

6100

267,500,00012

12p12

12100

2,675,000p

90 5 w 16.20.18 5 0.18w

0.18

16.2 5 0.18w

Per

cen

t

Ann

a

Car

la

Nik

kiR

ayle

ne

Free ThrowRecords

100

80

60

40

20

0

Per

cen

t

Did

not

Res

pond Ye

sM

aybe No

Barbecue SurveyResults

100

80

60

40

20

0

11. 12.

13. 14.

15. The equation (80)(0.07) 5 p represents Arizona’ssales tax p. (80)(0.07) 5 p; p 5 5.6, so Arizona’s sales taxis 5.6%. Use the equation (0.056)(25.85) 5 t to find thetax on the ticket in Arizona. (0.056)(25.85) 5 t; t < 1.45,so the sales tax on the ticket in Arizona is $1.45.16. 17.7 million is 25.8% of c, the number of householdswith cable in 2000. 17.7 5 0.258c; 5 ; 68.6; 68.6million households17. Let s 5 the total sales of her album.

Her album made $2,650,000.18. The total number of students is 22 ? 30 5 660;9 ? 30 5 270 students are 8th graders.

19. $899 3 1.053 5 $946.65 20. $899 3 1.04 5 $934.96

21. $899 3 1.05 5 $943.95 22. 5 0.95; 95%23. Answers may vary. Sample: Use a percent equation.Let p 5 the population of Florida in 2000. p 5

1,200,000(13.33) 5 15,996,000, or 15,996,000 people. Ichose a percent equation because it was easier to use13.33 than 1,333. 24. Answers may vary. Sample:Multiply the number by 0.13 or multiply the number by

. 25. Let p represent the amount your neighborreceived for the car. p 5 0.75(0.8x)(1.065) 26. 15% of60 5 0.15 ? 60 5 9; the correct choice is B.27. $899.99 1 $119.99 < 900 1 120 < 1020; 1020 4 24 5$42.50; the correct choice is F. 28. 5 ; 8x 5 10.4 ? 7;

5 ; x 5 9.1; the correct choice is A. 29. Convertthe fraction to a decimal. 5 1.25. Compare decimals.1.25 . 1.23, so is greater. 30. Convert the fraction to a decimal. 2 5 245. . Compare decimals.245. . 245.78, so 2 is greater. 31. Convert the fraction to a decimal. 5 0.0 . Compare decimals.0.0 . 0.015, so is greater.


1-2. Check students’ work. 3. 365 4 7 5 52 ; since 7 isnot a factor of 365, your birthday will never fall on thesame day of the week in two consecutive years. 4. 15%of $29.42; 15% 5 0.15 and $29.42 < $30; 0.15 ? 30 5 4.50;$29.50 1 $4.50 5 $34 5. 8% of $53.25 50.08 ? 53.25 5 $4.26; $53.25 1 $4.26 5 $57.516. 219.95 2 0.1(219.95) 5 $197.96; $197.96 , $200.7a-c. Check students’ work.

17

16615

15166

41297

74129

1512

1512

10.4 ? 78

8x8

10.48

x7

13100

12,457,350 tons13,113,000 tons

40.9% 5 p 270660 5

660p660

270 5 660p

2,650,000 5 s 53,0000.02 5 0.02s

0.02

53,000 5 0.02s

0.258c0.258

17.70.258

696 5 w 390 5 w 1740.25 5 0.25w

0.25 58.50.15 5 0.15w

0.15

174 5 0.25w 58.5 5 0.15w 11.1 5 w 445 5 w 0.7770.07 5 0.07w

0.07 3560.80 5 0.80w

0.80

0.777 5 0.07w 356 5 0.80w



1. 5 0.5 5 50% 2. 5 0.0909 5 9.09% 3. 5 0.375 5

37.5% 4. 5 2.5 5 250% 5. 5 0.4 5 40% 6. 19%

of 58 < 0.2 ? 60; or about 12 7. 0.66% of 36 < ;or about 0.24 8. 137% of 8 < ? 8; or about 11 9. 1.9%of 2 < 0.02 ? 2; or about 0.0410.

11. 20.5 5 0.41x; 5 ; 50 5 x 12. 16 5 320x; 5

; x 5 0.05; 5% 13. x 5 26(0.03); x 5 0.78 14. 0.08 5

0.32x; 5 ; x 5 0.25


1. Jacksonville: 753, 617 2 204,517 5 549,100, increase;Virginia Beach: 425,257 2 5,390 5 419,867, increase

2. Jacksonville: 5 268.5%; Virginia Beach:

5 7,789.7% 3. Answers may vary. Sample: Theanswer to Exercise 1 better describes which city’spopulation changed by the greater number of people.The answer in Exercise 2 better describes which city’spopulation changed by a greater percent of its originalpopulation.

5-5 Percent of Change pages 230–233

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. percent 2. 112.5%3. 27.3% 4. 26.7% 5. 366.7%

Quick Check 1. 4,475,000 2 3,748,000 5 727,000; P 5

5 0.194; 19.4% 2. 5 ? 12 5 60; 4 ? 12 1 9 5 57;

60 2 57 5 3; P 5 5 0.053 5 5.3% 3. 2,100 2 899 5

1,201; P 5 5 0.572 5 57.2%

Exercises 1. The percent of change is the percent aquantity increases or decreases from its original amount.

2. 40.379 2 27.287 5 13.092; 5 0.480; 48.0%

3. 15 2 12 5 3; 5 0.25; 25% increase 4. 27 2 36 5

29; 2 5 20.25; 25% decrease 5. 27 2 9 5 18; 5

2; 200% increase 6. 110 2 75 5 35; P 5 5 0.467 5

46.7% 7. 23 2 10 5 13; P 5 5 1.3 5 130%

8. 56 2 4 5 52; P 5 5 13 5 1,300% 9. 28 2 20 5

8; P 5 5 0.4 5 40% 10. 25 2 15 5 10; P 5 5

0.667 5 66.7% 11. 80 2 50 5 30; P 5 5 0.6 5 60%

12. 5.15 2 0.75 5 4.4; P 5 5 5.867 5 586.7%

13. 37 ? 12 1 6 5 450; 36 ? 12 1 3 5 435; 450 2 435 5 15;

P 5 5 0.034 5 3.4% 14. 20 ? 16 1 1 5 321;15435

4.40.75

3050

1015

820

524

1310

3575

189

936

312

13.09227.287

1,2012,100

357

727,0003,748,000

419,8675,390

549,100204,517

0.32x0.32

0.080.32

320x320

16320

0.41x0.41

20.50.41

n < 1,300,000 people

n 5 1,282,658

100n100 5

128,265,800100

100n 5 128,265,800

n5,130,632 5 25

100

118

23 ? 0.01 ? 36

1025

156

38

111

24

16 ? 16 1 4 5 260; 321 2 260 5 61; P 5 5 0.235 5

23.5% 15. 13 ? 16 1 5 5 213; 7 ? 16 1 3 5

115; 213 2 115 5 98; P 5 5 0.852 5 85.2%

16. 190 2 183 5 7; P 5 5 0.037 5 3.7%

17. 15 2 10 5 5; P 5 5 0.333 5 33.3%

18. 205 2 164 5 41; P 5 5 0.2 5 20% 19. 87 2 64 5

23; P 5 5 0.264 5 26.4% 20. 52 2 1 5 51; P 5 5

0.981 5 98.1% 21. 368 2 275 5 93; P 5 5 0.253 5

25.3% 22. 824 2 299 5 525; P 5 5 0.637 5 63.7%

23. 18% of 204,450,000 5 0.18 ? 204,450,000 5

36,801,000; 204,450,000 2 36,801,000 5 167,649,000;

167,649,000 acres 24. 9.6 2 1.4 5 8.2; P 5 5 5.857 5

585.7% increase. 25. 0.8 2 0.2 5 0.6; P 5 5 0.75 5

75%decrease. 26. 99.9 2 8.7 5 91.2; P 5 5 10.483 51,048.3% increase. 27. 5 2 1.25 5 3.75; P 5 5

0.75 5 75% decrease. 28. 130 2 1.4 5 128.6; P 5 5

91.857 5 9,185.7% increase. 29. 610.33 2 81 5 529.33;

P 5 5 0.867 5 86.7% decrease. 30. 6 ? 60 1 25 5

385; 6 ? 60 1 10 5 370; 385 2 370 5 15; P 5

5 0.041 5 4.1% 31. No; 20% of 100 is 20, so the result

of a 20% increase from 100 is 120. Then 20% of 120 is 24,

so the result of a 20% decrease from 120 is 96.

32. Convert the height to inches: 1 ? 12 1 3 5 15. Multiply

by the percent of increase: 15 ? 213 % 5 32 in. Since the

height increased by 32 inches, add 32 to the original

height of 15 in. to find the new height: 15 1 32 5 47 in.,

or 3 ft 11 in. 33. 3% of 30,000 5 0.03 ? 30,000 5 900;

30,000 1 900 5 30,900; the correct choice is C.

34. The x-coordinate will become negative and the y-

coordinate will remain the same, so the correct choice is

J. 35. 22 is 4 and 32 is 9. 7 is closer to 9 than it is to 4 so

is closest to 3; the correct choice is B.

36. 2.25 t 5 ? 5 2.25 ? 2,000 lb 5 4,500 lb

37. 6 qt 5 ? ? 5 6 ? 2 ? 2 c 5 24 c 38. 240 s 5

? ? 5 5 5 0.07 h

5-6 Markup and Discountpages 234–238

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. percent 2. 4 3. 2004. 1,100 5. 14,000

Quick Check 1. 19 2 10 5 9; 5 0.9 5 90%2. 1.80 ? 89.89 5 $161.80 3. 100 2 45 5 55;0.55 ? 182.75 5 $100.51

910

240 h3,600

(240)(1)(1)h3,600

1 h60 min

1 min60 s

240 s1

2 c1 pt

2 pt1 qt

6 qt1

2,000 lb1 t

2.25 t1

"7

13

15370

529.33610.33

128.61.4

3.755

91.28.7

0.60.8

8.21.4

525824

93368

5152

2387

41205

515

7190

98115

61260




4. Let t 5 the regular price.

Exercises 1. Markup is the amount of increase in price;the correct choice is C. 2. Sale price is the regular priceof an item minus the discount; the correct choice is A.3. The selling price is the cost of the item plus themarkup; the correct choice is B. 4. Markup adds to thecost of an item, but discount reduces the cost.

5. 39 2 26 5 13; 5 0.5 5 50% 6. 168.75 2 125 5

43.75; 5 0.35 5 35% 7. 90 2 75 5 15; 5 0.2 5

20% 8. 33 2 20 5 13; 5 0.65 5 65%

9. 1.60 ? 118.12 5 $188.99 10. 1.95 ? 22.05 5 $43.00

11. 1.35 ? 29.50 5 $39.83 12. 100 2 55 5 45; 0.45 ? 16.995 $7.65 13. 100 2 5 5 95; 0.95 ? 77.00 5 $73.15

14. 100 2 25 5 75; 0.75 ? 200 5 $15015. Let r 5 the regular price.

16. Let r 5 the regular price.

17. Let r 5 the regular price.

18. 100 2 30 5 70; 1.80 ? 5.25 ? 0.70 5 $6.6219. 1.6666 ? 71.99 5 $119.98 20. 1.375 ? 364.38 5$501.02 21. No difference; 250 ? 0.7 ? 1.1 5250 ? 1.1 ? 0.7; the final cost is $192.50 either way.22. 100 2 40 5 60; 0.60 ? 22.99 5 $13.794; 45.00 4 13.794 53.26; Your friend can buy 3 DVDs. 23. Answers mayvary. Sample: Divide the selling price by 1 plus thepercent of markup written in decimal form.24. 1.25 1 1.25 1 0 1 1.25 5 $3.75 25. 60 2 45 515; 5 0.25; 0.25 5 25%; the correct choice is B.26. The first point (21, 23) is represented only by graphG, so the correct choice is G. 27. A 10-pound box of Clementines for $3.99 is about $4 for 10 lb. 5 $0.40 per pound. Navel oranges are $0.99 < $1 per pound,which is $1.00 2 $0.40 5 $0.60 more per pound than theClementines; the correct choice is C.28. 29.

30. 31.

f 5 25 n 5 15

3.4f 5 85 16n 5 240

10f 5 3.4

8.5 1625 5 9.6

n

k 5 187.2 t 5 9

5k 5 936 8t 5 72

k234 5 4

5 38 5 t24

$410 lb

1560

r 5 $29

0.85r 5 24.65

r 2 (0.15r) 5 24.65

r 5 $16.25

0.8r 5 13

r 2 (0.20r) 5 13

r 5 $189.43

0.35r 5 66.30

r 2 (0.65r) 5 66.30

1320

1575

43.75125

1326

r 5 $116.47

0.85r 5 99

r 2 (0.15r) 5 99ACTIVITY LAB page 239

1. 6% of $55 5 0.06 ? $55 5 $3.30; $55 1 $3.30 5 $58.302. 35% of $28 5 0.35 ? $28 5 $9.80; $28 1 $9.80 5 $37.803. 25% of $17 5 0.25 ? $17 5 $4.25; $17 2 $4.25 5 $12.754. Answers may vary. Sample: Move the string until itcrosses 118% on the horizontal axis and $25 on thevertical axis. Then find the dollar amount where thestring crosses 100%.


1. Yes; 5 0.5 , which means, if you buy the sweater for$20, you are paying only 55.5% of the original price, orabout 44.5% off the original price. 2. No; for example, a25% markup on $100 would give you a cost of $125; ifyou subtract 25% of $125, the price is only $93.75.3. 20% of $36 5 0.20 ? $36 5 $7.20; $36 2 $7.20 5$28.80; 20% of $28.80 5 0.20 ? $28.80 5$5.76; $28.80 2 $5.76 5 $23.04; $36.00 2 $23.04 5

$12.96; Percent of discount 5 5 0.36, or 36%. Since

36% , 40%, the sweater should not be on the sale rack.4a. There was a 4.9% spending increase from 2002 to2003, so the 2003 spending is 100 1 4.9 5 104.9% the2002 spending. 4b. 4.9% more than the 2002 spendingequals the 2003 spending; 1.049x 5 440.3; x 5 419.73;$419.73 billion. 5a. To find how much more New Jerseyspent than the national average, take the amount NewJersey spent minus the national average; $12,202 2

$8,019 5 $4,183; 5 0.5216; 52.16%. 5b. To find the

percent increase for New Jersey, divide how much moreNew Jersey spent than the national average by how much New Jersey spent; < 52% 6. 1.34 2 1.25 5

0.09; 5 0.072; about 7%. 7. The greatest percent of increase in the average price of gasoline took place

between May and June. 8. Gasoline in Cleveland was$2.59 per gallon, and the price of gasoline in Boston was0.6% more than that. First find 0.6% of $2.59 5 0.006 ?$2.59 5$0.02. Add $2.59 1 $0.02 to get $2.61, the priceof gas in Boston. Since Seattle’s gas prices are 2.7%more than prices in Boston, find 2.7% of $2.61: 0.027 ?$2.61 < $.07. Now add $2.61 1 $.07 to get $2.68, theprice of gas in Seattle.

5-7 Simple Interest pages 242–244

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. formula 2. w 5

3. r 5 4. b 5 y 2 x 5. B 5

Quick Check 1. I 5 prt 5 3,600 ? 0.035 ? 5 5 $6302. I 5 prt 5 205 ? 0.08 ? 10 5 $164; 205 1 164 5 $369Exercises 1. The simple interest is the money earned based only on the deposit; C. 2. The interest is themoney earned by a depositor or lender; B. 3. Theinterest rate is the percent on which savings earnings are

3vh

dt

v/h

0.091.25

$4,183$8,019

$4,183$8,019

12.9636

52036


based; A. 4. 545 ? 0.05 ? 6 5 163.5; 545 1 163.5 5 708.5;$708.50 5. I 5 prt 5 970 ? 0.0425 ? 2 5 $82.45 6. I 5

prt 5 182 ? 0.06 ? 4 5 $43.68 7. I 5 prt 5

3,500 ? 0.075 ? 5 5 $1,312.50 8. I 5 prt 5

198 ? 0.04 ? 13 5 $102.96; 198 1 102.96 5 $300.969. I 5 prt 5 535 ? 0.06 ? 10 5 $321; 535 1 321 5 $85610. I 5 prt 5 6,000 ? 0.07 ? 4 5 $1,680; 6,000 1 1,680 5$7,680 11. 100 ? 0.05 ? 3 5 15; 100 1 15 5115; 115 ? 0.055 ? 4 5 25.3; 115 1 25.3 5 140.3;$140.30 12. 500 ? 0.0536 ? 3 5 80.4; 500 1 80.4 5 580.4;580.4 ? 0.0536 ? 3 5 93.32832; 580.4 1 93.32832 5673.72832; $673.73 13. The account that pays 1.3%simple interest, because 747(1 1 0.013) 5 $756.71 and747(1 1 0.02) 2 12 5 $749.94. 14. 180 months 5 15 years;1,000 ? x ? 15 5 1,240 2 1,000; 15,000x 5 240; 5

; x 5 0.016; 1.6% 15. 2,500 ? 0.06 ? 7 5

1,050; 2,500 1 1,050 5 3,550 16. 5 ; 2x 5 3 ? 7.5; 5

3 ? ; x < 11.25 17. 3 3 36 5 108; 108 students18. 3.62 5 12.96; 12.96 cm2 19. 9 3 11.4 5 102.6; 102.6 ft2


1. 154 2 14 5 140; 5 10 5 1,000% 2. 427 2 420 5 7;

5 0.016 5 1.6% decrease. 3. 2 2 0.4 5 1.6; 5 0.8 580% decrease 4. 456 2 123 5 333; 5 2.707 5

270.7% increase 5. 37 ? 12 1 6 5 450; 36 ? 12 1 3 5435; 450 2 435 5 15; 5 0.034; 3.4%6. 100 2 35 5 65%; Let r 5 the regular price.

0.65r 5 14.99

r < 23.06The regular price of the dog food is $23.06. 7. 26.99 222.94 5 4.05; 5 0.15; 15% 8. 250 ? 0.035 ? 5 5 43.75;$43.75 9. 95 ? 0.06 ? 3 5 17.1; $17.10


1-4. Check students’ work. 5. In 100 tosses, you wouldget about 50 heads and 50 tails. In 200 tosses, you wouldget about 100 heads and 100 tails. The reason is thatheads and tails are equally likely.

5-8 Ratios and Probabilitypages 246–250

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. ratio 2. 1 : 2 3. 4. 5. 6. 1 to 4

Quick Check 1. P 5 2. P 5 3% 1 25% 5 28%3. P 5 5 4. There are 8 possible outcomes, and three of those outcomes result in exactly 2 boys, so P 5 .Exercises 1. Answers may vary. Sample: An outcome isany of the possible results that can occur. An event isthe collection of possible outcomes in an experiment.An outcome can be an event if there is only one

38

12

1836

38

59

13

225

4.0526.99

0.65r0.65 5 14.99

0.65

15435

333123

1.62

7427

14014

7.52

2x2

3x

27.5

24015,000

15,000x15,000

possible result of the experiment. 2. If the jar has onlyred, white, and blue marbles, then you are certain topick a red, white, or blue marble, so the probability is100% or P 5 1.3. P 5 5 4. P 5 5 5. P 5 6. P 5 7. P 5

8. P 5 5 9. P 5 10. P 5 5 0 11. P 5 5 1

12. P 5 61% 1 22% 5 83% 13. P 5 3% 1 7% 5 10%

14. P 5 100% 2 22% 5 78% 15. P 5 16. P 5 5

17. P 5 5 18. P 5 5 19. P 5 5 20. P 5 5

21.

22. P 5 23. P 5 24. P 5 25. P 5 26. 45% of 200 5 0.45 ? 200 5 90; 200 2 90 5 110; 110 packages27. 50 1 80 1 100 1 20 5 250; P 5 5 or 20%

28. P 5 13.1% 1 13.2% 1 25% 5 51.3% 29. P 5 5

or 20% 30. P(silver) 5 5 or 40%

31. P(orange) 5 or 22.2% 32. No; reasons may vary.Sample: Probability cannot be greater than 1. 33. P 5

5 34. P 5 5 ; the correct choice is B. 35. Inorder to form a rectangle, point D must line up withpoint A on the x-axis so the widths will be even. PointA’s x-coordinate is 2.5. Point D must come down on they-axis as far as point C so the lengths will be even. PointC’s y-coordinate is 22.5. Point D will have the same x-coordinate as point A and the same y-coordinate aspoint C: (2.5, 22.5); the correct choice is H. 36. In orderto find 30% of 126, set up a proportion so that

5 : 5 ; the correct choice is D.

37. 120 lb : 4 lb 5 30 lb : 1 lb; 30 : 1 38. 5

5 5 ; 39. 9 h to 127 s 59 3 3,600 s to 127 s 5 32,400 s to 127 s; 32,400 to 127


1. 73% of 21; 73% < 75% and 21 < 20; 0.75 ? 20 5 15;the correct choice is B. 2. < 5 0.125, or 12.5%;the correct choice is G. 3. 44 out of 49 5 < 5 0.9,or 90%; the correct choice is C. 4. 15% of $23.04 50.15 ? $23.04 5 $3.46 < $3.50; the correct choice is H.


1. Markup is the amount by which a store increases theprice of an item. 2. The original deposit in a bankaccount is called the principal. 3. An outcome is any ofthe possible results that can occur in an experiment.4. The amount by which the price of an item on sale isreduced is the discount. 5. Interest calculated only on theprincipal of an account is simple interest. 6. 5 0.875 57

8

4550

4449

80640

78643

3,5201

3,520 ft1 ft

390,720 ft111 ft

74 3 5,280 ft111 ft

74 mi111 ft

30100

n126

percent100

partwhole

13

26

112

224

29

25

410

15

210

15

50250

18

38

38

18

Toss 1

H

T

Toss 2

H

T

H

T

Toss 3HTHTHTHT

OutcomeHHHHHTHTHHTTTHHTHTTTHTTT

14

416

12

816

18

216

14

416

12

816

316

88

08

38

12

48

18

18

16

12

36

13

26




87.5% 7. 5 1.0833 5 108.33% 8. 5 0.3125 5 31.25%9. 5 4.5 5 450% 10. 36% 5 5 11. 33 % 5 5

12. 124% 5 5 5 1 13. 27% 514–16. Estimations may vary. Samples are given.14. 24% of 97 < 25% of 100; about 25 15. 15% of $35.07 < 15% of 35; about $5.25 16. 68% of 89 < 70% of

90; about 63 17. 5 ; < and < ; 5 ;

100x 5 300; 5 ; x 5 3; about 3 students. 18. Letw 5 the number. 0.85w 5 170; w 5 200 19. P 5 5 0.4 540% 20. 150% of 12 5 1.5 ? 12 5 18 21. Let w 5 thenumber. 0.26w 5 39; w 5 150 22. 5 ; 7.5x 51,200;

5 ; x 5 160; 160 students 23. 13 2 9 5 4; <0.308 5 30.8% decrease 24. 88 2 2 5 86; 5 43 5

4,300% increase 25. 155 2 154 5 1; 5 0.006 5 0.6%increase 26. 18 2 3 5 15; < 0.833 5 83.3% decrease27. 100 2 20 5 80%; 80% of 249.99 5 0.8 ? 249.99 5$199.99 28. I 5 prt 5 475 ? 0.07 ? 3 5 99.75; 99.75 1 4755 $574.75 29. 710 ? 0.02 ? 7 5 99.4; 710 1 99.4 5 809.4;$809.40 30. 3,500 ? 0.07 ? 5 5 1,225; 3,500 1 1,225 54,725; $4,725 31. 3 1 5 1 1 5 9; P 5


1. 5 0.625 2. 0.6% , 0.6 3. , 0.34 4. , 85%5. < 0.8462 5 84.62% 6. < 2.4444 5 244.44%7. 5 0.0049 5 0.49% 8–12. Estimations may vary.Samples are given. 8. 76% of 48 < ? 48; about 369. 20% of $23.87 < 0.2 ? 24; about $4.80 10. 250% of 29 < 2.5 ? 30; about 75 11. 15% of $61.51 <0.1 ? 60 1 0.05 ? 60; about $9 12. 98,000 < 100,000;100,000 5 7,000,000x; 5 ; 0.014 < x;about 1.4%13. 37% of 134 5 0.37 ? 134 5 49.5814. 2% of 70 5 0.02 ? 70 5 1.4 15. 5 ; 5n 5 6,800;

n 5 1,360 16. 5 ; 350n 5 2,100,000; n 5 6,00017. 13% of 782 5 0.13 ? 782 5 101.66; 102 students walkto school. 18. n 5 132% of 65 5 1.32 ? 65 5 85.819. n 5 16% of 3 5 0.16 ? 3 5 0.48 20. Let w 5 thenumber. 0.6w 5 105; w 5 1,750 21. Let w 5 the number.1.2w 5 0.006; w 5 0.005 22. Let t 5 the tax. t 5

0.055 ? 49.95 5 $2.75 23. 163 2 99 5 64; < 0.6465 564.65% increase 24. 13 2 1 5 12; < 0.9231 5 92.31% decrease 25. 158 2 24 5 134; < 0.8481 5 84.81% decrease 26. 655 2 613 5 42; < 0.0685 5 6.85% increase 27. 6.75 2 6 5 0.75; 5 0.125 5 12.5% increase 28. 100 2 33 5 67; 0.67 ? 90 5 $60.3029. 1.15 ? 19.99 5 $22.99 30. Answers may vary. Sample:The student calculated the markup rate using the sellingprice instead of the store’s cost. The correct markup rateis or 25%. 31. Let / 5 the lower amount of money./ 5 0.5 ? 17 5 $8.50; Let u 5 the upper amount of money.u 5 0.65 ? 17 5 $11.05; Miguel should save between$8.50 and $11.05 each week. 32. I 5 prt 5 250 ?0.045 ? 3 5$33.75; 250 1 33.75 5 $283.75 33. 450 ? 0.06 ? 2 5 54;450 1 54 5 504; $504 34. 800 ? 0.06 ? 3 5 144; 800 1 1445 944; $944

14

0.756

42613

134158

1213

6499

350100

21,000n

5100

68n

7,000,000x7,000,000

100,0007,000,000

34

1205

229

1113

56

13

58

59

1518

1154

862

413

1,2007.5

7.5x7.5

7.5100

12x

0.82

300100

100x100

x20

15100

x20

x23

15100

13100

x23

13100

27100

625

3125

124100

13

3399

13

925

36100

276

516

1312

35a.

35b. P 5 5 35c. P 5 5

TEST PREP page 255

1. Find the pair with a GCF of 21. A: factors of 14: 1, 2, 7,14; factors of 21: 1, 3, 7, 21; the GCF is 7. B: factors of630: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70,90, 105, 126, 210, 315, 630; factors of 126: 1, 2, 3, 6, 7, 9, 14,18, 21, 42, 63, 126; the GCF is 126. C: factors of 84: 1, 2, 3,4, 6, 7, 12, 14, 21, 28, 42, 84; factors of 105: 1, 3, 5, 7, 15, 18,21, 35, 105; the GCF is 21; the correct choice is C. 2. The length of the HO boxcar: 50 ft 5 600 in.; 5 ; 87x 5

600; x 5 5 6.89 in. or about 7 in.; the correct choice

is H. 3. 4 2 (23 ) 5 4 1 3 5 7 5 8 ; the correct choice is D.4. 12% of x is 15

; the correct choice is J.5. Use the Pythagorean theorem. c2 5 a2 1 b2;52 1 122 5 25 1 144 5 169; 5 13; the correctchoice is B. 6. 35% off the regular price is 65% of the regular price. 65% is about ; 0.65 ? 79.99 < ? 80 < 53;the correct choice is G. 7. 4.5 5 4.5 ? 100% 5 450%; thecorrect choice is C.8.

; the correct choice is G.9.

; the correct choice is A.10. Use the order of operations. 64 2 42 4 8 564 2 16 4 8 5 64 2 2 5 62; the correct choice is H.11. When the triangle is reflected over the x-axis the x-coordinate remains the same and the y-coordinatechanges in sign, (x, y) (x, 2y); so (2, 24) becomes (2,4); the correct choice is D. 12. The prime numbers on a number cube are 2, 3, and 5. There are 6 possibleoutcomes and 3 of them are prime numbers. P(prime number) 5 , or 13. 2 1 1 7 5 1 1 5

14. [2] Let x 5 the number of boys on the sports team.

x 5 12

2x2 5 24

2

2x 5 24

32 5 x8

798

578

68

168

18

34

12

36

S

x 5 218

x 1 7 2 7 5 211 2 7

x 1 7 5 211

n 5 712

n 5 2312 1 10

12

n 2 56 1 5

6 5 214 1 5

6

n 2 56 5 21

4

23

23

!169

x 5 125

0.12x0.12 5 15

0.12

0.12x 5 15

512

1712

912

812

34

23

60087

x600

187

34

2736

518

1036

123456

1

(1, 1)(2, 1)(3, 1)(4, 1)(5, 1)(6, 1)

2

(1, 2)(2, 2)(3, 2)(4, 2)(5, 2)(6, 2)

3

(1, 3)(2, 3)(3, 3)(4, 3)(5, 3)(6, 3)

4

(1, 4)(2, 4)(3, 4)(4, 4)(5, 4)(6, 4)

5

(1, 5)(2, 5)(3, 5)(4, 5)(5, 5)(6, 5)

6

(1, 6)(2, 6)(3, 6)(4, 6)(5, 6)(6, 6)

phm07c3_sk_ch05 national.qxd 8/23/06 3:02 PM Page 60


There are 12 boys on the sports team. [1] minor error15. [2] I 5 prt 5 150(0.05)(4) 5 30; $30; The finalbalance is 150 1 30 5 180; $180; [1] incomplete answerOR minor error 16a–b. [4] Using the points (22, 1) and (2, 21), solve for slope. The slope is 5 5 2 ;

[3] minor error in graph;[2] minor error in graph andanalysis; [1] major error ingraph and analysis

y

xO

246

6

y 5 212x

y 2 1 5 212x 2 1

y 2 1 5 212(x 1 2)

(y 2 1) 5 212fx 2 (22)g

12

224

21 2 12 2 (22)


a. 1,000 1 60 1 150 1 50 1 100 5 $1,360/month1b. Let w 5 your earnings. 0.75w 5 1,360; w 5

$1,813.33/month 2a. 1,813.33 2 400 5 $1,413.33/month2b. Let p 5 the dealer’s profit. 0.25p 5 1,413.33; p 5

$5,653.32/month 2c. Let s 5 the monthly sales. 0.06s 5

5,653.32; s 5 $94,222/month 2d. 94,222 4 18,000 5 5.23;Since you can sell only whole cars and 5 is not enough,you will have to sell 6 cars/month. 3a. 2.50 ? 40 ? 4 5$400; 1,813.33 2 400 5 $1,413.33 3b. 15% of 25 50.15 ? 25 5 $3.75; 1,413.33 4 3.75 5 376.88, so 377customers per month; 377 4 4 5 86.25, so between 86 and87 customers per week; 94.25 4 40 5 2.35, so between 2and 3 customers per hour. 4. Check students’ work.




1. 8 1 15 1 (225) 5 23 1 (225) 5 22 2. 6 1 7 2 15 513 2 15 5 22 3. 14 2 8 1 8 5 6 1 8 5 144. 120 1 (26) 1 9 5 120 2 6 1 9 5 114 1 19 5 1235. 212 4 3 5 24 6. 23 4 (21) 5 37. 3(22 2 5) 4 7 5 3(27) 4 7 5 221 4 7 5 238. 6 ? (22) 4 (212) 5 212 4 212 5 1 9. 5

5 5 21 10. 5 5 5 5 1

11. 5 5 5 3 12. 5(c 2 3) 55 ? c 1 5 ? 23 5 5c 2 15 13. 22(w 1 8) 5

22 ? w 1 (22) ? 8 5 22w 2 16 14. 29(6 2 t) 529 ? 6 1 (29) ? (2t) 5 254 1 9t 15. 2(25 1 a) 52 ? 25 1 2 ? a 5 210 1 2a 16. 11(4 2 b) 511 ? 4 1 11 ? (2b) 5 44 2 11b 17. 21(x 2 2) 521 ? x 1 (21) ? (22) 5 2x 1 2


1–9. Check students’ work with algebra tiles.1. 2.

3. 4.

5. 6.

7. 8.

16x 1 36 2 36 5 100 2 36

9.

x 5 9

212x212 5 2108

212

212x 5 2108

46 2 12x 2 46 5 262 2 46

46 2 12x 5 262

x 5 4 x 5 25

16x16 5 64

16 28x28 5 40

28

16x 5 64 28x 5 40

215 2 8x 1 15 5 25 1 15

16x 1 36 5 100215 2 8x 5 25

x 5 22 x 5 2

3x3 5 26

3 2x2 5 4

2

3x 5 26 2x 5 4

3x 2 5 1 5 5 211 1 5 1 1 2x 2 1 5 5 2 1

3x 2 5 5 211 1 1 2x 5 5

x 5 6 x 5 1

2x2 5 12

2 2x–2 5 2

–2

2x 5 12 2x 5 2

2x 2 7 1 7 5 5 1 7 2x 2 4 1 4 5 22 1 4

2x 2 7 5 5 2x 2 4 5 22

x 5 23 x 5 1

23x3 5 29

3 22x22 5 22

22

3x 5 29 22x 5 22

3x 1 2 2 2 5 27 2 2 22x 1 5 2 5 5 3 2 5

3x 1 2 5 27 22x 1 5 5 3

31

2 2 (21)

2 1 (21)a 2 ba 1 b

44

2 1 24

2 2 2(21)4

a 2 2b4

222

(2)(21)2

ab2

10. Answers may vary. Sample: 22x 5 28; 2x 2 3 5 511. Answers may vary. Sample: Subtract 5 from eachside; 2x 1 5 2 5 5 x 2 1 2 5. Remove the zero pairs;2x 5 x 2 6. Subtract x from each side; 2x 2 x 5

x 2 6 2 x. Remove the zero pair; x 5 26. The solutionis 26.

6-1 Solving Two-Step Equationspages 261–264

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. to get the variable aloneon one side of the equation 2. 27 3. 6 4. 30

Quick Check1.

Check:

2.

4 min

Exercises 1. 3x 2 2 5 7 2. 22x 1 1 5 253–6. Answers may vary. Samples are given. 3. Add 8 toeach side. 4. Add 5 to each side. 5. Add 12 to each side.6. Subtract 9 from each side.

7. 10.67 1 5 38.9

< 11 1 5 39

about 568. Check:

9. Check:

g 5 24

27 5 27✔ 2g2 5 28

2

1 1 2(24) 0 27 2g 5 28

1 1 2g 5 27 1 2 1 1 2g 5 27 2 1

1 1 2g 5 27

x 5 21

3 5 3✔ 4x4 5 24

4

4(21) 1 7 0 3 4x 5 24

4x 1 7 5 3 4x 1 7 2 7 5 3 2 7

4x 1 7 5 3

x 5 56;

2 ? x2 5 2 ? 28

x2 5 28

11 1 x2 2 11 5 39 2 11

x2

x1.95

c 5 4;

0.85c0.85 5 3.40

0.85

0.85c 5 3.40

0.5 1 0.85c 2 0.5 5 3.90 2 0.5

0.5 1 0.85c 5 3.90

223.2 5 223.2✔ 4(28.7) 1 11.6 0 223.2

4g 1 11.6 5 223.2

g 5 28.7

4g4 5 234.8

4

4g 5 234.8

4g 1 11.6 2 11.6 5 223.2 2 11.6

4g 1 11.6 5 223.2

Chapter

6Equations and Inequalities pages 258–299


10. Check:

11. Check:

12. Check:

13. Check:

14. Check:

15. Check:

16. Check:

17. Let x 5 the cost of each CD.

Each CD costs $15.99.18. Let p 5 the number of pencils.

Anna Marie bought 7 pencils. p 5 7

0.39p0.39 5 2.73

0.39

0.39p 5 2.73

0.39p 1 1.19 2 1.19 5 3.92 2 1.19

0.39p 1 1.19 5 3.92

x 5 $15.99

4x4 5 63.96

4

4x 5 63.96

4x 1 5 2 5 5 68.96 2 5

4x 1 5 5 68.96

y 5 27

15 5 15✔ 3 ? 9 5 3 ?y3

15 0 273 1 6 9 5

y3

15 5y3 1 6 15 2 6 5

y3 1 6 2 6

15 5y3 1 6

b 5 338

30 5 30✔ 26 ? b26 5 26 ? 13

17 1 33826 0 30 b26 5 13

17 1 b26 5 30 17 2 17 1 b

26 5 30 2 17

17 1 b26 5 30

x 5 216

3 5 3✔ 4 ? x4 5 4 ? (24)

7 1 2164 0 3 x4 5 24

7 1 x4 5 3 7 2 7 1 x

4 5 3 2 7

7 1 x4 5 3

b 5 5

30 5 30✔ 2.6b2.6 5 13

2.6

17 1 2.6(5) 0 30 2.6b 5 13

17 1 2.6b 5 30 17 2 17 1 2.6b 5 30 2 17

17 1 2.6b 5 30

b 5 23.4

24.2 5 24.2✔ 8b8 5 227.2

8

23 1 8(23.4) 0 24.2 8b 5 227.2

23 1 8b 5 24.2 23 2 23 1 8b 5 24.2 2 23

23 1 8b 5 24.2

b 5 4

214 5 214✔ 26b26 5 224

26

26(4) 1 10 0 214 26b 5 224

26b 1 10 5 214 26b 1 10 2 10 5 214 2 10

26b 1 10 5 214

3 5 y15 5 15✔ 93 5

3y3

15 0 3(3) 1 6 9 5 3y

15 5 3y 1 6 15 2 6 5 3y 1 6 2 6

15 5 3y 1 6 19. Let c 5 the cost of a can of beans. To find c, subtractthe cost of the rice from the total cost. Then divide theresult by 6 to find c. Then add the value of c to $7.33 tosee if your $8.25 will cover the cost of one more can ofbeans.

Yes; one can of beans costs $.89, so it will cost a total of$8.22 to buy another can. 20. Wendy’s; Ben did not dothe order of operations in reverse or use the Dist. Prop.21. Let x 5 the recommended daily intake of zinc. To find x, add 4 to the daily intake of iron (18) and divide by 2.

11 mg22. Round 39.95 to 40 and 105.65 to 100. Solve:

23.Subtr. Prop. of EqualitySimplify.Div. Prop. of EqualitySimplify.

24. 25.

26.

27.

28.

1 5 s 33 5 3s

3

3 5 3s 1.2 1 1.8 5 3s 2 1.8 1 1.8

1.2 5 3s 2 1.8 26 5 v 1823 5 23v

23

18 5 23v 12 1 6 5 26 1 6 2 3v

12 5 26 2 3v t 5 219.8

22 ? t22 5 22 ? 9.9

t22 5 9.9

28.2 1 t22 1 8.2 5 1.7 1 8.2

28.2 1 t22 5 1.7

n 5 12.6 y 5 117

1.4 ? n1.4 5 1.4 ? 9 3 ?

y3 5 3 ? 39

n1.4 5 9 y3 5 39

n1.4 1 1 2 1 5 10 2 1 y3 2 9 1 9 5 30 1 9

n1.4 1 1 5 10

y3 2 9 5 30

b 5 3

7b7 5 21

7

7b 5 21

7b 1 3 2 3 5 24 2 3

7b 1 3 5 24

p 5 10; 24.27 is not reasonable.

6p6 5 60

6

6p 5 60

6p 1 40 2 40 5 100 2 40

6p 1 40 5 100

x 5 11;

2x2 5 22

2

2x 5 22

2x 2 4 1 4 5 18 1 4

2x 2 4 5 18

7.33 1 0.89 5 8.22

c 5 0.89

6c6 5 5.34

6

6c 5 5.34

6c 5 7.33 2 1.99



29.

30a. Student 1: Student 2:

30b. In the first equation, you need to subtract 60 fromeach side and then divide by 6. In the second equation,you need only to divide each side by 9.31. 0.5x 1 1.3 5 4.8

10(0.5x 1 1.3) 5 10(4.8)10(0.5x) 1 10(1.3) 5 10(4.8)

5x 1 13 5 48;5x 1 13 2 13 5 48 2 13

5x 5 355

x 5 7It is the same. You can avoid working with decimals bymultiplying both sides of the equation by 10. 32. Letn 5 the number of pets adopted last year. The number nof pets adopted last year is half of 35 more than 227:n 5 ; the correct choice is A. 33. Let x 5 thelength of the field for players under 10 years.

Let y 5 the length of the field for players under 8 years.Set up a proportion.

The diagram shows the width of the field for playersunder 8 years is 20 yd, and the solution for the length ofthe field is 30 yd. Since the formula for area is A 5 /w,A 5 30(20) 5 600, or 600 yd2; the correct choice is H.34. 1 ? 2 5 ? 5 5 4 ; if Sabrina had rounded 1

cups up to 2 cups, 2 ? 2 5 5, or 5 cups; the correct choiceis B.

35.


1. 3x 1 2; 2x 1 4 2a. 5 buses 2b. 6 students 3. 5x 1 6

x 5 22.8; 22.8 m

4x4 5 9.6 ? 9.5

4

4x 5 9.6 ? 9.5

49.5 5 9.6x

12

34

38

358

52

74

12

34

y 5 30

40y40 5

1,20040

40y 5 1,200

60y 5 40

20

x 5 60

40x40 5

2,40040

40x 5 2,400

227 1 352

355

5x5

x 5 2313; 231

3 h

6x 5 1406

x 5 2229; 222

9 h 6x 5 140

9x9 5 200

9 60 1 6x 2 60 5 200 2 60

9x 5 20060 1 6x 5 200

4.2 5 q 12.6

3 53q3

12.6 5 3q 10 1 2.6 5 3q 2 2.6 1 2.6

10 5 3q 2 2.6 4. The algebraic expression in Exercise 3 is the sum ofthe two expressions in Exercise 1. 5. 3x 1 4 6. 3x 1 67. 8; the sum of 3x and 5x is 8x.

6-2 Simplifying AlgebraicExpressions pages 266–269

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. No; 15 can be subtractedfrom 5. The simplest form is 3a 2 10. 2. 28r 2 243. 27s 1 35 4. 70 2 35t

Quick Check 1. 2t 1 t 2 17t 5 2t 1 1t 2 17t 5

(2 1 1 2 17)t 5 214t 2. Let b 5 the cost of a board.Let n 5 the cost of a box of nails. Let h 5 the cost ofa hammer.

3.

Exercises 1. No; the variable factors x2y5z11 and x2z5y11

are different.2.

3.

4.5.

6.

7. 8b 1 3b 5 (8 1 3)b 5 11b8. 9.

10.

11.

12.

13.

14. 5 24t

19t 2 t 1 6t 5 (19 2 1 1 6)t

5 23a

26a 1 a 1 28a 5 (26 1 1 1 28)a

5 2b

213b 2 17b 1 32b 5 (213 2 17 1 32)b

5 211t

225t 1 21t 2 7t 5 (225 1 21 2 7)t

5 z

5 1z

19z 2 24z 1 6z 5 (19 2 24 1 6)z

5 31x 5 31r 34x 2 3x 5 (34 2 3)x 9r 1 22r 5 (9 1 22)r

5 3.7a

1.3a 1 2.4a 5 (1.3 1 2.4)a

5 8a 1 15

5 (3 1 5)a 1 15

5 3a 1 5a 1 15

3a 1 5(3 1 a) 5 3a 1 15 1 5a

9m 1 2(2 1 n) 5 9m 1 4 1 2n

5 4x 1 7y 2 6

5 4x 1 (6 1 1)y 2 6

5 4x 1 6y 1 1y 2 6

4x 2 2 1 6y 1 y 2 4 5 4x 1 6y 1 y 2 4 2 2

5 22

5 (0)r 2 2

23r 1 2r 1 r 2 2 5 (23 1 2 1 1)r 2 2

5 9 2 6b 5 11 2 2 2 6b 5 11 2 6b 2 2

5 11 1 (26b) 2 2

5 11 1 f26b 1 (22)g 11 2 2(3b 1 1) 5 11 1 (22)(3b 1 1)

5 26b 1 3n 1 h 5 (16 1 10)b 1 (2 1 1)n 1 h 5 16b 1 10b 1 2n 1 1n 1 h

16b 1 2n 1 h 1 10b 1 n 5 16b 1 2n 1 h 1 10b 1 1n



15.

16.

17.

18.

19.

20.

21.

22. Let t 5 the cost of a T-shirt. Let s 5 the cost of a pairof shorts.

23.

24.

25.

26.

27.

28. 16b 2 4(c 1 3)24b 5 16b 2 4b 2 4(c 1 3)5 (16 2 4)b 2 4c 1 125 12b 2 4c 2 12

29. Let d 5 distance to the mall.

30. Let t 5 the cost of 1 lb of turkey. Let s 5 the cost of1 lb of cole slaw. Let c 5 the cost of 1 lb of cheese.

5 10t 1 5s 1 7c 5 6t 1 4t 1 3s 1 2s 1 4c 1 3c

6t 1 3s 1 4c 1 4t 1 2s 1 3c

5 6d 1 20

2d 1 2(10) 1 2(2d) 5 2d 1 20 1 4d

5 27b 1 2 5 f25 1 (22)gb 1 2 5 25b 1 (22b) 1 2 5 25b 1 f22b 2 (22)g

25b 2 2(b 2 1) 5 25b 1 (22)(b 2 1) 5 24.08 1 13.3c

4.3(5.6 1 c) 1 9c 5 24.08 1 4.3c 1 9c 5 227m 2 16 5 28m 2 19m 2 16

28(m 1 2) 2 19m 5 28m 2 16 2 19m 5 2t 1 63.5 5 7t 2 5t 1 59.5 1 4

7(t 1 8.5) 2 5t 1 4 5 7t 1 59.5 2 5t 1 4

5 23 2 5a

3 2 5(a 2 4) 5 3 2 5a 1 20

5 7t 1 3s

5 (3 1 4)t 1 (2 1 1)s 3t 1 2s 1 4t 1 s 5 3t 1 4t 1 2s 1 1s

5 10 2 3t 5 10 1 (23)t 5 (9 1 1) 1 (27 1 4)t

9 2 7t 1 1 1 4t 5 9 1 1 2 7t 1 4t 5 26z 2 2y 5 26z 1 (22)y 5 (2 2 8)z 1 (23 1 1)y

2z 2 3y 2 8z 1 y 5 2z 2 8z 2 3y 1 y 5 9n 2 3r 5 9n 1 (23)r 5 (5 1 4)n 1 (26 1 3)r

5n 2 6r 1 4n 1 3r 5 5n 1 4n 2 6r 1 3r 5 5n 2 3

n 1 4n 2 3 5 (1 1 4)n 2 3

5 5x 1 1

5 (2 1 3)x 1 1

2x 1 1 1 3x 5 2x 1 3x 1 1

5 4a 1 2

5 (3 1 1)a 1 2

5 3a 1 1a 1 2

3a 1 2 1 a 5 3a 1 a 1 2

5 18j

j 2 4j 2 15j 5 (1 2 4 2 15)j 31. Let b 5 the cost of a barrette. Let h 5 the cost of aheadband.

32.

33.

34.

35.

36.

37.

38. 9(a 1 1.4b) 1 8(b 2 16a)

39. 4.2x 1 8.1x 1 1.8x 2 2.1x

40. Similar categories of CDs are grouped together, andterms with similar variables are grouped together.41. Answers may vary. Sample: 2m 1 m 1 8;4m 1 2 2 m 1 6 42. Answers may vary. Sample: No;5a and 5b are not like terms, so they can not be combined,because the variables are different.43. 2.5(2t 2 8v) 2 3(3v 1 1.5t)

44. Since both the length and width of the larger squareare 7 units greater, the area of the smaller square must be multiplied by 72 and not just 7: 4 3 72 5 196; the correctchoice is C. 45. d 5 rt, 20 5 8t, t 5 5 2.5 h; the correct choice is G. 46. Translating 3 units up and 2 units to theleft is adding 3 to the y-coordinate and subtracting 2from the x-coordinate. (0 2 2, 3 1 3) 5 (22, 6); thecorrect choice is D.47. 48.

; 64% x 5 64 x 5 20

250x250 5 160 ? 100

250 80x80 5 16 ? 100

80

250x 5 160 ? 100 80x 5 16 ? 100

160250 5 x

100 16x 5 80

100

208

5 0.5t 2 29v 5 5t 2 4.5t 2 20v 2 9v 5 5t 2 20v 2 9v 2 4.5t 5 5t 2 20v 1 (29v 2 4.5t) 5 5t 2 20v 1 (23)(3v 1 1.5t)

5 12x

5 (4.2 1 8.1 1 1.8 2 2.1)x

5 2119a 1 20.6b 5 9a 2 128a 1 12.6b 1 8b 5 9a 1 12.6b 1 8b 2 128a

5 31.66y 1 8.4

33.7y 1 8.4 2 2.04y 5 33.7y 2 2.04y 1 8.4

5 22t 2 102 5 3t 2 5t 2 42 2 60 5 3t 2 42 2 5t 2 60 5 3t 2 42 1 (25t 2 60)

3(t 2 14) 2 5(t 1 12) 5 3t 2 42 1 (25)(t 1 12) 5 x 1 y 1 9 5 (5 2 4)x 1 y 1 9 5 5x 1 (24x) 1 y 1 9 5 5x 1 y 1 (24x) 1 9

(5x 1 y) 2 (4x 2 9) 5 5x 1 y 1 f24x 2 (29)g 5 6

5 0u 1 6 5 (25 1 1 1 4)u 1 6

25u 1 6 1 u 1 4u 5 25u 1 u 1 4u 1 6 5 3x 2 2y

x 1 2(x 2 y) 5 x 1 2x 2 2y 5 22b 1 5 1 c

7b 1 5 2 9b 1 c 5 7b 2 9b 1 5 1 c 5 5b 1 3h

3b 1 h 1 2b 1 2h 5 3b 1 2b 1 h 1 2h




1. 2.

3. 4.

5. 6.

7. 8.

9.

10. Let x 5 the cost of each tulip.

11.

12.

13.

14.

15.

16.

17. Let s 5 the cost of a sleeping bag. Let f 5 the cost of a flashlight. 6s 1 4f 1 5s 1 3f 5 11s 1 7f

5 168 2 3a

28 2 10(a 2 14) 1 7a 5 28 2 10a 1 140 1 7a

5 24.81j 2 18.27

2.9(1.1j 2 6.3) 2 8j 5 3.19j 2 18.27 2 8j

5 10k 1 0.11

2k 2 11(2k 2 0.01) 5 2k 1 11k 1 0.11

5 22h 1 20

2h 2 4(h 2 5) 5 2h 2 4h 1 20

5 8.1g 2 13.65

5 1.7g 2 0.85 1 6.4g 2 12.8

1.7(g 2 0.5) 2 6.4(2g 1 2)

5 28m 1 p 1 4

23m 1 4 2 5m 1 p 5 23m 2 5m 1 4 1 p x 5 $1.50

9x9 5

$13.509

9x 5 $13.50

$26.58 1 9x 2 $26.58 5 $40.08 2 $26.58

$26.58 1 9x 5 $40.08

$14.70 1 $11.88 1 9x 5 $40.08

6 ? $2.45 1 12 ? $.99 1 9x 5 $40.08

a 5 23

293 5 3a

3

29 5 3a

25 2 4 5 3a 1 4 2 4

25 5 3a 1 4

z 5 226.65 p 5 56.6

213 ? 2.05 5z

2.05 ? 2.05 23.420.06 5

20.06p20.06

213 5z

2.05 23.4 5 20.06p

215 1 2 5z

2.05 2 2 1 2 p ? 23.4p 5 20.06 ? p

215 5z

2.05 2 2 23.4p 5 0.06

m 5 228 15 5 y

22 ? m22 5 22 ? 14 75

5 55y5

m22 5 14 75 5 5y m22 1 7 2 7 5 21 2 7 49 1 26 5 5y 2 26 1 26

m22 1 7 5 21 49 5 5y 2 26

x 5 3 b 5 1

2x2 5 6

2 33 5 3b3

2x 5 6 3 5 3b

2x 1 5 2 5 5 11 2 5 29 1 12 5 3b 2 12 1 12

2x 1 5 5 1129 5 3b 2 12

v 5 9 q 5 5.5

21822 5 22v

22 2q2 5 11

2

218 5 22v 2q 5 11

16 2 34 5 22v 1 34 2 34 27 1 2q 1 7 5 4 1 7

16 5 22v 1 34 27 1 2q 5 4

6-3 Solving Multi-Step Equationspages 271–275

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. 3x, 2x, 2x 2. 12 2 26m3. 28 2 12r 4. 8q 1 5

Quick Check1.

Check:

2. Cost of student admission ? (the number of girls 1 thenumber of boys) 1 Cost of chaperone admission ? thenumber of chaperones 5 $380; the total cost. Let x 5

the number of boys.

There are 17 boys.

More Than One Way

Answers may vary.

Exercises 1. When you simplify an expression you combine like terms. 2. Distribute 24.3.

the correct choice is C.4. 5.

the correct choice is A. the correct choice is B.6. 7.

Check:

Check:

22 5 22✔

5(5) 1 2 2 5 0 22

5h 1 2 2 h 5 22

28 5 28✔ h 5 5

28 0 22 1 3(22) 4h4 5 20

4

28 5 z 1 3z 4h 5 20

22 5 z 4h 1 2 2 2 5 22 2 2

284 5

4z4 4h 1 2 5 22

28 5 4z 5h 2 h 1 2 5 22

28 5 z 1 3z 5h 1 2 2 h 5 22

x 5 3; x 5 28;

29 1 12 5 x 2 12 1 12 1622 5 22x

22

29 5 x 2 12 16 5 22x

x 5 11;

27 1 x 1 7 5 4 1 7

27 1 x 5 4

m 5 15.5;

3m3 5 46.5

3

3m 5 46.5

3m 2 19.5 1 19.5 5 27 1 19.5

3m 2 19.5 5 27

3(m 2 6.5) 5 27

x 5 17

10x10 5 170

10

10x 5 170

210 1 10x 2 210 5 380 2 210

210 1 10x 5 380

120 1 10x 1 90 5 380

10(12 1 x) 1 15(6) 5 380

215 5 215✔ 215 0 5(211) 1 12 2 2(211) 1 6

215 5 5b 1 12 2 2b 1 6

211 5 b 233

3 5 3b3

233 5 3b 215 2 18 5 3b 1 18 2 18

215 5 3b 1 18

215 5 5b 2 2b 1 12 1 6

215 5 5b 1 12 2 2b 1 6



8. 9.

Check: Check:

10. 21 5 6 2 x 2 4x 11.

Check: Check:

2(210) 1 8 2 4(210) 0 28

12.

Check:

13.

Check:

14. 15.

Check: Check:

14 5 14✔ 232 5 232✔

14 0 2(2 1 5) 4(211 1 3) 0 232

14 5 2(s 1 5) 4(m 1 3) 5 232

2 5 s m 5 211

42 5 2s2 4m

4 5 2444

4 5 2s 4m 5 244

14 2 10 5 2s 1 10 2 10 4m 1 12 2 12 5 232 2 12

14 5 2s 1 10 4m 1 12 5 232

14 5 2(s 1 5)4(m 1 3) 5 232

78 5 78✔

78 0 3(31) 1 12 2 31 1 4

78 5 3c 1 12 2 c 1 4

31 5 c 622 5 2c

2

62 5 2c 78 2 16 5 2c 1 16 2 16

78 5 2c 1 16

78 5 3c 2 c 1 12 1 4

78 5 3c 1 12 2 c 1 4

26 5 26✔

23(25) 1 4 1 5(25) 0 26

23y 1 4 1 5y 5 26

y 5 25

2y2 5 210

2

2y 5 210

2y 1 4 2 4 5 26 2 4

2y 1 4 5 26

23y 1 5y 1 4 5 26

23y 1 4 1 5y 5 26

28 5 28✔ 21 5 21✔

21 0 6 2 (23) 2 4(23)

2m 1 8 2 4m 5 28 21 5 6 2 x 2 4x

m 5 210

22m22 5 20

22 23 5 x 22m 5 20 15

25 5 25x25

22m 1 8 2 8 5 28 2 8 15 5 25x 22m 1 8 5 28 21 2 6 5 6 2 6 2 5x

2m 2 4m 1 8 5 28 21 5 6 2 5x 2m 1 8 2 4m 5 28

29 5 29✔4 5 4✔

3(7) 1 12 2 6(7) 0 293(3) 1 3 2 8 0 4

3a 1 12 2 6a 5 293b 1 b 2 8 5 4

a 5 7 b 5 3

23a23 5 221

23 4b4 5 12

4

23a 5 221 4b 5 12

23a 1 12 2 12 5 29 2 12 4b 2 8 1 8 5 4 1 8

23a 1 12 5 29 4b 2 8 5 4

3a 2 6a 1 12 5 29 3b 1 b 2 8 5 4 16. 17.

Check: Check:

18. 19.

Check: Check:

20.

You can buy 2 lb of apples.21. Let w 5 the weight of the letter.

Each letter weighed 6 oz.22. Let h 5 the number of hours worked.

The employee worked 41 hours.23.

The integers are 223 and 222. n 1 1 5 223 1 1 5 222

n 5 223

2n2 5 246

2

2n 5 246

2n 1 1 2 1 5 245 2 1

2n 1 1 5 245

n 1 (n 1 1) 5 245

h 5 41

10.50h10.50 5 430.50

10.50

10.50h 5 430.50

2122.50 1 122.50 1 10.50h 5 308.00 1 122.50

2122.50 1 10.50h 5 308.00

245 2 367.50 1 10.50h 5 308.00

245 1 10.50h 2 367.50 5 308.00

7.00(35) 1 10.50(h 2 35) 5 308.00

w 5 6

0.24w0.24 5 1.44

0.24

0.24w 5 1.44

0.15 2 0.15 1 0.24w 5 1.59 2 0.15

0.15 1 0.24w 5 1.59

0.39 1 0.24w 2 0.24 5 1.59

0.39 1 0.24(w 2 1) 5 1.59

g 5 2

1.20g1.20 5 2.40

1.20

1.20g 5 2.40

4.80 2 4.80 1 1.20g 5 7.20 2 4.80

4.80 1 1.20g 5 7.20

1.20(4 1 g) 5 7.20

284 5 284✔ 224 5 224✔

7(4 2 16) 0 284 22(21 2 9) 0 224

7(4 2 t) 5 284 22(x 2 9) 5 224

t 5 16 x 5 21

27t27 5 2112

27 22x22 5 242

22

27t 5 2112 22x 5 242

28 2 28 2 7t 5 284 2 28 22x 1 18 2 18 5 224 2 18

28 2 7t 5 284 22x 1 18 5 224

7(4 2 t) 5 28422(x 2 9) 5 224

16 5 16✔ 40 5 40✔

2(9 2 1) 0 16 40 0 5(10 2 2)

2(z 2 1) 5 16 40 5 5(d 2 2)

z 5 9 10 5 d 2z2 5 18

2 505 5 5d

5

2z 5 18 50 5 5d 2z 2 2 1 2 5 16 1 2 40 1 10 5 5d 2 10 1 10

2z 2 2 5 16 40 5 5d 2 10

2(z 2 1) 5 16 40 5 5(d 2 2)



24.

The integers are 15, 16, and 17.25.

The integers are 286, 285, and 284.26. Yes; as long as you do the same operation to eachside, the order of the steps does not affect the solution.27. 15 5 23(c 2 1) 28.

15 5 23c 1 3 1 915 5 23c 1 1215 5 23c 1 12 2 12

29.

30.

31.

32.

y 5 165 in.; 2y 5 2(165) 5 330 in.

3y3 5 495

3

3y 5 495

3y 1 505 2 505 5 1,000 2 505

3y 1 505 5 1,000

y 1 2y 1 505 5 1,000

m 5 4 ft

4m4 5 16

4

4m 5 16

4m 1 5 2 5 5 21 2 5

4m 1 5 5 21

m 1 m 1 m 1 m 1 5 5 21

s 5 5

8s8 5 40

8

8s 5 40

8s 2 35 1 35 5 5 1 35

8s 2 35 5 5

5s 1 3s 2 2 2 33 5 5

5s 2 2 1 3s 2 33 5 5

5s 2 2 1 3(s 2 11) 5 5

z 5 10

5z5 5 50

5

5z 5 50

5z 2 40 1 40 5 10 1 40

5z 2 40 5 10

2z 1 3z 2 40 5 10

2z 2 40 1 3z 5 10

2(z 2 20) 1 3z 5 10

n 5 521 5 c 23n23 5 215

233

23 5 23c23

23n 5 2153 5 23c 23n 1 8 2 8 5 27 2 8

23n 1 8 5 27

3n 1 8 2 6n 5 27

2(1.5n 1 4) 2 6n 5 27

n 1 2 5 286 1 2 5 284

n 5 286; n 1 1 5 286 1 1 5 285;

3n3 5 2258

3

3n 5 2258

3n 1 3 2 3 5 2255 2 3

3n 1 3 5 2255

n 1 n 1 n 1 1 1 2 5 2255

n 1 (n 1 1) 1 (n 1 2) 5 2255

n 5 15; n 1 1 5 15 1 1 5 16; n 1 2 5 15 1 2 5 17

3n3 5 45

3

3n 5 45

3n 1 3 2 3 5 48 2 3

3n 1 3 5 48

n 1 n 1 n 1 1 1 2 5 48

n 1 (n 1 1) 1 (n 1 2) 5 48 33. Let x 5 the cost of one jar of jelly.Set up an equation: (number of loaves ? cost of one loaf)1 (number of peanut butter jars ? cost of one peanutbutter jar) 1 (number of jelly jars ? cost of one jellyjar) 5 $14.56, the total cost of all the items.

$1.30.34.

35.

the correct choice is C.36. The Fab Store has a constant unit price of $4.50 peryard. Let y 5 the number of yards. $4.50y 5 total price,

so the correct choice is H. 37. 5 5 4 12 5 0.417, or41.7%; the correct choice is C.

38. 39.

40.

6-4 Solving Equations WithVariables on Both Sides

pages 276–278

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. inverse operations2. 9t 1 47 3. 60 2 12r 4. 23x 2 7

a 5 2128

8 ? a8 5 8 ? (216)

a8 5 216

a8 1 12 2 12 5 24 2 12

a8 1 12 5 24

x 5 275 n 5 44

25 ? x25 5 25 ? 15 4 ? n

4 5 4 ? 11

x25 5 15 n4 5 11

x25 2 7 1 7 5 8 1 7 n4 2 1 1 1 5 10 1 1

x25 2 7 5 8 n4 2 1 5 10

512

n 5 21;

5n5 5 105

5

5n 5 105

5n 1 95 2 95 5 200 2 95

5n 1 95 5 200

5(n 1 19) 5 200

a 5 2.12

1.25a1.25 5 2.65

1.25

1.25a 5 2.65

0.5 1 1.25a 2 0.5 5 3.15 2 0.5

0.5 1 1.25a 5 3.15

0.5 2 0.25a 1 1.5a 5 3.15 2 1.5a 1 1.5a

0.5 2 0.25a 5 3.15 2 1.5a

1.5 2 0.25a 2 1 5 3 1 0.15 2 1.5a

1.5 2 0.25(a 1 4) 5 3 1 3(0.05 2 0.5a)

x 5 1.30

2x2 5 2.60

2

2x 5 2.60

11.96 1 2x 2 11.96 5 14.56 2 11.96

11.96 1 2x 5 14.56

2(5.98 1 x) 5 14.56

2(2.79 1 3.19 1 x) 5 14.56

2(2.79) 1 2(3.19) 1 2x 5 14.56



Quick Check1.

2. $29.94 1 $.10 ? number of text messages 5$32.99 1 $.05 ? number of text messages.Let x 5 the number of text messages.

61 text messagesExercises 1. Like terms can be combined. Once ,22.8, 3, and 0 are converted to either decimals orequivalent fractions, they could be combined in anequation. These are all like terms. 2. Like terms havethe same variable factors. In this set, only the terms thatcontain both x and y variables can be like terms. xy andyx are like terms. 3. Like terms have the same variablefactors. Therefore, 11a and a are like terms, and 24.1a2

and a2 are like terms.

4.

no5. The student added x to the left-hand side, butsubtracted x from the right-hand side.

6. It is a negative integer. Combining like terms on theright gives you 22x 2 12. Adding 2x to each side givesyou 4x 5 212. A negative number divided by a positivenumber is a negative number.7.

Check:

226 5 226✔

2 1 14(22) 0 28 1 9(22) 2 1 14z 5 28 1 9z

z 5 22

5z5 5 210

5

5z 5 210 2 2 2 1 5z 5 28 2 2

2 1 5z 5 28 2 1 14z 2 9z 5 28 1 9z 2 9z

2 1 14z 5 28 1 9z

x 5 3 x 1 4 2 4 5 7 2 4

x 1 4 5 7 2x 2 x 1 4 5 7 1 x 2 x

2x 1 4 5 7 1 x 3x 1 4 2 x 5 7 1 x

26 2 31

21 2 8 2 7 0 35 2 4

3(7) 1 8 2 7 0 5(7) 2 4

3x 1 8 2 x 0 5x 2 4

279

x 5 61;

$0.5x$0.5 5

$3.05$0.5

$0.5x 5 $3.05

$29.94 1 $0.5x 2 $29.94 5 $32.99 2 $29.94

$29.94 1 $0.5x 5 $32.99

$29.94 1 $.10x 2 $.05x 5 $32.99 1 $.05x 2 $0.5x

$29.94 1 $.10x 5 $32.99 1 $.05x

b 5 2

6b6 5 12

6

6b 5 12

6b 2 2 1 2 5 10 1 2

6b 2 2 5 10

7b 2 b 2 2 5 b 2 b 1 10

7b 2 2 5 b 1 10

8.

Check:

9.

Check:

10.

Check:

11.

Check:

12.

Check:

13.

Check:

6.4 5 6.4✔ 8(4 2 3.2) 0 2(3.2)

8(4 2 a) 5 2a 3.2 5 a 3210 5 10a

10

32 5 10a 32 2 8a 1 8a 5 2a 1 8a

32 2 8a 5 2a 8(4 2 a) 5 2a 2126 5 2126✔

7(218) 0 9(218 1 4) 7m 5 9(m 1 4) m 5 218

22m22 5 36

22

22m 5 36 7m 2 9m 5 9m 2 9m 1 36

7m 5 9m 1 36 7m 5 9(m 1 4)

29 5 29✔ 29 0 9(9 2 10) 2k 5 9(k 2 10)

k 5 9

210k210 5 290

210

210k 5 290 2k 2 9k 5 9k 2 9k 2 90

2k 5 9k 2 902k 5 9(k 2 10)

13 5 13✔ 6(2) 1 1 0 15 2 2

6d 1 1 5 15 2 d d 5 2

7d7 5 14

7

7d 5 14 7d 1 1 2 1 5 15 2 1

7d 1 1 5 15 6d 1 d 1 1 5 15 2 d 1 d

6d 1 1 5 15 2 d 64 5 64✔

22 1 2(21) 0 37 1 6 1 21

22 1 2x 5 37 1 6 1 x x 5 21

22 2 22 1 x 5 43 2 22

22 1 x 5 43

22 1 2x 2 x 5 43 1 x 2 x 22 1 2x 5 43 1 x 22 1 2x 5 37 1 6 1 x

233 5 233✔

28 2 5(5) 0 12 2 9(5) 28 2 5y 5 12 2 9y

y 5 5

4y4 5 20

4

4y 5 20

28 1 8 1 4y 5 12 1 8

28 1 4y 5 12

28 2 5y 1 9y 5 12 2 9y 1 9y 28 2 5y 5 12 2 9y



14.

Check:

15. (3 ? $3.99) 1 cost of one video game 5(5 ? cost of one video game) 2 $.11. Let x 5 the cost ofone video game.

16. Let g 5 the weight of the golf ball.

A golf ball weighs 46 g.17. Efren and Gregory go the same distance when theycatch up to each other. d 5 rt; since the distances are thesame, we can set Elfren’s rt equal to Gregory’s rt. Letx 5 the time elapsed since Elfren left home.

about 9:57 A.M.18. Use inverse operations to combine the variables andthen isolate the variable on one side of the equation.19.

x 5 0.15

20.25 1 0.4 5 x 2 0.4 1 0.4

20.25 5 x 2 0.4

2x 2 0.25 2 2x 5 3x 2 0.4 2 2x

2x 2 0.25 5 3x 2 0.4

0.75 1 2x 2 1 5 3x 2 0.4

0.75 1 2(x 2 0.5) 5 3x 2 0.4

9:00 1 56.67 5

0.944 3 60 5 56.67

x < 0.944

4.254.5 5 4.5x

4.5

4.25 5 4.5x

0 1 4.25 5 4.5x 2 4.25 1 4.25

0 5 4.5x 2 4.25

4x 2 4x 5 8.5x 2 4.25 2 4x

4x 5 8.5x 2 4.25

4x 5 8.5(x 2 0.5)

46 5 g

46010 5

10g10

460 5 10g 460 1 g 2 g 5 11g 2 g

460 1 g 5 11g

x 5 3.02; $3.02

12.084 5 4x

4

12.08 5 4x

11.97 1 0.11 5 4x 2 0.11 1 0.11

11.97 5 4x 2 0.11

11.97 1 x 2 x 5 5x 2 x 2 0.11

11.97 1 x 5 5x 2 0.11

3(3.99) 1 x 5 5x 2 0.11

8 5 8✔ 8 2 3(4 2 4) 0 2(4) 8 2 3(p 2 4) 5 2p

4 5 p 205 5

5p5

20 5 5p 20 2 3p 1 3p 5 2p 1 3p

20 2 3p 5 2p 8 1 12 2 3p 5 2p 8 2 3p 1 12 5 2p

8 2 3(p 2 4) 5 2p 20. The perimeter or a square is equal to 4 times thelength of one side.

The side length of the square is 12 inches. grid 1221. 22. 5 5 0.1176 rounded to0.118; 11.8%23. 24.


1. No; if the family only visited on 2 days, the cost wouldbe $131.60, which is cheaper than a yearly membership.2. Yes; 43.90 5 2 ? 21.95 and 21.90 5 2 ? 10.95.Multiplying 21.95 and 10.95 by 2 is the same as addingthem to themselves.3. Let x 5 the cost of last year’s membership.

The cost of last year’s membership was $60 and the costof this year’s membership is $80. 4. Let x 5 the numberof granola bars the counselor can buy.

She can buy 10 granola bars and 30 drinks.5. Let x 5 the number of between–meal snacks theadults in this survey had in one year.

The children in the survey had about 1,655 snacks. 1.23(1,345.3) < 1,655

x < 1,345.3

2.23x2.23 5

3,0002.23

2.23x 5 3,000

x 1 1.23x 5 3,000

3(10) 5 30 x 5 10

2.4x2.4 5 24

2.4

2.4x 5 24 0.45x 1 1.95x 5 24

0.45x 1 3(0.65x) 5 24

60 1 20 5 80

x 5 60

0.25x0.25 5 15

0.25

0.25x 5 15

x 5 0.75x 1 15

x 5 0.75(x 1 20)

x 5 4

7x7 5 28

7 q 5 3

7x 5 28 2q2 5 6

2

7x 1 6 2 6 5 34 2 6 2q 5 6

7x 1 6 5 34 2q 1 3 2 3 5 9 2 3

7x 1 7 2 1 5 34 2q 1 3 5 9

7(x 1 1) 2 1 5 34 6q 1 3 2 4q 5 9

0.54.25

4.75 2 4.254.25

4.21.4 5 3

2x 1 8 5 2(2) 1 8 5 4 1 8 5 12

x 5 2

2412 5 12x

12

24 5 12x

32 2 8 5 12x 1 8 2 8

32 5 12x 1 8

8x 1 32 2 8x 5 20x 1 8 2 8x

8x 1 32 5 20x 1 8

4(2x 1 8) 5 20x 1 8




1.

2.3.

4.

5.

6. y , 24

7. p $ 25

8. k # 7

9. No; since 6 is equal to 6, it cannot also be more than 6.

6-5 Solving Inequalities by Addingor Subtracting pages 282–285

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. equation 2. 2183. 213 4. 24

Quick Check 1. 1 # u 2 41 1 4 # u 2 4 1 4

5 # u

2. Let a 5 number of seats available.

At most, 211 people can attend.

Exercises 1. An equation states that two expressionsare equal; an inequality compares two expressions thatare not usually equal. 2. n $ 22 3. 0.6 # x4. y 2 4 . 24 5. y 2 4 , 0 6. x , 12 7. x $ 658.

Check:

9.

Check:

26 , 23✔ 23 5 23✔

25 2 1 , 23 22 2 1 0 23

m 2 1 , 23 m 2 1 5 23

m , 22

m 2 1 1 1 , 23 1 1

m 2 1 , 23

22 . 18✔ 18 5 18✔

30 2 8 . 18 26 2 8 0 18

x 2 8 . 18 x 2 8 5 18

x . 26

x 2 8 1 8 . 18 1 8 282624 x 2 8 . 18

a # 211

a # 300 2 89

654

0 1 4 6 7 852 3

0

0

0 1 2 3�1

0 1 2

0 1 2 430

0

10.

Check:

11.

Check:

12.

Check:

13.

Check:

14.

Check:

15.

Check:

16.

Check:

17.

Check:

18.

Check:

19.

Check:

23 , 0✔ 0 5 0✔ 213 1 10 , 0 210 1 10 0 0

u 1 10 , 0 u 1 10 5 0 u , 210

u 1 10 2 10 , 0 2 10 u 1 10 , 0

2 $ 1✔ 1 5 1✔ 5 1 (23) $ 1 5 1 (24) 0 1

5 1 b $ 1 5 1 b 5 1 b $ 24

5 2 5 1 b $ 1 2 5 0 5 1 b $ 1

1 , 2✔ 2 5 2✔ 0 1 1 , 2 1 1 1 0 2 w 1 1 , 2 w 1 1 5 2

w , 1 w 1 1 2 1 , 2 2 1 210

w 1 1 , 2 25 $ 22✔ 22 5 22✔

24 1 1 $ 22 21 1 1 0 22 m 1 1 $ 22 m 1 1 5 22

m $ 21 m 1 1 2 1 $ 22 2 1 222120

m 1 1 $ 22 22 # 1✔ 1 5 1✔

3 1 25 # 1 3 1 (22) 0 1 3 1 t # 1 3 1 t 5 1

t # 22 3 2 3 1 t # 1 2 3 0

3 1 t # 1 12 $ 1✔ 1 5 1✔

0 1 12 $ 1 211 1 12 0 1

x 1 12 $ 1 x 1 12 5 1

x $ 211

x 1 12 2 12 $ 1 2 12 0 11 x 1 12 $ 1

214 , 212✔ 212 5 212✓

22 2 12 , 212 0 2 12 0 212

p 2 12 , 212 p 2 12 5 212

p , 0

p 2 12 1 12 , 212 1 12 20 p 2 12 , 212

211 . 216✔ 211 5 211✔

211 . 215 2 1 211 0 210 2 1

211 . w 2 1 211 5 w 2 1

210 . w 211 1 1 . w 2 1 1 1

211 . w 2 1

2 # 3✔ 2 5 2✔ 2 # 8 2 5 2 0 7 2 5

2 # n 2 5 2 5 n 2 5

7 # n 2 1 5 # n 2 5 1 5 0 7 14

2 # n 2 5

3 . 1✔ 1 5 1✔

16 2 13 . 1 14 2 13 0 1

a 2 13 . 1 a 2 13 5 1

a . 14

a 2 13 1 13 . 1 1 13 151413 a 2 13 . 1



20. Let x 5 number.

All numbers greater than or equal to 23 are solutions.21. Let x 5 available amps.

At most, 7.5 amps are available for other appliances.22. The family uses or 102 gallons ofwater for bathing, laundry, and cleaning. Let x 5 thegallons of water available to water the garden.

The family can use, at most, 148 gallons to water thegarden. 23. You can add or subtract the same numberfrom each side of an equation or inequality withoutchanging the value of the variable. They are different inthat an equation usually has one solution, but aninequality has an infinite number of solutions.24. x . 21 25. x # 0 26. After you write a check youhave $516.46 2 $26.47, or $489.99 in your account. Let x 5 the amount of money you need to deposit in orderto have free checking.

27. If x . y and y . z, then x . z. 28. If a . b,then b , a. 29. 6 30. 2 31. 2, 3, 4, 5, 6; 5 integers32.

33. Let w 5 the number of weeks it will take her to save$45. She saves $6 per week, which is represented by 6w,plus her original $15: 6w 1 15 5 45; the correct choice isD. 34. Add 97,066 km2 to Sweden’s land area andmatch this value to a country; 449, 964 1 97,066 5547,030, which is France’s land area; the correct choice isF. 35. Let n 5 Solana’s age now. Add 2 to her age now,multiply this by 5 and set this equal to 60 to get theequation: 5(n 1 2) 5 60; the correct choice is D.36. 1 5 1 5 37. 2 5 2 5

38. 1 5 1 5 5 1



322

2522

1122

1422

12

711

512

412

912

13

34

1945

1045

945

29

15

y . 2a y 1 2a 2 2a . a 2 2a

y 1 2a . a 2y 2 y 1 2a . a 2y 1 2a 2 y . a

2(y 1 a) 2 y . a

x . $10.01

x 1 $489.99 2 $489.99 . 500 2 $489.99

x 1 $489.99 . $500

x # 148

102 1 x 2 102 # 250 2 102

102 1 x # 250

50 1 27 1 25

x # 7.5 amps 12.5 2 12.5 1 x # 20 2 12.5

12.5 1 x # 20

x $ 23 x 2 18 1 18 $ 5 1 18

x 2 18 $ 5

2.

3.

4. Like terms are terms with exactly the same variablefactors5.

6. x 1 2x 1 3x 1 4x 1 5y 2 4y 1 3y 2 2y

7a–c. Check students’ work.


1. x $ 22 2. x , 13.

4. 5.

6. 7.

8.

y , 223

y 1 1 2 1 , 222 2 1

y 1 1 , 222

y 2 (21) , 222

g # 1 a $ 26

g 1 1.5 2 1.5 # 2.5 2 1.5 a 1 3.4 2 3.4 $ 22.6 2 3.4

g 1 1.5 # 2.5a 1 3.4 $ 22.6

z 5 21

22z22 5 2

22

m 5 228 22z 5 2

22 ? m22 5 22 ? 14 22z 1 6 2 6 5 8 2 6

m22 5 14 22z 1 6 5 8

m22 1 7 2 7 5 21 2 7 2z 2 z 1 6 5 8

m22 1 7 5 21 2z 2 (z 2 6) 5 8

f 5 29

213.51.5 5

1.5f1.5

213.5 5 1.5f

23.5 2 10 5 10 1 1.5f 2 10

23.5 5 10 1 1.5f

23.5 2 4f 1 4f 5 10 2 2.5f 1 4f

23.5 2 4f 5 10 2 2.5f

5 10x 1 2y

5 (1 1 2 1 3 1 4)x 1 (5 2 4 1 3 2 2)y

x 5 111

3x3 5 333

3

3x 5 333

3x 2 8 1 8 5 325 1 8

3x 2 8 5 325



9. Let b 5 the cost of a banana.4.99 1 b 5 13b

4.99 1 b 2 b 5 13b 2 b4.99 5 12b

5

0.42 < b; b < $.4210. Let x 5 the load weight. 28,500 1 x 5 64,000;28,500 1 x 2 28,500 5 64,000 2 28,500; x 5 35,500 lb


1. 6(3) , 12(3); 18 , 36; , ; 2 , 4;

6(2) , 12(2); 12 , 24; , ; 3 , 6;

6(1) , 12(1); 6 , 12; , ; 6 , 12;

6(0) 5 12(0); 0 5 0;

6(21) . 12(21); 26 . 212; . ; 26 . 212;

6(22) . 12(22); 212 . 224; . ; 23 . 26;

6(22) . 12(22); 218 .236; . ; 22 . 24;2a. The direction of the inequality stays the same whenyou multiply or divide by a positive number. 2b. Thedirection of the inequality changes when you multiply ordivide by a negative number. 3. 2a . 2b; 22a , 22b

6-6 Solving Inequalities byMultiplying or Dividing

pages 288–292

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. No; zero is not anegative number. 2. 24 3. 2101 4. 6.2 5. 28

Quick Check 1. Let n 5 the number of passengers thatthe elevator can safely hold.

The elevator can hold up to 12 passengers.2.

3.

Exercises 1. When you multiply or divide each side ofan inequality by a positive number, the relationshipbetween the two sides does not change. When youmultiply or divide by a negative number, the direction ofthe inequality sign reverses. 2. Any value that issubstituted for z must be negative in order to be asolution. Any positive value would not result in a truestatement. No; it will only include numbers less than orequal to 212.

p # 217

22p22 # 34

22

22p $ 34

b # 24

24 ? A b24 B # 24 ? 1 0

b24 $ 1

n # 12.5

160n160 # 2000

160

160n # 2000

1223

623

1222

622

1221

621

121

61

122

62

123

63

12b12

4.9912

3. 4.

5. 6.

7. 8.

9. 10.

11. Let s 5 number of specials.

At most, the math club can buy 4 luncheon specials.12. Let c 5 number of cases.

You can fit at most 96 CD cases on the shelf.13. 14.

15. 16.

17. 18.

19. 20.

21.

22. Let b 5 number of buses.

The school should reserve 4 buses.23. In either inequality, the answer

must be greater than 23,so 23 itself can never be a solution. x . 23; 23

2x21 . 3

21

2x , 3

b $ 3.475

48b48 $ 165

48

48b $ 165

48b $ 157 1 8

230 # r 2720.9 # 20.9r

20.90

27 $ 20.9r0 1 2 4 5 6 737 140

5 , q w . 7

21523 ,

23q23 22w

22 . 21422

215 . 23q 22w , 2140

x $ 24 212 . x 26x26 $ 24

26 22 ? 6 . 22 ? A x22 B

26x # 24 6 , x22

0 70 1400 48 96

140 # b z $ 96

27 ? (220) # 27 ? A b27 B 212 ? A z

212 B $ 212 ? (28)

220 $ b27

z212 # 28

200

m , 0 r $ 26

22 ? m22 , 22 ? 0 22 ? A r

22 B $ 22 ? 3

m22 . 0 r22 # 3

c # 96

0.375c0.375 # 36

0.375

0.375c # 36

s # 4.8057c

4.89s4.89 # 23.50

4.89

4.89s # 23.50

236 # x w # 29

218 ? 2 # x2 ? 2 6w

6 # 2546

218 # x2 6w # 254

y # 25 c , 2

4y4 # 220

4 5c5 , 10

5

4y # 220 5c , 10

220 , r y . 0

5 ? (24) , 5 ? A r5 B 2 ?

y2 . 2 ? 0

24 , r5

y2 . 0

b , 4 d . 12

2b2 , 8

2 3 ? A d3 B . 3 ? 4

2b , 8 d3 . 4



24. In 5x , 20, you must divide each side by a positivenumber to get x , 4. In 25x , 20, you must divide eachside by a negative number, which changes the directionof the inequality. You will also get 24 on the rightinstead of 4. So x . 24. 25. a and b must have oppositesigns because the product ab will then be negative. Theopposite of a negative number will then be positive andgreater than 0. 26. The product of a positive andnegative number will be less than 0. 27. a can bepositive or negative, but b must be positive. 28. a and bmust have the same sign and a 2 0 and b 2 0.29. Let x 5 the number of teachers. There must be oneteacher for every 5 kids, and the number of teachersmust be a whole number.

4 teachers30. Let x 5 the number of hours your brother works. Hemust work a whole number of hours to get paid.

; 27 h31. No; it is only true if b is positive. If b 5 0, theproblem is undefined. If b is negative, the inequality signneeds to change. 32. 75% of $26.99 5 $20.24; 70% of$29.99 5 $20.99; $20.24 , $20.99; the correct choice is D.33. Each percent is being divided by 4 and the number itis being multiplied by is being multiplied by 4 to keepthe answer 16; the correct choice is F.34. 5 5 2.5; the correct choice is D.35.

36.

37.


1. 435 3 5 290; 290 votes 2. 42 3 5 28; 157 3 5

104.67; 28 members of the Senate and 105 members ofthe House 3. No; an override requires two thirds of theSenate and two thirds of the House.


1. Like terms have the same variables. 2. An inequalityis a mathematical sentence that contains ,, ., #, $, or ?.3. A term is a number, a variable, or the product of anumber and a variable. 4. When you use theMultiplication Property of Inequality, you may need toreverse the direction of the inequality sign. 5. To solvethe inequality x 2 5 , 7, use the Addition Property ofInequality.

23 23 23

w $ 15

w 2 6 1 6 $ 9 1 6 1413 15 16 17 w 2 6 $ 9

a . 22

a 2 7 1 7 . 15 1 7 2221 23 24 25 a 2 7 . 15

y # 26

y 1 3 2 3 # 29 2 3 2423 25 26 27 y 1 3 # 29

52

6024

x $ 26.7

6.85x6.85 $ 182.89

6.85

6.85x $ 182.89

x $ 3.8;

5x5 $ 19

5

5x $ 19

6. Check:

7. Check:

8. Check:

9. Check:

10. Check:

11. Check:

12. Let x 5 the number of cans of cat food you bought.

15 cans13. Let x 5 the number of shirts you bought.

3 shirts14.

15.

16. 5 11x 2 12

8x 1 3(x 2 4) 5 8x 1 3x 2 12 5 3a 1 11

3(a 1 2) 1 5 5 3a 1 6 1 5

5 7 2 3f

4 2 3(f 2 1) 5 4 2 3f 1 3

x 5 3;

14.99x14.99 5 44.97

14.99

14.99x 5 44.97

125.89 1 14.99x 2 125.89 5 170.86 2 125.89

125.89 1 14.99x 5 170.86

79.90 1 45.99 1 14.99x 5 170.86

2 ? 39.95 1 45.99 1 14.99x 5 170.86

x 5 15;

$1.79x$1.79 5

$26.85$1.79

$1.79x 5 $26.85

$1.79x 1 $6.59 2 $6.59 5 $33.44 2 $6.59

$1.79x 1 $6.59 5 $33.44

w 5 40

4 ? Aw4 B 5 4 ? 10

20 5 20✔ w4 5 10

404 1 10 0 20 w4 1 10 2 10 5 20 2 10

w4 1 10 5 20 w4 1 10 5 20

s 5 256

12s12 5 210

12

28 5 28 12s 5 210

12 ? A 56 B 1 2 0 28 12s 1 2 2 2 5 28 2 2

12s 1 2 5 28 12s 1 2 5 28

c 5 29

28 5 28✔ 23 ? A c23 B 5 23 ? 3

2 5 2✔ c23 5 3

2923 2 1 0 2 c

23 2 1 1 1 5 2 1 1

c23 2 1 5 2 c

23 2 1 5 2

215 5 b 5 ? (23) 5 5 ? A b

5 B 21 5 21✔ 23 5 b

5

21 0 2155 1 2 21 2 2 5 b

5 1 2 2 2

21 5 b5 1 2 21 5 b

5 1 2

q 5 2113

3q3 5 211

3

27 5 27✔ 3q 5 211

4 1 3 A2113 B 0 27 4 2 4 1 3q 5 27 2 4

4 1 3q 5 27 4 1 3q 5 27 n 5 12

2n2 5 24

2

19 5 19✔ 2n 5 24 2(12) 2 5 0 19 2n 2 5 1 5 5 19 1 5

2n 2 5 5 19 2n 2 5 5 19



17.

Check:

18. Check:

19. Check:

20. Check:

21. Let x 5 the number of pounds of Swiss cheeseMarsha bought.

22. 23.

24.

25. c , 75 26. x $ 1500 11

t $ 211

4 2 4 1 t $ 27 2 4

4 1 t $ 27

0 2 419 380

u # 2 g . 19

u 1 3 2 3 # 5 2 3 g 2 7 1 7 . 12 1 7

u 1 3 # 5 g 2 7 . 12

x 5 2.5; 2.5 lb 4.50x4.50 5 11.25

4.50

4.50x 5 11.25

13.50 1 4.50x 2 13.50 5 24.75 2 13.50

13.50 1 4.50x 5 24.75

3 ? 4.50 1 4.50x 5 24.75

c 5 25

3c3 5 215

3

3c 5 215

210 5 210✔ 3c 1 5 2 5 5 210 2 5

3(25 1 4) 2 7 0 210 3c 1 5 5 210

3(c 1 4) 2 7 5 210 3c 1 12 2 7 5 210

3(c 1 4) 2 7 5 210

k 5 165 , or 3.2

165 5 5k

5

16 5 5k 18 2 2 5 5k 1 2 2 2

18 5 18✔ 18 5 5k 1 2

18 0 2(3 ? 165 1 1) 2 16

5 18 5 6k 2 k 1 2

18 5 2(3k 1 1) 2 k 18 5 6k 1 2 2 k18 5 2(3k 1 1) 2 k

b 5 5

3b3 5 15

3

3b 5 15

2 5 2✔ 3b 2 8 1 8 5 7 1 8

2(5) 2 8 0 2(5) 1 7 3b 2 8 5 7

2b 2 8 5 2b 1 7 2b 1 b 2 8 5 2b 1 b 1 7

2b 2 8 5 2b 1 7

29 5 29✔

4(24) 1 3 2 (24) 0 27 1 2 1 (24)

4a 1 3 2 a 5 27 1 2 1 a a 5 24

2a2 5 28

2

2a 5 28

2a 1 3 2 3 5 25 2 3

2a 1 3 5 25

3a 2 a 1 3 5 25 1 a 2 a 3a 1 3 5 25 1 a

4a 2 a 1 3 5 25 1 a 4a 1 3 2 a 5 27 1 2 1 a 27. 28.

29. 30.

31. 32.


1.

2.

3.

4.

5.

6.

7.

8.

9. 10.

11. 12.

c 5 22 m 5 9

22c22 5 4

22 4m4 5 36

4

22c 5 4 4m 5 36

22c 1 5 2 5 5 9 2 5 4m 2 9 1 9 5 27 1 9

22c 1 5 5 9 4m 2 9 5 27

a 5 1 z 5 235

2.5a2.5 5 2.5

2.5 6z6 5 2210

6

2.5a 5 2.5 6z 5 2210

a22 1 3a 5 2.5 2 3a 1 3a7 ? 6z7 5 7 ? (230)

a22 5 2.5 2 3a 6z7 5 230

9 5 y

2 1 7 5 27 1 y 1 7

2 5 27 1 y

2 1 y 2 y 5 27 1 2y 2 y

2 1 y 5 27 1 2y

x 5 113

3x3 5 11

3

3x 5 11

3x 1 7 2 7 5 18 2 7

3x 1 7 5 18

x 1 7 1 2x 5 18 2 2x 1 2x

x 1 7 5 18 2 2x

5 17s 1 6

5 13s 1 4s 1 6

13s 2 (26 2 4s) 5 13s 1 6 1 4s 5 25v 1 17

4v 1 17 2 9v 5 4v 2 9v 1 17

5 236a 2 5

24(7a 1 2a) 2 5 5 24(9a) 2 5

5 6m 2 4

2(3m 2 5) 1 6 5 6m 2 10 1 6

5 5 2 4t 5 1 (212t) 1 8t 5 5 2 12t 1 8t

5 2 2 4r 9 2 4r 2 7 5 9 2 7 2 4r

6 12 1800

z . 12 c , 220

24 ? A z24 B . 24 ? (23) 22 ? A c

22 B , 22 ? 10

z

24 , 23 c22 . 10

12802 4 6 80

w # 128 a , 7

8 ? Aw8 B # 8 ? 16 26a

26 , 24226

w8 # 16 26a . 242

00

y # 22 x , 23

217y217 # 34

217 4x4 , 212

4

217y $ 34 4x , 212



13. 14.

15. 16.

17. 18.

19.

Let b 5 number of quilt blocks.

The quilter needs 11 quilt blocks.20. Let a 5 cost of apples.

Each apple cost $.23.21. Let f 5 friend’s score.

f 5 103

2f2 5 206

2

2f 5 206

2f 1 6 2 6 5 212 2 6

2f 1 6 5 212

a 5 0.23

15a15 5 3.45

15

15a 5 3.45

15a 1 2.75 2 2.75 5 6.20 2 2.75

15a 1 2.75 5 6.20

b 5 11

4b4 5 44

4

4b 5 44

4b 1 4 2 4 5 48 2 4

4b 1 4 5 48

48 in.

4b

2 in. 2 in.

2 5 t c 5 29 42 5 2t

2

c 1 2 2 2 5 27 2 2 4 5 2t c 1 2 5 27 21 1 5 5 2t 2 5 1 5

2c 2 c 1 2 5 c 2 c 2 7 21 5 2t 2 5

2c 1 2 5 c 2 7 5t 2 5t 2 1 5 7t 2 5t 2 5

2(c 1 1) 5 c 2 75t 2 1 5 7t 2 5

3 5 b 2923 5 23b

23

29 5 23b 5 2 14 5 14 2 14 2 3b 10 5 d

5 5 14 2 3b 6 1 4 5 d 2 4 1 4

5 5 12 1 2 2 3b 6 5 d 2 4

5 5 12 2 3b 1 2 6 1 2d 2 2d 5 3d 2 2d 2 4

5 5 3(4 2 b) 1 26 1 2d 5 3d 2 4

h 5 21

r 5 285 23h23 5 3

23

25 ? A r25 B 5 25 ? 17 23h 5 3

r25 5 17 23h 2 21 1 21 5 218 1 21

r25 2 3 1 3 5 14 1 3 23h 2 21 5 218

r25 2 3 5 14 23(h 1 7) 5 218

22. Let c 5 weight of cricket ball.

A cricket ball weighs 5.5 oz.23. Answers may vary. Sample: You save $3 each weekfor a number of weeks. Then you spend $12 on a poster,leaving you with $6 from the money you saved. Howmany weeks have passed?

You have been saving for six weeks.24. Let d 5 the age of driver; d $ 16. 25. Let p 5 thenumber of passengers; p # 5. 26. Let w 5 the numberof weeks until vacation; w , 3. 27. Let t 5 the numberof tickets available; t # 75. 28. Let p 5 the number ofessay pages; p $ 4.29. Let x 5 the number.

The greatest value the number can be is 25.30. Let p 5 the number of pens.

You can buy up to 10 pens.31. Let w 5 the weight of your package. You cannotspend more than $3.00, and you cannot buy a fraction ofa stamp.

32.

33.

0 1 2 4 5 6 7 83

y . 5

y 2 12 1 12 . 27 1 12

y 2 12 . 275 10 15 200

15 . w 18 2 3 . w 1 3 2 3

18 . w 1 3

w # 10.875; 10 oz 0.24w0.24 # 2.61

0.24

0.24w # 2.61

0.39 1 0.24w # 3.00

p # 10

0.40p0.40 # 4

0.40

0.40p # 4

11 2 11 1 0.40p # 15 2 11

11 1 0.40p # 15

x # 25

23x23 # 15

23

23x $ 15

w 5 6

3w3 5 18

3

3w 5 18

3w 2 12 1 12 5 6 1 12

3w 2 12 5 6

5.5 5 c 336 5 6c

6

33 5 6c 42 2 9 5 6c 1 9 2 9

42 5 6c 1 9

42 1 2c 2 2c 5 8c 2 2c 1 9

42 1 2c 5 8c 1 9



34. 35.

36.

37.

38.

39.

40. You solve an inequality the same way that you solvean equation except that when you multiply or divide bya negative number, you must change the direction of theinequality. Examples:

TEST PREP page 297

1.

; the correct choice A.2. The sum of 2 times the width and 2 times the lengthgives the perimeter of the rectangle. Since its length is 10 cm more than its width, the equation to find thedimensions is 2w 1 2(w 1 10) 5 28; the correct choice is G.3.

; the correct choice is A.4.

22, 21, and 0 are all less than 2 and thus solutions to theinequality, so the correct choice is F.

x , 2

x 2 3 1 3 , 21 1 3

x 2 3 , 21

y 5 a 2 cb

y 5 c 2 a2b

2by 5 c 2 a

a 2 by 5 c

y , 4

9y9 , 36

9

9y , 36

x # 22 x 5 22

23x23 # 6

23 23x23 5 6

23

23x $ 6 23x 5 6 23x 1 4 2 4 $ 10 2 4 23x 1 4 2 4 5 10 2 4

23x 1 4 $ 10 23x 1 4 5 10

0

c , 29

29c29 , 81

29

29c . 81

0 3 5 6 741 2

b # 4

4b4 # 16

4

4b # 16

2 310

t # 1.5

22t22 # 23

22

22t $ 23

0 3 5 6 741 2

m , 4

3m3 , 12

3

3m , 12

05 10 15 200

s # 216 z # 15

24s24 # 64

24 3 ? A z3 B # 3 ? 5

24s $ 64 z3 # 5 5. A: 2(y 1 3) 5 2(y) 1 2(3); B: 2(y 1 3) 2 2y 1 3; the

correct choice is B.6.

; the correct choice is F.7. It costs 12 cents per photocopy, so k photocopies willcost 12k cents; the correct choice is B. 8. According tothe transitive property, if x . y and y . z, then x . z,which is the same as z , x; the correct choice is G.9. The team earned 0 ? 10, or 0 points for their losses and1 ? 7, or 7 points for their ties. They received 2 points foreach of their wins, so the equations to find the numberof wins they had is 2w 1 7 5 31; the correct choice is C.10. After purchasing a poster you have $10 2 $6, or $4left. $4.00 4 $0.08 5 50; you can purchase 50 copies ofthe flier; grid 50. 11. [2] x 5 number of tests; x # 3; [1]minor computational error OR incomplete answer12a–b. [4] Eli loses 2 pounds per month so he loses 2xpounds after x months. If he starts at 190 lb then theexpression to model his weight is 190 2 2x. 190 2 2(8) 5190 2 16 5 174; 174 lb; [3] minor error in one part; [2]minor error in two parts; [1] correct answer withoutwork shown


1a. Answers may vary. Sample: Bouncing Raisins fromPlanet 16 1b. Answers may vary. Sample: x 5 7; cost 53,000,000(7) 1 10,000,000 5 21,000,000 1 10,000,000 5$31,000,0002a. Answers may vary. Sample:

2b. Answers may vary. Sample: Let t 5 millions oftickets sold. profit 5 4t 2 31,000,000

Tickets Sold Profit

1,000,000 2$27,000,0002,000,000 2$23,000,0003,000,000 2$19,000,0004,000,000 2$15,000,0005,000,000 2$11,000,0006,000,000 2$ 7,000,0007,000,000 2$ 3,000,0008,000,000 $ 1,000,0009,000,000 $ 5,000,000

10,000,000 $ 9,000,00011,000,000 $13,000,00012,000,000 $17,000,00013,000,000 $21,000,00014,000,000 $25,000,00015,000,000 $29,000,000

5 4t 2 31,000,000

profit 5 money from ticket sales 2 cost

w . 25

2525 , 25w

25

25 . 25w



3a. Answers may vary. Sample:

The Lion King: running time 5 89 minutes;

budget 5 $79,300,000;

The cost per minute is about $891,011.< 891,011

579,300,000

89

cost per min 5Budget

Run Time

3b. Answers may vary. Sample (using The Lion Kingand a ticket price of $6.00):

For The Lion King, 13,216,667 tickets at a cost of $6 per ticket would need to be sold to make a profit.

< 13,216,667

579,300,000

6

number of tickets 5budget

price per ticket





1. 0.5 3 9 3 8 5 36 2. 2(3.14)(16) 5 100.48

3. 3 4(3 117) 5 3 4(20) 5 3 80 5 40

4. 5.

6. 7.

8. 9.

10. 11.

12. 13.

14.


Activity 1–3. Check students’ work. 4. m/1 5 m/3;m/2 5 m/4 5. If two lines intersect each other, theyform two pairs of angles with equal measures.

6. Sample:

m/1 1 m/2 5 1808

7. Sample:

m/2 1 m/3 5 1808

8. Answers may vary. Sample: The sum of the measuresof angles with a common side formed by the intersectionof two lines is 1808. 9. m/1 5 m/4 5 m/5 5 m/8 5508; m/2 5 m/3 5 m/6 5 m/7 5 1308 10. /1 >/4 > /5 > /8; /2 > /3 > /6 > /7 11. Answers mayvary. Sample: Four angles will have the same measures,

Trial

1

2

3

m∠2 � m∠3

17º � 163º � 180º

50º � 130º � 180º

102º � 78º � 180º

Trial

1

2

3

m�1 � m�2

163� � 17� � 180�

130� � 50� � 180�

78� � 102� � 180�

5 169 ft2 5 132

A 5 s2

5 28 in.2 5 216 m2

5 12(5 1 9)4 5 18 ? 12

A 5 12(b1 1 b2)h A 5 / ? w

c 5 35.7 w 5 84

7 ? 5.1 5 7 ? Ac7B 3.5 ? A w3.5 B 5 3.5 ? 24

5.1 5 c7 w3.5 5 24

k 5 1 214 5 11

7 g 5 15

1614 5 14k

14 4.2g4.2 5 63

4.2

16 5 14k 4.2g 5 63

p 5 32 s 5 23

10 1 22 5 p 2 22 1 22 44 2 44 1 s 5 41 2 44

10 5 p 2 2244 1 s 5 41

b 5 43 8 5 m b 1 13 2 13 5 56 2 13 25 2 17 5 17 2 17 1 m

b 1 13 5 5625 5 17 1 m

12

12

12

and the supplements of those angles will have the samemeasure. 12. Check students’ work.

7-1 Pairs of Angles pages 303–306

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. subtraction 2. 18 3. 314. 241 5. 229

Quick Check 1. /DBJ and /YBT are vertical angles.Adjacent angles may vary. Sample: /DBJ and /DBYare adjacent angles.2.

3. m/3 5 m/5 5 588

Exercises 1. No; they do not share a common side.2. Yes; they share a common vertex and a common side,but no common interior points. 3. No; they do not sharea common vertex. 4. No; only angles measuring lessthan 908 have complements. 5-7. Answers may vary.Samples are given. 5. Vertical angles: /MRQ and/NRP; adjacent angles: /NRP and /QRP; since /1 and /QRP are vertical angles, m/1 5 808.6. Vertical angles: /CKJ and /DKH; adjacent angles:/CKG and /GKH; since /1 and /DKH are verticalangles, m/1 5 908. 7. Vertical angles: /BDC and/TDY; adjacent angles: /CDV and /VDY; Since /1 and /BDC are vertical angles, m/1 5 408.8.

9.

10.

11.

12.

13.

m/4 5 908

m/3 5 628

288 1 m/3 5 908

m/2 1 m/3 5 908

m/2 5 288

m/1 5 1528

m/1 1 288 5 1808

x8 5 648

x8 1 1168 2 1168 5 1808 2 1168

x8 1 1168 5 1808

x8 5 1418

x8 1 398 2 398 5 1808 2 398

x8 1 398 5 1808

x8 5 358

x8 1 1458 2 1458 5 1808 2 1458

x8 1 1458 5 1808

x8 5 1568

x8 1 248 2 248 5 1808 2 248

x8 1 248 5 1808

x8 5 1668

x8 1 148 2 148 5 1808 2 148

x8 1 148 5 1808

m/4 5 908

m/4 1 908 5 1808

x8 5 1338

x8 1 478 2 478 5 1808 2 478

x8 1 478 5 1808

Chapter

7Geometry pages 300–351

phm07c3_sk_ch07_natl.qxd 8/22/06 5:19 PM Page 79


14.

15.

16. 908 2 408 5 508

17. Complement:

Supplement:

18. Complement: x8 1 778 5 908

Supplement: x8 1 778 5 1808

19. Complement:

Supplement:

20. Complement:

Supplement:

21. Complement: x8 1 6.18 5 908

Supplement: x8 1 6.18 5 1808

22. No; they do not share a common side. 23. No; theyare adjacent. 24-25. Answers may vary. Samples aregiven. 24. /1 and /2 25. /5 and /7 26. Yes; /5 issupplementary to /6. Since m/1 5 m/6, /1 and /5are supplementary angles. 27. Yes; two right angles aresupplementary and have measures of 908. 28. adjacent29. /KBL 30. m/KBL 5 m/RBT 5 1408

31. m/DBK 5 1408 2 648 5 768 32. Vertical angles areopposite each other, while adjacent angles share acommon side; the correct choice is B.33. 1808 2 (608 1 608 1 308) 5 1808 2 1508 5 308; thecorrect choice is A. 34. The percent of snowflakes thatIsabella made can be modeled by the equation 18 5 40x;the correct choice is G.

x8 5 173.98

x8 1 6.18 2 6.18 5 1808 2 6.18

x8 5 83.98

x8 1 6.18 2 6.18 5 908 2 6.18

x8 5 137.78

x8 1 42.38 2 42.38 5 1808 2 42.38

x8 1 42.38 5 1808

x8 5 47.78

x8 1 42.38 2 42.38 5 908 2 42.38

x8 1 42.38 5 908

x8 5 94.18

x8 1 85.98 2 85.98 5 1808 2 85.98

x8 1 85.98 5 1808

x8 5 4.18

x8 1 85.98 2 85.98 5 908 2 85.98

x8 1 85.98 5 908

x8 5 1038

x8 1 778 2 778 5 1808 2 778

x8 5 138

x8 1 778 2 778 5 908 2 778

x8 5 1488

x8 1 328 2 328 5 1808 2 328

x8 1 328 5 1808

x8 5 588

x8 1 328 2 328 5 908 2 328

x8 1 328 5 908

5 618

5 1808 2 (298 1 298 1 618) m/5 5 1808 2 (m/4 1 m/1 1 618)

5 298

5 1198 5 908 2 618

m/2 5 1808 2 618 m/4 5 908 2 m/3 5 298

m/3 5 618 m/1 5 908 2 618

m/4 5 1368

m/4 5 468 1 908

m/4 5 m/1 1 m/2 m/3 5 448

m/2 5 908

m/1 5 468

m/1 1 448 5 908 35. Let r 5 the regular price of the jacket.discount 5 0.30r

7-2 Angles and Parallel Linespages 307–310

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. 120° and 60° 2. 132°3. 61° 4. 113° 5. 49°

Quick Check 1a. alternate interior 1b. corresponding1c. neither 2. m/6 5 m/7 5 m/3 5 1178 3. Themeasure of each angle formed by lines t and < and lines tand m is 908. Since pairs of corresponding angles arecongruent, the lines are parallel.

Exercises 1-2. Answers may vary. Samples are given.

1. /2 and /4 2. /2 and /6 3. 4. /1, /3, /75. False; corresponding angles lie on the same side of atransversal, but alternate interior angles do not.6. alternate interior 7. corresponding 8. neither9. alternate interior 10. neither 11. corresponding12. corresponding 13. neither

14. 15. m/2 5 m/3 5 1228

16. m/6 5 m/3 5 1228 17. m/7 5 m/3 5 1228

18. m/8 5 m/4 5 588 19. m/5 5 m/4 5 588

20. Corresponding angles are congruent. 21. Alternateinterior angles are congruent. 22. Alternate interior anglesare congruent. 23. No; if the two lines were parallel, thenthe corresponding angles would be congruent.

24. m/2 5 1808 2 1388 5 428

m/3 5 m/1 5 1388

25. m is not parallel to / because alternate interiorangles are not congruent. 26. y 6 w becausecorresponding angles are congruent. 27. a i b; 708 and1108 are supplementary and adjacent. Correspondingangles are congruent and alternate interior angles arecongruent. 28. Answers may vary. Sample: Lines t andm are perpendicular, so they form a 908 angle. Since m isparallel to n, lines t and n must also form a 908 angle. So tis perpendicular to n. 29. m/1 5 708; m/2 5 708;m/11 m/3 5 1808; 7081 m/3 5 1808; m/3 5 1108; m/4 5m/3 5 1108 30. They are congruent; they are verticalangles of congruent alternate interior angles. 31a. m/15 808; m/3 5 608; m/2 5 1808 2 (m/1 1 m/3) 5

Not Parallel

m/4 5 588

1228 1 m/4 5 1808

*UV)

$90 5 r 630.70 5 0.70r

0.70

63 5 0.70r 63 5 r 2 0.30r

sale price 5 r 2 discount


1808 2 (808 1 608) 5 408 31b. sum of angles of triangle 5 808 1 608 1 m/2 5 808 1 608 1 408 5 1808

32. Vertical angles are always congruent; the correctchoice is B. 33. 5 5 0.7534.

35. 4 cups 5 1 quart; 3 1 2 1 1 2 1 1 2 5 5 1 1.5 5

6.5 quarts36. 37.

38. 39.


Exercises1.

(2 3 30 1 45)8 5 1058

(3 3 30 1 15)8 5 1058

2.

(2 3 24 1 15)8 5 638

(3 3 24 1 45)8 5 1178

3.

/1 5 (4x 1 5)8

/1 5 (4 3 10 15)8 5 458

4.

(10 3 12 1 15)8 5 1358

5. 1808 2 1358 5 458; sample answer: (165 2 10x)8

7-3 Congruent Polygonspages 312–316

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. equal 2. Not similar;corresponding sides are not in proportion.

Quick Check 1. nTRS > nKJL

x 5 12

726 5 6x

6

72 5 6x 90 2 18 5 6x 1 18 2 18

908 5 (6x 1 18)8

x 5 10

15 2 5 5 x 1 5 2 5

15 5 x 1 5

3x 1 15 2 3x 5 4x 1 5 2 3x

(3x 1 15)8 5 (4x 1 5)8

x 5 24

5x5 5 120

5

5x 5 120

5x 1 60 2 60 5 180 2 60

5x 1 60 5 180

(2x 1 15)8 1 (3x 1 45)8 5 1808

x 5 30

45 2 15 5 x 1 15 2 15

45 5 x 1 15

2x 1 45 2 2x 5 3x 1 15 2 2x

(2x 1 45)8 5 (3x 1 15)8

5 123.38 5 5.04 y 5 0.62 ? 199 y 5 0.14 ? 36

5 31.98 5 12.65 y 5 0.78 ? 41 y 5 0.23 ? 55

34

34

c 5 $13.50

c 5 17(0.50) 1 5

c 5 17t 1 5

34

1824

2a. 2b.

nXYZ > nRQP by SSS nLMJ > nLMK by SAS

3a. m/E 5 m/A 5 408 3b. m/ACB 5 m/ECD 5 508

Exercises 1. Congruent polygons have size and shape incommon. 2. When two polygons are congruent, you cantranslate, reflect, or rotate one so that it fits on top of theother one; true.3. 4.

nABC > nKHG by SAS. nMNO > nSRT by SSS.

5. > ; /EHF > /GHF; > ; /FEH >/HGF; > ; /EFH > /GHF 6. Michael;Corresponding vertices are not listed in the same order,and nEFH > nGHF by SAS, not ASA. 7. PALK >PSNK 8. nBCR > nBYD9. 10.

nXZY > nSCR by SAS. nABC > nDEC by ASA.

11. m/N 5 m/R 5 1048 12. m/T 5 m/L 5 868

13. RM 5 NX 5 0.9 cm 14. ND 5 RC 5 1.6 cm15. m/C 5 m/D 5 628 16. m/M 5 m/X 5 1088

17. XT 5 ML 5 1.4 cm 18. CL 5 DT 5 1.7 cm 19. Using the congruence statement, > . nFGHis the exact image of nPQR after a rotation of 908 aboutpoint R followed by a translation of 5 units to the rightand 1 unit up. Thus, point F is (6, 1). 20. Answers mayvary. Sample: Not congruent; the triangles have two pairsof congruent sides and a pair of congruent angles, butthe angles are not included between the two sides.21. Congruent; > ; /SPR > /TPM; > ;so the triangles are congruent by SAS using verticalangles. 22. Answers may vary. Sample: Similar triangleshave corresponding sides that are in proportion, whilecongruent triangles have corresponding sides that arecongruent.23. No; nABC RnDEF; similar triangles have congruentangles and proportional side lengths, so this means twotriangles with equal angles do not have to be congruent.

24. The angle between Lee St. and the road to Portersquare > the angle between Summit Ave. andWashington Rd.; Lee St. > Summit Ave.; the anglebetween Lee St. and Green St. > the angle betweenSummit Ave. and the road to Porter Square; so thetriangles are congruent by ASA.

FD

E

CA

B

RPMPTPSP

GHQR

/BCA > /ECD Angle ZY > CR Side

BC > EC Side /Z > /C Angle

/B > /E Angle XZ > SC Side

GHEF

FHFHGFEH

OM > TS Side BC > HG Side

NO > RT Side /B > /H Angle MN > SR Side AB > KH Side

KM > JM Side XY > RQ Side /LMK > /LMJ Angle ZX > PR Side

LM > LM Side YZ > QP Side




25. 26. The length of Green St. 5

road from Washington Rd. toPorter Square 5 0.13 km

27. The length of road past Porter Square 5 the lengthWashington Rd. 5 0.22 km; the length of road from PorterSquare to Green St. 5 0.22 2 the length of road fromWashington Rd. to Porter Square 5 0.22 2 0.13 5 0.09 km28. 5 :

z8 5 m/E 5 m/X 5 598; nVWX > nDFE by SAS orASA. 29. University Bookstore: 24.5 2 24.5(0.12) 524.5 2 2.94 5 $21.56; Carson Books: 28 2 28(0.20) 528 2 5.60 5 $22.40; $22.40 2 $21.56 5 $0.84; the correctchoice is A. 30. Point S is located farthest right alongthe x-axis; the correct choice is J. 31. 4 people workingat that rate could pick 4 ? 3, or 12 quarts in 40 minutes.Since they need to pick 15 quarts it will take , or the

time. ? 40 5 5 ? 10 5 50; the correct choice is B.32. 15% 5 0.15 33. 3.72% 5 0.0372 34. 180% 5 1.8035. 0.015% 5 0.00015 36. 0.49% 5 0.0049


1. vertical 2. alternate interior 3. corresponding4. adjacent 5. corresponding 6. adjacent 7. Answersmay vary. Sample: SAS, ASA, or SSS; > ; >

; > ; /D > /B; /K > /T; /J > /W;nJKD > nWTB.8. Complement:

Supplement:

9. Since /N > /K, m/N 5 1008 10. Since /P > /F,m/P 5 908 11. Since /O > /A, m/O 5 1208

12. Since > , 5 0.9 m 13. Since > ,5 1.6 m 14. Since > , 5 1.7 m

7-4 Classifying Triangles andQuadrilaterals pages 318–321

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. 90° 2. acute 3. obtuse

Quick Check 1a. The triangle has two congruent sidesand an obtuse angle; isosceles, obtuse. 1b. The triangle

DNSKDNDOSADOPKFNPK

y8 5 1138

678 2 678 1 y8 5 1808 2 678

678 1 y8 5 1808

x8 5 238

678 2 678 1 x8 5 908 2 678

678 1 x8 5 908

WBJDTW

KJBTDK

54

54

1512

5 10 5 10

5 5(3) 2 5 5 3(3) 1 1

DE 5 5x 2 5 VX 5 3x 1 1

3 5 x 62 5 2x

2

6 5 2x 1 1 5 5 2x 2 5 1 5

1 5 2x 2 5

3x 2 3x 1 1 5 5x 2 3x 2 5

3x 1 1 5 5x 2 5DEVX

has 3 congruent sides; equilateral, acute. 2a. VWXY hasfour right angles; rectangle. 2b. ABCD has exactly onepair of parallel sides; trapezoid.

Exercises 1. A rectangle has four right angles; thecorrect choice is C. 2. A rhombus has four congruentsides; the correct choice is B. 3. A trapezoid has exactlyone pair of parallel sides; the correct choice is D. 4. Asquare has four right angles and four congruent sides;the correct choice is A. 5. None of the sides arecongruent and the triangle contains an obtuse angle; thecorrect choice is B. 6. Two of the sides are congruentand the triangle contains a right angle; the correct choiceis C. 7. Two of the sides are congruent and the trianglecontains an acute angle; the correct choice is A. 8. Thetriangle has 3 congruent sides; equilateral, acute. 9. Thetriangle has an obtuse angle and 2 congruent sides;isosceles, obtuse. 10. The triangle has a right angle andno congruent sides; scalene, right. 11–14. Explanationsmay vary. 11. The quadrilateral has two pairs of parallelsides; parallelogram. 12. The quadrilateral has 4 rightangles; rectangle. 13. The quadrilateral has 4 congruentsides; rhombus. 14. The quadrilateral has 4 right anglesand 4 congruent sides; square. 15. one side: 36 4 3 5 12;perimeter: 12 3 4 5 48; 48 cm

16. 17.

18. 19.

20. Sample answer: right isosceles triangle: nDCJ; rightscalene triangle: nTCR; obtuse scalene triangle: nTKR;acute scalene triangle: nADJ; quadrilateral: ABRD;parallelogram: DRSJ; rectangle: ABGJ; square: CDGJ;trapezoid: TBDC 21. A square has four right angles, likea rectangle, and four congruent sides, like a rhombus.22. Opposite sides of a parallelogram are congruent, sothe fourth vertex must make the opposite side have ahorizontal length of 8 2 3, or 5. (1, 21) 1 (5, 0) 5(6, 21); (1, 21) 2 (5, 0) 5 (24, 21); (6, 21) or (24, 21)23. If a quadrilateral has two pairs of opposite sides thatare parallel, then it is a parallelogram. This statement isstill true. 24. If a rectangle is a square, then it has fourcongruent sides. This statement is still true. 25. If atriangle is an isosceles triangle, then it is an equilateraltriangle. This statement is not true. 26a–c. Answers mayvary. Samples are given.26a. P(4, 3)

4 6R

6

4

2

P

Q2


26b. P(5, 5)

26c. P(2, 6)

27. A trapezoid cannot have four right angles; the correct choice is D. 28. 5 2 5 2 5 2.5; the correct

choice is J. 29. 5 0.6; 5 0.625; 0.58, , , 0.65; the

correct choice is A.

30. 5 5 5 0.1 5 10% decrease

31. 5 5 0. < 63.6% increase

32. 5 < 0.332 < 33.2% decrease

33. 5 5 0.12 < 12.7% increase


1. Properties of Equality

6 � 3(2), so6 � 4 � 3(2) � 4

6 � 3(2), so6 � 4 � 3(2) � 4

Add. Prop.of Eq.

Subtr. Prop.of Eq.

Mult. Prop.of Eq.

4 �

3(4) � 3(

12 � 4(3), so

Div. Prop.of Eq.

, so123

)123

�122

4(3)2

661.5212

u12 2 13.52 u12

3.39.95

9.95 2 6.659.95

63711

u 11 2 18 u11

110

50500

500 2 450500

58

35

58

35

12

36

156

4 6R

6

4

2

P

Q2

4 6R

6

4

2

P

Q2

2.


1. Check students’ work. Sample:

2.

3a. The sum increases by 1808. 3b. The number oftriangles is two fewer than the number of sides.4a. Check students’ work. Sample:

4b. 4c. The sum ofthe exteriorangles of apolygon is 3608.

Numberof Sides

Sum ofAngles

360�

360�

360�

360�

3456

90º90º

90º

90º120º

120º

120º

60º60º

60º

60º

60º60º

72º

72º

72º

72º

72º

Numberof Sides

Number ofTrianglesFormed

12345

Sum ofAll AngleMeasures

180�

360�

540�

720�

900�

34567

Oppositesidesparallel

One pair ofopposite sidesparallel

4 sides

Quadrilateral

4 rt. angles and4 congruent sides

Parallelogram Trapezoid

4 rt. angles 4 congruentsides

Rectangle

Square

Rhombus




7-5 Angles and Polygonspages 324–327

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. You replace eachvariable in the expression with a number and thensimplify. 2. 27 3. 6 4. 36

Quick Check 1. A heptagon has 7 sides.

2. The sum of the interior angles:

Missing angle:

3.

Exercises 1. A regular polygon is a polygon with allsides congruent and all angles congruent. 2. pentagon3. heptagon 4. hexagon 5. octagon 6. Miranda; thesum of the angle measures of a dodecagon is (12 2 2)1808, not (6 2 2)1808 ? 2.7.

8.

9.

10.

11. (n 2 2)1808 5 (3 2 2)1808

12.

13.

14.

15.

16.

1,8008 4 12 5 1508

5 1,8008

(n 2 2)1808 5 (12 2 2)1808

1008 5 x8

9008 5 8008 1 x8

9008 5 1558 1 1168 1 1358 1 1358 1 1168 1 1438 1 x8

5 9008

(n 2 2)1808 5 (7 2 2)1808

1528 5 x8

1,2608 5 1,1088 1 x8

1 1238 1 1298 1 x8

1,2608 5 1358 1 1538 1 1178 1 1628 1 1358 1 1548

5 1,2608

(n 2 2)1808 5 (9 2 2)1808

838 5 x8

5408 5 4578 1 x8

5408 5 1138 1 1288 1 1228 1 948 1 x8

5 5408

(n 2 2)1808 5 (5 2 2)1808

5 1,8008

(n 2 2)1808 5 (12 2 2)1808

5 1808

5 1,4408

(n 2 2)1808 5 (10 2 2)1808

5 7208

(n 2 2)1808 5 (6 2 2)1808

5 1,0808

(n 2 2)1808 5 (8 2 2)1808

5 5408

(n 2 2)1808 5 (5 2 2)1808

5408 4 5 5 1088

5 5408

(n 2 2)1808 5 (5 2 2)1808

1518 5 x8

7208 5 5698 1 x8

7208 5 1428 1 848 1 1238 1 1308 1 908 1 x8

5 7208

(n 2 2)1808 5 (6 2 2)1808

5 9008

(n 2 2)1808 5 (7 2 2)1808

17.

9008 4 7 < 128.68

18.

1,4408 4 10 5 1448

19.

2,1608 4 14 < 154.38

20.

21.

2,8808 4 18 5 1608

22.

23. square24.

25.

26.

738

27. The angles in an irregular polygon are not allcongruent.28.

29.

Let x 5 m/1.

30.

3 sides: 1808 4 3 5 608; angles are multiples of 30. 5 1808

(n 2 2)1808 5 (3 2 2)1808

1358 5 x8

2708 5 2x8

5408 5 2708 1 2x8

5408 5 908 1 908 1 908 1 2x8

5 5408

(n 2 2)1808 5 (5 2 2)1808

1618 5 x8

9008 5 7398 1 x8

9008 5 1458 1 1158 1 1528 1 878 1 908 1 1508 1 x8

5 9008

(n 2 2)1808 5 (7 2 2)1808

(x 1 11)8 5 (86 1 11)8 5 978; (x 2 13)8 5 (86 2 13)8 5

868 5 x8

2588 5 3x8

3608 5 3x8 1 1028

3608 5 x8 1 x8 1 118 1 x8 2 138 1 1048

3608 5 x8 1 (x 1 11)8 1 (x 2 13)8 1 1048

5 3608

(n 2 2)1808 5 (4 2 2)1808

1058 5 a8

5408 5 4358 1 a8

5408 5 958 1 1248 1 1068 1 1108 1 a8

5 1068

b8 5 1808 2 748

5 5408

(n 2 2)1808 5 (5 2 2)1808

1358 5 n8

5408 5 4n8

7208 5 1808 1 4n8

7208 5 908 1 908 1 4n8

5 7208

(n 2 2)1808 5 (6 2 2)1808

n 5 16 sides

22.58n22.58 5 3608

22.58

22.58n 5 3608

1808n 2 157.58n 5 157.58n 1 3608 2 157.58n

1808n 5 157.58n 1 3608

1808n 2 3608 1 3608 5 157.58n 1 3608

1808n 2 3608 5 157.58n

(n 2 2)1808 5 157.58n

5 2,8808

(n 2 2)1808 5 (18 2 2)1808

2,3408 4 15 5 1568

5 2,3408

(n 2 2)1808 5 (15 2 2)1808

5 2,1608

(n 2 2)1808 5 (14 2 2)1808

5 1,4408

(n 2 2)1808 5 (10 2 2)1808

5 9008

(n 2 2)1808 5 (7 2 2)1808


4 sides:

3608 4 4 5 908; angles are multiples of 30.5 sides:

5408 4 5 5 1088; angles are NOT multiples of 30.6 sides:

7208 4 6 5 1208; angles are multiples of 30.8 sides:

1,0808 4 8 5 1358; angles are NOT multiples of 30.So, 3, 4, and 6 sided polygons have angles that aremultiples of 30:

P 5 5

or 60%31. 338 1 668 1 818 5 1808; m/A , m/B , m/C ,

908; the correct choice is B. 32. < 16.6; the correct choice is J. 33. 5 2 4 15,978 5 0.00013 ? 100 50.013; the correct choice is D.34. 35.

36. 37.

7-6 Areas of Polygons pages 328–332

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. A formula is a rule thatshows the relationship between two or more quantities.2. 80 cm2 3. 49 ft2

Quick Check 1.

More Than One Way Methods and explanations mayvary. Sample: I can subtract the area of the smaller unshaded triangle from the larger triangle to find thearea of the shaded region.

Big triangle:

Small triangle:

Area of shaded regions:

Exercises 1. Feet is a linear measure and cannot beused to express area; the correct choice is C.2. parallelogram 3. triangle 4. trapezoid

60 2 15 5 45, or 45 cm2

A 5 15

A 5 12 ? 5 ? 6

A 5 12bh

A 5 60

A 5 12 ? 10 ? 12

A 5 12bh

5 15 yd2 5 10.5 cm2

5 12(3)(3 1 7) 5 1

2 ? 7 ? 3

A 5 12h(b1 1 b2) A 5 1

2bh

x8 5 278 x8 5 538

1538 1 x8 5 1808 1278 1 x8 5 1808

x8 5 1328 x8 5 1158

488 1 x8 5 1808 658 1 x8 5 1808

215,978

!275

35

number of polygons with angle measures that are multiples of 30number of polygons

5 1,0808

(n 2 2)1808 5 (8 2 2)1808

5 7208

(n 2 2)1808 5 (6 2 2)1808

5 5408

(n 2 2)1808 5 (5 2 2)1808

5 3608

(n 2 2)1808 5 (4 2 2)1808 5. 6. 7.

8. 9.

10. 11.

12.

A 5 < 3 w 5 15 3 12 5 180; 180 yd2

13. Parking space area:

Area of spaces 5 8 ? 135 5 1,080


15. Area of a rectangle 5 < 3 w 5 8 3 5 5 40 m2

Area of a triangle 5 1 2bh 5 1 2(3)(4) 5 6 m2

Area of the shaded area 5 40 2 6 5 34 m2

16. Area of a square 5 s2 5 32 5 9 in.2

Area of one of the smaller squares 5 12 5 1 in.2

Area of the shaded region 5 9 2 4(1) 5 5 in.2

17. Area of a square 5 s25 182 5 324 cm2

Area of a triangle 5 1 2bh 5 1 2(18)(18) 5 162 cm2

Area of the shaded region 5 324 2 162 5 162 cm2

18a.

18b. c 5 < 4.3; do not round down because at least4.3 cases are needed, so round up to 5; 5 cases of tiles

18944

5 189 ft2 5 8 1 144 1 10 1 27

A 5 (2)(4) 1 (12)(8 1 4) 1 12(4)(5) 1 1

2(3)(10 1 8)

12

12

12

12

6

4

8

3

5 120 ft2 5 1,200 2 1,080

Unpaved section 5 total area 2 area of spaces

5 1,200

5 (15 1 15)(40)

Total area 5 bh 5 135 ft2 5 (9)(15)

A 5 bh

w 5 12

242 5 2w

2

24 5 2w 54 2 30 5 30 1 2w 2 30

54 5 30 1 2w 54 5 2(15) 1 2w P 5 2/ 1 2w

5 18 m2 5 52.5 ft2

5 12(4)(6 1 3) 5 1

2(5)(17 1 4)

A 5 12h(b1 1 b2) A 5 1

2h(b1 1 b2)

5 84 m2 5 165 mm2

5 12(6)(13 1 15) 5 1

2 ? 22 ? 15

A 5 12h(b1 1 b2) A 5 1

2bh

5 96 m2 5 20 in.2 5 50 cm2

5 12 ? 20 ? 9.6 5 1

2 ? 8 ? 5 5 (10)(5)

A 5 12bh A 5 1

2bh A 5 bh




18c. cost 5 39.16 ? 5 5 $195.80 19. Answers may vary.Sample: about 81,000 km2 20. A parallelogram can berearranged to form a rectangle, so both figures use theformula A 5 bh for area. 21. s ? s 5 s2; the area of a triangle is bh so the area is ? s ? s 5 s2; divide the

areas to find the ratio: 5 ; 1 : 2 22. 966 4 42 5 23;

the correct choice is A. 23. 2(16) oz 1 32 oz 1 3 c 1

c 1 5 c 5 1 1 3.5 1 0.5 1 5 5 4 1 4 1 3.5 1

0.5 1 5 5 17 c; 5 4.25 qt; Since you need to hold all

the ingredients with no overflow, you have to round up,

so the correct choice is G. 24. (n 2 2)1808 5

(3 2 2)1808 5 1808 25. (n 2 2)1808 5 (8 2 2)1808 5

1,0808 26. (n 2 2)1808 5 (16 2 2)1808 5 2,5208

27. (n 2 2)1808 5 (25 2 2)1808 5 4,1408


1. You can separate the pendant into four right trianglesand two trapezoids along the second, third, and fourth columns of pegs. 2. No; the sides are being reduced by ,

so, since the area is equal to s2, the area is reduced by ? , or , so the cost would be one fourth of $100.

3. 100 4 8 5 12.5 < 13 pendants 4. Area of the square5 42 5 16 in2; Subtract the unit squares and fractions ofsquares from the total area to find the area of the Ypendant: A 5 16 2 1 2(2)(1) 2 1 2(2)(4) 2 ( )(3)(1) 2 3.5 516 2 1 2 4 2 1.5 2 3.5 5 16 2 10 5 6 in.2

Y Team’s cost 5 6(0.75)($1.25)(10) 5 $56.25Subtract the unit squares and fractions of squares fromthe total area to find the area of the Z pendant:A 5 16 2 21 2(2)(3) 5 16 2 6 5 10 in2

Z Team’s cost 5 10(0.5)(1.25)(12) 5 $755. Area of the circle 5 22p < 12.6; Subtract the unitsquares and fractions of squares from the total area tofind the area of the shape: A 5 16 2 1 2(4) 5 14Difference of Area 5 14 2 12.6 5 about 1.4 in.2

6. 1 ton 5 2,000 lb25 ton 5 2,000 3 25 5 50,000 lb1 lb 5 900 mi long wire900 3 50,000 5 45,000,000 mi long wire45,000,000 4 25,000 5 1,800; about 1,800 times


1. parallelogram;

2. obtuse isosceles triangle;

3. trapezoid;

5 43.35 m2 5 1

2(5.1)(6.8 1 10.2)

A 5 12h(b1 1 b2)

5 1.7 in.2 5 1

2(2)(1.7)

A 5 12bh

5 100.86 cm2 5 12.3 ? 8.2

A 5 bh

12

12

12

12

12

14

12

12

12

174

328

2(16)8

12

12

12

12s2

s2

12

12

12

4.

5. Answers may vary. 6. Answers may vary.Sample: Sample:


1–2. Check students’ work. 3a. Answer may vary.Sample: the parallelogram has a height equal to thelength of one slice of pizza, which is the radius of the circle, or 4 in. Each side is made up of the crusts of 4, or

of the total pizza so the length of one side is equal to of the circumference of the circle. C 5 2pr 5 2(4)p 5 8p,so C 5 (8p) 5 4p; A 5 b ? h 5 4p ? 4 5 16p < 50 in.2;this area represents the area of a circle. 3b. Since A 5

4 ? 4 ? p and 4 is the length of the radius, A 5 r ? r ? p5 pr2.

7-7 Circumference and Area of aCircle pages 336–339

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Perimeter is thedistance around a figure. Area is the number of squareunits a figure encloses. 2. 45.5 ft2

Quick Check 1. C 5 pd 5 p(25) < 78.5 in.; A 5 pr2 5

p1 22 5 490.9 in.2 2. rectangle: A 5 bh 5 19.8 ? 13.2 5261.36; half circle: A 5 pr2 5 p(6.6)2 < 68.4; shaded area: A 5 261.36 2 68.4 < 193.0 m2

Exercises 1. The perimeter of a circle is called thecircumference. 2. Separate the figure into a rectangleand half a circle. 3. C 5 pd 5 p(2r) 5 2pr

4. C 5 pd 5. C 5 2pr

5 ? 21 5 ? 2(7)

5 ? 3 5 ? 2(1)

5 66 cm 5 44 km

6. C 5 2pr 7. C 5 pd

5 ? 2(3.5) 5 ? 28

5 ? 1 5 ? 4

5 22 m 5 88 in.8. 9.

< 113.1 m2 < 19.6 cm2 5 p(36)

5 pA52B2 5 pA12

2 B2 A 5 pr2 A 5 pr2

< 15.7 cm < 37.7 m

5 p(5) 5 p(12)

C 5 pd C 5 pd

221

221

227

227

221

221

227

227

12

12

252

12

12

12

12

x8 5 1338

5878 1 x8 5 7208

1438 1 1098 1 1248 1 1108 1 1018 1 x8 5 7208

5 7208

5 (6 2 2)1808

sum of interior angles 5 (n 2 2)1808


10. 11.

12. 13.

14. 15.

16. 17. triangle:

half circle:

shaded area 5 16 1 6.3

18. rectangle: 19. rectangle:

2 quarter circles:

half circle:

shaded area 5 19.22 2 15.1shaded area 5 900 1 353.4

20. rectangle: 21. circle:

2 half circles: triangle:

shaded area 5 153.9 2 49

22. square:

circle:

5 29.89 < 29.9 ft2shaded area 5 139.242109.35

< 109.35

5 p A 11.82 B 2

A 5 pr2 5 139.24

5 (11.8)2 A 5 s2

5 104.9 in.2 5 26.6 yd2shaded area 5 14 1 12.6

5 49 < 12.6

5 12(14)(7) 5 p A 4

2 B 2

A 5 12bh A 5 pr2

< 153.9 5 14

5 p(7)2 5 (3.5)(4)

A 5 pr2 A 5 bh

5 1,253.4 ft25 4.12 < 4.1 m2

< 353.4

5 12p A

302 B 2 < 15.1

A 5 12pr2 5 1

2p(3.1)2

5 900 A 5 12pr2

5 (45)(20) 5 19.22

A 5 bh A 5 bh

5 22.3 ft2

< 6.3 < 32.2 ft2

5 12p A

42 B 2 5 pA6.4

2 B2 A 5 1

2pr2 A 5 pr2 5 16 < 20.1 ft

5 12(4)(8) 5 p(6.4)

A 5 12bh C 5 pd

< 346.4 cm2 < 51.5 yd2

5 p(10.5)2 5 pA8.12 B

A 5 pr2 A 5 pr2 < 66.0 cm < 25.4 yd

5 p(10.5 ? 2) 5 p(8.1)

C 5 pd C 5 pd

< 973.1 mm2 < 63.6 cm2 5 p(17.6)2 5 p(4.5)2

A 5 pr2 A 5 pr2 < 110.6 mm < 28.3 cm

5 p(2 ? 17.6) 5 p(4.5 ? 2)

C 5 pd C 5 pd

< 615.8 yd2 5 pA9.2

2 B2 5 p(14)2 A 5 pr2 A 5 pr2

< 28.9 in. < 88.0 yd

5 p(9.2) 5 p(14 ? 2)

C 5 pd C 5 pd 23. Subtract the area of the smaller circle from the areaof the larger circle.larger circle: smaller circle:

area of ring 5 79 2 13 5 66 cm2

24. area of large half circle: area of small half circle:

two small rectangles: large rectangle:

area of 2 small rectangles: area of large rectangle:

area of purple shaded region:

25. area of circle: area of square:

A circle with a diameter of 2 in. has an area of 3.14 in.2,while a square with a side length of 2 in. has an area of 4 in.2. The square has a greater area than the circle.26. 27.

r 5 5 5 3.56 cm r 5 5 5 0.27 in.28. 29.

r 5 5 < 8.11 ft r 5 5 5 10.00 m30.

31. Area of Pizza: p(7)2 5 153.9 in.2

Area of Crust: 153.9 2 p(6)2 5 153.86 2 113.04 <40.8 in2

32a.

Large circle: small circle: A 5 pr2

The ratio of their areas is 9 : 1.32b. The area of a circle is pr2 so the ratio of areas withradii a and b is a2 : b2.

5 p(9r2) 5 9pr2 5 p(3r)2

A 5 pR2 A 5 pr2 R 5 3r

< 315.8 ft2 5 p(10.0268)2

A 5 pr2 10.0268 < r

632p < 2pr

2p

63 5 2pr C 5 2pr

20.002

d2

16.212

d2

20.00 m < d 16.21 ft < d

62.83 5 pd 50.94 5 pd

C 5 pd C 5 pd

0.542

d2

7.112

d2

0.54 in. < d 7.11 cm < d;

1.71 5 pd 22.35 5 pd C 5 pd C 5 pd

5 4 in.2 < 3.14 in.2

5 22 5 p A 22 B 2

A 5 s2 A 5 pr2

< 535.5 ft2 A 5 (612.7 1 144.375) 2 (56.5 1 165)

5 165 5 144.375 5 (13.75)(12) 5 2(5.25)(13.75)

A 5 bh A 5 2bh

5 19.75 2 6 5 13.75

b 5 39.52 2 6 h 5 39.5 2 12

2

< 56.5 < 612.7

5 12p(6)2 5 1

2p A39.5

2 B 2

A 5 12pr2 A 5 1

2pr2

< 13 < 79

5 4p 5 25p

5 p(2)2 5 p(2 1 3)2 A 5 pr2 A 5 pr2


< 66.5 in2



33.

34. Find the area of the circle: A 5 pr2 5 p(8)2 5

200.96; find the percent of the area that the shaded region represents: 5 64 4 200.96 5 0.318 3 100 531.8%35.

36. Subtract the sum of 120 and 30 from 180; the correctchoice is J. 37. 25 2 (6 3 5) 5 25 2 30 5 25; thecorrect choice is C. 38. $28.55 < $30; 30 ? 0.10 5 3;3 4 2 5 1.5; 3 1 1.5 5 4.5; $4.50 39. $64.82 < $64;64 ? 0.10 5 6.4; 6.4 4 2 5 3.2; 6.4 1 3.2 5 9.6; $9.6040. $13.97 < $14; 14 ? 0.10 5 1.4; 1.4 4 2 5 0.7;1.4 1 0.7 5 2.1; $2.10 41. $108.16 < $110; 110 ? 0.10 511; 11 4 2 5 5.5; 11 1 5.5 5 16.5; $16.50

EXTENTION page 340

1. , , , 2. , , , 3. ,, , , 4. , , , , , ,, , 5. , , or 6. , ,

, , , , , ,7. A diameter has both endpoints on a circle so, yes, adiameter is a chord, whereas a radius has only oneendpoint, so, no, a radius is not a chord. 8. C 5 pd 5

p8 5 4p

7-8 Constructions pages 341–343

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Congruent polygonshave the same size and shape. 2. /P > /T; /Q > /U;/R > /V; > ; > ; > 3. /A >/L; /B > /M; /C > /N; /D > /O; > ; >

; > ; >Quick Check 1.

2. d e

F

N

OLDANOCDMN

BCLMAB

VTRPUVQRTUPQ

12

12

FCE1

FCD1

EFD1

EFC1

DFC1

CDB1

CDF1 BCF

1BCE1

BED1

BFD1

BCD1

FC0

EB0

DF0 CE

0FB0

EF0

DE0

CD0

BC 0

HDWEDEBS

WHMTMNVNAVIJHKGHGK

d 5 785p < 250 ft; the correct choice is D.

785 5 pd

C 5 pd

64200.96

12 ft 5 r 144 5 r2 432 5 3r2

A 5 pr2 Exercises 1. A compass is a tool used to draw circlesand arcs. 2. No; the construction copies the anglewithout measuring it. 3. Place the compass tip at A anddraw an arc that intersects the sides of /A. Label thepoints of intersection C and D. 4. Parallel lines areformed by constructing corresponding angles; thecorrect choice is B.

5. 6.

7. 8.

9.

10. To construct /E congruent to /A, first draw a raywith endpoint E. Then adjust the compass width to thedistance between B and C. Now draw an arc thatintersects both sides of /A. The only unnecessary step isto adjust the compass width to the distance between Aand B; the correct choice is D. 11. First construct twoparallel lines. Then connect the parallel lines with twosegments that are not parallel. 12. Check students’ work.13.

14. Add the area of the 4 semicircles to the area of thesquare: 4( p12) 1 2(2) 5 2p 12(2); the correct choiceis J.15.

16. P(M, A, T, or H) 5 5 5

17. P(a letter before I) 5 5 5

18. P(a letter after Q) 5 5 926

sections with letters after Qtotal sections on spinner

413

826

sections with letters before Itotal sections on spinner

213

426

sections with M, A, T, or Htotal sections on spinner

n 5 96; the correct choice is B.

1922 5 2n

2

192 5 2n

262 2 70 5 70 1 2n 2 70

262 5 70 1 2n

c 5 70 1 2n

12

b 5 30 in.; the correct choice is C.

39013 5 13b

13

390 5 13b

390 5 A12B(26)b

A 5 12bh

a c

b

R

C



1. Check students’ work. Sample:

2a. Check students’ work. Sample:

2b. isosceles3a. Check students’ work. Sample:

3b. rhombus


1. The distance from K to Lis 4 times the distance fromJ to K so LK 5 4JK. Thedistance from J to L is 36yards more than 3 times thedistance from J to K so JL 5 36 1 3JK. Use substitution to solve for JK:

2. Opposite sides of arectangle are parallel and adjacent sides areperpendicular, so thecoordinates of I are (7, 6).Since the rectangle isreflected over x-axis the x-coordinates remainpositive and the y-coordinates will becomenegative, so the newcoordinates are (7, 26);the correct choice is J.

2

2 4 6

4

6

G

H

y

x

F

I

-6

-4

-2

JK 5 18; the correct choice is B.

2JK2 5 36

2

2JK 5 36

4JK 2 2JK 5 36 1 2JK 2 2JK

4JK 5 36 1 2JK

LK 5 36 1 2JK

LK 1 JK 2 JK 5 36 1 3JK 2 JK

LK 1 JK 5 36 1 3JK

JL 5 LK 1 JK

J K L

JK

36 + 3JK

4JK

A BC

D

A B

C

D

B

A

C

D

3. Julie climbed 28 yards less than twice the heightLogan climbed so J 5 2L 2 28. They climbed a total of95 yards so J 1 L 5 95. Use substitution to solve for L:


1. A transversal intersects two lines at different points.2. A triangle with no congruent sides is scalene.3. The measures of supplementary angles add up to 1808.4. A rhombus has four congruent sides. 5. All the sidesand angles of a regular polygon are congruent.6. 7.

8. isosceles, acute 9. scalene, obtuse 10. equilateral,acute11. Side

Angle

12. SideSide

13.

14.

1,0808 4 8 5 1358

15.

16.

17. 18. 19.

< 124.7 cm2 5 24 cm2 5 540 ft2

5 p(6.3)2 5 12(8)(6) 5 (30)(18)

A 5 pr2 A 5 12bh A 5 bh

2,8808 4 18 5 1608

5 2,8808

(n 2 2)1808 5 (18 2 2)1808

1,8008 4 12 5 1508

5 1,8008

(n 2 2)1808 5 (12 2 2)1808

5 1,0808

(n 2 2)1808 5 (8 2 2)1808

7208 4 6 5 1208

5 7208

(n 2 2)1808 5 (6 2 2)1808

KJ > NO Side; nJLK > nOMN; SSS

LK > MN JL > OM CD > HG Side; nCDE > nHGF; SAS

/D > /GED > FG

m/1 5 488 m/1 5 358

m/1 1 1328 5 1808 m/1 1 558 5 908

m/1 1 m/2 5 1808 m/1 1 m/2 5 908

m/2 5 1328 m/2 5 558

L 5 41 yd; the correct choice is A.

54 1 L 2 54 5 96 2 54

54 1 L 5 96

J 1 L 5 95

J 5 54 yd

3J3 5 162

3

3J 5 162

J 1 2J 5 162 2 2J 1 2J

J 5 190 2 2J 2 28

J 5 2(95 2 J) 2 28

L 5 95 2 J

L J




20. 21.


1. alternate interior 2. none of these 3. corresponding4. adjacent 5. none of these 6. vertical7.

8. Let x 5 the 9. Let y 5 the supplement of /D. complement of /D.

10. False; the sum of the measures of an obtuse angleand a right angle is greater than 1808. 11. True; a scalenetriangle can be acute, right, or obtuse. 12. True; a squareis a rhombus with four right angles. 13. scalene obtusetriangle; there are no congruent sides and there is oneobtuse angle. 14. rhombus; the four sides are congruentbut there are no right angles. 15. A rectangle has fourright angles. A parallelogram need not have four rightangles.16.

17. not congruent; SS is not a way to prove congruence.18. Side

AngleSide

nPRQ > nSRT by SAS

19–22. Answers vary. Samples are given.

19. 20.

21. 22.

23.

24.

25. 5 2,3408

(n 2 2)1808 5 (15 2 2)1808

5 9008

(n 2 2)1808 5 (7 2 2)1808

5 3608

(n 2 2)1808 5 (4 2 2)1808

RQ > RT /PRQ > /SRT

PR > SR

5408 4 5 5 1088

5 5408

(n 2 2)1808 5 (5 2 2)1808

y8 5 228 x8 5 1128

688 1 y8 5 908 688 1 x8 5 1808

/D 1 y8 5 908 /D 1 x8 5 1808

5 308 5 1508

m/4 5 m/2 m/5 5 m/3

5 308 5 1508

5 1808 2 1508 m/3 5 m/1

m/2 5 1808 2 m/1 m/1 5 1508

a b

P

T

26. 27.

28.

29.

TEST PREP pages 349

1. 112 5 121 and 122 5 144, so lies between 11and 12; the correct choice is C. 2. The ratio of pages shereads in time1 compared to the pages she reads in time2is proportional to the ratio of time1 compared to time2;

5 ; the correct choice is H. 3. 3 % 5 5 ;the correct choice is C.4.

; the correct choice is G.

5. 53 ? 52 5 5(3 + 2) 5 55; the correct choice is A.6. Angles 2 and 4 are angles of the same measurecreated by parallel lines intersecting one line; the correctchoice is J.7. Let p 5 the pay for 40 hours.

; the correct choice is B.8. F: 2(x 1 5) 5 2(x) 1 2(5); G: 2(x 1 5) 5 2(5 1 x);H: 2(x 1 5) 5 (x 1 5) 1 (x 1 5); J: 2(x 1 5) 2 5 1 2x;the correct choice is J. 9. The original point would be 6units right and 2 units down. (23 1 6, 22 2 2) 5 (3,24); the correct choice is D. 10. Draw a ray withendpoint E; the correct choice is G. 11. 3 : 2 5 9 : 6;9 1 6 5 15, so the painter needs 9 gallons of blue paint.12. [2] Use the Pythagorean theorem to find thedistance of the shortcut: c2 5 a2 1 b2 5 302 1 402 5

900 1 1600 5 2500; 5 50 m. Walking along the"2500

p 5 256

25p25 5 6400

25

25p 5 6400

16025 5

p40

C 5 12p

C 5 2p6

C 5 2pr

6 5 r

"36 5 #r2

36 5 r2

36pp 5 pr2

p

36p 5 pr2 A 5 pr2

7200

312

10012

12x

418

"135

H

G

< 176.7 cm2

5 p A 152 B 2 < 47.1 cm

5 p A d2 B 2 5 p(15)

A 5 pr2 C 5 pd

5 27 cm2 5 48 in.2 5 1

2(9)(6) 5 (6)(8)

A 5 12bh A 5 bh



sides would take him 30 1 40, or 70 m. He saves 70 2 50,or 20 meters by taking the shortcut. [1] minorcomputational error OR correct answer without workshown 13a-b. [4] They start off doing 6 pushups. Thenthey had to add 2(c 21) pushups for every class with cbeing what number class it is. p 5 6 1 2(c 2 1); p 5

6 1 2(9 2 1) 5 6 1 2(8) 5 6 1 16 5 22; [3] one minorcomputational error; [2] two minor computationalerrors; [1] correct answers without work shown


1. Drawing not to scale.

Green Boat (1): hypotenuse x 5 5 1 miles

Red Boat (2): hypotenuse y 5 5 1 mile

Blue Boat (3): hypotenuse z 5 5 mile

2. Since > , > , and > , nADC >nADB by SSS. 3a. m/BAC 5 908; m/ACD 5 458;m/CBA 5 458; m/BAD 5 458; m/CAD 5 458;m/CDA 5 908; m/BDA 5 908; the measures of theangles of each triangle are 458, 458, and 908. 3b. 458,458, and 908; when two legs of a right triangle arecongruent, the vertex of the two congruent sides must bethe 908 angle. The remaining angles are congruent,meaning each one must be half of (180 2 90)8, or 458.4a. > because nADC is an isosceles right ADDC

ADADCDBDACAB

34

34

33

12

32

xy

Boat 1 Boat 2 Boat 3

triangle. So AD 5 100 yd. 4b. Since nABC is anisosceles right triangle, AB 5 AC. So:

AC < 7.07 miles.5a. Boat 1: Let / 5 the length of a leg of 1 right triangle.

Boat 2: Let m 5 the length of a leg of 1 right triangle.

Boat 3: Let n 5 the length of a leg of 1 right triangle.

all threeboats follow the same length course.5b. The course will be about 4.24 mi no matter how manytimes the boat tacks. So if it tacks 10 times, the course will be 4.24 mi. 6. Answers may vary. Sample: Sailorsmay tack to avoid obstacles and other boats, but mightotherwise want to tack less because they lose some speedwith each tack.

5 8"0.28125 < 4.24 mi;

length of course 5 8n n 5 "0.28125

n2 5 0.28125

2n2 5 0.5625

2n2 5 (0.75)2

5 6"0.5 < 4.24 mi

length of course 5 6m m 5 "0.5

m2 5 0.5

2m2 5 1

2m2 5 (1)2

5 4"1.125 < 4.24 mi

length of course 5 4 ? / / 5 "1.125

/2 5 1.125

2/2 5 2.25

2/2 5 (1.5)2

7.07 < AC "50 5 AC

50 5 AC2 100 5 2AC2 100 5 AC2 1 AC2

BC2 5 AB2 1 AC2




1. A 5 pr2 5 p(1.5)2 5 2.25p < 7 ft2 2. A 5 pr2 5

p(2)2 5 4p< 13 m2 3. A 5 bh 5 12 ? 8 5 96 cm2 4. A 5

bh 5 ? 12 ? 9 5 54 mm2 5. A 5 bh 5 ? 8 ? 5 5

20 in.2 6. A 5 h(b1 1 b2) 5 ? 4(8 1 3) 5 22 cm2

7. 8.

9. 10.30h 5 360

h 5 12

8-1 Solids pages 354–357

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Congruent triangleshave the same shape and size. 2. scalene triangle3. parallelogram

Quick Check 1. The figure has two congruent parallelbases, so it is a prism. Prisms are named for the shape of

their bases, so this figure is a pentagonal prism. is alateral edge. Points J and K are vertices of the prism.2. The figures have two congruent parallel bases, so it isa prism. Prisms are named for the shape of their bases,so one figure is a trapezoidal prism and the other is a

rectangular prism. 3. Answers may vary. Sample:

and are intersecting line segments; they are not skewline segments because skew line segments do notintersect and do not lie in the same plane.

Exercises 1. Parallel lines lie in the same plane; skewlines do not. 2. Triangles, because the bases have threeedges. 3. Triangular, because prisms are definedthrough their two congruent parallel bases. 4. Lateral

edge, because is a line segment in the prism.5. Cylinder, because pencil contains two circular basesthat are parallel and congruent. 6. The base is circular.

The figure is a cone. is a radius of the base. 7. Thefigure has a square base. The figure is a square pyramid.

is a lateral edge. 8. The two bases are circles. The

figure is a cylinder. is a radius. 9. 3 rectangularprisms, 2 cylinders, and a triangular prism 10–12.

Answers may vary. Samples are given. 10. and

are skew line segments. and are parallel line

segments. 11. and are skew line segments.

and are parallel line segments. 12. and are

skew line segments. and are parallel lineKPLR

STJLEF

GDFHDE

HGDC

CGAD

PQ

PQ

PQ

CF

BC

AB

JK

b 5 2.5

26b 5 65

10h 5 30

36 265 5 13

b

a 5 7 x 5 3

27a 5 189 20x 5 60

a9 5 2127 x4 5 15

20

12

12

12

12

12

12

segments. 13. rectangular pyramid 12. triangular prism14. intersecting 15. skew 16. parallel 17. Checkstudents’ work. 18. Yes; Kenji is right in that there are 2parallel, congruent trapezoidal bases, and the lateralfaces are parallelograms. Esther is also right in that avertical cut could separate the figure into a rectangularprism and a triangular prism. 19. triangular prism 20. Answers may vary. Sample: The solid could bebroken down into one triangular prism, one rectangularprism, and one trapezoidal prism.21. A 5 / 3 w

336 5 28/

12 5 /; the correct choice is A.22. To find how many more barrels of oil the UnitedStates consumes than China and Japan consume, subtractthe number of barrels China and Japan consumes fromthe number of barrels the United States consume.Change mixed fractions into improper fractions: 20 5

; 6 5 ; 5 5 . Change the improper fractions so all three fractions have a common denominator: 5

5 ; 5 5 ; 5 5 .Subtract China’s and Japan’s oil consumption fromUnited States’ oil consumption: 2 ( 1 ) 5

2 5 5 5 8 ; the correct choice is J.

23. A trapezoid does not have four congruent sides, sochoice A is wrong. The formula for the area ofparallelogram is A 5 bh. Choice C is wrong becausethere are no right angles so the interior angles cannot bethe same. Choice D is wrong because the diagonal of aparallelogram divides the shape into two triangles. Thecorrect choice is B. 24. 15% of 506 <15% ? 500 5 75 25. 60% of 38 < 60% ? 40 5 2426. 94% of 440 < 95% ? 440 < 420

8-2 Drawing Views of Three-Dimensional Figures

pages 358–361

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. parallelograms2. rectangular prisms

Quick Check

1. 2.

Topview

Frontview

Rightview

2 221

1 Right

Front

35

8610

205211910

11910

20510

5410

6510

20510

5410

27 3 25 3 2

275

6510

13 3 52 3 5

132

20510

41 3 52 3 5

412

275

25

132

12

412

12

33628 5 28/

28

Chapter

8Measurement pages 352–409



3.

Exercises 1. An isometric view allows you to see the top,front, and right sides of an object in the same drawing.2. 8 grids because the front has 4 units and the right has2 units so the base is 4 by 2 units squared: 4 3 2 5 8.3. The bottom layer of the figure is a rectangle.4. 5. 6. 7.

8.

9.

10.


1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 3 3 3 3 3 3 3 3 3 3 3 3 3 2 1 1 2 3 4 4 4 4 4 4 4 4 4 4 4 3 2 1 1 2 3 4 5 5 5 5 5 5 5 5 5 4 3 2 1 1 2 3 4 5 6 6 6 6 6 6 6 5 4 3 2 1 1 2 3 4 5 6 7 7 7 7 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 8 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 8 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 7 7 7 7 6 5 4 3 2 1 1 2 3 4 5 6 6 6 6 6 6 6 5 4 3 2 1 1 2 3 4 5 5 5 5 5 5 5 5 5 4 3 2 1 1 2 3 4 4 4 4 4 4 4 4 4 4 4 3 2 1 1 2 3 3 3 3 3 3 3 3 3 3 3 3 3 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 2 2 2 1

1 1 1 1 1 1 2 2 2 1 1 2 3 2 1 1

11

1111

11

1111

1

Topview

Frontview

Rightview

Top view Front view Right view


22

2 1 11 1 1

2 2

1 1111

11 1 1 1

11

Topview

Frontview

Rightview

12. 13.

14.

15.

16. A plane that cuts parallel to the bases will make acircle. A plane that cuts perpendicular to the bases willmake a rectangle. 17. Cone; as the triangle is rotated3608 around the line of rotation, it forms a circular baseand it comes to a point at the other end forming a cone.18. Cylinder; as the rectangle is rotated 3608 around theline of rotation, it forms two circular bases generating acylinder. 19. 6, 8; 6, 8, 10

20. The top is almost a 3 by 3 square, which has a squaremissing from the bottom left and the right view have 3squares going up. The top and right views match the firstfigure; the correct choice is A. 21. House A sold for

5 187,000 4 2,200 5 $85 per square foot;

House B sold for 5 144,000 4 1,800 5 $80 per

square foot; the correct choice is F. 22. A 5 pr2 5

p(6.4)2 < 128.7 m2 23. A 5 pr2 5 p(1.95)2 <

11.9 in.2 24. A 5 pr2 5 p(83.5)2 < 21,904 cm2


1. 2.

3. 4.

p(1672 )2 5

p(3.92 )2 5

$144,000

1,800 ft2

$187,000

2,200 ft

2

8 Sides6 Sides 6 Sides 8 Sides 10 Sides

Top view Front view

2 23 3 2 2 Right

Front

21

2 2 2 3Right

Front

111 1

1 1 1 1

1 11 1 1 1

11

Right

Front



5. Check students’ work. 6–11. Answers may vary.Samples are given.6. 7.

8. 9.

10. 11.


Activity 1. Rectangular prism; the solid pattern forms arectangular prism. 2. Rectangles; the shapes that makeup its lateral faces and bases are all rectangles.

Exercises 1. Triangular prism; its two bases are trianglesand the three lateral sides are rectangles which makesup a triangular prism. 2. Cube; it has six equal squaresides making up a cube. 3. Square pyramid; its base is asquare with four triangles coming to a point making up asquare pyramid. 4. Check students’ work. 5. Cylinder;this pattern has two circles as the bases and a rectangleto connect the bases, this forms a cylinder. 6. Rectangle;its entire lateral surface makes up a rectangle.7. Triangles; the four faces of the solid make up triangles.8. Check students’ work.

8-3 Nets and Three DimensionalFigures pages 364–366

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. isometric 2.

Quick Check 1. Six congruent squares, there are manypossible arrangements. 2. The faces are triangles, so it isa pyramid. The base is a pentagon, so it is a pentagonalpyramid.

Exercises 1. A net is a two-dimensional pattern; a prismis a three-dimensional solid. 2. 2 trapezoids, 4 rectangles

3. The net of a cylinder will always include two circles.4. The correct choice is B. 5. The correct choice is C.6. The correct choice is A. 7. The base is a circle andthe lateral surface will come to a point so it is a cone.8. The base is a square, the four faces are triangles thatwill come up to make a point, so it is a square pyramid.9. The base is a square and two of the sides aretrapezoids, so it is a trapezoidal prism.10. The solid is a

rectangular prism.All 6 of its faces arerectangles.

11. The triangular prism will have two triangular facesand three rectangular faces, while the pyramid will havefour triangular faces. 12. The boxes are 16 in. high.7 ? 12 5 84 in.; 84 4 16 5 5.25; 5 boxes can be stacked.13.

14. Yes; the box can be represented by a net that fits in a26-in. by 32-in. rectangle, so the 36-in. by 36-in. wrappingpaper will cover it. 15. Let C equal circumference and dequal diameter. C 5 pd; 132 5 pd; 5 d; d < 42; thecorrect choice is C.16. Let s equals number of students.

17. 3 2 2 5 1; 1 ? 1808 5 1808; 1808 4 3 5 608 18. 5 2 2 53; 3 ? 1808 5 5408; 5408 4 5 5 1088 19. 8 2 2 5 6; 6 ? 1808

5 1,0808; 1,0808 4 8 5 1358 20. 14 2 2 5 12; 12 ? 1808 5

2,1608; 2,1608 4 14 5 154.38


1-3. Check students’ work. 4. Answers may vary.Sample: Lateral area is the perimeter of the base timesthe height. 5. Check students’ work. 6. L.A. 5 C ? h7. Check students’ work. 8. Surface area of a cylinder istwo circles and a rectangle. 2 1 5 2(pr2) 1 Ch 5

2pr2 1 pdh.us

s 5 16; the correct choice is H.

3s3 5 48

3

3s 5 48

3s 1 20 2 20 5 68 2 20

3s 1 20 5 68

132x

8 cm

4 cm

25 in.

15 in.

10 in.

7.5 in.

10 in.

7.5 in.



8-4 Surface Areas of Prisms andCylinders pages 368–372

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Multiply the lengthtimes the width. 2. 16.5 cm2 3. 12.6 ft2

Quick Check 1. Add the areas: S.A. 5 (18 3 15) 1 (183 15) 1 (18 3 6) 1 (18 3 6) 1 (15 3 6) 1 (15 3 6) 5270 1 270 1 108 1 108 1 90 1 90 5 936 cm2 2. S.A. 5

L.A. 1 2B 5 ph 1 2B 5 (2 ? 8 1 2 ? 5)(12) 1 2(8 ? 5) 5(26)(12) 1 2(40) 5 312 1 80 5 392; about 392 in.2

3. S.A. 5 L.A. 1 2B 5 2(pr2) 1 2prh 52p( )(10) 1 2p( )2 5 40p 1 8p 5 48p < 151 m2

Exercises 1. The lateral area of a prism is the sum ofthe areas of the lateral faces. The surface area includesthe lateral area plus the area of the two bases.2. 32 ? 24 5 768; 768 in.2 3. 16 ? 24 5 384; 384 in.2

4. 16 ? 32 5 512; 512 in.2 5. 2(768) 1 2(384) 5 2,304;2,304 in.2 6. S.A. 5 L.A. 1 2B 5 ph 1 2B 5

(20 1 18 1 18)60 1 2( ? 20 ? 15) 5 3,360 1 300 53,660 in.2 7. S.A. 5 6(4 ? 4) 5 6(16) 5 96; 96 cm2

8. L.A. 5 ph 5 (10 1 10 1 12 1 12) ? 105 44 ? 105 440; 440 ft2

9. S.A. 5 6s2 5 6 ? 102 5 600 cm2 10. S.A. 5

L.A. 1 2B 5 ph 1 2A bhB 5 (3 1 4 1 5) ? 7 1 2A ? 3 ? 4B 5

84 1 12 5 96 in.2 11. S.A. 5 L.A. 1 2B 5 ph 1 2B 5

(10 1 10 1 6 1 2) ? 8 1 2 A6 ? 2 1 ? 6 ? 8B 5 224 1 72 5296 ft2 12. S.A. 5 L.A. 1 2B 5 2prh 1 2pr2 5

2p ? 4 ? 6 1 2p ? 42 5 48p1 32p5 80p< 251 in.2

13. S.A. 5 L.A. 1 2B 5 2prh 1 2pr2 5

2p ? ? 9 1 2p ? ( )2 5 63p 1 24.5p 5 87.5p <275 cm2 14. L.A. 5 ph 5 (105 1 105 1 126 1 126) ? 45 5

20,790 ft2 15. Find the surface area of each box: S.A. 5

2(9 1 5.5) ? 11.75 1 2(9 1 5.5) 5 340.75 1 99 5 439.75, or439.75 in2; S.A.: 2(8 1 6.25) ? 10.5 1 2(8 1 6.25) 5299.25 1 100 5 399.25,or 399.25 in.2The 9-cm by 5.5-cm by11.75-cm box will require more cardboard because it hasa greater surface area. 16. Answers may vary. Sample:Using a formula is preferable to using a net becauseusing a formula is quicker. 17a. Treat the lighthouse as acylinder. Multiply 3 3 30 3 150 to estimate the lateralarea. L.A. < 13,500 ft2 17b. Since the lateral area isabout 13,500 ft2 and half the lateral area is black andhalf is white, there is about 13,500 4 2, or about 6,750 ft2

of each color. Since one gallon covers about 350 ft2, ittakes about 6,750 4 350, or about 20 gallons of blackpaint and 20 gallons of white paint to cover the lateralsurface of the lighthouse. 18. L.A. 5 2prh 5 2p ? 6 ?12 5 144p < 452 ft2; S.A. 5 L.A. 1 2pr2 5 144p 1 2p ?

62 5 144p 1 72p 5 216p < 679 ft2 19. L.A. 5 ph 5

(15 1 15 1 15.8 1 10) ? 12 5 55.8 ? 12 5 670 m2; S.A. 5

L.A. 1 2B 5 670 1 2 ? (10 1 15)15 5 670 1 375 5

1,045 m2

12

72

72

12

12

12

12

42

42

20. L.A. 5 ph 5 (6 1 8 1 10) ? 7 5 24 ? 7 5 168 ft2;

S.A. 5 L.A. 1 2B 5 168 1 2A bhB 5 168 1 6 ? 8 5

168 1 48 5 216 ft2 21. None; the area of the three new surfaces of figure A is exactly the same as the area of three surfaces of cube B. 22. L.A. 5 2prh 5 2p(1.5)(8) 524p < 75; the correct choice is D.

23. 16% of original cost of gasoline is $0.34 per gallon.

24.

25. 1808 2 628 5 1188 26. 908 2 788 5 128


1. triangular prism 2. rectangles 3.

4.

5. L.A. 5 ph 5 (18 1 18 1 8 1 8) ? 9 5 52 ? 9 5 468; 468 ft2


1-4. Check students’ work.

8-5 Surface Areas of Pyramids and Cones pages 374–378

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. hypotenuse 2. 10 ft2

Quick Check

1. S.A. 5 4A bhB 1 s2 2. L.A. 5 2b/5 2 ? 8 ? 10 1 82 5 2 ? 755 ? 611 5 160 1 64 5 922,610 ft2

5 224 cm2

3. S.A. 5 L.A. 1 B 4. S.A. 5 L.A. 1 B5 2b< 1 b2 5 pr/ 1 pr2

5 2(755)(611) 1 (755)2 5 p ? 4 ? 5 1 p ?

42

5 922,610 1 570,025 5 20p 1 16p5 1,492,635; 1,492,635 ft2 5 36p < 113 yd2

Exercises 1. Lateral area is less than surface areabecause it does not include the area of the square base.2. 10.25 1 5.3 5 15.55; 15.55 m2 3. slant height, < 5 14m 4. L.A. 5 pr/ 5 p(4)(14) 5 56p 5. S.A. 5 L.A. 1 B;S.A. 5 56p 1 p(4)2; S.A. 5 56p 1 16p 5 72p; theexpression is 56p 1 16p.

12


22 1 1

!450 5 c < 21; the correct choice is C.

450 5 c2 225 1 225 5 c2 152 1 152 5 c2

c < $2.13; the correct choice is G.

5 2.125

c 5 3416

16c 5 34

16c 5 (0.34)(100)

16100 5 0.34

c

12



6. S.A. 5 4A bhB 1 s2

5 2 ? 20 ? 32 1 202

5 1,280 1 400

5 1,680 cm2

7. S.A. 5 4A bhB 1 s2

5 2 ? 1 ? 1.2 1 12

5 2.4 1 1

5 3.4 yd2

8. S.A. 5 4A bhB 1 s2

5 2 ? 7 ? 13 1 72

5 182 1 49 5 231 in.2

9. L.A. 5 2b<5 2 ? 30 ? 50 5 3,000; 3,000 in.2;

S.A. 5 L.A. 1 B5 2b< 1 b2

5 2 ? 30 ? 50 1 302

5 3,000 1 900 5 3,900; 3,900 in.2

10. L.A. 5 2b< 5 2 ? 14 ? 16.5 5 462; 462 m2; S.A. 5

L.A. 1 B 5 2b< 1 b2 5 2 ? 14 ? 16.5 1 142 5

462 1 196 5 658; 658 m2 11. L.A. 5 2b< 5 2 ? 3 ? 4 5 24;24 cm2; S.A. 5 L.A. 1 B 5 2b< 1 b2 5 2 ? 3 ? 4 1 32 5

24 1 9 5 33; 33 cm2 12. S.A. 5 L.A. 1 B 5 pr< 1 pr2 5

p ? 4 ? 11 1 p ? 42 5 44p1 16p5 60p< 188 ft2

13. S.A. 5 L.A. 1 B 5 pr< 1 pr2 5 p ? ? 8 1 p ? ( )2 5

24p 1 9p 5 33p < 104 m2 14. S.A. 5 L.A. 1 B 5

pr< 1 pr2 5 p ? ? 7.5 1 p ? 3.52 5 26.25p 1 12.25p 5

38.5p < 121 in.2 15. The lateral area of the roof is L.A. 5

2b< 5 2 ? 5 ? 4 5 40. The cost to put new shingles in is$1.25 per square foot, so the total cost is 40 ? 1.25 5 50;$50. 16. The student used 8 for the radius, rather than 4;the correct solution is about 88 cm2. 17a. 8532 1 72.52 5

727,609 1 5,256.25 5 732,865.25; < 856 ft17b. L.A. 5 2b/ 5 2 ? 145 ? 856 5 248,240 ft2 18. L.A. 5

pr/ 5 p ? 8 ? 18 5 144p< 452 yd2 19. L.A. 5 pr/ 5

p ? 8 ? 25 5 200p< 628 cm2 20. L.A.5 pr/ 5 p ? 2.5 ? 3 5

"732,865.25

72

62

62

12

13

7

12

12

1

12

32

20

7.5p 5 24 ft2 21. Yes, because it is equivalent to pr2 1 pr/. 22. Yes, because pr/ 5 p(2r) .

23. Answers may vary. Sample: L.A. 5 2b/ 5 2 ? 9 ? 15 5270 m2. L.A. 5 2b/ 5 2 ? 8.8 ? 15.2 5 268 m2 24. Thepyramid; since the base areas are the same, pr2 5 b2 or b 5 r . The lateral area of the cone is pr<, and thelateral area of the pyramid is 2b< or 2(r )<. Comparepr< to 2 r<, because p , 2 ; the pyramid has thelarger surface area.25.

3 cm2 is the closest; the correct choice is D.26. 10% of $5,500 5 0.10 ? 5,500 5 550; $5,500 1 $550 5$6,050; 30% of $6,050 5 0.30 ? 6,050 5 1,815;$6,050 2 $1,815 5 $4,235; $4,235 ? 4 5 $16,940; thecorrect choice is H.27.


1.

2. Answers may vary. Sample: The volume is the basearea times the height.3. 4. V 5 pr2h

8-6 Volumes of Prisms andCylinders pages 380–384

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. No; the base of acylinder is a circle, not a polygon. 2. 105 ft2 3. 207 m2

Quick Check 1. V 5 Bh 5 (16 ? 2.5)3.5 5 52.5, or 52.5 ft3 2a. V 5 Bh 5 pr2 ? h < (3)( )2(12) 5 2,025;

about 2,025 mm3 2b. V 5 Bh 5 pr2 ? h 5 p( )2(12) 5675p < 2,120; 2,120 mm3

More Than One Way Methods may vary. Sample: V 5

Bh 5 pr2h 5 p ? 122 ? 4.5 5 648p < 2,036 ft3

Exercises 1. Answers may vary. Sample: ft3, in.3, cm3

2. 2.7 in.2 < 3 in.2; 2.3 in. < 2 in.; V 5 Bh 5 3 ? 2 5 6;

152

152

3 6 18

3 14 42

2 12.6 25.2

Height Base area Volume of prism

2 � 4

3 � 5

3 24

3

8

15 45

Base dimensions Height Base area Volume of prism

K L

5 3.4 cm2 5 2.4 1 1

5 2 ? 1 ? 1.2 1 12

5 4 ? 12bh 1 b2

S.A. 5 L.A. 1 B

!p!p!p

!p

A ,2 B



about 6 in.3 3. 10 ? 10 ? 10 5 1,000; the correct choice isB. 4. 7 ? 7 ? 10 5 49 ? 10 5 490; the correct choice is A.5. 100 ? 8 5 800; the correct choice is C. 6. V 5 Bh 5

/wh 5 25 ? 30 ? 25 5 18,750 cm3 7. Find the area of the base. The base is a triangle, so Bprism 5 bh. Bprism 5

(26)(10); Bprism 5 130. Use the base area to find the

volume. V 5 Bprismh; V 5 (130)(30); V 5 3,900 mm3.

8. Find the area of the base. The base is a trapezoid, soBprism 5 Ab1 1 b2Bh. Bprism 5 A20 1 16B20; B 5 360.

Use the base area to find the volume. V 5 Bprismh; V 5

(360)(15); V 5 5,400 cm3. 9. Find the area of the base.The base is a trapezoid, so Bprism 5 Ab1 1 b2Bh. Bprism 5

A3 1 2B4; Bprism 5 10. Use the base area to find the

volume.V 5 Bprismh; V 5 (10)(2); V 5 20 ft3. 10. V 5

Bh 5 /wh 5 33 ? 42 ? 20 5 27,720 in.3 11. V 5 Bh 5

bhn ? h 5 ? 10 ? 13 ? 9 5 585 in.3 12. V 5 Bh 5 bhn ? h 5

? 28 ? 28 ? 2 5 784 ft3 13. V 5 Bh 5 pr2h 5 p ? 42 ? 6 596p < 302 m3 14. V 5 Bh 5 pr2h 5 p ? 3.52 ? 16 5196p < 616 in.3 15. V 5 Bh 5 pr2h 5 p ? 22 ? 4 5 16p <50 ft3 16. Divide the pool into three sections. The shallow rectangular prism, the deep rectangular prism,and the trapezoidal prism. V 5 1,792 1 1,440 1 576 53,808 ft3 17. V 5 Bh 5 pr2h 5 p ? 5.52 ? 6.2 5 187.55p<589 ft2; check students’ work. 18. 48 4 4 5 12; Thepossible dimensions are 1 and 12, 2 and 6, 3 and 4.19. doubling the radius, since the radius is squared incalculating the volume 20a. V 5 Bh 5 /wh 5 6 ? 2.5 ? 4 5

60 in.3; 60 ? 240 5 14,400 in.3 20b. 14,400 4 1,728 58.3 ft3 21. Subtract the cutout from the whole prism: V 5

LWH 2 /wh 5 (8 ? 20 ? 15) 2 (8 ? 10 ? 7.5) 5 2,400 2 600 51,800 m3 22. Subtract the cutout from the whole prism.V 5 LWH 2 /wh 5 (18 ? 12 ? 14) 2 (6 ? 8 ? 12) 53,024 2 576 5 2,448 m3 23. Answers may vary. Sample:Start with the equation pr2h 5 565.5. Divide each sideby 20p, which results in r2 5 9.0002. Take the square rootof each side to find the radius. r < 3 in. 24. The volumeof the cake with a 12 in. diameter is V 5 Bh 5 pr2 ? h 5

p( )2 ? 3 5 108p. The volume of the cake with a 3 in.

diameter is V 5 Bh 5 pr2 ? h 5 p( )2 ? 3 5 6.75p. The volume of how much cake is served is 108p 2 6.75p 5

101.25p < 318; about 318 in.3. 25. L.A. 5 ph; 308 5 11p;p 5 28 ft; 28 4 4 5 7 ft; The side length of the base is 7 ft. A 5 /wh 5 7 ? 7 ? 11 5 539 ft3 26. 30 in. 5 ft 52 ft, or 2.5 ft; 5 ft5 5.5 ft; 2.5 ? 2.5 ? 5.5 < 34; the correct choice is B. 27. L.A. 5 2prh 5 2p( )(1.8) 54.32p < 13.5; the correct choice is G.28. 20% of regular price is 12.

12 5 0.20p

5

p 5 60; the correct choice is C.29. 5 5 0.3529 ? 100% 5 35.3%

30. 5 5 0.7982 ? 100% 5 79.8%

31. 100 2 5 5 0.14 ? 100% 5 14.0%14100

100 2 86100

364456

456 2 92456

1234

34 2 2222

0.20p0.20

120.20

2.42

612

612

3012

32

122

12

12

12

12

12

12

12

12

12

12


1. Check students’ work. 2. The numbers 2,500 and 390were changed to 2,400 and 400. 3. The formula for the volume of a cylinder is V 5 pr2h; h 5 11 and r 5 , or 8;V 5 p(8)2 ? 11 5 704p < 2,211.68; about 2,212 cm3

4. A diagram shows how many cupped hands it wouldtake for each person to hold the full bottle of water.354 4 5 5 70.8; 354 4 4 5 88.5; 354 4 4.5 < 78.667;354 4 3.5 5 101.143; Sara’s capacity is about 71 mL,Jan’s capacity is about 89 mL, Bill’s capacity is about 79 mL, and Juanita’s capacity is about 101 mL.

5. There is a total of71.6 1 31.6 1 15.3 114.4 1 13.2 1 12.5 120.8, or 179.4 milliontons of trash. 1 ton 52,000 lb, so there are179,400,000 ? 2,000, or358,800,000,000 lbs oftrash. The average

American throws away 358,800,000,000 4 296,000,000,or about 1,212 lb of trash. 6. The total area of thegeoboard is 4 ? 4, or 16 units. The area covered by the geoband is 2 ? 3 1 ? 2 ? 3 1 ? 2 ? 1 5 6 1 3 1 1, or 10 units. The fraction of the geoboard that is covered is

, or . The portion of the geoboard that is outlined is

worth ? $1,000, or about $625.


1. 10 ? 10 5 100; both base areas are 100 cm2.2. The height of the cube is 10 cm. The height of the square pyramid is also about 10 cm. 3. 3 4. 5. Check students’ work. 6. The diameter of the base of cylinder is 8 cm, so the radius is 5 4; 4 cm. Area of the

cylinder’s base is A 5 pr2; A 5 p( )2 5 p(4)2 5 16p <50 cm2. Circumference of the base of the cone is 25 cm,thus the radius of the circle is C 5 2pr; 25 5 2pr;25 4 2p 5 2pr 4 2p; r 5 p < 4. Area of the circle with radius 4 is A 5 pr2; A 5 p(4)2 5 16p < 50 cm2. Bothbase areas are about 50 cm2. 7. The height of the coneis 10 cm, and the height of the cylinder is also about 10 cm. 8. 3 9. 10. Check students’ work.

8-7 Volumes of Pyramids andCones pages 388–391

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. The base of a pyramid isa polygon, whereas the base of a cone is a circle.2. 429 in.2

Quick Check 1. V 5 Bh 5 s2h 5 (30)2 ? 64 519,200 in.3 2. V 5 Bh 5 pr2h 5 p(3)2 ? 12 5 36p <113 m3

13

13

13

13

13

13

13

252

82

82

13

58

58

1016

12

12

354 mL 354 mL

354 mL

JanSara

354 mL

JuanitaBill

162



3. V 5 Bh 5 ? pr2 ? h

360 5 pr2(9)

360 5 3pr2

5

38.1972 5 r2

r 5 < 6.2 cm

Exercises 1. V 5 Bh 5 ? 9 ? 5 5 15; 15 m3 2. Thebase of this figure is a square, and the faces are triangles,so the figure is a square pyramid. Because the base is asquare, and each side is 4 cm, the area of the base of thepyramid is B = S2, or B = 42; the correct choice is C.3. The base and faces of this figure are triangles, so thisfigure is a pyramid. When the base of a pyramid is atriangle, the formula for area is B 5 Bh, so B = (4)(3);the correct choice is B. 4. The base of this figure is acircle and the lateral surface has no edges, so the figureis a cone. To find the area of the circle, use the formula ispr2. The area of the base is B 5 pr2 or B = pr2(42); thecorrect choice is A. 5. V 5 Bh 5 s2h 5

(6)2 ? 6 5 72 in.3 6. V 5 Bh 5 s2h 5 (6)2 ? 8 5

96 cm3 7. V 5 Bh 5 s2h 5 (2)2 ? 1.8 5 2.4 < 2 m3

8. V 5 Bh 5 pr2h 5 p(12)2 ? 30 5 1,440p< 4,524 cm3

9. V 5 Bh 5 pr2h 5 p(2)2 ? 3 5 4p < 13 ft3

10. V 5 Bh 5 pr2h 5 p(5)2 ? 14 5 116.67p < 367 m3

11. V 5 Bh 5 pr2 ? h

419 5 pr2

419 ? 5 pr2 ?

5 r2

25.01 5 r2

r 5 < 5 cm12. V 5 pr2h; 500 5 pr2 ? 12; 500 5 4pr2; 5 ;r2 < 39.8; r < 6.3. The diameter is twice the radius, so 2r 5 2(6.3) 5 12.6 < 13 cm. Check the reasonableness ofthe answer by substituting 13 cm into the formula for volume of a cone: B 5 pr2 5 p( ) 5 42.25p; V 5 Bh 5

(42.25p)12 < 530, so the estimate is reasonable. 13. Thefigure is 2 congruent cones, so the volume of the wholefigure is twice the volume of one cone: V 5 2 ? Bh 5

2 ? pr2h 5 2 ? p(62) ? 8 < 603 cm3. 14. The figure is asquare pyramid and a rectangular prism, so the volumeis the sum of the volumes of each figure: V 5 Bh 1 Bh 5

S2h 1 S2 5 2.52 ? 1 1 (2.5)2 ? 3 5 6.25 1 6.25 5 12.5 <13 m3 15. No; because the radius is squared in theformula, and the height is not.

16. V 5 Bh 5 pr2 ? h 17. V 5 Bh

47 5 p(3)2 ? h 15 5 (27)h

47 5 3ph 15 5 9h5 5

h < 5 in. h 5 1.67 ft18. Suppose the original volume is (b2)h. If thedimensions are doubled, the new volume is (2b)2(2h),1

3

13

9h9

159

3ph3p

473p

13

13

13

13

13

13

13

13

13

13

13

13

13

132

2

4pr2

4p5004p

13

13

"25.01

1,25716p

316p

163

316p

163

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

13

12

12

13

13

"38.1972

3pr2

3p3603p

13

13

13 which simplifies to b2h. The new volume is 8 times the

original. 19. Each volume formula involves the productof the height h and the base area B. You can substitutethe appropriate area formula for B when finding thevolume. For cones and pyramids, you must also multiplythe product by . 20. Solve for the radius of the coneusing the lateral area equation with given lateral areaand slant height.

L.A. 5 pr/106 5 pr(7.5)

5

4.5 5 rFind the height of the cone using the PythagoreanTheorem with the radius as side 1 and the slant height asthe hypotenuse.

r2 1 h2 5 /2

(4.5)2 1 h2 5 (7.5)2

20.25 1 h2 5 56.25h2 5 36

h 5 5 6Find the volume of the cone with the calculated radius and the height. V 5 pr2h 5 p(4.5)2 ? 6 5 2p(20.25) 5

40.5p < 127; about 127 in.3 21. V 5 Bh 5

? (11 ? 11) ? 8 5 ? 121 ? 8 < 323; the correct choice isA. 22. L.A. 5 C ? h 5 pd ? h 5 p(18)(30) 5 540p <1,696; the correct choice is H. 23. Add 28 and 25 andthen subtract 6 from the result; the correct choice is A.24. S.A. 5 C ? h 1 2(pr2) 5 p(24) ? 24 1 2p( )2 5

576p 1 288p 5 864p < 2,714 ft2


1. S.A. 5 L.A. 1 B 5 2b/ 1 /w 5 2 ? 21 ? 17 1 212 5

1,155 cm2; V 5 Bh 5 ? 212 ? 13 5 1,911 cm3

2. S.A. 5 L.A. 1 B 5 pr/ 1 pr2 5 p ? 14 ? 26 1 p ? 142 <1,759 in.2; V 5 Bh 5 pr2h 5 p ? 142 ? 22 < 4,516 in.3

3. S.A. 5 L.A. 1 B 5 2b/ 1 lw 5 2 ? 42 ? 57 1 422 5

6,552 cm2; V 5 Bh 5 /wh 5 ? 422 ? 53 5 31,164 cm3

4. V 5 Bh 5 pr2 ? h 5 p( )2 ? 10 5 40p < 126 m3

5. V 5 Bh 5 bh ? h 5 ? 6 ? 12 ? 9 5 324 in.3

6. V 5 /wh 5 50 ? 40 ? 20 5 40,000 cm3

7. V 5 pr2 ? h; 22 5 pr2 ? 21; 22 5 7pr2; 5

; r2 < 1; r 5 5 1; about 1 ft8. V 5 Bh 5 ? 52 ? 5 < 42; about 42 ft3

8-8 Spheres pages 393–396

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. The radius is half thediameter. 2. about 48 cm2 3. about 108 m2 3. about 27ft2 4. about 217 in.2

13

13

!17pr2

7p

227p

13

13

12n

12

42

13

13

13

13

13

13

13

13

242

13

13

13

13

13

"36

7.5pr7.5p

1067.5p

13

83



Quick Check1. S.A. 5 4pr2 2. V 5 pr3

5 4p(72) 5 p(203)

5 196p< 616 ft2 < 33,510 in.3

Exercises 1. A cone has exactly one circular base andone vertex; the correct choice is C. 2. A cylinder hastwo bases that are parallel, congruent circles; the correctchoice is A. 3. A sphere is a set of all points in spacethat are the same distance from a center point; thecorrect choice is B. 4. The surface area of a sphere isS.A. 5 4pr2. The S.A. of a sphere with radius of 1 m is4(3.14)(1)2. 5. S.A. 5 4pr2 5 4(3.14)(1)2 5 12.6 m2

6. V 5 pr3 5 p(13) 5 4.2 m3 7. S.A. 5 4pr2 5 4p ?

122 < 1,810 cm2; V 5 pr3 5 p ? 123 < 7,238 cm3

8. S.A. 5 4pr2 5 4p ? 52 < 314 in.2; V 5 pr3 5 p ? 53 <

524 in.3 9. S.A. 5 4pr2 5 4p ? < 95 m2; V 5

pr3 5 p ? < 87 m3 10. S.A. 5 4pr2 5 4p ? 82 <

804 yd2; V 5 pr3 5 p ? 83 < 2,145 yd3 11. S.A. 5

4pr2 5 4p ? 5.52 < 380 ft2; V 5 pr3 5 p ? 5.53 < 697 ft3

12. S.A. 5 4pr2 5 4p ? 6.42 < 515 mm2; V 5 pr3 5

p ? 6.43 < 1,098 mm3 13. V 5 pr3 5 p ? 33 < 110;about 110 cm3 14. S.A. 5 4pr2 5 4p ? 6,5002 <5.3093 3 108; 70% of 5.3093 3 108 5

0.70 ? 5.3093 3 108< 3.7165 3 108 km2 15. Larger Ball:S.A. 5 4pr2 5 4p ? (1.47)2 < 27.2 in.2; Smaller Ball:S.A. 5 4pr2 5 4p ? (1.43)2 < 25.7 in.2; 27.2 2 25.7 5 1.5;about 1.5 in.2 16. C 5 2pr; 12.5 5 2pr; r 5 <1.99 < 2 in.; S.A. 5 4pr2 5 4p ? 22 < 50 in.2 17. V 5 pr3,so V 5 p (5)3 5 p (125) 5 < 167p ft3; yourclassmate forgot to divide by 3. 18. S.A. 5 4pr2 5

4p ? 32 < 113 cm2; V 5 pr3 5 p ? 33 < 113 cm3

19. S.A. 5 4pr2 5 4p ? 202 < 5,027 mm2; V 5 pr3 5

p ? 203 < 33,510 mm3 20. S.A. 5 4pr2 5 4p ? 22 <

50 mm2; V 5 pr3 5 p ? 23 < 34 mm3 21. S.A. 5 4pr2 5

4p ? 0.62 < 5 cm2; V 5 pr3 5 p ? 0.63 < 1 cm3

22a. The volume of 3 tennis balls: V 5 3 ? pr35

4p ? 1.253 < 25 in.3 22b. The volume of the can: V 5

Bh 5 pr2h 5 p ? 1.252 ? (2.5 ? 3) < 37 in.3

23. semicircle: S.A. 5 ? 4pr2 5 2p ? 2.252 < 32 in.2;V 5 ? pr3 5 p ? 2.253 < 24 in.3; cylinder: S.A. 5

L.A. 1 B 5 pdh 1 pr2 5 p(4.5)(2.5) 1 p ? 2.252 5

11.25p 1 5.0625p 5 16.3125p < 51 in.2; V 5 Bh 5

pr2 ? h 5 p ? 2.252 ? 2.5 < 12.65625p < 40 in.3;Total S.A. 5 32 1 51 5 83 in.2; Total volume 524 1 40 5 64 in.3 24. Since S.A. 5 4pr2, you can solve for r by dividing and taking the square root.

Therefore, r 5 . Then you can substitute into pr3

to get the volume of the sphere.

43"S.A.

4p

S.A.4p

23

43

12

12

43

43

43

43

43

43

43

43

43

500p3

43

43

43

12.52p

43

43

43

43

43

43

43

43

A 5 ? 52 B 24

343

A 5 ? 52 B 2

43

43

43

43

43

43

532,000p

3

43

43

25. V 5 pr3

1.642 3 1011 5 pr3

? 1.642 3 1011 5 ? pr3

3.92 3 1010 5 r3

5

r 5 3,396.99; about 3,397 km26. V 5 pr3 5 p ? 4.33 < 106p < 333 in.3: grid 33327. S.A. 5 L.A. 1 B 5 pdh 1 2pr2 5

p ? 10 ? 19 12 ? p ? 52 5 190p 1 50p 5 240p < 754 ft2:grid 754 28. C 5 2pr 5 2p ? 42 5 84p <264; 2(74) 1 264 5 412 m2: grid 412 29. V 5 Bh 5

/w ? h 5 ? 3 ? 4 ? 3.5 5 14 in.3 30. V 5 Bh 5

(pr2) ? h 5 ? p(42) ? 8 5 < 134 cm3 31. V 5

Bh 5 /w ? h 5 ? 8 ? 7 ? 6 5 112 ft3


1. S.A. 5 6(1 ? 1) 5 6 sq. units 2. V 5 / ? w ? h 5

1 ? 1 ? 1 5 1 cubic unit3.

4.

5. The ratios of surface areas are equal to the ratios ofsides squared and the ratios of volumes are equal to theratios of sides cubed. 6. A 4 3 4 3 4 cube has a S.A. 5

6(4 ? 4) 5 96; V 5 4 ? 4 ? 4 5 64; the ratio of the sidelengths of the 4 3 4 3 4 cube to the 1 3 1 3 1 cube is 96 : 6 : 4 : 14 : 1, the ratio of the surface area is 16 : 1, theratio of the volume is 64 : 1 7. Figure I contains half theamount of water as the square prism because Figure I ishalf the size of the square prism. Figure II also containshalf as much as water as the square prism because bothfigures are the same size and Figure II is only half full.Figure III also contains only half the amount of liquid asthe square prism because Figure II is two times threefourths of the square prism that is only one third full.Figures I, II, and III contain about half as much water asthe square prism; the correct choice is D.

8-9 Exploring Similar Solidspages 398–401

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. A proportion is an

Cubes

A : B

B : C

C : A

1 : 2

2 : 3

3 : 1

1 : 4

4 : 9

9 : 1

1 : 8

8 : 27

27 : 1

Ratio ofSide

LengthsRatio ofVolumes

Ratio ofSurfaceAreas

CubeABC

Dimensions VolumeSurface

Area62454

18

27

13

13

13

128p3

13

13

13

13

13

13

43

43

3"(r3)3"(3.93 3 1010)

43

34p

34p

43

43



volumes is A B3, or . Use each ratio to set up a proportion to find the surface area and volume of thesimilar figure.

14. 5 ; S.A. 5 ? 78 5 19.5 ft2 15. If the ratio of their heights is the same as the ratio of their radii, they

are similar. 16. The ratio of surface areas is , so 5 .17. V 5 /wh 5 8 ? 8 ? 8 5 512 cm3; 512 ? 2 5 1,024 cm3;V 5 /wh; 1,024 5 s3; s < 10.1 cm 18. In a cube alldimensions are equal. The volume of the larger cube is V 5 <wh; V 5 3x 3 3x 3 3x; the volume for the smallercube is V 5 <wh; V 5 x 3 x 3 x: x3; Simplify the largercube’s volume, 216 5 3x 3 3x 3 3x; 216 5 27x3; 8 5 x3

and compare with the smaller cube’s volume, V 5

x 3 x 3 x; V 5 x3. So the volume of the smaller cube is V 5 x3 5 8. The correct choice is B. 19. Find some ofthe possible combinations for the 3 sides of fence.The combinations are 25 3 250, 50 3 200, 75 3 150, and100 3 100. 25 3 250 is 6,250; 50 3 200 and 100 3 100 areboth 10,000; and 75 3 150 is 11,250. The dimensions ofthe enclosed area cannot be any greater because 2(75 1 150) 5 300, and he only has 300 yd of fencing.Choice J is too great and choices F and G are both toosmall. So the greatest area that can be enclosed is 11,250;the correct choice is H. 20. Take the minutes of a yearand multiply that by the rate a teenager’s heart beats tofind how many times a teenager’s heart beats in a year.5.256 3 105 ? 80 5 420.48 3 105; keep the answer inscientific notation by moving the decimal place 2 placesto the left to get a factor greater than or equal to one butless than 10, and add 2 to the exponent of 105;4.205 3 107; the correct choice is C. 21. 75,000; Movethe decimal place 4 places to the left to get a factorgreater than or equal to one but less than 10, and use 4as the exponent of 10; 7.5 3 104 22. 0.00194; Move thedecimal place 3 places to the right to get a factor greaterthan or equal to one but less than 10, and use 23 as theexponent of 10; 1.94 3 1023 23. 0.000083; Move thedecimal place 5 places to the right to get a factor greaterthan or equal to one but less than 10, and use 25 as theexponent of 10; 8.3 3 1025


1. 34 1 16.9 5 50.9 < 51; since the least number ofsignificant digits in the computation is 2 the summationis rounded to 51 ft. 2. 1.1 1 1.01 5 2.11 < 2.1; since theleast number of significant digits in the computation is 2the summation is rounded to 2.1 cm. 3. 60 2 22.80 537.2 < 40; since the least number of significant digits inthe computation is 1 the answer is rounded to 40 in.4. 42.00 2 21.0 5 21.00 < 21.0; since the least number of

21

!4!1

a2

b2

14

14A 1

2 B 2

V < 2,382 ft3 S.A. < 1,274 ft2 x < 2,381.6 x < 1,273.5

216x216 5

514,425216 36x

36 545,847

36

216x 5 514,425 36x 5 45,847

216x 5 75(6,859) 36x 5 127(361)

6,859216 5 x

75 36136 5 x

127

6,859216

196

equation stating that two ratios are equal. 2. 1.753. 43.2 4. 9

Quick Check1.

2.

Exercises 1. Two solids are similar if they have thesame shape and all their corresponding lengths are proportional. 2. 5

3. ( )2 5 4. ( )3 5

5 5

x 5 6 ? 9 5 54 cm2 x 5 1 ? 27 5 27 cm3

5. 6.

7. The edge length of the small cube is 5 of the

bigger cube. The S.A. ratio is ( )2 5 ; using the S.A. of the big box the S.A. of the small box can be calculated. S.A. of the small box: 5 ; 25x 5 25,200;

; x 5 1,008 m2; using the edge length ratio

the volume ratio is ( )3 5 . With the given volume of

the big box and the volume ratio, the volume of the

small box is 5 ; 125x 5 259,200; 5 ;

x < 2,074 m3. 8. 5 ; ( )2 5 ; S.A. 5 5 ; 4x 5

356; 5 ; x 5 89 ft2; ( )3 5 ; V 5 5 ; 8x 5 507;

5 ; x < 63 ft3 9. 5 ; ( )2 5 ; S.A. 5 5 ;

9x 5 31,360; 5 ; x < 3,484 in.2; ( )3 5 ; V 5

5 ; 27x 5 21,696; 5 ; x < 804 in.3

10. 5 ; S.A. 5 ? 6,000 5 3,375 cm2 11. 5 ;

18b 5 20 ? 4.5; b 5 ; b 5 5 m 12. Answers may

vary. Sample: about 20 times as great. 5 , V < 16;

5 , V < 27; So the volume would be between

16 and 27 times as great. 13. First find the surface areaand volume of the original figure.

f g

The ratio of corresponding dimensions is , so the ratio

of the surface areas is A B2, or , and the ratio of the 36136

196

196

5 127 ft2 5 102 1 25

5 75 ft3 5 (17) ? 6 1 2(12.5)

5 12.5(6)A 12 B (5)(5) 5 (5 1 5 1 7) ? 6 1 2

V 5 Bh S.A. 5 L.A. 1 2B

v1

33

13

v1

2.53

13

20 ? 4.518

4.5b

1820

916

916A 3

4 B 2

21,69627

27x27

x339

6427

6427

43

31,3609

9x9

x1,960

169

169

43

43

86

5078

8x8

x507

18

18

12

3564

4x4

x356

14

14

12

12

2.44.8

259,200125

125x125

x4,050

64125

64125

45

25x25 5

25,20025

x1,575

1625

1625

45

45

1215

y 5 6.75 cm x 5 8.4 in.

4y 5 27 2x 5 16.8

94 5y3 72 5 x

2.4

127

1x

19

6x

127

13

19

13

1x

13

V 5 27 ? 27 5 729 in.3

V27 5 271

volume of large boxvolume of small box 5 33

13 5 271

x 5 9 ? 54 5 486 in.2

x54 5 91

surface area of large boxsurface area of small box 5 32

12 5 91

h 5 8.8 m

5h 5 44

4h 5 511



significant digits in the computation is 3 the summationis rounded to 21.0 m2. 5. 372 3 278 5 103,416 <103,000; since the least number of significant digits in thecomputation is 3 the product is rounded to 103,000 mi2.6. 189.9 3 5.40 5 1,025.46 < 1,030; since the leastnumber of significant digit in the computation is 3 theproduct is rounded to 1,030 km2. 7. 6 4 0.0569 5105.44815 < 100; since the least number of significantdigit in the computation is 1 the quotient is rounded to100. 8. 124.6 4 8.101 5 15.380817 < 15.38; since theleast number of significant digit in the computation is 4the quotient is rounded to 15.38.


1. S.A. 5 L.A 1 B 5 pr< 1 pr2 5 p(3)(4) 1 p(32) 512p1 9p5 21p, so choice A cannot be the answer andchoice D is too big to be the answer; 21p5 65.94 < 66 m2;the correct choice is B. 2. 1.3 3 10–5, so the decimalmoves 5 places to the left, Choices F and G moved thedecimal to the right, and choice H did not move farenough left. The standard form is 0.000013; the correct choice is J. 3. 12 in. 5 1 ft; 24 in. 5 2 ft, 8 in. 5 5 ft,

6 in. 5 5 ft; V 5 Bh 5 /w 3 h 5 2( ) 3 5 3 5

ft3; compare using like fractions. 5 , 5 , 2 5 ,3 5 , 6 5 ; ft3 is closest to ft3; the correct choice is A.


1. The volume of an object is the number of cubic unitsin the object. 2. A cone has one base and one vertex,but it is not a polyhedron. 3. Both lateral area andsurface area are measured in square units. 4. Both acylinder and a prism have two parallel, congruent bases.5. An isometric view shows all the surfaces of a solid inone view. 6. rectangle, parallelograms 7. square,triangles 8. circle, curved surface

9.

10.

11.

12. cone 13. triangular prism 14. cube 15. L.A. 5 ph 5

(3 1 4 1 5) ? 1 5 12 ? 1 5 12 m2; S.A. 5 L.A. 1 2B 5

12 1 2 ? bhn 5 12 1 3 ? 4 5 24 m2; V 5 Bh 5 bhn ? h 5

? 3 ? 4 ? 1 5 6 m3 16. L.A. 5 2prh 5 2p ? 2.5 ? 10 <12

12

12

112

21

Top viewBase plan Front view Right view

1121

111


111

2 1


23

12

366

186

1516

12

36

12

46

23

23

12

43

12

23

12

612

23

812

157 cm2; S.A. 5 L.A. 1 2B 5 157 1 2 ? pr2 5 157 1 2 ?p ? 2.52 < 196 cm2; V 5 Bh 5 pr2h 5 p ? 2.52 ? 10 <196 cm3 17. L.A. 5 ph 5 (13 1 13 1 13 1 13) ? 13 5676 in.2; S.A. 5 L.A. 1 2B 5 676 1 2/w 5 676 1 2 ? 13 ?13 5 1,014 in.2; V 5 Bh 5 /wh 5 13 ? 13 ? 13 5 2,197 in.3

18. L.A. 5 2b/ 5 2 ? 4 ? 9.2 5 74 m2; S.A. 5 L.A. 1 B 5

74 1 s2 5 74 1 4 ? 4 5 90 m2; V 5 Bh 5 s2 ? h 5

? 42 ? 9 5 48 m3 19. L.A. 5 pr/ 5 p ? 4 ? 16.5 < 207 cm2;S.A. 5 L.A. 1 B 5 207 1 pr2 5 207 1 p ? 42 < 258 cm2;V 5 Bh 5 pr2h 5 p ? 42 ? 16 < 268 cm3 20. L.A. 5

pr/ 5 p ? 5 ? 7.1 < 112 ft2; S.A. 5 L.A. 1 B 5 112 1 pr2 5

112 1 p ? 52 < 190 ft2; V 5 Bh 5 pr2h 5 p ? 52 ? 5 <131 ft3 21. r 513,000 4 2 5 6,500; S.A. 5 4pr2 5

4 3 p 3 6,5002 5 169,000,000p < 5.3 3 108; V 5 pr3 5

3 p 3 6,5003 < (3.66 3 1011)p < 1.15 3 1012;5.3 3 108 km2; 1.15 3 1012 km3 22. S.A. 5

L.A. 1 2B 5 2prh 1 2pr2 5 2p ? 4.5 ? 20 1 2p ? 4.52 <693 yd2; 693 ? 5 444 yd2; V 5 Bh 5 pr2h 5

p ? 4.52 ? 20 < 1,272 yd3; 1,272 ? 5 651 yd3 23. S.A. 5

L.A. 1 2B 5 ph 1 2/w 5 24 ? 4 1 2 ? 6 ? 6 5 168 in.2;

168 ? 5 108 in.2; V 5 Bh 5 /wh 5 6 ? 6 ? 4 5 144 in.3;

144 ? 5 74 in.3 24. S.A. 5 L.A. 1 B 5 pr/ 1 pr2 5

p ? 3 ? 11.4 1 p ? 32 < 136 m2; 136 ? 5 87 m2; V 5

Bh 5 pr2h 5 p ? 32 ? 11 < 104 m3; 104 ? 5 53 m3


1. cone, one circular base 2. pyramid, one rectangularbase 3. rectangular prism, two rectangular bases4. cylinder, two circular bases 5–6. Answers may vary.Samples are given. 5. A pair of skew line segments is

, ; a pair of parallel line segments is ,

6. A pair of skew line segments is , ; a pair of

parallel line segments is ,

7. 8.

9.

10.

11. cone 12. cube 13–14. Answers may vary. Samplesare given.


Topview

Frontview

Rightview

31111

111

111

112222

122

JKHI

IJGH

EDBCCDAB

A 45 B 31

313

13

A 45 B 2

A 45 B 3

A 45 B 2

A 45 B 3

A 45 B 2

43

43

13

13

13

13

13

13

13

13

13



13. 14.

15. L.A. 5 ph 5 35 ? 5 5 175 yd2; S.A. 5 L.A. 1 2B 5

175 1 2/w 5 175 1 2 ? 10 ? 7.5 5 325 yd2 16. L.A. 5

2b/ 5 2 ? 9 ? 13.8 5 248 m2; S.A. 5 L.A 1 B 5

248 1 /w 5 248 1 9 ? 9 5 329 m2 17. L.A. 5 pr/ 5

p ? 7 ? 15.7 < 345 cm2; S.A. 5 L.A. 1 B 5 345 1 pr2 5

345 1 p ? 72 < 499 cm2 18. L.A. 5 2prh 5 2p ? 11 ? 22 <1,521 in.2; S.A. 5 L.A. 1 2B 5 1,521 1 2pr2 5

1,521 1 2p ? 112 < 2,281 in.2 19. V 5 Bh 5 s2h 5

? 12 ? 0.75 5 0.25 ft3 20. V 5 Bh 5 pr2h 5 p ? 62 ? 20 <

2,262 in.3 21. V 5 Bh 5 pr2h 5 p ? 3.52 ? 7.5 < 96 m3

22. V 5 Bh 5 /wh 5 7 ? 3 ? 2 5 42 ft3 23. Since pr2h multiplies three linear units together, the result will be in cubic units, which is appropriate for volume.

24. To find a, use the proportion 5 ; 30a 5 520; 5

; a 5 17 in. To find b, use the proportion 5 ;

20b 5 1,200; 5 ; b 5 60 in. To find c, use the

proportion 5 ; 20c 5 840; 5 ; c 5 42 in.25. r 5 2; S.A. 5 4pr2 5 4 3 p 3 22 5 16p < 50; V 5

pr3 5 3 p 3 23 5 p 3 8 5 p < 34; 50 in.2; 34 in.3

26. r 5 5; S.A. 5 4pr2 5 4 3 p 3 52 5 4p 3 25 5100p < 314; V 5 pr3 5 3 p 3 53 5 p 3 125 <(1.67 3 10 2)p< 523; 314 ft2; 523 ft3 27. r 5 6 42 5 3;S.A. 5 4pr2 5 4 3 p 3 32 5 4p 3 9 5 36p < 113;

V 5 pr3 5 3 p 3 33 5 p 3 27 5 36p < 113;113 m2; 113 m3 28. r 5 8 4 2 5 4; S.A. 5 4pr2 5

4 3 p 3 42 5 4p 3 16 5 64p < 201; V 5 pr3 5

3 p 3 43 5 p 3 64 < (8.53 3 102)p < 268;201 cm2; 268 cm3

43

43

43

43

43

43

43

43

43

323

43

43

43

84020

20c20

c28

3020

1,20020

20b20

b40

3020

13

52030

30a30

a26

2030

13

13

13

13

13

13

TEST PREP page 407

1. As the circle grows the circumference being read perunit of time will have increased, so there will be moredata per second as the circle grows; the correct choice is C. 2. C 5 2pr 5 2p( r) 5 pr; the correct choice is H.3. The disc will spin slower as the data circle grows because the circumference will be growing as well.The correct choice is C. 4. As shown in problem 2,the circumference at the outer edge is twice thecircumference halfway to the outer edge so the speedhalfway to the outer edge will be 200% of the speed atthe outer edge; the correct choice is J 5. The moleculestraveling over the wing have to travel 15% farther andstill reach the other side first so their speed has to beover 15% faster than the molecules traveling under thewing. a . 1.15u 6. The surface area of the bottom of thewing will be about 15% less so it will be about 85% thesurface area of the top of the wing. 85% of 16 is 0.85 ? 16, or about 14 m2; the correct choice is G.


1. Check students’ work.2.

3. 768 4 96 5 8; 8 times4. 384 4 96 5 4; 4 times5. Answers may vary. Sample: The larger bird requireseight times as much lift, but its wings provide only fourtimes as much lift. For the bird to fly, its wings wouldhave to be able to carry twice as much bird volume persquare centimeter of wing.6. Check students’ work.

RatioVolume

VolumeWing Area

Size ofBird

WingArea

Small

Large

96 cm3 96 cm2 9696

768 cm3 384 cm2 768384

1121

=

=

12


Using Graphs to Analyze Data pages 410–467



1–9.

10. 11.

12. 13.

14. 26% 5 5 15. 48% 5 16.

17. 72% 5 18. 19.

20. 50% 5 21.

22. 5% 5 5

9-1 Finding Mean, Median, andMode pages 412–416

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. subtraction 2. 18 3. 314. 241 5. 229Quick Check 1. Find the mean:

5 514; find the median: 8, 11, 11, 15, 16, 18, 19; 15; find the mode: 11.2. The greatest value is 224.2 and the least value is233.1., so subtract 224.2 2 (233.1), to get 8.9.3a. The outlier is 1. Find the mean with the outlier:

5 5 10.875.Find the mean without the outlier:

5 5 12. . The outlier,1, lowers the mean by about 1.4. 3b. The outlier is 218.Find the mean with the outlier:

5 5

23. . Find the mean without the outlier:3

2309

(25) 1 (23) 1 0 1 2 1 (21) 1 (218) 1 (26) 1 3 1 (22)9

285714867

11 1 14 1 9 1 12 1 15 1 12 1 137

878

11 1 14 1 9 1 1 1 12 1 15 1 12 1 138

987

11 1 19 1 11 1 15 1 16 1 18 1 87

120

5100

10% 5 10100 5 1

1050

100 5 12

47% 5 4710020% 5 20

100 5 15

72100 5 18

25

13% 5 13100 48

100 5 1225

1350

26100

m 5 5

3m3 5 15

3 s 5 24

3m 5 15 s 5 2 ? 12

3m 5 35 2 5 s

12

3m 5 75125 63 5 s

12

a 5 24 ? 1412 5 28 x 5 9 ? 16

8 5 18

12a 5 24 ? 14 8x 5 9 ? 16

a24 5 1412 89 5 16

x

4

4

4 Ox

y

4

5 5

21.5. 218; it lowers the mean by approximately 1.8.

4. Find the mean: 5 5

81.5; find the median: 72, 72, 82, 84, 88, 91; 5

5 83; find the mode: 72; find the range: 91 2 72 5 19;the median makes the scores seem greatest.Exercises 1. No, because none of the data values arerepeated, there is no mode. 2. 23 1 (22) 1 (29) 1(28) 1 2 1 0 1 1 1 15 1 6 1 11 1 7 1 11 5 313. There are 12 data values. 4. 5 2.58 5. 29, 28, 23,

22, 0, 1, 2, 6, 7, 11, 11, 15; median: 5 5 1.5; mode:

11 6. 15 is the greatest value; 29 is the least value.

7. Find the mean: 5 5

1. Find the median: the middle number is 1. Find themode: the number that occurs most often is 0. Find therange: 3 2 0 5 3.The mean, median, mode, and range,respectively are 1, 1, 0, 3. 8. Find the mean:

5 5 86. Find the median:the middle numbers are 84 and 90, and 5 87.Find the mode: no number occurs more often than theothers. Find the range: 100 2 70 5 30. The mean,median, mode, and range, respectively are 86, 87, no mode, 30. 9. Find the mean:

5 5 8. . Find the median: the middle number is 9. Find the mode: thenumber that occurs most often is 9. Find the range:10 2 7 5 3. The mean, median, mode, and range,respectively are 8. , 9, 9, 3. 10. Find the mean:

5 5 2.5. Find the median: the middle two numbers are 2 and 3, and

5 2.5. Find the mode: the number that occurs mostoften is 3. Find the range: 6 2 0 5 6. The mean, median,mode, and range, respectively are 2.5, 2.5, 3, 6. 11. Find

the mean: 5 5

0.375; find the median: 22, 21, 0, 0, 0, 0, 2, 4: 0; find themode: 0; find the range: 4 2 (22) 5 6. The mean, median,mode, and range, respectively are 0.375, 0, 0, and 6.12. Find the mean:

5 5 5. .Find the median of the ordered data: 29, 23, 21, 7, 7,8, 8, 14, 16, the middle number is 7. Find the mode: thenumbers that occur more than the others are 7 and 8, sothere are two modes. Find the range: 16 2 (29) 516 1 9 5 25. The mean, median, mode, and range,respectively are 5. , 7, 7 and 8, 25. 13. The numberwhose value is farthest from the rest of the data is 10.Find the mean with the outlier:

5 5 2.625. Find the218

1 1 0 1 3 1 10 1 0 1 2 1 4 1 18

2

2479

(21) 1 16 1 7 1 8 1 7 1 14 1 8 1 (23) 1 (29)9

38

2 1 0 1 (22) 1 4 1 0 1 0 1 0 1 (21)8

2 1 32

2510

0 1 1 1 1 1 2 1 2 1 3 1 3 1 3 1 4 1 610

7

7799

7 1 8 1 8 1 9 1 9 1 9 1 9 1 10 1 109

84 1 902

5166

70 1 80 1 84 1 90 1 92 1 1006

99

0 1 0 1 0 1 0 1 1 1 1 1 2 1 2 1 39

32

1 1 22

3112

1662

82 1 842

4896

82 1 84 1 88 1 72 1 91 1 726

2128

(25) 1 (23) 1 0 1 2 1 (21) 1 (26) 1 3 1 (22)8

Chapter

9


mean without the outlier: 5 <1.571.The outlier raises the mean by about 2.625 2 1.571 51.054. Outlier: 10; it raises the mean by about 1.05.14. The number whose value is farthest from the rest ofthe data is 12. Find the mean with the outlier:

5 5 30. Find the

mean without the outlier: 5

5 33. The outlier lowers the mean by 33 2 30 5 3.Outlier: 12; it lowers the mean by 3. 15. The number whose value is farthest from the rest of the data is $20.50. Find the mean with the outlier:

5 5 10.00;$ 10.00. Find the mean without the outlier:

5 5 7.90; $7.90.The outlier raises the mean by 10.00 2 7.90 5 2.10;$2.10. Outlier: $20.50; it raises the mean by $2.10.16. Find the median: 20,000, 22,000, 34,000, 42,000,43,000, 50,000, 80,000: $42,000. Find the mean:

5

< $41,571. There is no mode. The most persuading measure of central tendency is the median,$42,000. 17. If the mean of 9 values is 5, then their sumis 9 ? 5, or 45. If the mean of 10 values is 6, then their sumis 10 ? 6, or 60. The tenth value is 60 2 45, or 15.18. Find the median: 1.25, 1.75, 2.75, 2.75, 3.00: 2.75. Find

the mean: 5 5 2.3.Find the mode: 2.75. The median and the mode are themost impressive measure of central tendency. 19. If themean of 5 values is 8, then their total sum is 8 ? 5, or 40.The sum of four values is 11 1 5 1 11 1 5, or 32, so thefifth value is 40 2 32, or 8. 20. If the mean of 5 values is8, then their total sum is 8 ? 5, or 40. The sum of fourvalues is 7 ? 4, or 28, so the fifth value is 40 2 28, or 12.21. If the mean of 5 values is 8, then their total sum is 8 ? 5, or 40. The sum of four values is 18 1 0 1 18 1 6, or42, so the fifth value is 40 2 42, or 22. 22. Find the mean:

5 5 29.625.

Find the median:The middle numbers are 34 and 26,and 530. Find the mode: The number that occurs most often is 25. The mean, median, and mode,respectively, are 29.625, 30, 25. 23. Yes; without the U.S.

data, the mean is 5 5

32; the U.S. brings the mean down more than 2 days.24a. You want 6 test scores to have an average of 87, sotheir total points should be 87 ? 6, or 522. You alreadyhave 89 1 92 1 78 1 83 1 83, or 425 points, so you need522 2 425, or 97 points more; 97. 24b. Order the testscores: 78, 83, 83, 89, 92. The current median is 83.When you add the next test score, you will have twomiddle numbers.You want their mean to be 85, so thesum of the two numbers must be 85 ? 2, or 170. Youalready have 83 points, so you need 170 2 83, or 87points more; 87. 25. Since the median is 7, then themiddle number is 7. If the mean is 11, then the sum ofthe three numbers is 11 ? 3, or 33, and the sum of the first

2247

42 1 37 1 35 1 34 1 26 1 25 1 257

34 1 262

2378

42 1 37 1 35 1 34 1 26 1 25 1 25 1 138

11.55

1.25 1 1.75 1 2.75 1 2.75 1 3.005

2910007

20,000 1 22,000 1 34,000 1 42,000 1 43,000 1 50,000 1 80,0007

39.505

8.00 1 7.50 1 8.00 1 8.00 1 8.005

60.006

8.00 1 7.50 1 8.00 1 8.00 1 8.00 1 20.506

1986

28 1 37 1 36 1 30 1 32 1 356

2107

28 1 12 1 37 1 36 1 30 1 32 1 357

117

1 1 0 1 3 1 0 1 2 1 4 1 17

and last numbers is 33 2 7, or 26. Since the range is 14,the difference between the first and last numbers is 14.Use try, check, and revise to find two numbers whosesum is 26 and difference is 14; the numbers are 6 and 20.So, the three numbers are 6, 7, and 20. 26. Find the

mean: 5 5 14. Find themode: 15. Find the range: 16 2 11 5 5. Find the median:

11, 13, 14, 15, 15, 16: 5 14.5. The correct choiceis D. 27. The surface area of a cube is S.A. 5 6s2. So thearea of one face of the cube is 337.5 4 6 5 56.25. Thearea of a square is A 5 s2. So the length of any one side

is 5 7.5; the correct choice is F. 28. 5 ; 20x 5

2,900; x 5 5 145; $145; the correct choice is B.

29. The signs are different, so the product is negative:15(220) 5 2300. 30. The signs are the same, so theproduct is positive: 27(211) 5 77. 31. The signs are the

same, so the quotient is positive: 5 5 20.32. The signs are different, so the quotient is negative:

5 2 5 215.


1–2. Check students’ work. 3. Mean; 7 ft 2 in. is anoutlier that raises the mean. 4. The median describesthe group best; the mean is affected by the outlier, andthe mode may be too high or too low.5. 5 5 19; 19 in.6. 45 in.; the data are very spread out, and the meandoes not indicate this.

Exercises 1–4. Check students’ work.

9-2 Displaying Frequencypages 418–422

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. range 2. 7.9; 8; 7 and 8; 43. 0.875; 1; no mode; 9

Quick Check 1.

2. Find the median: 101.58; find the mode: 1018.3. The data are from $4.00 to $9.00. The range is 9 2 4, or 5. Consider 3 to 5categories. Answers may vary. Sample:

FrequencyCost

(Dollars)

4–5.99

6–7.99

8–9.99

4

6

4

98

Human Body Temperatures

999796 100

1146

48 1 9 1 10 1 3 1 26 1 186

604

6024

1206

212026

2,90020

29x

20100!56.25

(14 1 15)2

846

16 1 14 1 15 1 15 1 13 1 116



Exercises 1. A histogram is a bar graph with no spacesbetween the bars. Histograms are used for data that iscontinuous. 2. There are no values less than 25 inthe data. 3. 5

5 27.4 4.

5.

6. Find the mean:

5

5 < 2.8. Find the median:the middle term is the ninth term, 3. Find the mode:the value occurring most frequently is 5. The mean,median, and mode are 2.8, 3, and 5. 7. Find the mean:

5

5 5 0.7; find the median:1; find the mode: 0, 1, and 3.

8.1512963

(�4)–(�1) 0–3 4–7

Freq

uenc

y

Low Temperatures

1622

2 6 1 (22) 1 0 1 5 1 4 1 1522

2 2 ? 3 1 (21) ? 2 1 0 ? 5 1 1.5 1 2 ? 2 1 3 ? 522

4817

0 1 3 1 4 1 12 1 4 1 252 1 3 1 2 1 4 1 1 1 5

2 ? 0 1 3 ? 1 1 2 ? 2 1 4 ? 3 1 1 ? 4 1 5 ? 52 1 3 1 2 1 4 1 1 1 5

16 18Gigabytes

Hard-Drive Size

201412108 22 24

2Hours

Hours Spent on Homework

310 4

41115

25 ? 3 1 26 ? 2 1 27 ? 4 1 28 1 29 ? 2 1 30 ? 315

Cost (dollars)

Fre

qu

ency

8–9.99

8

4

0

6–7.994–5.99

9.

10.

11. The multiple of 10 less than or equal to the leastnumber, 58, is 50; and the multiple of 10 greater than orequal to the greatest number, 100, is 100. Answers mayvary. Sample: 50–59, 60–69, 70–79, 80–89, 90–99, 100–109.12. The multiple of 20 less than or equal to the leastnumber, 305, is 300; and the multiple of 20 greater thanor equal to the greatest number, 458, is 460. Answersmay vary. Sample: 300–319, 320–339, 340–359, 360–379,380–399, 400–419, 420–439, 440–459.13. Find the mean:

5

5 26. Find the median: the middle two terms are 26

and 26. 5 26. Find the mode: the values occuringmost frequently are 24, 26, and 28.14. Find the mean:

(60 1 60 1 62 1 62 1 62 1 66 1 67 1 67 1 67 1 73 173 1 75 1 76 1 78 1 78 1 78) 4 16 5 5 69. Find the median: the middle two terms are 67 and 67.

5 67. Find the mode:the values occuring most frequently are 62, 67, and 78.15. Find the mean:

5 < 6.39. Find the median: the middle term is 6.Find the mode: the valueoccuring most frequently is 6.16. The data are from 2 to 21,so the range is 21 2 2, or 19.Consider 3 to 10 categories. Answers may vary.

14723

5 ? 6 1 6 ? 7 1 7 ? 5 1 8 ? 523

67 1 672

110416

60 62 64 66 68 70 72 74 76 78

Ages of Members of theSeniors Hiking Club

26 1 262

31212

21 1 23 1 24 1 24 1 25 1 26 1 26 1 27 1 28 1 28 1 29 1 3112

20 22 24 26 28 30

Cars Sold Per Month

5 6 74321 8 9 10 11 12

3

2

1

0–4 5–9 10–14

Freq

uenc

y

Number of Gold Medals


2 4 6 8 10

Keystrokes inComputer Passwords


17. The data are from 25 to 5, so the range is 5 2 (25),or 10. Consider 3 to 5 categories. Answers may vary.Sample:

18. The data are from 140 to 512, so the range is 512 2140, or 372. Consider 3 to 8 categories. Answers mayvary. Sample:

19. Answers may vary. Sample: The bars will not be ashigh and the graph will be wider when using smallintervals. 20. The Smith family had 8 families attendingwithout children and the Baker family had 3 familiesattending without children; the Smiths. 21. The Smithfamily has 3 1 1 1 2, or 6 families of 3 or more children,and the Baker family has 8 1 1 1 3, or 12 families of 3or more children; the Bakers. 22. The mean for the Smith family is

5 5 1.56 < 1.6.The median, or middle value from the ordered data, forthe Smith family is 1. The mode, or most frequent value,for the Smith family is 0. The mean for the Baker family is 5 < 2.4. The median, or middle value from the ordered data, for the

5623

3(0) 1 3(1) 1 5(2) 1 8(3) 1 1(4) 1 3(5)

3 1 3 1 5 1 8 1 1 1 3

3925

8(0) 1 6(1) 1 5(2) 1 3(3) 1 1(4) 1 2(5)

8 1 6 1 5 1 3 1 1 1 2

Payment (dollars)

Fre

qu

ency

500–

599

8

6

4

2

400–

499

300–

399

200–

299

100–

199

0–99

FrequencyMonthly

Car Payment

0–99

100–199

200–299

300–399

400–499

500–599

0

2

3

7

1

1

Fre

qu

ency

4–61–3

Golf Scores

15

12

9

6

3

FrequencyScore

1

15

11

5

TVs Sold

Fre

qu

ency

10

6

2

20–2

4

15–1

9

10–1

4

5–9

0–4

FrequencyTVs Sold

0–4

5–9

10–14

15–19

20–24

1

10

6

2

1

Baker family is 3. The mode, or most frequent value, forthe Baker family is 3. Smith: 1.6, 1, 0; Baker: 2.4, 3, 323. The data range from 9 to 53, so the intervals shouldstart at or below 9 and end at or above 53. Answers mayvary. Sample:

24. There is only one 9 in the set of data, so the correct choice is B. 25. 16% 5 5 ; the correct choice is F.

26. 20% 5 5 27. 33 % 5 5 28. 1.75% 5

5


1.

2.

9-3 Venn Diagrams pages 424–426

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. additive inverses. 2. 163. 21 4. 7

Quick Check 1.

Exercises 1. In a Venn diagram, the region of theoverlapping circles represent objects or people that fallinto both categories. 2. 1 dog 3. 72 2 12 5 60; 60students

2 124

Left Right

Freq

uenc

y

100

1

2

3

140 180 220 260 300

Freq

uenc

y

9 10111213141516

12345

7400

1.75100

13

33.33100

13

15

20100

425

16100

Number of Carsper 100 People

Fre

qu

ency

50–5

9

4

2

0

40–4

9

30–3

9

20–2

9

10–1

9

0–9

FrequencyCars

0–9

10–19

20–29

30–39

40–49

50–59

1

1

0

2

3

1



4. 5.

6. 7.

5 campers8.

10 is the GCF of30 and 40.

9.

Only 2 is primebut not odd.1 number

10. The number of students who only take math is 11 2 5, or 6. There are 15 students in summer school, so P(only math) 5 .

11. In a Venn diagram, if the circles don’t overlap,nothing falls in both categories. 12. Check students’work. 13. There are 105 favorable outcomes and 105 180 1 195 1 200, or 580 possible outcomes, so P(neither a cat nor a dog) 5 , or 0.181. 18.1%. 14. 8 2 2 5 6; the correct choice is D. 15. Subtract the volume of thecircular center with radius 3 4 2, or 1.5 ft, from theentire volume of the fountain. A 5 pr12h 2 pr22h 5

p(52)(2.5) 2 p(1.52)(2.5) 5 p(25)(2.5) 2 p(2.25)(2.5) 562.5p 2 5.625p 5 56.875p < 178; 178 ft2; the correctchoice is H. 16. The total area of the garden is 80 ? 125,or 10,000 ft2. The area of square fountain is 82, or 64 ft2.The area of the garden reserved for plants is 10,000 2 2,500 2 64, or 7,436 ft2.

105580

5 46

Math English6

15

21 9 1537

13

51117

19

Odd Prime

Factors of 30

125

10

Factors of 40

12458

102040

12356

101530

Climbing

8 57

CanoeingDownhill

26 2549

Cross-Country

8 4 8

red shapes triangles

7 11 4

sport band 17.

18.


1. 103 2 100.5 5 2.5; $2,500; 5 0.0249; 2.5% increase. 2. The manager started the vertical scale at100 instead of 0 and made the increments very small.3. The operating expenses for the corporate office inSeptember were $20,000. The operating expenses inJanuary were $10,000. The percent of increase is

5 5 1 3 100%, or 100%. 4. The manager used a vertical scale with large increments thatwent much higher than the data. 5. Answers may vary.Sample: While the monthly sales only increased by 2.5%,the operating expenses went up 100%. The business isnot doing well.

Exercises 1–2. Check students’ work.

9-4 Reading Graphs Criticallypages 428–431

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. A bar graph comparesamounts.

OperatingExpenses

Exp

ense

s (t

hous

and

s o

f $)

MonthJ F M A M J J A S

2

6

10

14

18

22

4

8

12

16

20

Monthly Sales

Sal

es (t

hous

and

s o

f $)

MonthJ F M A M J J A S

20

40

60

80

100

120

10,00010,000

20,000 2 10,00010,000

2.5100.5

6

4

2

250–274

275–299

300–324

Freq

uenc

y

Weekly Earnings

FrequencyWeekly

Earnings

250–274

275–299

300–324

6

1

3

6

4

2

21–22 23–24 25–26

Freq

uenc

y

Lengths ofWood

FrequencyLengths of

Wood

21–22

23–24

25–26

3

4

5



2.

Quick Check 1. The graph at the right starts at 0 in thevertical axis, so the difference between the airports isportrayed more accurately. 2. The second graph withthe break symbol shows the data more clearly becausethe scale is more spread out.

Exercises 1. Answers may vary. Sample: not starting atzero on the vertical scale, using intervals that are toosmall, too large, or unequal. 2. 2003 3. No, the breaksin the scale make the differences appear greater thanthey are. 4. The bar that appears to be about twice as long as the one for Music3 is Digital World; DigitalWorld. 5. The circulation for Music3 is about 8.3. Themagazine having twice that circulation, 2 ? 8.3, or 16.6million, is Sports Fan. 6. The horizontal scale does notstart at 0, so the differences are exaggerated. 7. Startthe horizontal scale at 0.

8. Boston MarathonWinning Women’s

Times

Tim

e (h

:min

)

Year19

7019

7519

8019

8519

9019

9520

0020

05

2:20

2:30

2:40

2:50

3:00

3:10

Sports Fan

Teen Life

Digital World

Music3

4 8Circulation (millions)

Magazine Circulation

12 16

Preferred Color

Num

ber

of

Stu

den

ts

Color

12108642

Red Blue Yellow

9.

You can approximate the amounts better on the graphwith the break, but the differences are exaggerated.10.

The graph with the break allows you to approximate the population more closely, but the changes areexaggerated. 11. Start the scale at 0 and use a largescale to de-emphasize change.

’98 ’99 ’00 ’01 ’02 ’03 ’04

70

50

30

10

Year

Per

cent

Recycling of Drink Containers

1 2 3 4 5

80

70

60

50

Year

Population Density

Po

pul

atio

n /

mi2

1 2 3 4 5

80

60

40

20

Year

Population Density

Po

pul

atio

n /

mi2

Titanic

Star Wars

Shrek 2

ET

400Dollars (millions)

Top Films

500 600

Titanic

Star Wars

Shrek 2

ET

100 200Dollars (millions)

Top Films

300 400 500 600



12. Use a break symbol and use a small scale toemphasize change.

13. In the first graph, starting the vertical scale at 0minimizes the appearance of change. In the secondgraph, the differences are exaggerated.

14.

15.

16. The second graph is more accurate because theenrollment only grew about 17%. The first graph makesthis difference look much larger. 17a. The differencesbetween consecutive labels are 5, 10, 20, and 40.17b. No; the time differences are not the same, which ismisleading. 17c. Yes; each interval is twice the size ofthe interval before it. 18. x2 5 9.752 1 12.752 5 257.625;x 5 16.05; the correct choice is C. 19. 7 2 3 ? 2 5

2 3 ? 5 2 5 ; the correct choice is G. 20. A 5

pr2 5 p(8)2 5 64p< 201.1;201.1 cm221. A 5 pr2 5 (142) 5196p < 615.8; 615.8 in.2 22. A 5 pr2 5 p(9.6)2 5 92.16p< 289.5; 289.5 m2 23. A 5 pr2 5 p(1.22) 5 1.44p < 4.5;4.5 ft2

34

274

304

94

152

14

12

Public SchoolEnrollment in

the U.S.

Enr

ollm

ent

(tho

usan

ds)

Year19

7019

7519

8019

8519

9019

9520

0020

05

10,000

20,000

30,000

40,000

50,000

60,000

Public SchoolEnrollment in

the U.S.

Enr

ollm

ent

(tho

usan

ds)

Year19

7019

7519

8019

8519

9019

9520

0020

05

48,000

50,000

52,000

54,000

56,000

58,000

60,000

62,000

’98 ’99 ’00 ’01 ’02 ’03 ’04

6462605856545250

Year

Per

cent

Recycling of Drink Containers


1.

2.

3. The second graph; the first graph visually exaggeratesthe change in the number of visitors.


1. 5

5 94.5 2. 80, 83, 85, 88, 88, 90, 100, 101, 106, 109,110: The median is 90. 3. The mode is 88. 4. The rangeis 110 2 80 5 30 5. Answers may vary. Sample:

6.


Fre

qu

ency

91–10081–90

Scores

Math Scores

71–8061–70

7

6

5

4

3

2

1

68 72 76 80 84 88 92 96 100

FrequencyScores

61–70

71–80

81–90

91–100

1

5

5

6

1,04011

80 1 83 1 88 1 88 1 90 1 106 1 100 1 101 1 110 1 109 1 8511

’98 ’99 ’00 ’01 ’02 ’03 ’04

500

300

100

Year

Visitors to National Parks

Vis

ito

rs (m

illio

ns)

’98 ’99 ’00 ’01 ’02 ’03 ’04

440

430

420

410

Year

Visitors to National Parks

Vis

ito

rs (m

illio

ns)



8.

Answers may vary. Sample: The graph without the breaksymbol shows that the number of students per computerare similar for each school.

9-5 Stem-and-Leaf Plotspages 433–437

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. the frequency of eachdata value 2. 29.2 3. 30 4. 40

Quick Check 1.

More Than One Way Median: 41.5; mode: 34; checkstudents’ work.

Quick Check 2. The mean and median for the citymileage is < 22.6 mi/gal and 22 mi/gal, respectively. The mean and median for thehighway mileage is 5

30 mi/gal and 28 mi/gal, respectively. Both the mean andmedian give the impression that the highway mileage ofthe new cars is higher than the city mileage.

Exercises 1. 6 is the stem; 7 is the leaf. 2. 6, 7, 8, 9 arethe stems. 3. 8, 8 are the leaves. 4. There are 24 dataitems. 5. Find the median: 84%; find the mode: 78%.

24 1 25 1 27 1 28 1 33 1 33 1 407

18 1 18 1 19 1 22 1 24 1 27 1 307

Monthly HighTemperatures

Key: 13 4 means 134

611104

77

30 5 6

89

10111213

ElementarySchool

Average Number of Studentsper Computer

MiddleSchool

HighSchool

12

8

4

ElementarySchool

Average Number of Studentsper Computer

MiddleSchool

HighSchool

14

13

12

11

10

6.

There are 26 items, so the median is the mean of the 13th and 14th values: 5 17.5. The stem 1 has thedigits that repeat the most, and the digits that repeat the most are 8 and 9, so there are two modes: 18 and 19.7. 8.

9.

10. The mean of blood pressure for men: 68 1 76 12(77) 1 79 1 81 1 2(84) 1 871 88 1 2(89)1 2(90) 1921 941 951 981 1001 102 5 1,740 4 20 5 87. Themean of blood pressure for women: 2(65) 1 66 1 68 170 1 2(71) 1 72 1 75 1 76 1 2(78) 1 79 1 2(80) 1 83 185 1 86 1 90 1 91 5 1,529 4 20 < 76.5. The median of blood pressure for men is 5 88.5. The median of

blood pressure for women is 5 77. The mean andmedian for the men’s blood pressure are 87 and 88.5,respectively, whereas the mean and median for thewomen’s blood pressure are 76.5 and 77, respectively.11. Both measures of central tendency indicate that thewomen’s blood pressure in the survey was considerablyless than the men’s blood pressure.12.

There are 8 leaves for saw A, so the median is the meanof the 4th and 5th leaves: 5 57.5. The leaf 4repeats on stem 5, so the mode for saw A is 54. There are8 leaves for saw B, so the median is the mean of the 4th and 5th leaves: 5 54.5. No stems for saw B have leaves that repeat, so saw B has no mode. 13. The meanfor the men’s score is

5

< 277.77. There are 22 leaves on the men’s side,so the median is the mean of the eleventh and twelfthscores: 278. There are three modes on the men’s side:276, 279, and 280. The mean for the women’s score is

5

< 280.23. There are 22 leaves on the women’s 6,16522

2 ? 272 1 273 1 2 ? 274 1 276 1 2 ? 277 1 2 ? 278 1 3 ? 280 1 282 1 2 ? 283 1 284 1 285 1 287 1 3 ? 2902 1 1 1 2 1 1 1 2 1 2 1 3 1 1 1 2 1 1 1 1 1 1 1 3

6,11122

3 ? 272 1 4 ? 276 1 2 ? 277 1 3 ? 278 1 4 ? 279 1 4 ? 280 1 282 1 2853 1 4 1 2 1 3 1 4 1 4 1 1 1 1

52 1 572

57 1 582

6 3 means 63Key: 61 means 1

4567

3232

574

Saw BLength of Wood

97 4

4

Saw A

8 43

21

76 1 782

88 1 892

2 means 3.2Key: 3

2103

7307

529

89

3456

1 means 131Key: 13

5621

7644

97 8 8

10111213

8 means 48Key: 4

0013

8274

9386

498

4567

17 1 182

6 means 6Key: 0

600

717

827

82

83 6 6 7 8 8 8 8 8 9 9 9 9 9

012



side, so the median is the mean of the eleventh andtwelfth scores: 280. There are two modes on the women’sside: 280 and 290. The mean, median, and mode for themen’s golf scores are around 278 strokes, while thewomen’s scores were around 280. This indicates that thedifference in scores isn’t very large. However, the factthat one of the modes for the women’s scores was 290shows that women frequently do have a higher numberof strokes.14a. 14b. Answers may

vary. Sample: The newdata include decimalvalues. You mightchoose to use theinteger part as stemsto avoid decimals inthe leaves. 15. Whena set of data containsnumbers in the 30s,40s and 60s only, it is

not necessary to put a 5 on the stem of a stem-and-leafplot, but it would help show the range of data.16. The median for the left side is 43.5, so the medianfor the right side is 43.5. So, the missing digits for stem 4on the right side are 2 and 5, or 3 and 4. Thus, the modeon the right side is 42, or 42 and 50, so the mode on theleft side is 42, or 42 and 50. The mode on the left sidecannot be 42, so the missing leaves in stem 4 on the rightare 3 and 4, and the mode for both sides must be 50. Themissing leaf for stem 5 on the left side, then, is 0. The range for the right side is 51 2 31, or 20, so the range forthe left side is 20. Since the high value on the left is 50,the low value must be 50 2 20, or 30. Thus, the missingleaf for stem 3 on the left is 0.

17. Each plot has 8 numbers so the median is theaverage of the 4th and 5th largest numbers. For plot B, itis , or 3.2; the correct choice is B. 18. 9.25 in fraction form is . Order the numbers from least to

greatest; , , , 10 , ; the correct choice is F.

19. Find the mean:5

5 180.3; find the median: 177, 178, 179, 179, 180,

180, 180, 182, 183, 185: 180; find the mode: 180; find therange: 185 2 177: 8. 20. Find the mean:

5

5 6.7; find the median: 2, 4, 4, 4, 4, 4, 6, 6, 6, 8, 8, 8, 8,10, 10, 10, 12: 6; find the mode: 4; find the range:12 2 2 5 10.

11467

4 1 2 1 4 1 8 1 10 1 12 1 10 1 6 1 4 1 8 1 4 1 6 1 8 1 4 1 6 1 8 1 1017

1,80310

178 1 179 1 180 1 182 1 177 1 183 1 185 1 180 1 180 1 17910

101695

691391

4

914

3.1 1 3.32

Life Spans ofDifferent Animals

0 1 3 4 5 6 7 7

1 0 0 0 2 2 3 5 5 5 5 5 8

2 0 0 0 0 2 5 5

3

4 0

9-6 Box-and-Whisker Plotspages 438–441

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Median 2. 24 3. 4 4. 95

Quick Check 1. Answers may vary. Sample: The rangefor the girls’ heights is greater than the boys’. Overallthe boys tend to be taller than the girls. The girls’ upperquartile is equal to the boys’ lower quartile. 2. Theordered data are 4 10 11 12 16 21 24 24 25 26 26 2931 35 47 53, and the median is 5 24.5.The lower quartile is the median of the lower half of the data: 4 1011 12 16 21 24 24; 5 14. The upper quartile is the median of the upper half of the data: 25 26 26 2931 35 47 53; 5 30. The least and greatest values are 4 and 53, respectively. Draw a number line thatincludes the least and greatest values. Mark points belowthe number line to represent the least and greatestvalues, the median, and the upper and lower quartiles.Use the lower and upper quartiles to form a box. Draw avertical line through the median.

Draw the whiskers fromthe box to the least andgreatest values.Exercises 1. The median

is the middle quartile of a data set. 2. C 3. E 4. B5. Answers may vary. Sample: the median income formen exceeded that of women. The range for women’sincomes was greater than men’s. The men’s incomeswere more consistent than the women’s. 6. Answersmay vary. Sample: the range of percents of on-timearrivals is about the same for Atlanta and Denver.Overall, Denver had a greater percent of on-timearrivals per day in 2004 than Atlanta. The median forDenver is about the same as the upper quartile forAtlanta.

48 2 37 5 11. They had the same range.7. Find the median in the ordered data: 152 161 161180 184 193 199 221 229 267 271 273; 196. Find thelower quartile: 152 161 161 180 184 193; 170.5. Findthe upper quartile: 199 221 229 267 271 273; 248. Theleast and greatest values are 152 and 273. Plot 152, 170.5,196, 248, and 273 below the number line, form a boxwhose ends are the upper and lower quartiles, draw avertical line at the median, and draw the whiskers.

8. Find the median in the ordered data: 2 4 5 5 5 5 66 6 6 7 8 8 8 9 9 9 10 11 12 13 13 14 18; 8. Find

200150 250

30 35 40 45 50

American

National

0 10 20 30 40 50

29 1 312

12 1 162

24 1 252



the lower quartile: 2 4 5 5 5 5 6 6 6 6 7 8; 5.5. Findthe upper quartile: 8 8 9 9 9 10 11 12 13 13 14 18;10.5. The least and greatest values are 2 and 18. Plot 2,5.5, 8, 10.5, and 18 below the number line, form a boxwhose ends are the upper and lower quartiles, draw avertical line at the median, and draw the whiskers.

9. American League: 43 2 32 5 11. National League:48 2 37 5 11. They had the same range. 10. The medianis the dot or vertical line inside the box; 85. 11. The lower quartile is the left end of the box; 70. 12. 100 2 45 555 13. The data are skewed. The two middle quartiles ofthe data are not evenly spread out. 14. Find the mean inthe ordered data: 134 135 143 156 156 162 162 173; 156.Find the lower quartile: 134 135 143 156; 139. Find theupper quartile: 156 162 162 173; 162. The least andgreatest values are 134 and 173. Plot 134, 139, 156, 162,and 173 below the number line. Form a box whose endsare the upper and lower quartiles, draw a verticalline at the median, anddraw the whiskers.15. Yes; it would move the upper quartile from 162 to167.5, and the lower quartile would move from 139 to149.5. 16. Since there are 10 pieces of data, the mean ofthe fifth and sixth values is the median. So, if x representsthe fifth value, then 5 60.5; x 1 71 5 121; x 5 50. Thefifth piece of data is 50. 17. The median is the middlevalue of the box-and-whisker plot; the median is 67, sothe correct choice is C.18.

; The correct choice is J.19. 3.14 ? 3 ? 12 5 113; the correct choice is C20.


1.

2.



1 2 3 4 5 6 7 8 9 10111213

35 40 45 50 55

0 means 130Key: 13

800

931

32

4 5 5 6 6 7111213

n 5 5 153 5 3n

3

15 5 3n 18 2 3 5 3n 1 3 2 3

18 5 3n 1 3 18 2 2n 1 2n 5 n 1 3 1 2n

18 2 2n 5 n 1 3

x 1 712

130140150160170180

0 5 10 15 20

9-7 Making Predictions FromScatter Plots pages 443–447

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. It identifies the locationof a point.

2–3.

Quick Check 1.

2.

Exercises 1. A scatter plot is used to compare two setsof data. 2. negative 3. no trend 4. positive

5. 6.

2 4Hits

Ru

ns

6 8 10

6

4

2

1 2Number of Roommates

Mo

nthl

y R

ent

(do

llars

)

3 4x

y

800

600

400

200

0

2 4 6 8Age (yr)

Valu

e (d

olla

rs) 14,000

10,000

6,000

2,000

4 20

Age

Sle

ep T

ime

(h)

8 12 16

14

12

10

8

6

4

2

0

4

A

Ox

y

4B



7. Negative trend 8. Negative trend

9.

about 62 billion barrels10. No trend; age does not determine the number ofpets a person has, so people of all ages own varyingnumbers of pets. 11. Negative trend; as thetemperatures increase, you wear fewer layers of clothing.12. No; it depends on how close the points are on theline; also, the farther your prediction point is from thelast point used to create the trend line, the less accurateyour predictions may be.13a–b.

13c. At 500 at-bats, the trend line shows about 140 hits;about 140 hits. 13d. about 800 14. No; there is norelationship between these two variables—one did notcause the other. 15. 45 16. 57, 66, 67, 69, 69, 72, 75, 81,85: 69 is the middle number because when the numbersare sorted from least to greatest it is the fifth numberfrom the right and left, which makes it the median.17. 149,597,870.691 5 1.496 ? 10x; x 5 8 18. Order thedata and determine the median and quartiles:1 3 4 6 6 7 7 7 8 8 8 8 9 9 9 10 10. Under the

250 350At-Bats

Hit

s

450 550 650

170

130

90

500

40World Oil Production (billion barrel)U

S P

erce

nt o

f W

orl

d O

il P

rod

ucti

on

45 50 55 60

25

20

15

10

5

065 70 75

X

Oil Production (1960-2000)

2Number of Farms (millions)

Ave

rag

e S

ize

(acr

es)

3 4 5 6

400

300

200

100

010 20

Age

Life

Exp

ecta

ncy

(yr)

30 40 50

80

60

40

20

0

number line, plot the low point 1; plot the lower quartile6; plot the median 8, plot the upper quartile 9, and plotthe high point 10. Draw a box having ends at the upperand lower quartile. Connect the high and low points tothe box with segments.


1. DeWayne: 2 because 2 3 3 5 6, which equals the sizeof their household; Tom: 8 because it is the highestquantity of cell phones; Jack: 6 because 6 familymembers corresponds to either 2 cell phones or 6 cellphones since DeWayne’s family has 2 cell phones Jack’sfamily should have 6 cell phones; Rita: 4 because itequals the number of family members in Rita’s family;Manny: 6 because it is only the remaining data point.2. Art: 80% because 8 3 10 5 80; Sam: 85% because nohair corresponds to 85; Dee Dee: 100% because perfectscore is 100; Barb: 80% because it approximately equalsSam’s; Wilma: 70% because it is the lowest score.3–4. Check students’ work.


1. 2.

3.

4. As the populationincreases, the electoralvotes increase, so thedata show a positivetrend.

9-8 Circle Graphs pages 450–453

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. A proportion is anequation stating that two ratios are equal. 2. 24 3. 304. 28 5. 41Quick Check 1. The color in the key for 50 or oldermatches the part of the circle marked 22%. Find 22% of21.3 million: 22% ? 21,300,000 5 0.22 ? 21,300,000 5

23

100 20Population (millions)

Ele

cto

ral V

ote

s

30 40

60

40

20

0

0 5 10 15

Ages of WWII Veterans

7 3 3 4 5 6 9

8 0 3 6 7 8 9

9 1 1 2 5 5

8 means 68%

Grades

Key: 6

82000

521

533

775

78 9

6789

10

0 2 4 6 8 10



4,686,000; 4,686,000 people. 2.

Total number of vehicles:75 1 55 1 37 1 1 5 168.Cars: = , so m < 1618.

Vans: = , so m < 1188.

Trucks: = , so m < 798.

Other: = , so m < 28.

Exercises 1. The sum of themeasures of the central angles of a circle is 3608.2. $10.84 because it is the amount in the light blueshaded section of circle. 3. The key identifies eachsector. 4. Football was chosen by the most students.5. football: 200 ? 0.30 5 60; baseball/softball: 200 ? 0.27 554; soccer: 200 ? 0.21 5 42; basketball: 200 ? 0.12 5 24;swimming: 200 ? 0.06 5 12; tennis: 200 ? 0.04 5 8 6. 30%of x is 90: 0.3 ? x 5 90; 90 4 0.3 5 300; 300 students7. Yes; it would be the smallest sector. 8. The total number of people is 200. Find the central angles: 5

, so a < 1488; 5 , so r < 1558; 5 , so h <

408; 5 , so s 5 188.

9. The percents are 28%, 48%, 7%, and 17%. Find the central angles:

10. The total number of patients is 340. Find the central angles:

5 , so a 5

368; 5 ,so b< 318; 5

, so c < 438;

5 , so d <

778; 5 ,

so e < 698; 5

, so f < 1048.

11. Find the central angles: 5 , so p < 1568; 5 ,s360

2081

p360

3581

f360

98340

e360

65340

d360

73340

c360

41340

b360

29340

a360

34340Miles of Running

Lessthan 329%

3miles19%

10%

12%

5 miles

More than 6

6 miles

4 miles21% 9%

x 5 360 ? 0.17 < 618

g 5 360 ? 0.07 < 258

m 5 360 ? 0.48 < 1738

s 5 360 ? 0.28 < 1018Vehicle Types

Small28%

Large7%

Luxury17%

Midsize48%

Favorite Books

Adventure41%

Science Fiction5%

Horror11%Romance

43%

s360

10200

h360

22200

r360

86200

a360

82200

m3608

1168

m3608

37168

m3608

55168

m3608

75168

Fuel Use

Cars45%

Other 1%

Trucks22%

Vans33%

so s < 898; 5 , so h 5 808; 5 , so g < 368.

12. Circle graph; it allows you to show all the parts as awhole. 13a. Find the central angles: 17.7% of 3608 <648; 37.4% of 3608 < 1358; 44.9% of 3608 < 1628.

13b. 37.4% of 400 5 0.374 ? 400 < 150; 150 women13c. (17.7% 1 37.4%) of 400 5 55.1% of 400 50.551 ? 400 < 220; 220 women 14. The total number ofresponses is 11 1 17 1 24 1 17 1 13 1 8, or 90. Divide11, 17, 24, 17, 13, and 8 by 90 to find the correspondingpercents. Multiply each of the percents by 360 to find the corresponding angle measures. The circle graph is amore appropriate display of the data than a bar graph,because the circle graph shows the proportions clearly.

15. $70 is the largest value and $30 is the smallest valueand graph B is the only graph that shows $70 as thelargest and $30 as the smallest piece of the pie, so thecorrect choice is B. 16. The sales of insect repellentwould increase as mosquito population increases, so thetrend would be positive; the correct choice is F.17.

200 40Height (in.)

Wei

ght

(lb

)

60

80

60

40

20

0

Color of Cell Phones

Silver17

Green17

Red24

8Black

11White

Blue13

Magazine Covers

44.9%Celebrities

Athletes37.4%

17.7%Models

Favorite Lunch

Pizza43%

22%Hamburger

Grilledcheese

10%25%

Spaghetti

g360

881

h360

1881




1. Like terms were combined to get 6 x 5 100, and each

side was divided by 6 . 2. The biggest section looks like

of the circle, so 75% makes sense. The other two sections look like about 25% of the circle with one beingslightly less than the other. 3. Let x 5 the percent ofwhite perch in a lake. The percent of fish that aresmallmouth bass is twice the percent of white perch, or2x. The percent of sunfish is one third the percent of white perch, or x. x 1 2x 1 x = 100%, or 3 x = 100%;

x = 100%; ? x = 100% ? = 30%, so the percent ofwhite perch is 30%. Smallmouth bass = 2(30%) = 60%;sunfish = (30%) = 10%.4. 5. positive

6. Answers mayvary. Sample:70 oz; no, becausethe largest drinksize probabilitywill not continueto increase asquickly now thatthe largest size isso big.

7. About half of the data values fall between the lowerand upper quartiles.

9-9 Choosing an Appropriate Graphpages 456–459

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. frequency

2.

Quick Check 1a. Bar graph; scatter plots need to benumerical; bar graphs represent categorical data.1b. Scatter plot; you are looking to see if there is a trend or a relationship. 1c. Line graph; it shows change over time.

FrequencyValues

0–1.9

2–3.9

4–5.9

6–7.9

8–9.9

5

6

2

2

2

6.5 7.5 8.5

70

60

50

40

30

20

10

01970 1980 1990 2000 2010

Year

Siz

es A

vaila

ble

(oz)

Available Drink Sizesat a Convenience Store

13

310

310

103

103

13

13

13

34

23

23

2. A circle graph shows comparisons of the parts of a whole.

Exercises 1–3. Check students’ work. 4. Scatter plot;if there are two sets of data, you can see if there is arelationship. 5. Line graph; this graph is better forshowing data over time. 6. Double bar graph; this graphcan show a comparison of the two groups. 7. Circlegraph; a circle graph is a good way to compare parts of awhole. 8–10. Answers may vary. Samples are given.8. Line graph; it shows data over time well.

9. Box-and-whisker plot; itgives a good summary ofdata, including high andlow, median, and upper andlower quartiles.

10. Stem-and-leaf plot; itshows a data set arranged inorder.

11. Double bar graph; it shows a comparison of each category.

12–14. Check students’ work. 15a. The data do notshow parts of a whole.

16 to24

25 to34

35 to44

45 to54

55 to64

65 andolder

0

2

4

6

8

10

12

Less Than $10 $10 or More

Num

ber

of

Wo

rker

s (m

illio

ns)

Workers Paid Hourly Rates

Age

0 means 606

1000

411

712

723

9

7

3456

52 56 60 64 68

’99 ’01Year

Florida’s Resident Population

Po

pul

atio

n (t

hous

and

s)

’03

17,800

17,400

17,000

16,600

16,200

15,800

15,400

15,000

Weekly Budget

Lunch30%

Clothes35%

Savings20%

15%

Recreation



15b. A line graph shows change over time.

16. Any datathat representparts of awhole can bedisplayed incircle graphsor bar graphs.17. Answersmay vary.Sample: Youcould choose ahistogram with

intervals. The intervals cut down the amount of spaceneeded to show the data. 18. Box–and–whisker plotsare used to organize very large data sets, so using one torepresent this data would be most appropriate; thecorrect choice is D. 19. There are 2 1 1 1 5 1 6 1 3, or17 students participating in the read–a–thon. 6 of themread between 9 and 11 books. < ; the correct choice is J. 20. 37 1 x 5 180; x 5 180 2 37 5 143; 1438

21. 95 1 n 5 180; n 5 180 2 95 5 85; 858 22. 42 1 a 5

180; a 5 180 2 42 5 138; 1388 23. 170 1 k 5 180; k 5

180 2 170 5 10; 108 24. 64 1 w 5 180; w 5 180 2 64 5116; 1168




1. Each side of each square is about 0.4 cm, so the areaof each square is 0.42, or about 0.16 cm2. The lateralsurface area of the bead is 0.16 ? 6, or about 1 cm2; thecorrect choice is B. 2. The length of each side of thebase of the pyramid is about 1.5 cm, so the area of thebase is 1.52, or about 2.25 cm2. The height of each triangle is about 1 cm, so the area of each triangle is ? 1.5 ? 1, or about 0.75 cm2. The total surface area is

2.25 1 4(0.75), or about 5.25 cm2; the correct choice is H.


1. Quartiles divide a data set into four equal parts. 2. Ascatter plot displays two sets of data as ordered pairs.3. An angle whose vertex is the center of the circle is acentral angle. 4. A display that shows numeric data inorder is a stem-and-leaf plot. 5. Find the mean:

5

5 15.18; find the median: 10, 12, 12, 14, 15, 15, 15, 16,16, 18, 24: 15; find the mode: 15; find the range: 24 2 10 514. 6. Find the mean:

5

5 9.82; find the median: 9.0, 9.1, 9.1, 9.4, 9.5, 9.8, 9.9,10.2, 10.3, 10.3, 10.5, 10.7: 9.85; find the mode: 9.1 and10.3; find the range: 10.7 2 9.0 5 1.7.

117.812

9.1 1 10.2 1 9.5 1 10.3 1 10.5 1 9.1 1 9.0 1 9.8 1 9.9 1 9.4 1 10.7 1 10.312

16711

15 1 12 1 10 1 16 1 24 1 16 1 12 1 15 1 18 1 14 1 1511

12

13

617

’94 ’96Year

Percent of U.S. HomesWith Personal Computers

Per

cent

’98 ’00 ’02 ’04

60

40

20


8. 22 1 8 5 30; 30 2 25 5 5; 5 artists

9.

Answers may vary. Samples: The graph with no breakgives a realistic comparison between the data sets. Thegraph with the break symbol shows the data moreclearly because the scale is more spread out.10. Find the median of the ordered data set: 63 65 67 7275 78 78 79 79 79 85 85 89 90 99; 79 is the median. Thenumber that appears most often is the mode, and 79 appears 3 times in the data set so it is the mode.

11. 72; 85

From the stem-and-leaf plot in Exercise 10, the leastvalue is 63, the lower quartile is 72, the median is 79, theupper quartile is 85, and the greatest value is 99.

60 70 80 90 100

0 means 90Key: 9

3250

5559

789

8 9 9 96789

1 2Year

Boys

Girls

Num

ber

3 4 5

42

38

34

30

1 2Year

School Chorus Members

BoysGirls

Num

ber

3 4 5

40

30

20

10

0

Fre

qu

ency

50–5

4

4

2

0

55–5

960

–64

65–6

970

–74

75–7

980

–84

FrequencyNumber

50–54

55–59

60–64

65–69

70–74

75–79

80–84

2

3

3

2

2

4

2



12.

13. Answers may vary. Sample: Scatter plot; it shows therelationship between two sets of data.

14. Answers may vary. Sample:Stem-and-leaf plot; it showsnumerical data arranged in order.


1. Find the mean:5 5 2.125

rounds to 2.13; find the median: 23, 22, 21, 21, 3, 5, 7, 9:1; find the mode: 21; find the range: 9 2 (23) 5 12.2. Find the mean:

5

5 6.1 rounds to 6.12; find the median: 5.7, 5.8, 5.9,6.0, 6.2, 6.3, 6.3, 6.4, 6.5: 6.2; find the mode: 6.3; find the range: 6.5 2 5.7 5 0.8. 3. Mean with the outlier:

5 5 ;Mean without the outlier:

5 5 13.625;13.625 2 12.333 < 1.3. It lowers the mean by about 1.3.

1098

3(12) 1 10 1 14 1 18 1 15 1 168

12.31119

3(12) 1 10 1 14 1 18 1 2 1 15 1 169

255.19

5.8 1 5.9 1 6.3 1 6.5 1 5.7 1 6.2 1 6.4 1 6.0 1 6.39

178

(21) 1 9 1 (22) 1 3 1 (21) 1 5 1 (23) 1 78

0 means 30Key: 3

500

613

73 9

123

50 55Temperature (�F)

Num

ber

of

Stu

den

ts

60 65 70 75 80

10

8

6

4

2

0

400

800

1,20

01,

600

2,00

02,

400

Length and Water Flow of Rivers

Length (mi)

Flo

w (1

,000

ft3 /

s)

300

200

100

00

4. 5.

6. Find the mean:

5

5 5 2.25. The middle value of the ordered data is the median: 2. The mode isthe value that occurs most often: 2. The mean, median,and mode are 2.25 movies, 2 movies, and 2 movies.

7.

8.

9. 45% of 600 students 5 0.45 ? 600 5 270; 270 students10. 20% of 600 is 0.20 3 600, or 120 students.

1,300–1,599

1,000–1,299

700–999

400–699

Salary ($)

Fre

qu

ency

Monthly Salary

8

6

4

2

FrequencySalary

400–650

700–950

1,000–1,250

1,300–1,550

2

7

4

1

11–129–10Hours

Number of Hours of Sleep

7–85–6

8

6

4

2Fre

qu

ency

FrequencyHours

5–6

7–8

9–10

11–12

3

9

4

1

4520

0 1 4 1 12 1 9 1 8 1 5 1 0 1 73 1 4 1 6 1 3 1 2 1 1 1 0 1 1

3(0) 1 4(1) 1 6(2) 1 3(3) 1 2(4) 1 1(5) 1 0(6) 1 1(7)3 1 4 1 6 1 3 1 2 1 1 1 0 1 1

4 5 63210 7

FrequencyMovies

0

1

2

3

4

5

6

7

3

4

6

3

2

1

0

1



11. 100 2 45 5 55; 55% do not work at a restaurant.55% of 600 5 0.55 ? 600 5 330; 330 students.12.

13a. Answers may vary. Sample:

13b. The earnings oftop male golfersrange from $14.5million to $21.9million, with half ofthem earning over

$15.3 million. The top female golfers earn from $6.3million to $10.2 million, with half earning more than $7.3 million. Each of the top male golfers makes morethan the top female golfer.14. Box graph; it shows the relative size of categories.

15. Line graph; it shows the changes over time.

16. Bar graph; it shows the relative size of categories

17. 100 2 67 5 33; 33 mothers

Per Capita Freshwater Use

State

Gal

lon

s p

er D

ay

AlaskaOre.

Ky.Ohio

Calif.Fla.

2,000

1,000

0

’99 ’00 ’01 ’02 ’03 ’04

90

80

70

60

Year

Percent of Music Soldon Compact Discs

Per

cent

Leading U.S.Clothing Businesses

Bill

ion

s o

f D

olla

rs

Nik

e

10

8

6

4

2

0

VF

Jon

es

Liz

Cla

ibo

rne

Re

eb

ok

6 8 10 12 14 16 18 20 22

MalesFemales

3 means 83.3Key: 83

013

05

3 3 8 8 9818283

TEST PREP page 465

1. Find the median: 6, 7, 7, 7, 7, 8, 8, 9, 9, 9; the median is= , or 7.5; find the mode: 7; the correct choice is B.

2. The measure of central tendency that is best todescribe your classmates’ favorite brand of sneakers isthe mode, the most frequently occurring item. The modeis appropriate for non-numerical data; the correct choiceis F. 3. Find the mean:

= = 5.1; find themedian: 4.6, 4.8, 5.1, 5.1, 5.2, 5.3, 5.6; the median is 5.1, sothe correct choice is B. 4. A soup can has the shape of acylinder, not of a prism; the correct choice is J. 5. Thetrend is negative; a trend line made through the middleof the points shows one set of values increasing whilethe other set of values tends to decrease; the correctchoice is B. 6. A line graph shows how a categorychanges over time; the correct choice is J.

7. 5

x 5 12 ? 30x 5 360; the correct choice is D.

8. x 1 (x 1 1) 1 (x 1 2) 5 423x 1 3 5 42

3x 1 3 2 3 5 42 2 33x 5 39

5

x 5 13; the correct choice is H.9. In this sequence, the difference between eachconsecutive term is 1 less than the difference from theprevious term. Since the difference between 22 and 23is 21, the difference between 23 and 25 is 22, and soon. Therefore, to find the first missing term, find thedifference between 28 and 212: 212 2 (28) 5 24. Thedifference between the 12 and the missing numbers willbe one less: 24 1 (21) 5 25. 212 1 (25) 5 217. Thefirst missing number is 217, so find the differencebetween 217 and 223: 223 2 (217) 5 26. Thedifference between 223 and the missing number will beone less: 26 1 (21) 5 27. 223 1 (27) 5 230, so thesecond missing number is 230; the correct choice is B.10. The width is 2(48), or 96 m. The length is 3(48) or 144m. The correct choice is G. 11. 3.0481 rounds to 3.05;grid 3.05 12. If there are 2 cubits in a yard, which isequal to 3 feet. Then there are 1.5 feet in a cubit. 1.5 ? 125 18; 18 inches; grid 18 13. [2] She spent $50.00 2 $7.04,or $42.96, when she went shopping. She spent $42.96 2$18.99, or $23.97 on the three books, so she spent , or $7.99 for each book. [1] minorcomputational error OR no work shown 14. [4] Put the data in order: 19, 21, 23, 24, 25, 25, 25, 25,26, 26, 27, 29, 31, 33, 33, 34, 40

n 5 17median: 26lower quartile: 24.5

5 24.5upper quartile: 32

5 3231 1 332

24 1 252

$ 23.973

393

3x3

30x

112

35.77

5.1 1 5.6 1 5.3 1 5.1 1 4.8 1 4.6 1 5.27

152

7 1 82



[3] minor error in one part; [2] minor error in two parts;[1] answer correct, but work not shown


1–5. Answers may vary. Samples are given for wheat.1. 5 ; 16x 5 4.9; x < 0.306 lb 2. 13.9 in.3

3. 5 ; x 5 3,200 million lb;

3.2 3 109 lb 4. 5 ; 0.306x 5 44.48 ? 109;

x 5 1.45 3 1011in.3 5a. 1.45 3 1011 5 (4,110)3; about4,110 in. or 342.5 ft 5b. 2(342.5) 5 685; about 685 6. 1.6 million tons, or 3.2 3 109 lb; this is the amount ofwheat the world eats per day.

23p

x in3

3.2 3 109 lb

13.9 in3

0.306 lb

1 ton2,000 lb

1.6 million tonsx lb

16 oz1 lb

4.9 ozx lb

32282420 36 40




Probability pages 468–509


1. ? 5 5 2. ? 5 ? 5 3. ? 5

? 5 ? 5 4. ? 5 ? 5 ? 5 ? 5

5. ? 5 ? 5 ? 5 6. ? 5 ? 5

7-8. Answers may vary. Samples are given.

7. 5 ; 5 ;

5 8. 5 ;

5 ; 5

9. There are 8 sections and 3 are yellow, so P(yellow) is . 10. There are 8 sections and 2 are green, so P(green)

is , or . 11. There are 8 sections and 1 is purple, so

P(purple) is . 12. There are 8 sections, of which 2 are

green and 2 are blue, so P(green or blue) 5 5 5 .13. There are 8 sections, and 2 are blue and 3 are yellow, so P(blue or yellow) is , or . 14. There are 8 sections, and 2 are green and 1 is purple, so P(green or purple) is , or .

10-1 Theoretical and ExperimentalProbability pages 470–473

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. sample space 2. 1, 2, 3,4, 5, 6 3. 4. 5.

Quick Check 1. 8 heads occurred in 20 tosses, so the experimental probability of getting heads is , or ; 0.4.2. Theoretical; the result is based on the number ofpossible outcomes. 3. Since the odds in favor ofselecting a yellow ball at random are 2 : 5, the oddsagainst it are 5 : 2.

Exercises 1. When you conduct trials to gather data,you are finding experimental probability.2. P(cereal with nuts) 5 5 3. P(cereal with whole

grains) 5 5 4. Odds in favor of an event is the ratio: number of favorable outcomes : number of unfavorable outcomes. For the baseball team, the odds

of winning are , or . 5. 5 5 0.272 6. 5

5 0.376 7. The number of zinnias are

250 2 (68 1 94 1 8) 5 80; 5 5 0.32.8. Experimental; the result is found by repeating an

825

80250

47125

94250

34125

68250

32

6342

310

2480

15

1680

25

820

13

12

16

38

2 1 18

58

2 1 38

12

48

2 1 28

18

14

28

38

1020

number of white sectionsnumber of yellow sections

1030

number of white sectionsnumber of all sections

2030

number of yellow sectionsnumber of all sections

22

number of white sectionsnumber of yellow sections

42

number of all sectionsnumber of white sections

24

number of white sectionsnumber of all sections

217

11

217

15

1017

917

11

917

21

934

23

2734

13

11

13

31

19

38

89

1232

89

38

14

32

74

314

712

914

425

425

11

2425

16

314

3 ? 17 ? 2

12

37

experiment. 9. Theoretical; the result is based on the number of possible outcomes: 5

5 5 . 10. There is 1 favorable outcome and 12 possible outcomes, so the odds in favor are 1 : (12 2 1),or 1 : 11. 11. There are 819 different animal species atthe zoo, so the number of possible outcomes is 819.There are 115 mammal species, so the number offavorable outcomes is 115. The probability of choosing a fact sheet about a mammal is .12. 1 : (4 2 1), or 1 : 3 13. No, since the odds in favor are 2 : 3, the probability would be 5 . 14. The total number of children surveyed is 171, so P(9:30) 5

. 15. The total number of children surveyed is 171, so

P(8:30) 5 . 16. The total number of children

surveyed is 171, so P(7:3028:30) 5 5 .17. The total number of children surveyed is 171, so P(not 9:00) 5 5 . 18. The total number of children surveyed is 171, so P(after 8:30) 5

5 . 19. The total number of children

surveyed is 171, so P(before 9:30) 5 5

. 20. There are 36 square units on the board and 4

green units, so 5 5 .21. The total number of marbles that Tammy pulledfrom the bag was 8 1 7, or 15. Of the 15 marbles, 8 weregreen. You can use this ratio to set up a proportion topredict how many of 20 marbles are green.

22. The total surface area of the eraser is equal to thenet for the eraser. h < 1.5 in., w < 1.5 in.; 1.5 3 1.5 52.25; 2 triangles 5 1 square: s 5 0.5 in.; 0.5 3 0.5 5 0.25;2.25 1 0.25 5 2.5; the correct choice is J.23. h 5 222(75 2 65) 5 222(10) 5 2,220; the correctchoice is D. 24. 25% of 3608 5 0.25 ? 360 5 90, or 908

25. 10% of 3608 5 0.10 ? 360 5 36, or 368 26. 20% of3608 5 0.20 ? 360 5 72, or 728 27. 15% of 3608 5

0.15 ? 360 5 54, or 548


1–3. Check students’ work. 4. The series ends when ateam wins 4 games, so Team H needs to win one moregame or Team T needs to win all 3 remaining games.

x < 11; the correct choice is B.

15x15 5 8 ? 20

15

15x 5 8 ? 20

815 5 x20

19

436

number of favorable outcomesnumber of possible outcomes

135171

24 1 31 1 38 1 42171

78171

42 1 36171

129171

24 1 31 1 38 1 36171

93171

24 1 31 1 38171

38171

36171

25

23 1 2

115819

12

36

33 1 3

favorable outcomespossible outcomes

Chapter

10

phm07c3_sk_ch10national.qxd 8/22/06 5:54 PM Page 120


5.

6. Team H wins at least once in 7 of the possible 8 gameseries, so P(Team H wins the series) 5 . Team T wins allthree times in only one of the 8 possible game series soP(Team T wins the series) 5 . 7. No; he should bewilling to do your chores for 7 weeks since his team is 7times more likely to win.

10-2 Making Predictionspages 475–478

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. cross 2. 135 3. 1364. 4.5

Quick Check 1. ? 500 5 ? 25 5 5 12 ; about 13

winning caps 2. ? 1,200 5 ? 20 5 380 votes

Exercises 1. ? 600 5 ? 6 5 18; 18 cars 2. The probability of getting heads on a single coin flip is 1 in 2,

or ; ? 10 5 ? 5 5 5. 5 heads are likely. 3. The

probability of getting heads on a single coin flip is 1 in 2,





or ; 3 599 5 5 299 ; Round up to 300 since you

cannot have a head. 300 heads are likely. 6. ? 60 5

? 3 5 9 7. ? 600 5 ? 30 5 90 8. ? 12,000 5

? 600 5 1,800 9. ? 54 5 5 8 5 8 5 8.1; round

down to 8. 10. ? 80 5 ? 8 5 8 11. ? 95 5 5

14 5 14 5 14.25; round down to 14. 12. ? 12,000 5

? 120 5 2,640; 2,640 people 13. ? 12,000 5 ? 120 5

2,400; 2,400 people 14. ? 12,000 5 ? 120 5 2,280;2,280 people 15. ? 12,000 5 ? 120 5 1,440;

1,440 people 16. ? 12,000 5 ? 120 5 2,040;

2,040 people 17. ? 12,000 5 ? 120 5 1,200;1,200 people 18. The probability that a planted bean will grow is , or . The number of favorable outcomes is 24. Use the probability and the desired

34

4 2 14

101

10100

171

17100

121

12100

191

19100

201

20100

221

22100

14

520

28520

320

11

110

110

220

16220

320

31

320

21

320

31

320

12

12

5992

12

12

11

12

12

11

12

12

11

12

12

31

3100

191

1960

12

252

12

140

18

78

H

T T

H

T

H

T

H

T

H

H

TH

T

T

T

TH

T

H

H

H

T

T T

T T

H

-

-

-

-

-

-

-

-

H

H

H

H

-

-

-

-

-

-

-

-

Outcome Probability

H

T

H

T

H

T

1818181818181818

number of favorable outcomes to write a proportion tofind how many plants must be planted in order toachieve this number.

19. ? 1,400 5 ? 28 5 5 5 5 5.6; about 6 bats

20. ? 125 5 ? 25 5 100; 100 flights 21. ? 9,000 5

? 60 5 3,000; 3,000 votes 22. ? 9,000 5 ? 60 5

900; 900 votes 23. ? 9,000 5 ? 60 5 3,480; 3,480 votes 24. Answers may vary. Sample: Experimentalresults are not necessarily the same as the actual results.For example, the survey results could have been basedon a small percentage of the people voting. 25. 16% of600 5 0.16 ? 600 5 96; 96 students 26. 45% of 600 50.45 ? 600 5 270; 270 students 27. 48% of 600 5 0.48 ?600 5 288; 288 students 28. 23% of 600 5 0.23 ? 600 5138; 138 students 29. The probability of being an eighth grader at the Sunrise Middle School is and the probability of being an eighth grader in Mr. Shelton’s math class is , so the probability of being in Mr.

Shelton’s eighth-grade math class is equal to ? , or .Since there are 630 students in the school, you can multiply this number by in order to predict how many of the students are in Mr. Shelton’s eighth-grade math class. ? 630 5 ? 30 5 60; 60 students. 30. of 450 5

? 450 5 ? 225 5 5 112 ; 11331.

32. L.A. 5 (2pr)< 5 pr< 5 (3.14)(8)(32) 5

803.84; 804 yd2 33. L.A. 5 4 ? ( b<) 5 2b< 5

(2)(2)(3.5) 5 14; 14 ft2

EXTENSION page 479

1. P(complement of 2) 5 1 2 P(2) 5 1 2 5

2 5 2. P(not odd) 5 1 2 P(odd) 5 1 2 5

2 5 5 3. P(not 3,5, or 10) 5 1 2 P(3,5, or 10) 5

1 2 5 2 5 5


1. P(dinner) 5 5 < 0.95

2. P(lunch) 5 5 < 0.94

3. P(breakfast) 5 5 <0.77 4. Experimental; the results are based on actual meals eaten by students. 5. 50% of 20 5 ? 20 5

? 20 5 10; 10 heads 6. ? 5,670 5 ? 9 5 9; 9 toys11

1630

11

12

1,1501,493


1,4031,493


1,4131,493


34

912

312

1212

312

12

612

612

1212

612

1112

112

1212

112

12

12

x 5 6

3x3 5 2 ? 9

3

3x 5 2 ? 9

2x 5 39

12

2252

12

14

14

21

221

221

221

27

13

27

13

581

58150

151

15150

501

50150

41

45

35

285

15

1250

x 5 32; 32 beans

3x3 5 24 ? 4

3

3x 5 24 ? 4

34 5 24x



10-3 Conducting a Surveypages 480–483

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Experimentalprobability is based on running numerous trials orexperiments, whereas theoretical probability is based on the mathematical likelihood of events. 2. 3. 4.

Quick Check 1. Not a random sample; people who are18–30 years old may not represent all people. 2. Itassumes you either in-line skate or ice skate; answersmay vary. Sample: Do you like to in-line skate or iceskate, or neither? 3. No; she would not get a randomsample of all shoppers.

Exercises 1. Researchers use samples because there areusually too many objects or people in a population tosurvey. 2. Students from one bus do not represent allstudents traveling to school. 3. Answers may vary.Sample: Do you like reality television or homework, orneither? 4. Answers may vary. Sample: Biasedquestions may lead to invalid conclusions. 5. This is arandom sample; the population is the students in theclass. 6. This is not a random sample; 25 friends may notbe representative of all the students in the school.7. This is not a random sample; students at one middleschool may not represent all middle school students.8. This is not a random sample; students in the eighthgrade are not representative of all the students in the school. 9. Biased; it makes roses sound moreappealing than carnations. 10. Not biased; it does not try to influence your answer. 11. Not biased; itdoes not try to influence your answer. 12. Yes; you areusing a random sample. 13. No; not everyone walkingon the street is a visitor. 14. Answers may vary. Sample:Biased surveys may lead to misleading probabilityvalues and statistics. 15a. The population is people whoregister a car during the year. 15b. P($20,000–$24,999) 5

5 16. Remove the descriptions showing preference or dislike. Answers may vary.Sample: Do you prefer to watch baseball or figureskating, or neither? 17. Remove the descriptionsshowing preference or dislike. Answers may vary.Sample: Do you prefer to swim in a pool or in the ocean,or neither? 18. Biased; it assumes you like eggs.19. The sample only represents people who swim at thepool; the correct choice is C. 20. Katie has already read19 books this year and plans to read 2 books each weekfor the rest of the year. In order to find the number ofbooks she will have read after six more weeks, multiply 6by 2 and add 19; the correct choice is J. 21. The moneyKim will have left after x days will be 30 dollars minusthe number of 2 dollar lunches Kim has. y 5 30 2 2x; thecorrect choice is B. 22. There are 4 numbers less thanfive on a number cube, and 2 numbers greater than orequal to five, so the odds are 4 to 2, or 2 : 1.

1241

1215 1 8 1 12 1 6

518

29

12




1. Check students’ work. 2. The number of possibleoutcomes is 10 and the number of favorable outcomes is 4, so P(green cube) 5 , or . 3. When you replace the cube, the probability does not change, so P(green cube) 5 , or . 4. The number of possible outcomes is now 10 2 1, or 9 and the number of favorable outcomes is now 4 2 1, or 3, so P(green cube) 5 , or . 5. The probability with replacement is greater than theprobability without replacement.6–10. Check students’ work. 11. The probability ofselecting two yellow cubes will be greater withreplacement since you will have more yellow cubes tochoose from.

10-4 Independent and DependentEvents pages 486–489

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. You can set up aproportion to solve, or you can multiply the theoreticalprobability by the population size. 2. about 8 3. about 84. 0 5. about 25

Quick Check 1. Orange and black are independentevents, so P(orange, then black) 5P(orange) ? P(black) 5 ? 5 , or 0.0525.2. P(boy, then girl) 5 P(boy) ? P(girl after boy) 5 ? 5

? 5 3a. Independent; the outcome of the first coin flip does not affect the outcome of the second coin flip.3b. Dependent; since you do not replace the name afteryou pick it, the outcome of the first pick affects theoutcome of the second pick.

Exercises 1. If the outcome of the first event affects theoutcome of the second event, the events are dependent.If the outcome of the first event has no effect on theoutcome of the second event, the events areindependent. 2. Independent; the outcome of the cointoss will have no effect on the roll. 3. Dependent; afterthe first card is chosen, the remaining collection of cardshas changed. 4. These events are dependent;P(green, then red) 5 P(green) ? P(red after green) 5

? 5 , or 5. The events are independent.

P(3, then 4) 5 P(3) ? P(4) 5 ? 5 6. P(A, then B) 5

P(A) ? P(B) 5 ? 5 7. P(C, then X) 5

P(C) ? P(X) 5 ? 5 8. P(I, then a vowel) 5

P(I) ? P(vowel) 5 ? 5 9. P(2 vowels) 5

P(vowel, then vowel) 5 P(vowel) ? P(vowel) 5 ? 5

10. The total number of marbles is 20;P(red, then blue) 5 P(red) ? P(blue after red) 5

25676

526

526

5676

526

126

1676

126

126

1676

126

126

136

16

16

310

620

34

25

310

12

35

24

35

21400

320

720

13

39

25

410

25

410



? 5 ? 5 ? 5 11. The total numberof marbles is 20; P(red, then yellow) 5 P(red) ? P(yellowafter red) 5 ? 5 ? 5 12. The totalnumber of marbles is 20; P(orange, then blue) 5P(orange) ? P(blue after orange) 5 ? 5 ? 5

13. The total number of marbles is 20; P(red, then red) 5 P(red) ? P(red after red) 5 ? 5 ? 5

? 5 14. Independent; the outcome of the second draw is not dependent on the first draw. 15. Independent;the first spin does not affect the second spin.16. Dependent; the second selection is affected by thefirst selection. 17. After picking one paper, it is notreplaced before picking the second paper. There is noreplacement, the events are dependent. P(both yourfavorites) 5 P(favorite one) ? P(favorite two after favorite one) 5 ? 5 , or 18. The portion of the

spinner that is green is ? 1 ? 5 1 5 1 5

; P(3, then green) 5 P(3) ? P(green) 5 ? 5 <0.052 5 5.2% 19. The prime numbers on a numbercube are 2, 3, 5, so there are 3 prime numbers, and the portion of the spinner that is blue is ? 1 ? 1 ? 5

1 1 5 ; P(prime, then blue) 5

P(prime) ? P(blue) 5 ? 5 ? 5 < 0.156 5 15.6%

20. The portion of the spinner that is yellow is

1 ? 5 1 5 ; P(5, then yellow) 5

P(5) ? P(yellow) 5 ? 5 ? 5 < 0.063 5 6.3%21. The number 8 does not appear on a number cube,and the portion of the spinner that is yellow is 1 ? 5

1 5 ; P(8, then yellow) 5 P(8) ? P(yellow) 5 0 ? 5

0 5 0% 22. The even numbers on a number cube are 2,4, and 6, so there are 3 of them, and the portion of thespinner that is green is ? 1 ? 5 1 5 1 5

; P(an even number and green) 5 P(an even number) ?P(green) 5 ? 5 ? 5 < 0.156 5 15.6% 23. For each roll, there are 6 possible outcomes and 1 favorable outcome, so the probability for guessing two rolls correctly is ? , or . 24. For independent events, the outcome of the first event does not affect the outcome of the second event. For dependent events, the outcome of the second event is affected by the outcome of the first event. 25. If two events are dependent and P(A,then B) 5 P(A) ? P(B) 5 and P(B after A) 5 P(B) 5 .

26. ? 5 ; the correct choice is B. 27. The ninth figure in the pattern will be an upward pointingarrow with horizontal lines because it will look likefigures 3 and 6; an upward arrow rotated 2708 will be

140,000

1200

1200

P(A) 5 615, or 25

P(A) ? 13 ? 3

1 5 215 ? 3

1

P(A) ? 13 5 2

15

13

215

136

16

16

532

516

12

516

36

516

216

316

18

316

14

12

14

34

38

38

18

14

14

12

14

116

18

12

38

16

38

18

14

14

12

14

532

516

12

516

36

516

116

18

18

14

14

14

12

14

12

596

516

16

516

216

316

18

316

14

12

14

34

310

620

24

35

338

119

32

519

310

6 2 120 2 1

620

295

219

15

220 2 1

420

9190

319

310

320 2 1

620

395

119

35

219

310

220 2 1

620

a leftward pointing arrow; a 2708 rotation of the ninthfigure will be a leftward pointing arrow with verticallines; the correct choice is J.28.

29.

30.


1. No; people at the music store are not representativeof all the people who read. 2. Yes; it makes watching amovie seem more appealing than reading a book.3. The events are independent; P(I, then N) 5P(I) ? P(N) 5 ? 5 5 4. The events are independent; P(I, then vowel) 5 P(I) ? P(vowel) 5

? 5 5 5. The events are independent; P(N, then

vowel) 5 P(N) ? P(vowel) 5 ? 5 5 6. The events are independent; P(A, then not U) 5P(A) ? (1 2 P(U)) 5 ? (1 2 ( )) 5 ? 5

7. There are 14 cards in all, so P(3 and 0) 5P(3) ? P(0 after 3) 5 ? 5 ? 5 8. Thereare 14 cards in all and 7 of them are even, so P(3 and an even number) 5 P(3) ? P(an even number after 3) 5

? 5 ? 5 5 9. There are 14 cards in all and 7 of them are odd, so P(5 and an odd number) 5P(5) ? P(an odd number after 5) 5 ? 5 ? 5

? 5 10. There are 14 cards in all and 13 of themare not 11, so P(2, then not 11) 5 P(2) ? P(any numberother than 11 after 2) 5 ? 5 ? 5 ? 5

10-5 Permutations pages 491–495

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. a collection of allpossible outcomes 2. 12 3. 36 4. 4

691

613

17

1213

114

13 2 114 2 1

114

391

313

17

613

114

7 2 114 2 1

114

126

7182

713

114

714 2 1

114

1182

113

114

114 2 1

114

9100

910

110

110

110

120

5100

510

110

110

10100

510

210

150

2100

110

210



Quick Check 1a. Check students’ work. The treediagram should be set up such that each book has fourbranches in the first line. In the second line, each of thefour branches should have another three branches. In

the third line, each ofthese three branchesshould have two branchesand in the last line each ofthe two branches shouldhave one branch. This is atotal of 24 permutationsper book; 24 multiplied by5 equals 120 ways.

1b. Check students’ work. The tree diagram should beset up such that each goose has three branches in thefirst line. In the second line, each of the three branchesshould have two branches and in the last line these twobranches should have one branch. This is a total of 6permutations per goose; 6 multiplied by 4 equals 24 ways.

2. 7 ? 6 ? 5 5 210; 7 ? 6 ? 5 ? 4 5 840; 5 4; there are 4 times as many ways, or 840 ways. 3a. 2! 5 2 ? 1 5 23b. 6! 5 6 ? 5 ? 4 ? 3 ? 2 ? 1 5 720 3c. 4! 5 4 ? 3 ? 2 ? 1 5 24

More Than One Way 20 ? 19 ? 18 ? 17 5 116,280;116,280 arrangements; check students’ work.

Exercises 1. A permutation is an arrangement of a setof objects in a particular order. 2. 6 ? 5 ? 4 5 6 ? 20 5120 3. 10 ? 9 ? 8 5 10 ? 72 5 720 4. 3! 5 3 ? 2 ? 1 5 65. 10P2 5 10 ? 9 5 90

840210

1

2

4

3

342423

434232

3

1

4

2

241412

424121

4

2

5

3

341413

434131

4

1

3

2

231312

323121

2

3

5

4

453543

545334

3

2

5

4

452524

545242

4

2

5

3

352523

535232

5

2

4

3

342423

434232

1

6. Let 1, 2, 3, and 4 represent the four students.24 ways

7.

6 orders8. 10 ? 9 ? 8 5 720; 720 orders 9. 6 ? 5 ? 4 5 120; 120orders 10. 5! 5 5 ? 4 ? 3 ? 2 ? 1 5 120 11. 7! 57 ? 6 ? 5 ? 4 ? 3 ? 2 ? 1 5 5,040 12. 9! 5 9 ? 8 ? 7 ? 6 ? 5 ? 4 ?3 ? 2 ? 1 5 362,880 13. 10! 5 10 ? 9 ? 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2? 1 5 3,628,800 14. 11! 5 11 ? 10 ? 9 ? 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2? 1 5 39,916,800 15. 6! 5 6 ? 5 ? 4 ? 3 ? 2 ? 1 5 720; 720ways 16. 10P4 5 10 ? 9 ? 8 ? 7 5 5,040; 5,040 ways17. 25P3 5 25 ? 24 ? 23 5 13,800 18. 18P2 5 18 ? 17 5306 19. 32P3 5 32 ? 31 ? 30 5 29,760 20. 8P4 5

8 ? 7 ? 6 ? 5 5 1,680 21. 400P2 5 400 ? 399 5 159,60022. 10P3 5 10 ? 9 ? 8 5 720; 720 ways 23. 10P5 5

10 ? 9 ? 8 ? 7 ? 6 5 30,240; 30,240 ways 24. 10P7 5

10 ? 9 ? 8 ? 7 ? 6 ? 5 ? 4 5 604,800; 604,800 ways 25. 10P9 5

10 ? 9 ? 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2 5 3,628,800; 3,628,800 ways26. 10P10 5 10 ? 9 ? 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2 ? 1 5 3,628,800;3,628,800 ways 27. 25P3 5 25 ? 24 ? 23 5 13,800; 13,800arrangements 28. 4 ? 3 5 12; 12 frames 29. 21 ? 20 ? 19 ?18 ? 17 ? 16 5 39,070,080 orders; check students’ work.30. You can multiply 12 by each positive integer lessthan 12 or you can use the factorial key. 31. Thenumber of arrangements is 8! 5 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2 ? 1 540,320. The number of hours you need to complete this project is ? ? ? 5 ? ? ? 5

? ? ? 5 168 ? 3 ? 1 ? 1 5 504; 504 h 32. 9% of 3608 5 14

11

31

6721

160

11

451

6721

1 h60 min

1 min60 s

45 s1 row

40,320 rows1

1

2

4

3

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3

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3

1

4

2

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0.09 ? 3608 5 32.48; the correct choice is C. 33. Thefourth option has 3 vertices in quadrant II and a vertexwith an x-coordinate of 23; the correct choice is J.34. The total price is found by taking 25% off the $55price and then adding on an 8% sales tax. 25% of $55 50.25 ? 55 5 13.75; $55.002 $13.75 5 $41.25; 8% of $41.255 0.08 ? 41.25 5 3.30; $41.25 1 $3.30 5 $44.55; Emily isgoing to pay her brother in four equals payments, to findthe amount of each payment divide the total price of theCD player by 4. $44.55 4 4 5 $11.14; the correct choiceis A. 35. Circle graph; it shows how the total time usingcomputers is broken into parts. 36. Line graph; it showschange over time.

10-6 Combinations pages 496–499

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. permutation 2. 42 3. 244. 90 5. 999,900

Quick Check 1. Lists may vary. Sample: If the fourstudents are A, B, C, and D, the groups are ABC, ABD,

, ACD, , , , , , BCD,, , , , , , , ,, , , , , ; 4 groups.

2a. 7C5 5 5 5 5 7 ? 3 5 21

2b. 8C4 5 5 5 5 2 ? 7 ? 1 ?

5 5 70 2c. 5C3 5 5 5 5 5 ? 2 5 10

Exercises 1. In a permutation, the order matters. In acombination, order does not matter. 2. Yes; it is apermutation because it is a specific order. 3. No; it is acombination because the order is not considered.4. No; it is a combination because the order is not considered. 5. 5 5 6. 5 5

126 7. Let numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 representthe toppings. The combinations of toppings are 12, 13,14, 15, 16, 17, 18, 19, , 23, 24, 25, 26, 27, 28, 29, , , 34,35, 36, 37, 38, 39, , , , 45, 46, 47, 48, 49, , , , ,56, 57, 58, 59, , , , , , 67, 68, 69, , , , , ,

, 78, 79, , , , , , , , 89, , , , , , ,, ; 36 ways 8. Let numbers 1, 2, 3, 4, and 5 represent

the members. The combinations of members are 12, 13,14, 15, , 23, 24, 25, , , 34, 35, , , , 45, , , ,

; 10 ways 9. 4C3 5 5 5 5 4 10. 4C2 5

5 5 5 2 ? 3 5 6 11. 4C1 5 5 5 4

12. 6C5 5 5 5 5 6 13. 6C4 5 5

5 5 3 ? 5 5 15 14. 10C1 5 5 5 10

15. 10C9 5 5 5 5 10

16. 7C4 5 5 5 5 7 ? 5 5 35

17. 3C1 5 5 5 3 18. 9C6 5 5

5 5 3 ? 4 ? 7 5 84 19. 10C3 59 ? 8 ? 73 ? 2 ? 1

9 ? 8 ? 7 ? 6 ? 5 ? 46 ? 5 ? 4 ? 3 ? 2 ? 1

9P

66!

31

3P

11!

7 ? 6 ? 53 ? 2 ? 1

7 ? 6 ? 5 ? 44 ? 3 ? 2 ? 1

7P

44!

101

10 ? 9 ? 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 29 ? 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2 ? 1

10P

99!

101

10P

11!

6 ? 52 ? 1

6 ? 5 ? 4 ? 34 ? 3 ? 2 ? 1

6P

44!

61

6 ? 5 ? 4 ? 3 ? 25 ? 4 ? 3 ? 2 ? 1

6P

55!

41

4P

11!

2 ? 31 ? 1

4 ? 32 ? 1

4P

22!

41

4 ? 3 ? 23 ? 2 ? 1

4P

33!54

535251434241323121

9897

9695949392918786858483828176

75747372716564636261

54525251434241

323121

3,02424

9 ? 8 ? 7 ? 64 ? 3 ? 2 ? 1

5 ? 4 ? 3 ? 24 ? 3 ? 2 ? 1

5 ? 42 ? 1

5 ? 4 ? 33 ? 2 ? 1

5P

33!

2 ? 7 ? 6 ? 51 ? 3 ? 2 ? 1

8 ? 7 ? 6 ? 54 ? 3 ? 2 ? 1

8P

44!

7 ? 62 ? 1

7 ? 6 ? 5 ? 4 ? 35 ? 4 ? 3 ? 2 ? 1

7P

55!

DCBDCADBCDBADACDAB

CDBCDACBDCBACADCABBDCBDA

BCABADBACADCADBACB

5 5 10 ? 3 ? 4 5 120; 120 groups 20. There are 16 different songs to choose from and the diskjockey will pick 10. This is a combination because the order does not matter. 16C10 5

5

5 5

5 2 ? 1 ? 14 ? 13 ? 2 ? 11 5 8,008;8,008 groups 21. Permutation; the order of selectionmatters. 22. Combination; the order of selection does

not matter. 23. 10C2 5 5 5 5 ? 9 5 45;

45 games 24a. 6C2 5 5 3 ? 5 5 15; 15 groups

24b. 6C622 5 6C4 5 5 5 3 ? 5 5 15;15 groups 25. The number of combinations is equal tothe number of permutations divided by r!. The numberof permutations is greater. 26. No; Sanjay found thenumber of permutations instead of combinations. Theorder of the sweaters does not matter. 27. Since the ordermatters, use the permutation. There are 14 ? 13 ? 12 52,184 possible choices and only 1 desired choice, so the probability is . 28. These are dependent events because there is no replacement. P(grape, then grape) 5

P(grape) ? P(grape, after grape) 5 ? 5 5 ;the correct choice is B. 29. There is a total of 40possible outcomes and 15 1 1 1 6, or 22 favorableoutcomes. P(not meet on Monday) 5

5 5 ; the correct choice is

H. 30. 153,000 5 1.53 3 100,000 5 1.53 3 105

31. 45 5 4.5 3 10 32. 53,200,000 5 5.23 3 10,000,000 55.23 3 107 33. 8,693 5 8.693 3 1,000 5 8.693 3 103


1. an arrangement of objects in a particular order2. theoretical; based on a theory 3. Free from influence;outcome of one event does not affect the other.4. having hidden assumptions or suggesting a preferredanswer 5. by chance 6. based on an experiment7. dependent


1. The number of ways you can pick 3 from 6 gymnastswhere order does not matter. 2. Dependent; theselection of the second gymnast depends on theselection of the previous gymnast. 3. Because orderdoes not matter, the total number of permutations isdivided by the number of ways of arranging threegymnasts in order, to remove the duplicate groups.4. There are five members on the bowling team and only two are being chosen; 5C2 5 5 5 10; there are 10 possible combinations and 1 favorable combination,so P(Carlos and Kareem) 5 . 5. There are four countries left and you will choose two of them; 4C2 5

5 5 6; there are 6 possible combinations, 3 of 2 ? 31 ? 1

4 ? 32 ? 1

110

2 ? 21 ? 1

5 ? 42 ? 1

1120

2240


120

12240

315

416

12,184

6 ? 52 ? 1

6 ? 5 ? 4 ? 34 ? 3 ? 2 ? 1

6 ? 52 ? 1

10 ? 92 ? 1

10P

22!

16 ? 1 ? 14 ? 13 ? 2 ? 112 ? 4

16 ? 15 ? 14 ? 13 ? 2 ? 116 ? 5 ? 4

16 ? 15 ? 14 ? 13 ? 12 ? 116 ? 5 ? 4 ? 3 ? 2 ? 1

16 ? 15 ? 14 ? 13 ? 12 ? 11 ? 10 ? 9 ? 8 ? 710 ? 9 ? 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2 ? 1

10 ? 9 ? 83 ? 2 ? 1

10P

32!



which contain Germany, so P(one country is Germany) 5, or . 6. There are five toppings and three are chosen

randomly. 5C3 5 5 5 10; there are 10 possible combinations.Where < is lettuce, t is tomato, c ischeese, s is sour cream, and g is guacamole, thecombinations are: <tc, <ts, <tg, <cs, <cg, <sg, tcs, tcg, tsg,and csg. Of the 10 combinations, 6 contain guacamole. SoP(one topping is guacamole) 5 5 . 7. There are 5events during each of the two days; 5! ? 5! 5 5 ? 4 ? 3 ? 2 ?1 ? 5 ? 4 ? 3 ? 2 ? 1 5 120 ? 120 5 14,400; 14,400 ways8. The chances of winning the game show are 6 out of 53;

53C6 5 5 5

22,957,480; The chance of getting hit by lightning is 1 in3,000; there is a greater chance of being hit by lightning,your chance of winning the game show is only 1 out of22,957,480.


1. This is a dependent event because there is noreplacement. P(Jana, then Cooper) 5 P(Jana) ?P(Cooper after Jana) 5 ? 5 ; the correct choice is B.

2. of the packages produced will be underweight, so out of 300 packages the number that are underweight are of 300; ? 300 5 ? 12 5 24; the correct choice is H. 3. The probability of rolling a number cube 5 timesand getting all ones is an independent probability, it isfound by multiplying all the individual probabilities together; ? ? ? ? 5 ; the correct choice is A.


1. Theoretical probability describes how likely it is thatan event will happen based on all the possible outcomes.2. People often conduct surveys on a random sample sothat each object in the population has an equal chanceof being selected. 3. To calculate the number of ways aclass can line up, you need to find the number ofpossible permutations. 4. When the outcome of oneevent does affect the outcome of a second event, theevents are dependent events. 5. You have 9 bills in all,and 5 “favorable” bills, so the odds of choosing a one-dollar bill is 5 : (9 2 5), or 5 : 4. 6. You have 9 bills in all,and 3 “favorable” bills, so the odds of choosing a five-dollar bill is 3 : (9 2 3) 5 3 : 6, or 1 : 2. 7. You have 9bills in all, and 1 “favorable” bill, so the odds of choosing a ten-dollar bill is 1 : (9 2 1), or 1 : 8. 8. ? 7,800 5

? 15 5 15; about 15 cases 9. ? 225 5 ? 75 5 ? 75 5

5 100; about 100 students 10. Random, because the people being interviewed were chosen randomly.11. Not random; because only people buyingskateboards are being chosen. 12. Independent; theoutcome of the second roll is not dependent on the firstroll. 13. Dependent; the probability of the second pickis affected by the first pick. 14. Find the number ofcombinations of 2 people from a group of 12: 12C2 5

3003

43

86

818

11

1520

17,776

16

16

16

16

16

21

225

225

225

142

16

17

53 ? 13 ? 17 ? 5 ? 49 ? 81 ? 1 ? 1 ? 1 ? 1 ? 1

53 ? 52 ? 51 ? 50 ? 49 ? 486 ? 5 ? 4 ? 3 ? 2 ? 1

35

610

5 ? 21

5 ? 4 ? 33 ? 2 ? 1

12

36

5 6 ? 11 5 66; 66 games.15. Find the number of permutations of 10 magazines taken 2 at a time: 10C2 5 5 5 ? 9 5 45; 45 ways


1. P(Brand X) 5 5 2. P(Brand Y) 5 5

3. P(crack) 5 5 ; P(not crack) 5 1 2 P(crack) 5

1 2 5 4. The events are independent; ? 5

5. The number of possible outcomes is 100, and the number of favorable outcomes is 1, so P(85) 5 .6. 105 is not one of the possible outcomes, so P(105) 5 0.7. Numbers from 1 to 100 that are divisible by 9 are 9,18, 27, 36, 45, 54, 63, 72, 81, 90, 99, so there are 11favorable outcomes and 100 possible outcomes:P(number divisible by 9) 5 . 8. From 1 to 39, thereare 4 fours; from 40 to 50, there are 10 numberscontaining a four; and from 51 to 100, there are 5 fours;for a total of 19 favorable outcomes; P(numbercontaining a 4) 5 . 9. P(yellow then blue) 5P(yellow) ? P(blue after yellow) 5 ? 5 ? 5

? 5 10. P(2 green) 5 P(green) ? P(green after

green) 5 ? 5 ? 5 ? 5

11. P(green then blue) 5 P(green) ? P(blue after green) 5

? 5 ? 5 ? 5 12. P(2 yellow) 5

P(yellow) ? P(yellow) 5 ? 5 ? 5 ? 5

13. The events are independent; ? 25 5 4.167; about

4 times 14. 8! 5 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2 ? 1 5 40,320

15. 5! 5 5 ? 4 ? 3 ? 2 ? 1 5 120 16. 4P3 5 4 ? 3 ? 2 5

24 17. 5 5 6 ? 5 ? 4 ? 3 5 360

18. 18C2 5 5 9 ? 17 5 153 19. 10C7 5 5

5 5 5 5 ? 3 ? 8 5

120 20. ? 235 5 ? 47 5 5 79.9; about 80

students 21. Random; every patron of the movietheater has the same chance of being asked. 22. Notrandom; teenagers do not represent all customers.

23. 12C3 5 5 2 ? 11 ? 10 5 220; 12C9 5

5 5 2 ? 11 ? 10 5

220; yes, both equal 220. 24. 12C3 5 5

2 ? 11 ? 10 5 220; 5

5 12 ? 11 ? 10 51,320; no, 12C3 is equal to 220 and is equal to 1,320.

25. 12C3 5 ; 5 ;

yes, 12C3 5 , which is the same as .

26. 12C3 5 5 2 ? 11 ? 10 5 220; 12P3 5

12 ? 11 ? 10 5 1,320; no, 12C3 5 , but 12P3 5

12 ? 11 ? 10. 27. 5 5 5

8 ? 7 5 56; 56 combinations 28. Answers may vary.Sample: Order does not matter in combinations, so

8 ? 7 ? 11 ? 1 ? 1

8 ? 7 ? 63 ? 2 ? 1

8 ? 7 ? 6 ? 5 ? 45 ? 4 ? 3 ? 2 ? 1

12 ? 11 ? 103 ? 2 ? 1

12 ? 11 ? 103 ? 2 ? 1

12 ? 11 ? 103!

12 ? 11 ? 103 ? 2 ? 1

12 ? 11 ? 103 ? 2 ? 1

12 ? 11 ? 103!

12 ? 11 ? 103 ? 2 ? 1

12!9!

12 ? 11 ? 10 ? 9 ? 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2 ? 19 ? 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2 ? 1

12!9!

12 ? 11 ? 103 ? 2 ? 1

12 ? 11 ? 103 ? 2 ? 1

12 ? 11 ? 10 ? 9 ? 8 ? 7 ? 6 ? 5 ? 49 ? 8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2 ? 1

12 ? 11 ? 103 ? 2 ? 1

79910

1710

1750

5 ? 3 ? 81 ? 1 ? 1

10 ? 9 ? 83 ? 2 ? 1

10 ? 9 ? 8 ? 7 ? 6 ? 5 ? 47 ? 6 ? 5 ? 4 ? 3 ? 2 ? 1

10P

77!

18 ? 172 ? 1

6 ? 5 ? 4 ? 3 ? 2 ? 12 ? 1

6!2!

16

119

119

11

419

14

5 2 120 2 1

520

27190

319

910

619

920

620 2 1

920

1895

219

95

819

920

9 2 120 2 1

920

338

319

12

619

14

620 2 1

520

19100

11100

1100

136

16

16

1718

118

118

7126

15

80400

23100

92400

10 ? 92 ? 1

12 ? 112 ? 1



different arrangements of the same outcomes are notcounted multiple times.

TEST PREP page 507

1. There are 8 different possibilities for each note, so forthe first two notes there are 8 ? 8, or 64 outcomes; thecorrect choice is D. 2. There are 8 ? 8 ? 8, or 512 differentpossibilities; the correct choice is J. 3. There are 8n

outcomes for n notes; the correct choice is D. 4. If n 5

10, 8n 5 810; the correct choice is F. 5. There are 3officers to select from 20 members and order does matter.

20P3 5 20 ? 19 ? 18 5 6,840; the correct choice is C. 6. There are n members and 2 people to group and

order does not matter. nC2 5 n(n 2 1); the correct choice is F. 7. 4 members must be selected out of

20 people and order does not matter. 20C4 5 5

5 5 4,845; the correct choice is B.8. Selecting 4 member out of 20 1 4, or 24 people, whenorder does not matter can be found using 24C4. So thedifference in the number of ways 4 leaders can be foundis 24C4 2 20C4. The correct choice is H.

116,28024

20 ? 19 ? 18 ? 174 ? 3 ? 2 ? 1

20P4

4!


1. Check students’ work. 2a–c. Check students’ work.2d. Answers may vary. Sample: The differences occurdue to the random nature of the recapture. It is unlikelythat the same number of beans will be recaptured everytime. 3. Answers may vary. Sample: The population isusually not fixed in the wild, because animals can enteror leave the area and new ones may be born or old onesdie. Animals may lose their tags or markings. Scientistsmight try to control for these factors by closing the areatemporarily or doing the second capture soon after thefirst. But if the second capture is done too soon, theanimals will not have had a chance to mix properly andthe results will be skewed.



Functions pages 510–557


1. 5 35 4 (27) 5 25 2. 5 272 4 12 5 26

3. 5 254 4 9 5 26 4. 5 240 4 5 5 28

5. 5 224 4 (26) 5 4 6. 5 63 4 (221) 5 23

7–9.

10. The second quadrant is to the upper left; P11. Point S is 3 units to the left and 2 units below theorigin; (23, 22)

12. y 5 x 1 2;

13. y 5 27x 2 14;

2 4Ox

y14

2 4Ox

y

4

34

O

y

x�2 2

2

�2

�4

�6

�8

4

4 6 8

8.

7.

9.

63221

22426

2405

2549

27212

3527

14. y 5 x 2 4;

11-1 Sequences pages 512–516

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Replace each variablewith a number and then simplify. 2. n 1 7 3. 5n 4. 12d

Quick Check 1a. You find each term by adding 7 to theprevious term; 33, 40, 47. 1b. You find each term byadding 5 to the previous term; 24, 29, 34. 1c. You findeach term by adding 10 to the previous term; 42, 52, 62.

2.

3. 22n; 22(20) 5 2404. The common ratio is 10. The rule is “Start with 0.1 and multiply by 10 repeatedly”; 1,000;10,000; 100,000.

Exercises 1. A common ratio involves multiplication ordivision. A common difference involves addition orsubtraction. 2. Add 2 to find the next term in thesequence. The common difference is 2. 3. Add 21 tofind the next term in the sequence. The commondifference is 21. 4. Answers may vary. Sample: 1, 1 , 2,2 , . . . 5. Multiply by 2 to find the next term in thesequence. The common ratio is 2. 6. Multiply by 3 tofind the next term in the sequence. The common ratio is3. 7. 2 ? 4 5 8; 8 ? 4 5 32; 2, 8, 32 8. You find each termby adding 4 to the previous term; 19.5, 23.5, 27.5. 9. Youfind each term by subtracting 1 from the previous term;2 , 21 , 22 . 10. You find each term by adding 7 to theprevious term; 32, 39, 46.

14

14

14

12

12

n

2 6 8O x

y

2

67

Chapter

11



11.

12.

13.

14.

15. 3n; 3(20) 5 60 16. n; (20) 5 10 17. 24n; 24(20) 5280 18. The common ratio is 0.1. The rule is start with750 and multiply by 0.1 repeatedly; 0.075, 0.0075,0.00075. 19. The common ratio is 4. Start with 1 andmultiply by 4 repeatedly; 256; 1,024; 4,096. 20. The common ratio is . The rule is start with 1 and multiply by

repeatedly; , , . 21. The common ratio is 2.The rule is start with 3 and multiply by 2 repeatedly; 48, 96,192. 22. The common ratio is 3. The rule is start with0.12 and multiply by 3 repeatedly; 3.24, 9.72, 29.16.23. The common ratio is . The rule is start with 125 and

multiply by repeatedly; , , . 24. Answers may vary. Sample: 3n 1 2; The sequence based on the numberof outer edges is 5, 8, 11. The common difference d is 3.Add d to 5 once to get the second term. Add d to 5 twiceto get the third term. The rule is start with 2 and add 3repeatedly. To get the nth term, start with 2 and add 3 ntimes: 3n 1 2. 25. In this sequence, each new weight is 2oz greater than the last. Since each term differs from thenext by a fixed number, it is an arithmetic sequence.26. The terms in this sequence do not vary by a fixednumber, so the sequence is not arithmetic. The termscannot be found by multiplying the previous term by afixed number, so the sequence is not geometric. Thesequence is therefore neither. 27. Yes, if the sequencehas enough terms; if you start with any number andrepeatedly add a negative number, you eventually will

1125

125

15

15

15

164

132

116

12

12

12

12

TermNumber

n

Term ofSequence

1

2

3

4

TermNumber

n

Term ofSequence

1

2

3

4

end up with a negative answer. 28. arithmetic; you findeach term by adding 0.3 to the previous term; 3.2, 3.5,3.8. 29. neither; you find each term using the expressionn2 1 1; 26, 37, 50. 30. arithmetic; you find each term byadding 26 to the previous term; 23, 29, 215.31. geometric; you find each term by multiplying theprevious term by 3; 162, 486, 1,458. 32. neither; you findeach term using the expression 1 1 0.1n; 1.0001, 1.00001,1.000001. 33. geometric; you find each term by multiplying the previous term by ; 0.125, 0.0625, 0.03125.34a. 1 week is 7 days: 6 ft 5 (12 ? 6) in. 5 72 in.:72 2 7(3) 5 51 in., or 4 ft 3 in. 34b. half his original height 5 3 ft 5 36 in.; he shrinks 36 in. in days, or 12days. 36. Arithmetic; start with 72 in. and add 23repeatedly. 37. Answers may vary. Sample: 15.5 2 3n;15.5 2 3(20) 5 15.5 2 60 5 244.5 38. Answers mayvary. Sample: 3 1 4n; 3 1 4(20) 5 3 1 80 5 8339a. Side length 2: V 5 23 5 8; side length 3: V 5 33 5 27;side length 4: V 5 43 5 64; side length 5: V 5 53 5 125.39b. Volume is the length of the side cubed. 39c. n3,where n is the length of each side 40. n 5

1: 400 ? 1 2 1 5 400 ? 1 5 400; n 5 2: 400 ? 2 2 1 5

400 ? 5 200; n 5 3: 400 ? 3 2 1 5 400 ? 5 100; n 5

4: 400 ? 4 2 1 5 400 ? 5 50; geometric 41. Start at 2 and add 0.3 for every term after; the correct choice isC. 42. You have 2 favorable outcomes and 6 possibleoutcomes for the first roll, and you have 4 favorableoutcomes and 6 possible outcomes for the second roll.

? 5 5 ; the correct choice is H.43. 7.5% ? 3 ? $245 5 0.075 ? 3 ? $245 5 $55.13;the correct choice is B. 44. P(black, then red) 5P(black) ? P(red, after black) 5 ? 5 5

45. P(red, then blue) 5 P(red) ? P(blue, after red) 5

? 5 5 46. P(blue, then blue) 5

P(blue) ? P(blue, after blue) 5 ? 5 5

47. P(blue, then black) 5 P(blue) ? P(black, after blue) 5

? 5 5


1. Press 23.5 . Press repeatedly.

The first five terms are 23.5, 22.8, 22.1, 21.4, 20.7.

2. Press 900 . Press 283 . Press

repeatedly.The first five terms are 900, 817, 734,

651, 568. 3. Press and enter 3x 1 4. Use the

feature. Use the feature. The sequence is 5, 6, 7, 8, 9. The verbal description is start with 5 and

add 1 repeatedly. 4. Press and enter 5 ? 3x. Use the

feature. Use the feature. The sequence is 15, 45, 135, 405, 1,215; the verbal description is start

with 15 and multiply by 3 repeatedly. 5. Press and Y5

TableTblSet

Y5

TableTblSet

Y5

ENTER

ENTERENTER

ENTERENTER

7171

14342

718

219

1171

2342

118

219

10171

20342

218

1019

35171

70342

1018

719

29

836

46

26

18B1

2A

14B1

2A12

B12AB1

2A

363

12



enter 24x 1 30. Use the feature. Use the

feature. The sequence is 26, 22, 18, 14, 10; start

with 26 and add 24 repeatedly. 6. Press and enter

2x 1 4. Use the feature. Use the feature. The sequence is 6, 8, 10, 12, 14. The verbal description is start with 6 and add 2 repeatedly.

11-2 Relating Graphs to Eventspages 518–522

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Line graphs best displaychanges over time. 2–3. Answers may vary. Samples aregiven. 2. Line plots best display frequency of data-forexample, displaying the number of siblings each classmember has. 3. Bar graphs compare amounts indifferent categories-for example, the number of studentsin each grade.

Quick Check 1. 40 mi/h

2.

Exercises 1. Line graphs best display changes over time.2. The student should put time on the horizontal scaleand distance on the vertical scale. 3. The line is parallelto the horizontal axis when the bus is stopped. 4. Theline is farthest away from the horizontal axis when thebus is farthest from the transit center. 5. Highway; thebus travels a greater distance over a shorter period oftime on the highway. 6. from week 10 to week 20; 11weeks 7. reach peak at week 10; 10 weeks 8. fourthand fifth weeks 9. week 25: 30; week 24: 40; 30 2 40 5210 km 10. Answers may vary. Sample:

11.Answers may vary. Sample:

Dis

tan

ce

Time

6 A.M. Noon 6 P.M. Midnight 6 A.M.

Time

Tem

per

atur

e

0

Dis

tanc

e

5Time (min)

10 15 20

TableTblSet

Y5

Table

TblSet 12. For Cam, Ben, and Abel, distance from the labincreases with time. Cam is represented by the steepestline because he was walking faster than anyone.

13. The blue line begins farther down the time axis,meaning it began at a later time. The blue line representsAl. 14. The red line extends farther along the time axis,so the blue line completed the full distance in less time.Since Carlos is represented by the red line and Al by theblue, Al went the full distance before Carlos did, so Alwon the race. 15. The red line goes flat in one part,meaning time went by, but no distance was gained. Thisrunner stopped during the race. The red line representsCarlos. 16. Al ran the same distance in a shorter periodof time. Al won.

17.

18.

19.

20.

21. Maritza walked a positive distance, which is onlyrepresented by graph B; the correct choice is B.22. The longest side of triangle ABC is 10 units long, andthe longest side of triangle DEF is 5 units long. The ratiois 5 : 10, or ; 5 ; the correct choice is F. 23. The firstnumber has to be 2 1 3(1), or 5; the correct choice is D.

12

510

510

X

1 2 3 4OTime (seconds)

Hei

gh

tA

rea

Side Length

60 12 18 24Time (min)

Sp

eed

Hei

gh

t

Time

Dis

tanc

e Fr

om

Lab

Time

Cam

Ben

Abel

DanErin



24. 9C3 5 5 5 84 25. 7C5 5 5

5 21 26. 5C2 5 5 5 10

27. 7C3 5 5 5 35


1a. The value increased by about $45 2 $30, or about $15.1b. The value increased the greatest amount betweenSeptember and October. 2–3. Check students’ work.


1. Add 13 repeatedly. 52 1 13 5 65, 65 1 13 5 78,78 1 13 5 91; 65, 78, 91 2. Add repeatedly. 3 1 5 3 ;

3 1 5 4 ; 4 1 5 5 ; 3 , 4 , 5 3. Subtract 7 repeatedly. 228 2 7 5 235; 235 2 7 5 242; 242 2 7 5249; 235, 242, 249 4. Naomi was driving 20 mi/h.5. 20 mi/h ? 1 h 5 20 mi 6. Naomi’s speed first increasedafter 1 hour. 7. Her speed increased to 40 mi/h.8. Naomi’s final speed was 65 mi/h.

11-3 Functions pages 523–526

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. a 2. 8 3. 53 4. 9 5. 25

Quick Check 1.

2.

3. f(6) 5 2(6) 5 12; f(6) is the total cost of buying 6 fish.

Exercises 1. A function rule is an equation thatdescribes a function. 2. No; a function assigns exactlyone output value to each input value. 3. Alwayspositive; the product of two negative numbers is alwayspositive. 4. f(1) 5 3 1 1 5 4; f(2) 5 3 1 2 5 5; f(3) 53 1 3 5 6; 4, 5, 65. 6.

7. 8.

9. 10.

11. 12. E(h) 5 0.04h

5 230.4

f(216.7) 5 2(216.7) 1 3

f(x) 5 2x 1 3

5 23 5 7

f(10) 5 2(10) 1 3 f(2) 5 2(2) 1 3

f(x) 5 2x 1 3 f(x) 5 2x 1 3

5 21 5 3

f(22) 5 2(22) 1 3 f(0) 5 2(0) 1 3

f(x) 5 2x 1 3 f(x) 5 2x 1 3

pm

2

6

13

5.50

13.50

27.50

tn

44

132

165

4

12

15

5 0 5 40

5 212 1 12 5 28 1 12

f(3) 5 24(3) 1 12 f(27) 5 24(27) 1 12

f(x) 5 24x 1 12 f(x) 5 24x 1 12

dc

5

10

15

$.50

$1.00

$1.50

14

12

34

14

34

12

12

34

34

34

34

34

7 ? 6 ? 53 ? 2 ? 1

7P

33

5 ? 42 ? 1

5P

22

7 ? 6 ? 5 ? 4 ? 35 ? 4 ? 3 ? 2 ? 1

7P

5

5!9 ? 8 ? 73 ? 2 ? 1

9P

33!

13. Let b 5 the number of paintbrushes you buy. LetC(b) 5 the total cost of b paintbrushes.

5 48.33; $48.3314. Each input only has one output; yes. 15. The inputs2 and 3 each have more than one output; no. 16a. w 5

40(6) 5 240; the number of gallons of water used towash 6 loads of laundry. 16b. <; the number of loads,which is the input, is the domain. 16c. The number w ofgallons of water used is dependent on the number < ofloads of laundry in the washing machine, so thedependent variable is w. 17. Answers may vary. Sample:

(0, 22), (2, 4), (7, 19); each solution (x, y) equals an input/output pair for the function f(x) 5 3x 2 2;f(0) 5 22, f(2) 5 4, f(7) 5 19.18. y 5 4x 19. d 5 50t

20.

21a f(1) 5 100 2 4(1) 5 100 2 4 5 96; f(2) 5 100 2 4(2)5 100 2 8 5 92; f(3) 5 100 2 4(3) 5 100 2 12 5 88; f(4)5 100 2 4(4) 5 100 2 16 5 84; 96, 92, 88, 84, arithmetic21b. f(1) 5 1(4 2 1) 5 1(3) 5 3; f(2) 5 2(4 2 2) 5 2(2)5 4; f(3) 5 3(4 2 3) 5 3(1) 5 3; f(4) 5 4(4 2 4) 5 4(0)5 0; 3, 4, 3, 0; neither 22. 52 1 7 ? 2.50 5 52 1 17.50 569.50 23. The height of the large cylinder is 5 timeslarger than the small cylinder, and since the cylinders aresimilar the radius of the large cylinder is 5 times largerthan the small cylinder.V(large cylinder)

V(small cylinder)

5 2724. 4n; 4(5) 5 20; 4(6) 5 24; 4(7) 5 28; 20, 24, 2825. 21n; 21(5) 5 25; 21(6) 5 26; 21(7) 5 27;25, 26, 27


1. The rate of change is 2; the person grows 2 in./yr.2. The rate of change is 3; it rains 3 mm/h. 3. The rate of change is ; the person runs 25 m every 4 s. 4. The rate

of change is ; the temperature drops 38C every 500 m ascended.

23500

254

53,375125

5 (p)(r2)(x)

3,375125 5 (p)r2(x)

3,375125 5

125(p)(r2)(x)

125

3,375 5 125(p)(r2)(x)

5 (p)((5r)2)(5x)

5 3.50; $ 3.50

5 1.50 1 2.00

f(4) 5 1.50 1 0.50n

f(n) 5 1.50 1 0.50n

Input t Output d

50100150200

1234

Input x Output y

20283644

579

11

5 19 5 4 5 22

5 3(7) 2 2 5 3(2) 2 2 5 3(0) 2 2

y 5 3x 2 2 y 5 3x 2 2 y 5 3x 2 2

C(27) 5 1.79(27)

C(b) 5 1.79b



11-4 Understanding Slopepages 528–531

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. no 2. 24 3. 14 4. 265. 22Quick Check 1a. 5 1b. 5

2 5 2 2. 5 ; undefined

3. 2 5 22;

Exercises 1. The slope of a line is the rise over the run.2. Check students’ work. 3. 5 5 2

4. 5 5 2 5. 5

6. 5 2 7. 5 ; 2

8. 5 2;

9. 5 21;

10. 5 5 25; the supply of rice decreases

by 5 lb/wk. 11. Your classmate found instead of .

12. 5 1.71; 5 2; the roof with a rise of 8 and a run of4 is steeper because it has a greater slope. 13. Answersmay vary. Sample:Add 2 to the y-coordinate and 1 to thex-coordinate, or subtract 2 from the y-coordinate and 1from the x-coordinate. 14. False; if two lines have thesame slope, their equations describe the same line orparallel lines. 15. A line graph is the best choice forevents involving time; the correct choice is A.16. $54 1 4 ? $75 2 4 ? $94 5 $54 1 $300 2 $376 52$22; the correct choice is F. 17. < 6; the correctchoice is A.

!35

84

127

riserun

runrise

2102

15 2 252 2 0

Ox

y3

211

2 4 6 8Ox

y

4

2

21

21

3 2 122 2 (23)

14

23 2 (22)

5 2 1

35

1 2 (22)

3 2 (22)34

324

2 2 ( 2 1)2 2 6

13

226

3 2 10 2 6

2Ox

y

2

21

30

1 2 (22)3 2 3

12

24

0 2 22 2 (22)

25

4 2 22 2 (23)

18–21.

EXTENSION page 532

1. perpendicular 2. neither 3. neither 4. perpendicular5. parallel 6. parallel 7. Find the parallel slope: 5

5 1; find the perpendicular slope: 1 ? m 5 21; m 5 21;1, 21 8. Find the parallel slope: 5 ; find the

perpendicular slope: ? m 5 21, 4 ? ? m 5 21 ? 4, m 5

24; , 24. 9. Find the parallel slope: 5 5

2 ; Find the perpendicular slope: 2 ? m 5 21,

2 ? ( ) ? m 5 2 ? (21), m 5 ; 2 , .


1.

2.

3.

y

x �3 �2 �1 0 1 2 3

0 � �2 �423 � 43 � 83 � 10

3

yx

�3 2

�4

O

y

x �3 �2 �1 0 1 2 3

�3 �1 1 3 5 7 9

y

x�3 2

2

O

y

x �3 �2 �1 0 1 2 3

�9 �7 �5 �3 �1 1 3

y

x�2 2

2

�2

O

53

35

53

53

235

53

35

35

325

1 2 (22)22 2 3

14

14

14

14

2 2 121 2 (25)

22

4 2 23 2 1

4Ox

y

4C

ABD



4.

5. The lines are parallel. 6. They intersect at the sameplace on the y-axis but have different slopes.

11-5 Graphing Linear Functionspages 534–538

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. Divide the change in yby the change in x. 2. 3. 0 4. 21

Quick Check

1.

2.

1 2 3 4 5 6O

4,000

3,000

2,000

1,000

(0, 4,000)

(3, 2,200)

Time (minutes)

Hei

ght

(fee

t)

Time

Height

0

4,000

1

3,400

2

2,800

3

2,200

4

1,600

5

1,000

6

400

2 4 6 8 10O

100

80

60

40

20

Number of Adult Tickets

Co

st (d

olla

rs)

Tickets

Cost

0

0

1

15

2

30

3

45

4

60

5

75

6

90

7

105

267

y

x �3 �2 �1 0 1 2 3

�17 �12 �7 �2 3 8 13

y

x�2 2

5

�5

O

More Than One Way Explanations may vary.

Exercises 1. Discrete data involve a count of items.Continuous data are for which numbers between anytwo data values have meaning. 2. It shows continuousdata. 3. Find the slope 5 4; find the y-intercept 5 21.4. Find the slope 5 1; find the y-intercept 5 4.

5.

6. discrete;

7. continuous;

x

p

10 20 30O

3

2

1

Depth (ft)

Pre

ssu

re (

atm

)px

0

10

20

30

1

1.3

1.6

1.9

x

d

2 4CDs

O

40

20

Mo

ney

Lef

tdx

0

1

2

40

25

10

y

x�2 2

69

3

�6�9

�3 O

y

x �3 �2 �1 0 1 2 3

�9 �6 �3 0 3 6 9

yx

�3 2

�4

O



8. continuous;

9. e 5 20.25n 2 10

10. 11.

12.

13. 14. y

x�2 2

5101520

�15�10

�5

y

x�2 1

4

�4

�12

2 4 6Ox

y

2 4Ox

y

2

2Ox

y

4

2

e

1 2 3 4 5 6 8 9 10 7 O n

80 70

10090

60 50 40 30 20 10

x

y

20 40 60 80 100O

240

180

120

60

Degrees Celsius

Deg

rees

Fah

ren

hei

t

yx

0

50

100

32

122

212

15. 16. Check students’ work.

17a. 17b. 8 cm

17c.

18. 5 17.5 Calories per cracker

19.

They are parallel but have different y-intercepts.

O x

y

2

2

4

4

x

y

4 8 12O

200

100

Crackers Eaten

Cal

ori

es

CaloriesCrackers

0

4

8

12

16

0

70

140

210

280

140 Calories8 crackers

16 h 5 t 28 5 21

2t

0 5 8 2 12t

h 5 8 2 12t

h

t

4 8 12 16O

8

4

Time (h)

Hei

gh

t (c

m)

2Ox

y

4

2



20. Company A: y 5 5 1 2x; Company B: y 5 10 1 x

21. y 5 2.3x; y 5 2.35x

22. y 5 2x 2 1 had a slope of 2 and a y–intercept of 21;the correct choice is A. 23. The factors of 72 are 1, 2, 3,4, 6, 8, 9, 12, 18, 24, 36, and 72. The factors of 90 are 1, 2,3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. The GCF of 72 and 90is 18, so the largest size of square tile that can be usedwithout being cut is 18 in.2; the correct choice is H.24. 5 5 ; the correct choice is D.25. 30, 35, 60, 70, 80; the median is 60 26. 30, 35, 60; thelower quartile is 35. 27. 60, 70, 80; the upper quartile is70. 28. The least value is 30.


1. f(21) 5 23(21) 2 2 5 3 2 2 5 1 2. f(5) 523(5) 2 2 5 215 2 2 5 217 3. f(0) 5 23(0) 2 2 50 2 2 5 22 4. f(210) 5 23(210) 2 2 5 30 2 2 5 285. C(p) 5 0.99p 6. The line is horizontal so the slope is

0. 7. (3, 3), (1, 0); 5 8. (2, 22), (21, 1);

5 5 21 9. A hill with a rise of 5 and a run

of 3 is steeper because it is rising 1 units for eachhorizontal unit. The other hill is rising only unit foreach horizontal unit.

35

23

323

1 2 (22)21 2 2

32

3 2 03 2 1

1625

3250

12 1 2050

2 4 6 8 10O

12

16

20

24

8

4

Number of Gallons

Co

st (

do

llars

)

Cost to Fill Tank

2 4 6 8 10O

30

20B

A10

Hours Used

Tota

l Co

st (

do

llars

)

Internet Costs

10.

11-6 Writing Rules for LinearFunctions pages 540–543

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. y 5 mx 1 b, where m isthe slope and b is the y-intercept. 2. 3; 22 3. 1; 5 4. 8; 0

Quick Check 1. Let x 5 the number of music standsbought. Let y 5 the balance in the treasury. y 5

298 2 42x 2. ratios: 5 ; 5 ; 5 ;the ratios are not the same, so the function is not linear.3. Use the slope, 2 , and the point (22, 1).

Exercises 1. The slope-intercept form is an example ofthe linear function rule. 2a. (2, 1), (1, 0); Find the slope5 5 5 1. 2b. Answers may vary. Sample: y 2 2 51(x 2 3) 3. Let c 5 the number of cars Mrs. Savin sells.Let p 5 Mrs. Savin’s total pay. p 5 1,200c 1 5004. Let x 5 the number of minutes that have passed.Let y 5 the amount of water over the dam. y 5 500x5. ratios: 5 ; 5 ; 5 ;

yes; y 5 23x 1 2 6. ratios: 5 ; 5 ;

5 ; yes; y 5 22x 1 8 7. Find the slope:

5 ; find the equation for the line: y 2 2 5(x 2 0), y 5 2 x 1 2. 8. Find the slope: 5 ; find

the equation for the line: y 2 0 5 (x 2 0), y 5 x.

9. 5 1.25n 1 2.25n 5 3.50n10. Determine the change between each successiveinput and output value. If the ratios of the change ofoutputs to the change in inputs are the same, it is a linearfunction. 11a. y 5 30 1 2x 11b. When x 5 12, y 5 54;his payment is $54 for the space and the 12 drawings hesold; f(12) 5 30 1 2(12) 5 54.12. Use the slope, , and the point (2, 25).

y 1 5 5 34(x 2 2)

y 2 (25) 5 34(x 2 2)

y 2 y1 5 m(x 2 x1)

34

y 5 1.25n 1 (0.75 ? 3)n

25

25

25

2 2 05 2 0

32

232

232

2 2 (21)0 2 2

221

2 2 43 2 2

221

4 2 62 2 1

221

6 2 81 2 0

231

21 2 21 2 0

231

2 2 50 2 (21)

231

5 2 821 2 (22)

11

1 2 02 2 1

y 2 1 5 245(x 1 2)

y 2 1 5 245fx 2 (22)g

y 2 y1 5 m(x 2 x1)

45

11

8 2 73 2 2

31

7 2 42 2 1

21

4 2 21 2 0

0 2Hours (h)

Mo

ney

(d

olla

rs)

14

28

42

56

4 6 8

HoursWorked

012345678

MoneyEarned

07

14212835424956



13. Use the slope, 2 , and the point (4, 21).

14.

15.;

The $30 plan is cheaper for someone who plans to go on many (30 or more) rides. 16. The slope is , or 50, and the y–intercept is 100, so the equation is b 5

50h 1 100; the correct choice is D. 17. (18 1 24) 3 6 5

(42) 3 6 5 21 3 6 5 126; the correct choice is H.18. 25 , 22 , 1 , 4; the correct choice is B.19. Experimental; because the probability is from eventsthat occurred. 20. Theoretical; because the probabilityis calculated from how many pens and pencils there are.


1. Yes; the function rule works for any positive number.2. The conclusion was made using a table and a graph;there are no other conclusions. 3. Let the year 2000 5 0.The slope is 5 1.09 < 1.1; (y 2 36.3) 51.1(x 2 4); y 5 1.1x 2 4.4 1 36.3 5 1.1x 1 31.9; y 5

1.1x 1 31.9 5 1.1(20) 1 31.9 < 22 1 32 5 54; about 54million senior citizens

2010 2020 2030 2040 2050

100

80

60

40

20

Year

Po

pul

atio

n (m

illio

ns)

0

86.7 2 36.350 2 4

12

12

150 2 1001 2 0

r

c

10 20 30 40

40

30

20

10

Number of Rides

Co

st (

do

llars

)

O

C 5 30 1 0.50r

C 5 15 1 r

y 5 212x 1 1

y 5 212x 1 2 2 1

y 1 1 2 1 5 212(x 2 4) 2 1

y 1 1 5 212(x 2 4)

y 1 1 5 212(x 2 4)

y 2 (21) 5 212(x 2 4)

y 2 y1 5 m(x 2 x1)

12

4.

The plane will have traveled 8.8 miles horizontally. Theairplane can climb 3,000 feet per mile so the rate ofascent is 3,000 ft/mi. A 5 3,000m5.

About 287 hats will sell if hats are priced at $5 each.6.

The landfill will contain 50,000 tons of trash in 60months.

11-7 Quadratic and Other NonlinearFunctions pages 546–549

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. The rate of change isconstant.

10 20 30 40 50

50,000

45,000

40,000

35,000

30,000

25,000

20,000

Months

Tons

of

tras

h

0 60

m 5 60

30,000

500 5 500m500

30,000 5 500m

50,000 2 20,000 5 20,000 2 20,000 1 500m

50,000 5 20,000 1 500m

t 5 20,000 1 500m

2 4 6 8 10 12

(5, 287)X

O

400

300

200

100

Price per Hat (dollars)

Nu

mb

er o

f H

ats

m 5 8.8

26,4003,000 5

3,000m3,000

26,400 5 3,000m

5 ? 5,280 5 3,000m

A 5 3,000m



2.

3. y 5 x2 2 2

Exercises 1. Graphs of linear functions are straight lines,and graphs of quadratic functions are parabolas.2. 3.

4.

5.

2Ox

y

15

9

3

xy

3

18

0

0

1

2

2

8

2O xy

xy

0

0

x

y

0 1

1 7 17 31

2 3 4

Ox

y

x

–3

–1

0

2

4

x2

9

1

0

4

16

y

7

–1

–2

2

14

5 10 150 x

y160

120

80

40

0

Sp

eed

(m

iles)

Time (hours)

15

13 13

t

y

1

200

5

40

8

25

10

20

20

10

2.

3.

4.

5.

Quick Check

1.

2Ox

y

2

xy

2

3

y

x�2�4 2 4

2

8

�4

�8

O

y

x�4 2 4

2

�2

�6

�8

O

y

x�2�4 2 4

2

4

6

�2

O

y

x24 2 4

2

2



6.

7.

8.

9.

10.

2 4O x

y8

4

3

3 13

4

2 12

x

y

1

10

2

5

5

2

2Ox

y24

16

8

xy

3

27

0

9

1

11

2

17

2O

x

y

xy

0

0

2Ox

y

8

4

xy

3

11

0

2

1

3

2

6

2Oxy

xy

0

0

11.

12.

13.

14. 15.

y 5 x2 2 20 y 5 2x2

16. 17.

y 5 x2 1 5 y 5 x2 2 4

18. When too many treesare planted per acre,production decreases.

x

y

20 40Trees Per Acre

Bus

hels

Per

Acr

e

60O

12

6

x –2–1 0 1 4

y0

–3–4–312

2x410116

x 0

1 2 3 4

y569

1421

2x510916

x 0

1 2 3 4

y0

–1–4–9–16

2x014916

x –10

–5 0 5 10

y805

–20580

2x10025025100

2 4O x

y20

10

5

3

3

5 1315

x

y

1

16

2

8

4

4

2 4O x

y20

10

5

4

3

6 23

x

y

1

20

2

10

4

5

2 4O x

y8

4

5

1

3

2 2335

x

y

1

8

2

4

4

2



19.

20.

21.

22.

1O x

y

xy

0

0

1

0

2Ox

y25

15

5

xy

3

26

0

2

1

6

2

14

2O

x

y

xy

0

0

2

Are

a (y

d2 )

4Ox

y

8

4

Width x Length

54321

12345

Area y

58985

23a. 23b. Answers may vary.Sample: Both graphs arenonlinear and havepositive y values forpositive x values. Thegraph of y 5 n2 is aparabola but the graph ofy 5 n3 is not.24. III25. I26. II

27.

28.

29.

30a.

30b.

The graph is the same shape as thegraph in part (a), but it is shifted two units to the right.

2 4Ox

y

4

2

3

319

13

127

x

y

0 1 2

1

4

9

5

27

2Ox

y

4

2

1

319

13

127

x

y

0

1

2

9

3

27

2Ox

y

8

4

32

x

36

1224

2 4O x

y8

4

7xx

95.54.33.75

1234

2Ox

y6

4

2

x

5Ox

y25

15

5



30c.

The graph is the same shape as thegraph in part(a) and (b), but it isshifted two units to the left frompart (a).

30d.

The graph is the same shape as thegraph in part (a), but it is reflected through the x-axis

31. The graph of d 5 216s 1 125 is linear and has anegative slope; the correct choice is D. 32. (3.14)(1.52)1 3 ? 7 5 3.5325 1 21 < 24.5; the correct choice is G.33. f(2) 5 2(2) 1 5 5 4 1 5 5 9 34. f(22) 52(22) 1 5 5 24 1 5 5 1 35. f(13) 5 2(13) 1 5 526 1 5 5 31 36. f(27) 5 2(27) 1 5 5 54 1 5 5 59


1. Function Rule: y 5 3 1 2x2

2.

3. Function Rule: y 5 10 1 8x

4. Answers may vary. Sample: It is easier to use a graphwhen looking for an estimate or prediction, and it is easier to use a function rule when you have a known value.

2Ox

y24

16

8

n

P

2 4O

120

80

40

Pn

0

1

2

3

4

5

5

15

45

135

405

1,215

yx

11

5

3

5

11

12

O xy

19

13

127

x

y

Ox

y

4

2

19

13

x

y

0

9

1

27


1. 258 north latitude has a temperature of about 758F;the correct choice is D. 2. As latitude increases, thetemperature decreases, so F is not supported by thegraph; the correct choice is F. 3. At 608F the latitude isabout 358 N; the correct choice is C.


1. The U-shaped graph of an equation like y 5 x2 2 2 isa parabola; the correct choice is E. 2. A function whosepoints lie on a line is a linear function; the correct choiceis D. 3. A sequence is a set of numbers that follows apattern; the correct choice is A. 4. Each number in asequence is called a term; the correct choice is C. 5. Afunction is a relationship that assigns exactly one outputto each input value; the correct choice is B. 6. Eachterm is found by multiplying the previous term by ; the common ratio is ; start with 160 and multiply by repeatedly; the next three terms are 0.625, 0.05625, and0.0390625. 7. Each term is found by adding 7 to theprevious term; the common difference is 7; start with 14and add 7 repeatedly; the next three terms are 42, 49,and 56. 8. Each term is found by multiplying theprevious term by 22; the common ratio is 22; start with21 and multiply by 22 repeatedly; the next three termsare 216, 32, and 264. 9. Each term is found by adding 4to the previous term; the common difference is 4; startwith 13 and add 4 repeatedly; the next three terms are29, 33, and 37.

10.

11.

1

1

2

3

4

TermNumber

Term ofSequence

(1) =1414

14

(2) =1414

24

(3) =1414

34

(4) =1414

14 – 11(1) = 31

14 – 11(2) = –82

14 – 11(3) = –193

14 – 11(4) = –304

TermNumber

Term ofSequence

14

14

14



12.


14. 15.

16. 17.

18. 5 5 0 19. 5 5

20. 5 5

21. 5 5 2122. 23.

24. ratios: 5 ; 5

; 5 ; 5 ; yes;

slope 5 and y-intercept 5 1;

y 5 x 1 1

25. ratios: 5 23; 5

23; 5 23; 5 23; yes;slope 5 23 and y-intercept 5 10;y 5 23x 1 10

22 2 14 2 3

1 2 43 2 2

4 2 72 2 1

7 2 101 2 0 x

0–1 2 3 4

y10741

–2

2x014916

12

12

12

3 2 24 2 2

12

2 2 12 2 0

12

1 2 00 2 (22)

12

0 2 (21)

22 2 (24) x –4–2 0 2 4

y–10123

2x1640416

2O

x

y2

3Ox

y

6

4

2

10210

8 2 (22)22 2 8

2 314

2314

6 2 910 2 (24)

85

2825

27 2 10 2 5

04

2 2 21 2 (23)

5 25 5 227

f(12) 5 4(1

2) 2 7 f(25) 5 4(25) 2 7

f(x) 5 4x 2 7 f(x) 5 4x 2 7

5 27 5 5

f(0) 5 4(0) 2 7 f(3) 5 4(3) 2 7

f(x) 5 4x 2 7 f(x) 5 4x 2 7

Dis

tan

ce

Time

1

2

3

4

TermNumber

Term ofSequence

23 + 1 = 24

23 + 2 = 25

23 + 3 = 26

23 + 4 = 27

26.

27.

28.

29.


1. arithmetic; 4,500. 2. arithmetic; 2303. geometric; 3 4. 125 2 5 124 ; 124 2 5 124;124 2 5 123 ; 124 , 124, 123

5. 6.

7.

5 0

5 0 2 0

f(c) 5 2(0)2 2 3(0)

f(x) 5 2x2 2 3x

5 218 5 218

5 29 2 9 5 236 2 (218)

f(3) 5 2(3)2 2 3(3) f(26) 5 2(26)2 2 3(26)

f(x) 5 2x2 2 3x f(x) 5 2x2 2 3x

12

12

12

12

12

12

12

12

x

y

2

4

6

8

21 3 4 5

x

y

1 2

7 3

3 4 592

113

134

5 10 15O x

y

4

2

1412

2113

x

y

1

7

7

1

2Ox

y

1

xy

0

2

1

1

2Ox

y4

2

xy

2

4



8.

9. 10.

11. 12.

13. IV 14. III 15. II 16. I 17. The line with a slope of210 is steeper because it decreases more sharply thanthe line with a slope of 7 increases.18a.18b.

19. Check students’ work. 20. 5

21. 5 2 22. 5 5

23. 5

24. y 5 x2 1 1

25.

10 2Time (s)

Dis

tanc

e fr

om

Gro

und

(ft)

30

40

20

10

0

x

y0

40

0.5

36

1

24

1.5

4

2

�24

x x 2 y

4 5

1 2

0 1

1 2

4 5

0

1

2

74

6 2 (21)

5 2 1

317

23 217

4 2 7212 2 5

67

267

23 2 39 2 2

310

13 2 106 2 (24)

5 100; about 100 grams

f(20) 5 5(20)

f(n) 5 5n

$1.00 5 20 nickels

f(n) 5 5n

2 4O x

y

20

10

O x

y

1

2

4

6

�2 2Ox

y4

22 4O

y1

5 9,000 people

5 4,000 1 5,000

5 400(10) 1 5,000

p 5 400t 1 5,000

tp

0

5,000

1

5,400

2

5,800

5

7,000

10

9,000

The stone hits the ground at d 5 216t2 1 40; 0 5216t2 1 40; 0 2 40 5 216t2 1 40 2 40; 240 5 216t2;

5 5 t2; t 5 < 1.6, or about 1.6 s.26. 5 5 27. 5 5 2 28. No; afunction has exactly one output value for each inputvalue, and when 8 is the input, the output is either 24 or22, which is not possible for a function.

TEST PREP pages 555–556

1. 35,306,000 5 3.5306 3 107; the correct choice is B.2. The white population in 2000 was < 0.75, or about 75% of the entire population. The non-whitepopulation is 100% 2 75% 5 25%; the correct choice is H.3. The Asian American population increased by 10,243,000 2 6,909,000 5 3,334,000; < 0.48 548%; the correct choice is C. 4. The Latino population in2000 was < 0.125, or about 12.5%; the correct choice is G. 5. A line would because line graphs showevents over periods of time; the correct choice is D.6. The Bay of Fundy has a long and narrow shape, whichis similar to the shape of a rectangle. A 5 < ? w 5

170 ? 35 5 5,950; the correct choice is G. 7. The averagetidal range is 39.4 ft. The increase is 53 ft 2 39.4 ft. Thepercent increase is 3 100; the correct choice is D.


1.Price

pNumber Sold

n

�2.5(100)2 � 39,400 � 14,400100

�2.5(95)2 � 39,400 � 16,83895

�2.5(90)2 � 39,400 � 19,15090

�2.5(85)2 � 39,400 � 21,33885

�2.5(80)2 � 39,400 � 23,40080

�2.5(75)2 � 39,400 � 25,33875

�2.5(70)2 � 39,400 � 27,15070

�2.5(65)2 � 39,400 � 28,83865

�2.5(60)2 � 39,400 � 30,40060

�2.5(55)2 � 39,400 � 31,83855

�2.5(50)2 � 39,400 � 33,15050

�2.5(45)2 � 39,400 � 34,33845

�2.5(40)2 � 39,400 � 35,40040

�2.5(35)2 � 39,400 � 36,33835

�2.5(30)2 � 39,400 � 37,150 30

53 2 39.439.4

35,306,000282,000,000

3,334,0006,909,000

211,461,000282,000,000

14

124

2 2 124 2 0

12

24

4 2 24 2 0

"2.5216t2

216240216



2.Sales in Dollars

s � p � n

100 � 14,400 � 1,440,000

95 � 16,838 � 1,599,563

90 � 19,150 � 1,723,500

85 � 21,338 � 1,813,688

80 � 23,400 � 1,872,000

75 � 25,338 � 1,900,313

70 � 27,150 � 1,900,500

65 � 28,838 � 1,874,438

60 � 30,400 � 1,824,000

55 � 31,838 � 1,751,063

50 � 33,150 � 1,657,500

45 � 34,338 � 1,545,188

40 � 35,400 � 1,416,000

35 � 36,338 � 1,271,813

30 � 37,150 � 1,114,500

3.

4. Answers may vary. Sample: The best price is about$72.50, which yields an income of $1,900,400. Prices that are higher or lower than that yield a lower income.5. Check students’ work.

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

30 50 70 90 n

Number Sold

s

Sal

es In

com

e (M

illio

ns

of

Do

llars

)

0



Polynomials and Properties of Exponents pages 558–597


1.

2.

3.

4.

5.

6.

7. 5 1 4(a 2 3) 5 5 1 4a 2 12 5 4a 2 78.

9.

10.

11.

12.

13. 7 ? 7 ? 7 ? 7 ? 7 5 75 14. 5 ? 5 ? c ? c 5 52 ? c2

15. a ? a ? b ? b ? b 5 a2 ? b3 16. x ? y ? x ? y ? x 5 x3 ? y2

17. (3x) ? (3x) ? (3x) 5 (3x)3 18. c ? d ? g ? d ? g 5 c ? d2 ? g2

19. 42 5 4 ? 4 5 16 20. (24)2 5 24 ? 24 5 1621. 242 5 2(4 ? 4) 5 216 22. 2(22)5 5

2(22 ? 22 ? 22 ? 22 ? 22) 5 2(232) 5 32 23. 102 5

10 ? 10 5 100 24. 103 5 10 ? 10 ? 10 5 1,000


Activity 1. Your age is one less than the answer; Kwamesubtracts one from the answer. 2. x 1 1; since theanswer is one more than the age. 3. Your age is onemore than the answer; Kwame adds one to the answer.4. x 2 1; since the answer is one less than the age.Exercise 1–3. Check students’ work.

5 5y 2 5

20y 2 (15y 1 5) 5 (20 2 15)y 2 5

5 20.44 2 5.7c

5 20.44 1 (7.3 2 13)c

7.3(2.8 1 c) 2 13c 5 20.44 1 7.3c 2 13c

5 212x 2 45

5 (6 2 18)x 2 45

6x 2 9(2x 1 5) 5 6x 2 18x 2 45

5 36f 2 88

5 (28 1 44)f 2 88

28(f 1 11) 1 44f 5 28f 2 88 1 44f

5 29b 1 21

5 (22 2 7)b 1 21

22b 2 7(b 2 3) 5 22b 2 7b 1 21

5 28t 1 x 2 6

5 (7 2 15)t 1 x 2 6

7t 2 6 2 15t 1 x 5 7t 2 15t 1 x 2 6

5 36r 1 34

8r 1 34 2 2r 1 30r 5 (8 2 2 1 30)r 1 34

5 43f 2 23g 1 3

5 (6 1 37)f 2 23g 1 3

6f 2 23g 1 3 1 37f 5 6f 1 37f 2 23g 1 3

5 65w 2 49

5 (2 1 63)w 2 49

5 2w 1 63w 2 42 2 7

5 2w 2 42 2 7 1 63w 5 2w 2 42 1 f27 2 (263w)g

2w 2 42 2 7(1 2 9w) 5 2w 2 42 1 (27)(1 2 9w)

5 27v 1 73

4v 1 65 2 11v 1 8 5 (4 2 11)v 1 65 1 8

5 22d 2 4

13d 1 9d 2 4 5 (13 1 9)d 2 4

12-1 Exploring Polynomialspages 561–565

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. yes; all the terms includethe same variable, x. 2. 22 2 t 3. 12w 2 10 4. 35k 2 5

Quick Check 1a. x2 2 2x 1 2 1b. 22x2 1 2x 2 32a. Check students’ work; 22x2 2 x 1 6 2b. Checkstudents’ work; 6x2 2 3x 1 2

3a.

3b.

More Than One Way Methods may vary.Sample: 22x2 1 5x 2 6x 1 5 2 2x2

Exercises 1. A constant is a term that does not contain avariable; the constants are 63 and 35. 2. Commutativeproperty because the order of the terms was changed;the correct choice is B. 3. Associative property becauseliked terms were grouped; the correct choice is A.4. Distributive property because x was taken out of thegrouped term and was multiplied by it; the correctchoice is C. 5. 2x2 2 x 1 3 6. x2 1 3x 2 5 7. 22x2 1 x2 2 8. 2x2 1 5x 1 1 9. 3x2 1 2x 2 4 10. x2 1 x 1 111. 2x2 1 2x12. 3x2 2 8 1 2x 2 4x 1 3 2 5x2

13. 21 1 2x2 2 2x 1 2 1 3x

14. 3 2 7x 1 3x2 1 2x2 1 2x

5 5x2 2 5x 1 3

5 (3 1 2)x2 1 (27 1 2)x 1 3

5 (3x2 1 2x2) 1 (27x 1 2x) 1 3 5 3x2 1 2x2 2 7x 1 2x 1 3

5 2x2 1 x 1 1

5 2x2 1 (22 1 3)x 1 1

5 2x2 1 (22x 1 3x) 1 1 5 2x2 2 2x 1 3x 2 1 1 2

5 22x2 2 2x 2 5

5 (3 2 5)x2 1 (2 2 4)x 2 5

5 (3x2 2 5x2) 1 (2x 2 4x) 2 5

5 3x2 2 5x2 1 2x 2 4x 2 8 1 3

5 24x2 2 x 1 5

5 (22 2 2)x2 1 (5 2 6)x 1 5

5 (22x2 2 2x2) 1 (5x 2 6x) 1 5

5 22x2 2 2x2 1 5x 2 6x 1 5

5 25y2 1 2y 1 7

5 25y2 1 (3 2 1)y 1 7

5 25y2 1 (3y 2 y) 1 7

3y 2 5y2 2 y 1 7 5 25y2 1 3y 2 y 1 7

5 2g2 1 2g

5 (4 2 2)g2 1 (25 1 7)g

5 (4g2 2 2g2) 1 (25g 1 7g)

4g2 2 5g 2 2g2 1 7g 5 4g2 2 2g2 2 5g 1 7g

Chapter

12

phm07c3_sk_ch12national.qxd 8/23/06 10:32 AM Page 144


15. area of small rectangle 5 3x; area of large rectangle 5 5x; total area 5

16. 22x2 1 3x 1 x2 1 5 2 3x 2 2

17. 2x2 2 x2 1 x 2 3x 1 2 2 3

18.

19. 25n 1 2n 1 k 1 k 1 10n

20. 13 1 g 2 3r 1 10g 1 14r

21. 5 31 22. 2 23. 324. 1 25. 5 26. pr2 1 pr2 1 pdh 5 2pr2 1 pdh27. Answers may vary. Sample: The prefix poly means“several” or “many.” This meaning can be combined withthe meaning of the root word, as in polygon, whichmeans “many sided.” 28. 23x3 1 2x 2 9xy 2 z5y5 1 12 4y2 1 5yx 1 x3 2 6y 1 y5z5 5 23x3 1 x3 2 4y2 2 9xy1 5yx 1 2x 2 6y 2 z5y5 1 y5z5 1 1 5 (23 1 1)x3 2 4y2

1 (29 1 5)xy 1 2x 2 6y 1 (21 1 1)z5y5 1 1 522x3 2 4y2 2 4xy 1 2x 2 6y 1 1 29. On the bar graph,women are represented by the pink bar. For the agegroup of 18–24, the pink bar stops at about 22; thecorrect choice is C. 30. $1,295 < $1,300; $74.99 5 $75.00;$1,300 1 $75.00 5 $1,375; 8% of $1,375 5 0.08 ? 1,375 5110; $1,375 1 $110 5 $1,485; the correct choice is G.31. The data tends to decrease from left to right; thecorrect choice is B.32.

t y � 3t 2 � 12

�3 3 (�3)2 � 12 � 15

�2 3 (�2)2 � 12 � 0

�1 3 (�1)2 � 12 � �9

0 3 (0)2 � 12 � �12

1 3 (1)2 � 12 � �9

2 3 (2)2 � 12 � 0

3 3 (3)2 � 12 � 15

2y2 2 y 1 3 5 2(4)2 2 4 1 3 5 11g 1 11r 1 13 5 (1 1 10)g 1 (23 1 14)r 1 13 5 (g 1 10g) 1 (23r 1 14r) 1 13 5 g 1 10g 2 3r 1 14r 1 13

5 7n 1 2k 5 (25 1 2 1 10)n 1 (1 1 1)k 5 (25n 1 2n 1 10n) 1 (k 1 k) 5 25n 1 2n 1 10n 1 k 1 k

5 0 ft 5 144 2 144

5 48(3) 2 16(3)2 height 5 48t 2 16t2

5 x2 2 2x 2 1

5 (2 2 1)x2 1 (1 2 3)x 2 1

5 (2x2 2 x2) 1 (x 2 3x) 1 2 2 3

5 2x2 1 3

5 (22 1 1)x2 1 (3 2 3)x 1 3

5 (22x2 1 x2) 1 (3x 2 3x) 1 3 5 22x2 1 x2 1 3x 2 3x 1 5 2 2

(3 1 5)x 5 8x

3x 1 5x 5

33.

34. x y � 2x 2 � 2

�3 2 (�3)2 � 2 � 16

�2 2 (�2)2 � 2 � 6

�1 2 (�1)2 � 2 � 0

0 2 (0)2 � 2 � �2

1 2 (1)2 � 2 � 0

2 2 (2)2 � 2 � 6

3 2 (3)2 � 2 � 16

m y � m 2 � m

�3 (�3)2 � (�3) � 12

�2 (�2)2 � (�2) � 6

�1 (�1)2 � (�1) � 2

0 (0)2 � (0) � 0

1 (1)2 � 1 � 0

2 (2)2 � 2 � 2

3 (3)2 � 3 � 6



12-2 Adding and SubtractingPolynomials pages 566–569

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. 1 2. 2y2 2 2y 3. 6x2 2 14. 8z 2 5z2

Quick Check 1a. (c2 1 3c 2 5) 1 (4c2 2 c 1 7) 5(c2 1 4c2) 1 (3c 2 c) 1 (25 1 7) 5(1 1 4)c2 1 (3 2 1)c 1 (25 1 7) 5 5c2 1 2c 1 21b. (x2 1 3x 2 1) 1 (2x2 2 6) 5(x2 1 2x2) 1 (3x) 1 (21 1 26) 5(1 1 2)x2 1 (3)x 1 (21 1 26) 5 3x2 1 3x 2 7

2a.

2b.

3. (4y2 2 3y 1 1) 2 (6y2 2 3y 1 3)

5 (4y2 2 3y 11) 1 (26y2 1 3y 2 3)

5 (4y2 2 6y2) 1 (23y 1 3y) 1 (1 2 3)

5 (4 2 6)y2 1 (23 1 3)y 1 (1 2 3)

5 22y2 2 2

Check:y 5 1; (4y2 2 3y 1 1) 2 (6y2 2 3y 1 3) 0 22y2 2 2

4(1)2 2 3(1) 1 1 2 6(1)2 1 3(1) 2 3 0 22(1)2 2 24 2 3 1 1 2 6 1 3 2 3 0 22 2 2

24 5 24

Exercises 1. A coefficient is a number that is multipliedby a variable. 2. 2, 3 3. 21, 21 4. 24 5. 5m 6. 24x

7. (3p2 2 2p 1 1) 1 (5p2 1 4p)

8. (7t2 1 t 2 3) 1 (26t2 1 3)

9.

10. (2b2 1 b 2 3) 1 (2b2 2 b 2 3)

11.

12.

13.

5 6x 2 5

5 (x 1 2x 1 3x) 1 (22 2 3)

P 5 x 1 (2x 2 2) 1 (3x 2 3)

5 12x 1 26

5 (2x 1 2x 1 4x 1 4x) 1 (5 1 5 1 8 1 8)

P 5 (2x 1 5) 1 (2x 1 5) 1 (4x 1 8) 1 (4x 1 8)

5 4x 1 6

5 (x 1 x 1 x 1 x) 1 (3 1 3)

P 5 x 1 x 1 (x 1 3) 1 (x 1 3)

5 4b2 2 6

5 (2 1 2)b2 1 (1 2 1)b 1 (23 2 3)

5 (2b2 1 2b2) 1 (b 2 b) 1 (23 2 3)

5 4k2 1 k 5 (1 1 3)k2 1 (3 2 2)k

(k2 1 3k) 1 (3k2 2 2k) 5 (k2 1 3k2) 1 (3k 2 2k)

5 t2 1 t 5 (7 2 6)t2 1 t 1 (23 1 3)

5 (7t2 2 6t2) 1 t 1 (23 1 3)

5 8p2 1 2p 1 1

5 (3 1 5)p2 1 (22 1 4)p 1 1

5 (3p2 1 5p2) 1 (22p 1 4p) 1 1

5 10m 2 2

5 (5m 1 2m 1 3m) 1 (23 1 1)

P 5 (5m 2 3) 1 (2m) 1 (3m 1 1) 5 10c 1 24 5 (3c 1 3c 1 2c 1 2c) 1 (8 1 8 1 4 1 4)

P 5 (3c 1 8) 1 (3c 1 8) 1 (2c 1 4) 1 (2c 1 4)

14. (4x 2 4) 1 (2x 1 5) 1 (4x 2 4) 1 (2x 1 5)5 (4x 1 2x 1 4x 1 2x) 1 (24 1 5 2 4 1 5)5 (4 12 1 4 1 2)x 1(24 1 5 2 4 1 5)5 (12x 1 2) ft

15. (2x2 1 5x 1 7) 2 (3x2 1 7x)

16. (2a2 1 5a 1 7) 2 (a2 2 3a 2 1)5 (2a2 1 5a 1 7) 1 (2a2 1 3a 1 1)5 (2a2 2 a2) 1 (5a 1 3a) 1 (7 1 1)5 (2 2 1)a2 1 (5 1 3)a 1 (7 1 1)5 a2 1 8a 1 8

17. (g2 1 7) 2 (3g2 1 2g 1 1)

18. (3r2 2 4r 2 1) 2 (2r2 1 r 2 4)

19. For x5 45; (25x 2 30) 2 (13x 1 400) 5 (25 ? 45 230) 2 (13 ? 45 2 400) 5 (1,125 2 30) 2 (585 1 400) 5(1,095) 2 (985) 5 110; $11020. (12x3 1 2x2 2 4) 1 (9x2 1 5x)

21. (x3 1 x2 1 1) 2 (x2 1 9x)

22. (3x3 2 1) 2 (5x2 2 2x 2 4)

23. (23x3 2 2x2 1 5) 1 (2x3 1 2x)

24. (2x2 2 2x 1 3) 1 (2x2 1 x 1 2)

25. (12x2 1 4x) 2 (6x2 2 12x)

26. Perimeter

5 7a 1 4b 5 (4a 1 a 1 a 1 a) 1 (b 1 b 1 b 1 b) 5 (4a) 1 (a 1 b) 1 (a 1 b) 1 (a) 1 (b) 1 (b)

f(a 1 b) 2 ag 5 (4a) 1 (a 1 b) 1 (a 1 b) 1 (a) 1 (b) 1

5 6x2 1 16x 5 (12 2 6)x2 1 (4 1 12)x 5 (12x2 2 6x2) 1 (4x 1 12x)

5 (12x2 1 4x) 1 (26x2 1 12x)

5 x2 2 x 1 5

5 (2 2 1)x2 1 (22 1 1)x 1 (3 1 2)

5 (2x2 2 x2) 1 (22x 1 x) 1 (3 1 2)

5 2x3 2 2x2 1 2x 1 5

5 (23 1 2)x3 2 2x2 1 2x 1 5

5 (23x3 1 2x3) 1 (22x2) 1 (2x) 1 (5)

5 3x3 2 5x2 1 2x 1 3

5 (3x3) 1 (25x2) 1 (2x) 1 (21 1 4)

5 (3x3 2 1) 1 (25x2 1 2x 1 4)

5 x3 2 9x 1 1

5 x3 1 (1 2 1)x2 2 9x 1 1

5 (x3) 1 (x2 2 x2) 1 (29x) 1 (1)

5 (x3 1 x2 1 1) 1 (2x2 2 9x)

5 12x3 1 11x2 1 5x 2 4

5 12x3 1 (2 1 9)x2 1 5x 2 4

5 (12x3) 1 (2x2 1 9x2) 1 (5x) 1 (24)

5 r2 2 5r 1 3

5 (3 2 2)r2 1 (24 2 1)r 1 (21 1 4)

5 (3r2 2 2r2) 1 (24r 2 r) 1 (21 1 4)

5 (3r2 2 4r 2 1) 1 (22r2 2 r 1 4)

5 22g2 2 2g 1 6

5 (1 2 3)g2 2 2g 1 (7 2 1)

5 (g2 2 3g2) 1 (22g) 1 (7 2 1)

5 (g2 1 7) 1 (23g2 2 2g 2 1)

5 2x2 2 2x 1 7

5 (2 2 3)x2 1 (5 2 7)x 1 7

5 (2x2 2 3x2) 1 (5x 2 7x) 1 7

5 (2x2 1 5x 1 7) 1 (23x2 2 7x)



27. Answers may vary. Sample: Like adding integers,you add the coefficients of like terms; however, unlikeadding integers, there are different kinds of terms—some with variables of differing powers and somewithout variables. 28. Write an expression for the area

of figure 1: A 5 h(b1 1 b2) 5 (x)(2x 1 3x) 5 x2.Write an expression for the area of figure 2: A 5 bh 5

(x)(2x) 5 x2 5 x2. Write an expression for the total

area of the two figures: A 5 x2 1 x2 5 x2 1 x2 5 x2.

29. 5 (1); 5 (2); 1 5 (3); 5 (4); x; the correct choice is B. 30. median: $127,000, $127,000,$156,000, $164,000, $170,000: $156,000; mode: $127,000;mean:

5

5 $148,800; range: $170,000 2 $127,000 5$43,000; The median is the largest, the correct choice is F.31. 20P5 5 20 ? 19 ? 18 ? 17 ? 16 5 1,860,480 32. 8P3 5 8 ?7 ? 6 5 336 33. 4P2 5 4 ? 3 5 12 34. 12P4 5

12 ? 11 ? 10 ? 9 5 11,880


1. 2x 2 2 2. x2 1 2x 1 2 3. x2 1 2x 4. 22 2 6x 1 5x2

2 2x 16 5 5x2 1 (26 2 2)x 1 (6 2 2) 5 5x2 2 8x 1 45. 9x2 1 3 2 10x 2 3 1 7x2 5 (9 1 7)x2 2 10x 1 (3 2 3)5 16x2 2 10x

6. (3a2 1 2a 2 1) 1 (23a2 2 9)5 (3a2 2 3a2) 1 (2a) 1 (21 2 9)5 (3 2 3)a2 1 (2)a 1 (21 2 9)5 2a 2 10

7. (11b2 2 7) 1 (15b2 2 b)5 (11b2 1 15b2) 2b 1 (27)5 (11 1 15)b2 2b 2 75 26b2 2 b 2 7

8. (c2 2 9c 2 5) 2 (2c2 2 8c 2 10)5 (c2 2 9c 2 5) 1 (c2 1 8c 1 10)5 (c2 1 c2) 1 (29c 1 8c) 1 (25 1 10)5 (1 1 1)c2 1 (29 1 8)c 1 (25 1 10)5 2c2 2 c 1 5

9. (2d2 2 9d) 2 (24d2 1 20d 1 17)5 (2d2 2 9d) 1 (4d2 2 20d 2 17)5 (2d2 1 4d2) 1 (29d 2 20d) 1 (217)5 (2 1 4)d2 1 (29 2 20)d 2 175 6d2 2 29d 2 17

10. P 5 (5x 1 2) 1 (5x 1 2) 1 (3x 1 1) 1 (3x 1 1)5 (5x 1 5x 1 3x 1 3x) 1 (2 1 2 1 1 1 1)5 16x 1 6

11. P 5 (10x 2 7) 1 (7x 2 3) 1 (5x)5 (10x 1 7x 1 5x) 1 (27 2 3)5 22x 2 10

$744,0005

$ 127,000 1 $ 127,000 1 $ 156,000 1 $ 164,000 1 $ 170,0005

13

13

43

13

13

23

13

13

72

22

52

52

22

12

12

52

12

12


1.

2a. The sum of the exponents in the first cell is equal tothe exponent in the last cell. 2b. Yes, the relation holdstrue for the other rows in the table. For example 21 ? 22 5

23. 3. am ? an 5 am 1 n

12-3 Exponents and Multiplicationpages 571–574

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. x 2. 1 3. 9 4. 29 5. 21

Quick Check 1a. 65

1b. (24)8 1c.

m12 2a. (2 3 106)(4 3 103) 5 (2 ? 4)(106 3 103) 5 8 3 109 2b. (3 3 105)(2 3 108) 5(3 ? 2)(105 3 108) 5 6 3 1013 2c. 12(8 3 1020) 5(12 ? 8) 3 1020 5 96 3 1020 5 9.6 3 1021 3. (3.00 3 105)(3.6 3 103) 5 (3.00 ? 3.6)(105 3 103) 5 10.8 3 108 5 1.083 109. In 3.6 3 103 s, light travels 1.08 3 109 km.

Exercises 1. 8 because when two exponential terms withthe same base are multiplied the answer have the samebase and the exponents are added together, thus themissing base has to be equal to the base of the first termand the answer. 2. 3 because when two exponentialterms with the same base are multiplied the answer havethe same base and the exponents are added together,thus the missing exponent has to be 6 2 3 5 3.3. (26)2 ? (26)2 5 (26)(2 1 2) 5 (26)4 4. (22)8 ? (22)3 5

(22)(8 1 3) 5 (22)11 5. 72 ? 78 5 7(2 1 8) 5 710 6. 45 ? 46

5 4(5 1 6) 5 411 7. Instead of just adding the exponents,the student multiplied the bases and then added theexponents. 8. 4.17 3 1020 ? 103 5 4.17 3 10(20 1 3) 5

4.17 3 1023 9. y3 ? y5 5 y(3 1 5) 5 y8 10. m10 ? m100 5

m(10 1 100) 5 m110 11. 3.43 ? 3.410 5 3.4(3 1 10) 5 3.413

12. 125 ? 1250 5 12(5 1 50) 5 1255 13. 4.510 ? 4.510 5

4.5(10 1 10) 5 4.520 14. (25)5 ? (25) 5 (25)(5 1 1) 5

(25)6 15. 0.45 ? 0.410 5 0.4(5 1 10) 5 0.415 16. x ? x0 5

x(1 1 0) 5 x1 17. (2 3 103)(4 3 106) 5 (2 ? 4)(103 3 106) 5

8 3 109 18. (7 3 102)(9 3 105) 5 (7 ? 9)(102 3 105) 563 3 107 5 6.3 3 108 19. 90(8 3 109) 5 720 3 109 5

7.2 3 1011 20. (3 3 105)(5 3 107) 5 (3 ? 5)(105 3 107) 515 3 1012 5 1.5 3 1013 21. (9 3 105)(5 3 109) 5(9 ? 5) (105 3 109) 5 45 3 1014 5 4.5 3 1015

22. (5.1 3 104)(2 3 107) 5 (5.1 ? 2)(104 3 107) 510.2 3 1011 5 1.02 3 1012 23. (4.8 3 1019)(9.47 3 1026) 5(4.8 ? 9.47)(1019 3 1026) 5 45.456 3 1045 < 4.55 3 1046.

m(1111) 5

m1 ? m11 5(24)(117) 5(24) ? (24)7 5

62 ? 63 5 6(213) 5

Product as aRepeated Factor

TwoExponents

SingleExponent

22

23

24

25

StandardForm

48

1632



There are about 4.55 3 1046 water molecules on Earth.24. E 5 mc2 5 (1)(3.0 3 108)2 5 (3.0)2 3 (108)2 5

9.0 3 1016 joules 25. Answers may vary. Sample: 4 ? 411;42 ? 410; 46 ? 46 26. The bases are not the same.27. 2(3.4 3 1012) 5 6.8 3 1012 28. 4x ? 4t 5 4(x 1 t)

29. 3m ? 3n 5 3(m 1 n) 30. 1.58 ? 1.5t 5 1.5(8 1 t)

31. (24)x ? (24)y 5 (24)(x 1 y)32. 23 ? 2 ? 28 5

2(3 1 1 1 8) 5 212 33. a5 ? a4 ? a 5 a(5 1 4 1 1) 5 a10

34. 912 ? 96 ? 93 5 9(12 1 6 1 3) 5 921 35. 3a ? 32a ? 33a 5

3(a 1 2a 1 3a) 5 36a 36. xy ? x2y3 5 x(1 1 2)y(1 1 3) 5 x3y4

37. c2d ? cd3 5 c(2 1 1)d(1 1 3) 5 c3d4 38. x ? x3 ? x5 5

x(1 1 3 1 5) 5 x9 39. 3x2 ? x5 ? x 5 3x(2 1 5 1 1) 5 3x8

40. (3.5 3 106)(2.79 3 107) 5 (3.5 3 2.79)(106 3 107) 59.765 3 1013; about 9.77 3 1013 ft2

41. 42.

43.

44. S.A. 5 4pr2 5 4p(6.05 3 103)2 5 4p(6.05)2 3 (103)2

5 4p(36.6 3 106) < 4.60 3 108; about 4.60 3 108 km2

45. (h 1 h)(h ? h) 5 2h(h ? h) 5 2h3. Since 2h3 5 16, h3 5

8, and h 5 2. 46. 415 5 230 because the pattern showsthat the exponent with base 4 is half as much as theexponent with the base 2; the correct choice is C.

47. Lana: 5 9004 5 5 180 words per minute; Sierra:

5 980 4 7 5 140 words per minute; 180 2 140 5 40words per minute; the correct choice is H.

48. 5 $5/book 49. 5 mi/h 5

42.85714 cmi/h < 43 mi/h 50. 5 $.60/lb


1. (3.5 3 1012)(2.3 3 109) 5 8.05 3 1021 2. (2.99 3 1016)(4.36 3 1012) 5 1.30364 3 1029 3. (2.75 3 104)2 5

7.5625 3 108 4. (5.54 3 106) 1 (1.38 3 106) 56.92 3 106 5. (4.02 3 1013) 2 (2.01 3 1013) 5 2.01 3 1013

6. (9.22 3 1011)3 < 7.84 3 1035 7. 1020 5 1.0 3 1020

8. The area of the square is (1.5 3 104)2 5 2.25 3 108

square units

12-4 Multiplying Polynomialspages 576–579

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. exponents 2. x15

3. (2a)10 or a10

Quick Check

1.

2. 3r(5r 1 5) 5 3r ? 5r 1 3r ? 5 5 15r2 1 15r3a. 2x2 1 7x 1 6

x

11

x x 1 1 1

5 8y4 5 8 ? y3 ? y

(2y3)(4y) 5 (2)(4) ? y3 ? y

$150250 lb

3007

150 mi3.5 h

$7515 books

9807

9005

516 . 510 516 j 58 ? 52

62 , 64 46 . 45 36 j 62 ? 62 46 j 43 ? 42

3b. 6x2 1 11x 1 4

3c. 2x2 1 7x 1 5

Exercises 1. A monomial has one term, whereas abinomial has two terms.

2. 3. 5a ? 3a 5 15a2 4. x5 ? x 5 x6 5. (x 1 4)(2x 1 3)6. (x 1 4)(2x 1 3) 5 2x2 1 11x 1 127.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19. x(2x 1 4) 5 x ? 2x 1 x ? 4 5 2x2 1 4x20. (x 1 3)(2x 1 3) 5 2x2 1 9x 1 921. (2x 1 1)(2x 1 2) 5 4x2 1 6x 1 2 22. A 5 <w; A 5

2(2x 1 4) ? 3(x 2 4) 5 (4x 1 8)(3x 2 12) 54x ? 3x 1 8 ? 3x 1 4x ? (212) 1 8 ? (212) 512x2 1 24x 2 48x 2 96 5 12x2 2 24x 2 96;

5 23d3 1 12d2 23d2(d 2 4) 5 23d2 ? d 2 (23d2) ? 4

5 10k2 2 2k 2k(5k 2 1) 5 2k ? 5k 2 2k ? 1

5 23y3 1 18y2 23y(y2 2 6y) 5 23y ? y2 2 (23y) ? 6y

5 21s2 1 7

7(3s2 1 1) 5 7 ? 3s2 1 7 ? 1

5 2m2 2 14m 2m(m 2 7) 5 2m ? m 2 2m ? 7

5 a2 2 3a a(a 2 3) 5 a ? a 2 a ? 3

5 220c7 5 220 ? c3 ? c4

(5c3)(24c4) 5 (5)(24) ? c3 ? c4 5 240s3 5 240 ? s2 ? s

(10s2)(24s) 5 (10)(24) ? s2 ? s 5 214x5 5 214 ? x2 ? x3

(7x2)(22x3) 5 (7)(22) ? x2 ? x3 5 26z5 5 26 ? z3 ? z2

(2z3)(6z2) 5 (21)(6) ? z3 ? z2 5 12g7

5 12 ? g4 ? g3 4g4 ? 3g3 5 (4)(3) ? g4 ? g3

5 12t5 (23t2)(24t3) 5 (23)(24) ? t2 ? t3

5 216y25 216 ? y ? y (28y)(2y) 5 (28)(2) ? y ? y

x

1xx 1 1 1 1 1

x

x

x

1111

xx 1



(12x2 2 24x 2 96) ft2

23. 24.

25.

26. 2w2(w2 1 2w 2 4)

27. Model x 1 1 along the vertical and model x 1 2along the horizontal. Since length times width is the areaof a rectangle, complete the rectangle. The area of thearray of tiles is x2 1 3x 1 2. 28. binomial29. monomial 30. polynomial 31. monomial32a. GCF is 3:

32b. GCF is 5y:

32c. GCF is 4a:

33. Alec: 5 ft 10 in. Harry: 5 ft 10 in. 1 4 in. 5 6 ft 2 in.Caitlin: 5 3 ft 1 in. Jordan: 3 ft 1 in. 2 2 in. 5 2 ft11 in. Andrea: 2(2 ft 11 in.) 5 4 ft 22 in. 5 5 ft 10 in; thecorrect choice is D. 34. The first choice matches the topand side views; the correct choice is F.35. y 5 7 2 3x 36. y 5 8x 1 10

37. y 5 2x 1 2


1. 4.76 ? 4.715 5 4.7(6 1 15) 5 4.721 2. (24a2)(24a2) 5

(24a)(2 1 2) 5 (24a)4 3. xy5 ? x3y7 5 x ? x3 ? y5 ? y7 5

x(1 1 3) ? y(5 1 7) 5 x4y12 4. 50(6 3 103) 5 300 3 103 5

3.0 3 105 5. (3 3 107)(5 3 104) 5 3 ? 5 3 10(7 1 4) 5

6ft 2in.2

5 4a(2a2 1 a 1 3)

8a3 1 4a2 1 12a 5 4a ? 2a2 1 4a ? a 1 4a ? 3

5 5y(y 1 2)

5y2 1 10y 5 5y ? y 1 5y ? 2

5 3(x2 1 3)

3x2 1 9 5 3 ? x2 1 3 ? 3

5 2w4 2 2w3 1 4w2

5 2w2 ? w2 1 (2w2) ? 2w 2 (2w2) ? 4

5 4x2 1 2x 5 2x ? 2x 1 2x ? 1

5 (2x 1 1)2x A 5 bh

5 32x2 2 2x

5 12(3x2 2 4x) 5 6x2 1 4x

5 12f(3x ? x) 2 (4 ? x)g 5 2x ? 3x 1 2x ? 2

5 12(3x 2 4)(x) 5 2x(3x 1 2)

A 5 12bh A 5 / ? w

15 3 1011 5 1.5 3 1012 6. (4 3 104)(9 3 102) 5

4 ? 9 3 10(4 1 2) 5 36 3 106 5 3.6 3 107 7. 7f5 ? 4f3 5

(7)(4) ? f(5 1 3) 5 28f 8 8. (3.1g6)(5g2) 5 (3.1)(5) ? g(6 1 2) 5

15.5g8 9. (28h8)(2.2h10) 5 (28)(2.2) ? h(8 1 10) 5

217.6h18 10. 25j(j2 2 9j) 5 (25j) ? j2 1 (25j) ? (29j) 5(25)(1) ? j(1 1 2) ? (25)(29) ? j(1 1 1) 5 25j3 1 45j2

11. 6k(k 2 1) 5 6k ? k 1 6k ? (21) 5

(6)(1) ? k(1 1 1) 1 (6)(21) ? k 5 6k2 2 6k

12. 10m2(3m 2 4) 5 10m2 ? 3m 1 10m2 ? (24) 5

(10)(3) ? m(2 1 1) 1 (10)(24) ? m2 5 30m3 2 40m2

13. (2x 1 3)(4x 1 1) 5 8x2 1 14x 1 3

14. (x 1 3)(2x 1 2) 5 2x2 1 8x 1 6

12-5 Exponents and Divisionpages 581–585

Check Skills You’ll Need For complete solutions seeDaily Skills Check and Lesson Quiz Transparencies orPresentation Pro CD-ROM. 1. power 2. 74 3. 43 4. 52

5. 15

Quick Check 1. 5 w(8 2 5) 5 w3 2. 5

3 5 3 1 5 8.5 3 1; 8.5 min 3a. (29)0 5 1

3b. (2r)0 5 1 3c. 2r0 5 2 ? r0 5 2 ? 1 5 2 4a. 321 5 5

4b. w24 5 4c. (22)23 5 5 5 2

Exercises 1. Positive; any nonzero number to the power

zero is equal to one. 2. 5 123(5 2 4) 5 123 3. 5

5 2(6 2 5) 5 21 4. 5 5

3(4 2 2) 5 32 5. 5 5 8(5 2 3) 5 83 6. 5

a(5 2 3) 5 a2 7. 5 x(9 2 5) 5 x4 8. 5 c(7 2 2) 5 c5

9. 5 (21)(5 2 4) 5 (21)1 10. 5 23(12 2 8) 5 234

11. 5 135(10 2 1) 5 1359 12. 5 (27)(99 2 98) 5

(27)1 13. 5 (29)(32 2 15) 5 (29)17

14. 5 3 5 8.07 3 10(8 2 7) 5

8.07 3 101; 80.7 min 15. 40 5 1 16. (23)0 5 1 17. u0 5

1, u ? 0 18. (3t)0, t ? 0 5 1 19. 1022 5 5

20. b26 5 21. x24 5 22. 721 5 23. 5

3 10(9 2 4) 5 0.22 3 105 5 2.2 3 104. China’s population is about 2.2 3 104 times greater than

Marshall Islands’ population. 24. 5

3 10(6 2 4) , 1.09 3 102. The sun’s diameter is about

1.09 3 102, or about 109 times greater than Earth’s diameter. 25. 12 26. 2 27. 2 28. 27 29. (w 1 x)24 5

(21 1 2)24 5 (1)24 5 5 1 30. xw 5 221 5

31. 22(w 1 2x) 5 22(21 1 2 ? 2) 5 22(21 1 4) 5

12

1

14

1.391.28

1.39 3 106

1.28 3 104

1.35.9

1.3 3 109

5.9 3 104

17

1

x41

b6

1100

1

102

108

107

8.881.1

8.88 3 108

1.1 3 107

(29)32

(29)15

(27)99

(27)98

13510

1351

2312

238

(21)5

(21)4

c7

c2x9

x5

a5

a38 ? 8 ? 8 ? 8 ? 8

8 ? 885

82

3 ? 3 ? 3 ? 33 ? 3

34

322 ? 2 ? 2 ? 2 ? 2 ? 2

2 ? 2 ? 2 ? 2 ? 2

26

251235

1234

18

128

1

(22)3

1

w4

13

131

9.31.1

107

107

9.31.1

9.3 3 107

1.1 3 107

w8

w5



223 5 28 32. (2x)w 1 1 5 (2 ? 2)21 1 1 5 40 5 1

33. 5 3 5 1.12 3 10(6 2 3) 5

1.12 3 103; 1.12 3 103 ft/s 34. False; 40 5 1 and 421 5 .

35. False; 821 5 and (28)1 5 28. 36. True; 21 ? 221 5

2(1 1 21) 5 20. 37. False; (22)21 5 5 2 and 2 2 2.38. 3.0 3 105 km/s ? 3,600 s/h 5 10,800 3 105 5

1.08 3 109 km/h; 5 3 5 11.2 3 1 5

11.2; 11.2 h 39a. 5 2 5 2n3 2 4

39b. 5 1 1 5

2m6 1 3m3 1 1 40. L.A. 5 2bl 5 2 ? 1.5 ? 1.5 5 4.541. c 5 8.95 1 0.95s 5 8.95 1 0.95(23) 5 8.95 1 21.85 5

30.80 42. The ratio of the sides is , so the ratio of the

areas is ( )2 5 ; 5 ; x 5 9 ? 12 5 108 43. 58x 5 17

5

x 5 0.2931x 5 29.31%

44. x 5 0.125 ? 34.5x 5 4.31

EXTENSION page 586

1. (33)7 5 3(3 ? 7) 5 321 2. (92)25 5 9(2 ? 25) 5 9210

3. (w22)26 5 w(22 ? 26) 5 w12 4. (r2)3 5 r(2 ? 3) 5 r6

5. (3x)2 5 32 ? x2 5 9 ? x2 5 9x2 6. (a2b3)4 5

(a2)4 ? (b3)4 5 a8 ? b12 5 a8b12 7. (10x5)2 5

102 ? (x5)2 5 100 ? x10 5 100x10 8. (y2 ? 22)4 5

(y2)4 ? (22)4 5 y8 ? 28 5 y8 ? 256 5 256y8


1. Yes; 10% of 889 is 88.9, 88.9 1 889 5 977.9. Since977.9 , 1,000, 1,000 will be enough. 2. Work a simplerproblem. Find how many dominos you would need for n 5 10 rows. 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 5

55; (102 1 10) 5 (100 1 10) 5 (110) 5 55; Both

Wanda and Jake are correct. 3. 110 ? 2.36 5 259.6 lb;259.6 4 110 5 2.36; It is 2.36 times your weight on Earth.

4.

; 15 miles

5. 5 5 0.25 ? 70.7 5 17.7;17.7 seconds

0.25"5,000t 5 0.25"d

5 15

5 "225

d 5 "32 ? 150

d 5 "32h

"32h 5 "d2

32 ? h 5 d2

32 ? h 5 23d2 ? 3

2

h 5 23d2

12

12

12

1758

58x58

12x

19

19

13

13

2m3

2m3

6m6

2m3

4m9

2m3

4m9 1 6m6 1 2m3

2m3

12n2

3n2

6n5

3n2

6n5 2 12n

3n2

2

109

109

12.11.08

12.1 3 109

1.08 3 109

12

12

122

18

14

106

1034.023.6

4.02 3 106 feet

3.6 3 103seconds


1. Let g 5 4. Then 33 ? 4 5 132. Since 132 2 297, choiceA is wrong. Let g 5 6. Then 33 ? 6 5 198. Since 198 2297, choice B is wrong. Let g 5 9. Then 33 ? 9 5 297.Since 297 5 297, the correct choice is C. 2. Let r 5 5.2.Then 5.2 3 1.5 5 7.5. Since 7.5 2 13.1, choice A iswrong. Let r 5 8.7. Then 8.7 3 1.5 5 13.1. Since 13.1 513.1, the correct choice is G.


1. 6x2 1 3x 2 2 is an example of polynomial. 2. A termthat does not contain a variable is a constant. 3. Apolynomial such as 4y is called a monomial. 4. In thepolynomial 5z2 12, 5 is a coefficient. 5. A binomial is apolynomial with two terms. 6. 2x2 1 8 7. x2 1 3x 1 48. 5x2 1 6 2 4x 1 9x2 1 17x

5 (5 1 9)x2 1 (24 1 17)x 1 65 14x2 1 13x 1 6

9. 8 2 3x 1 11x2 1 2x2 2 10 1 7x5 (11 1 2)x2 1 (23 1 7)x 1 (8 2 10)5 13x2 1 4x 2 2

10. 4 2 3x2 1 2x 2 x2 1 35 (23 2 1)x2 1 2x 1 (4 1 3)5 24x2 1 2x 1 7

11. 2x2 1 4x 1 7 2 2x 1 9x5 2x2 1 (4 2 2 1 9)x 1 75 2x2 1 11x 1 7

12. (2x 2 5) 1 (14x 1 10)5 (2x 1 14x) 1 (25 1 10)5 (2 1 14)x 1 (25 1 10)5 16x 1 5

13. (24x2 1 7x) 1 (x2 2 7x 1 3)

14. (8x2 2 7x 1 3) 1 (3x2 1 x 2 5)

15. (5x2 1 3) 1 (2x2 2 3x 2 1)5 (5x2 1 2x2) 1 (23x) 1 (3 2 1)5 (5 1 2)x2 1 (23x) 1 (3 2 1)5 7x2 2 3x 1 2

16.

17. (2x2 2 4x 2 8) 2 (x2 2 5x 13)5 (2x2 2 4x 2 8) 1 (2x2 1 5x 2 3)5 (2x2 2 x2) 1 (24x 1 5x) 1 (28 2 3)5 (2 2 1)x2 1 (24 1 5)x 1 (28 2 3)5 x2 1 x 2 11

18. (7x2 1 6) 2 (2x 2 7)5 (7x2 1 6) 1 (22x 1 7)5 (7x2) 1 (22x) 1 (6 1 7)5 7x2 2 2x 1 13

5 24x 2 7

5 (5 2 9)x 1 (24 2 3)

5 (5x 2 9x) 1 (24 2 3)

(5x 2 4) 2 (9x 1 3) 5 (5x 2 4) 1 (29x 2 3)

5 11x2 2 6x 2 2

5 (8 1 3)x2 1 (27 1 1)x 1 (3 2 5)

5 (8x2 1 3x2) 1 (27x 1 x) 1 (3 2 5)

5 23x2 1 3

5 (24 1 1)x2 1 (7 2 7)x 1 3

5 (24x2 1 x2) 1 (7x 2 7x) 1 3



19. (5x2 1 9x 2 7) 2 (2x2 1 3x)5 (5x2 1 9x 2 7) 1 (22x2 2 3x)5 (5x2 2 2x2) 1 (9x 2 3x) 1 (27)5 (5 2 2)x2 1 (9 2 3)x 1 (27)5 3x2 1 6x 2 7

20. 810 ? 89 5 8(10 1 9) 5 819 21. (23)4 ? (23)9 5

(23)(4 1 9) 5 (23)13 22. 2.612 ? 2.612 5 2.6(12 1 12) 5 2.624

23. 115 ? 116 5 11(5 1 6) 5 1111 24. (3 3 106) ? (2 3 1012) 5

(3 ? 2) 3 10(6 1 12) 5 6 3 1018 25. 5 ? (1.4 3 106) 5

(5 ? 1.4) 3 106 5 7 3 106 26. (6 3 109) ? (5 3 104) 5

(6 ? 5) 3 10(9 1 4) 5 30 3 1013 5 3 3 1014

27. (2.1 3 107) ? (7 3 1012) 5 (2.1 ? 7) 3 10(7112) 5

14.7 3 1019 5 1.47 3 1020

28.

29.

30.

31.

32. (2x 1 1)(x 1 4) 5 2x ? x 1 1 ? x 1 2x ? 4 1 1 ? 4 5

2x2 1 9x 1 4 33. (x 1 1)(x 1 3) 5

x ? x 1 x ? 3 1 1 ? x 1 1 ? 3 5 x2 1 4x 13

34. 5 5(10 2 7) 5 53 35. 5 (28)(12 2 2) 5

(28)10 36. 5 76(11 2 5) 5 766 37. 5 1.8(6 2 5) 5

1.81 38. 80 5 1 39. (216)0 5 1 40. g0 5 1 41. (8b)0 5 1

42. 524 5 5 43. x29 5 44. 922 5 5

45. h28 5


1. 3x 1 12 2 4 1 9x5 3x 1 9x 1 12 2 45 (3x 1 9x) 1 (12 2 4)5 (3 1 9)x 1 (12 2 4)5 12x 1 8

2. 4x2 2 6 1 x2 1 5x 2 105 4x2 1 x2 1 5x 2 6 2 105 (4x2 1 x2) 1 (5x) 1 (26 2 10)5 (4 1 1)x2 1 (5x) 1 (26 2 10)5 5x2 1 5x 2 16

3. 4 2 2x 1 9 1 3x2 1 7x 2 6x2

5 3x2 2 6x2 2 2x 1 7x 1 4 1 95 (3x2 2 6x2) 1 (22x 1 7x) 1 (4 1 9)5 (3 2 6)x2 1 (22 1 7)x 1 (4 1 9)5 23x2 1 5x 1 13

4. 14x 2 1 1 5x2 1 10x2 2 45 5x2 1 10x2 1 14x 2 1 2 45 (5x2 1 10x2) 1 (14x) 1 (21 2 4)5 (5 1 10)x2 1 (14)x 1 (21 2 4)5 15x2 1 14x 2 5

5. 2x2 2 x2 2 2x 1 4 2 1 5 x2 2 2x 1 3

1

h8

181

1

92

1

x9

1625

1

54

1.86

1.85

7611

765

(28)12

(28)2

510

57

5 5x3 2 15x2 5x(x2 2 3x) 5 5x ? x2 2 5x ? 3x

5 230x2 1 20x 210x(3x 2 2) 5 210x ? 3x 2 (210x) ? 2

5 14x2 (22x)(27x) 5 (22)(27) ? x ? x

5 218x4 (26x)(3x3) 5 (26)(3) ? x ? x3

6. (5x2 2 4x 1 2) 1 (3x2 2 3x 2 5)5 (5x2 1 3x2) 1 (24x 2 3x) 1 (2 2 5)5 (5 1 3)x2 1 (24 2 3)x 1 (2 2 5)5 8x2 2 7x 2 3

7. (x2 2 3x 1 5) 1 (2x2 1 4x 1 4)5 (x2 2 x2) 1 (23x 1 4x) 1 (5 1 4)5 (1 2 1)x2 1 (23 1 4)x 1 (5 1 4)5 0x2 1 1x 1 95 x 1 9

8. (2x2 1 7x 2 6) 1 (4x2 1 3x 2 2)5 (2x2 1 4x2) 1 (7x 1 3x) 1 (26 2 2)5 (2 1 4)x2 1 (7 1 3)x 1 (26 2 2)5 6x2 1 10x 2 8

9. (7x2 2 x 1 2) 2 (x2 1 4x 2 4)

10. (2x2 1 3x 1 4) 2 (2x 2 7)5 (2x2 1 3x 1 4) 1 (22x 1 7)5 (2x2) 1 (3x 2 2x) 1 (4 1 7)5 (2x2) 1 (3 2 2)x 1 (4 1 7)5 2x2 1 x 1 11

11. (9x2 1 5x 2 10) 2 (22x2 1 4x 1 3)5 (9x2 1 5x 2 10) 1 (2x2 2 4x 2 3)5 (9x2 1 2x2) 1 (5x 2 4x) 1 (210 2 3)5 (9 1 2)x2 1 (5 2 4)x 1 (210 2 3)5 11x2 1 x 2 13

12a.

12b.

13. 107 ? 106 5 10(7 1 6) 5 1013 14. a5 ? a2 5 a(5 1 2) 5 a7

15. 3.43 ? 3.46 5 3.4(3 1 6) 5 3.49 16. (2h)5 ? (2h)8 5

(2h)(5 1 8) 5 (2h)13 17. 23 ? 26 ? 25 5 2(3 1 6 1 5) 5 214

18. r3 ? r4 ? r10 5 r(3 1 4 1 10) 5 r17

19.

20.

21.

22.

23. 5(7 3 104) 5 (5 3 7) 3 104 5 35 3 104 5

3.5 3 101 3 104 5 3.5 3 105 24. 11(8 3 102) 5(11 3 8) 3 102 5 88 3 102 5 8.8 3 101 3 102 5

8.8 3 103 25. (9 3 105)(3 3 1012) 5(9 3 3) 3 (105 3 1012) 5 27 3 1017 5 2.7 3 101 3 1017 5

2.7 3 1018 26. (12 3 107)(2 3 106) 5(12 3 2) 3 (107 3 106) 5 24 3 1013 5 2.4 3 101 3 1013 5

2.4 3 1014 27. (6 3 103)(6 3 1010) 5(6 3 6) 3 (103 3 1010) 5 36 3 1013 5 3.6 3 101 3 1013 5

3.6 3 1014 28. t23 ? t0 5 t23 ? 1 5 t23

5 2x3 2 12x2

2x(x2 2 6x) 5 2x ? x2 2 2x ? 6x 5 x3 1 17x2

x2(x 1 17) 5 x2 ? x 1 x2 ? 17

5 3x2 1 5x x(3x 1 5) 5 x ? 3x 1 x ? 5

5 218x2

(29x)(2x) 5 (29)(2) ? x ? x

5 2x2 2 3x 5 x ? 2x 2 x ? 3

area 5 x(2x 2 3)

5 6x 2 6

5 (1 1 1 1 2 1 2)x 1 (23 2 3)

5 (x 1 x 1 2x 1 2x) 1 (23 2 3)

perimeter 5 x 1 x 1 (2x 2 3) 1 (2x 2 3)

5 6x2 2 5x 1 6

5 (7 2 1)x2 1 (21 2 4)x 1 (2 1 4)

5 (7x2 2 x2) 1 (2x 2 4x) 1 (2 1 4)

5 (7x2 2 x 1 2) 1 (2x2 2 4x 1 4)



29. 5 (23)(5 2 2) 5 (23)3 30. 5 14(8 2 4) 5 144

31. 5 c(6 2 2) 5 c4 32. (x 1 1)(4x 1 2) 5

x ? 4x 1 1 ? 4x 1 x ? 2 1 1 ? 2 5 4x2 1 4x 1 2x 1 2 5

4x2 1 6x 1 2 33. 20 5 1 34. r0 5 1 35. 70 5 1

36. d0 5 1 37. 425 5 5 38. a28 5 39. r22 5

40. 924 5 5 41. x26 5 42. 623 5 5

43. Answers may vary. Sample: Since you subtract exponents to find the quotient of two numbers with the same base, any nonzero number divided by itself will give you a number to the zero power, and any nonzero

number divided by itself is always 1. For example, 5

5(4 2 4) 5 50 5 1. 44. 4.2 3 106 3 14 5 (4.2 3 14)3 106 5 58.8 3 106 5 5.88 3 101 3 106 5 5.88 3 107

TEST PREP pages 593–595

1. A: Find the median: 14, 14, 14, 16, 18; the median is 14;find the mean: 5 5 15.2; themean is not 14.8, therefore 14, 14, 14, 16, 18 is not thecorrect data set. B: Find the median: 12, 14, 14, 15, 20; the median is 14; find the mean: 5 5

15; the mean is not 14.8, therefore 12, 14, 14, 15, 20 is notthe correct data set. C: Find the median: 13, 14, 14, 16, 17;the median is 14; find the mean: 5

5 14.8; find the mode: 14; find the range: 17 2 13 5 4,therefore this data set is correct. The correct choice is C.2. The first circle has 8 out of 10 pieces shaded in, andthe second circle has 12 out of 15 pieces shaded in. 5

is the proportion of the number of piecesshaded to the total number of pieces on each circle.

5 is the proportion of the number of pieces notshaded to the number of pieces shaded on each circle.5 cannot be represented by the model at the

right; 5 is the simplified proportion of the firstcircle equal to the actual proportion of the first circle;the correct choice is H. 3. y 5 2x2 2 3; for all values ofx, y must be greater than or equal to 23 because x2 willnever be negative; 25 cannot be a value of y because itis less than 23; the correct choice is D. 4. The graphrepresents the inequality a . 23; solving the equation

, 1 for x simplifies the equation to x . 23 which isshown graphically on a number line with an open circleat 23 and the line pointing in the positive direction fromthere; the correct choice is F. 5. Find the LCM of 5 and6: the multiples of 5 are 5, 10, 15, 20, 25, 30, . . . Themultiples of 6 are 6, 12, 18, 24, 30, . . . The LCM is 30.Divide the LCM by 6 because Tia has art class everysixth day of school: 30 4 6 5 5, therefore every 5th weekTia will have art class on a Monday; the correct choice isB. 6. 1 gram is equal to 0.001 kilograms. 500 gramsequals 500 times 0.001 kilograms which is 0.5 kilograms.The correct choice is G. 7. Use the Pythagoreantheorem. 32 1 42 5 9 1 16 5 25. The hypotenuse equalsthe square root of 25, or 5. The correct choice is C.

2x3

810

45

215

310

312

28

810

1215

745

13 1 14 1 14 1 16 1 175

755

12 1 14 1 14 1 15 1 205

765

14 1 14 1 14 1 16 1 185

54

54

1216

163

1x6

16,561

194

1r2

1a8

11,024

1

45

c6

c2

148

144

(23)5

(23)2

8. F: 2(x 2 3) 5 2(x) 2 2(3)G: 2(x 2 3) 5 2(23) 1 2xH: 2(x 2 3) 5 (x 2 3) 1 (x 2 3)J: 2(x 2 3) 5 2x 2 6; 2(x 2 3) ? 2x 2 3

The correct choice is J.9. The original coordinates are A(22, 2), B(1,1), C(1, 21);after a translation of 2 units left and 3 units down,(x, y) (x 2 2, y 2 3), the new coordinates will beA9(24, 21), B9(21,22), C9(21, 24); the correct choiceis A. 10. The only integers that have an absolute valueless than 3 are 22, 21, 0, 1, and 2. The correct choice is H.11. There are 2 favorable outcomes with the 2 greenshirts, out of 9 possible outcomes, all the shirts Deidreowns. The probability of the shirt being green is . Thecorrect choice is C. 12. The shaded area is equal to thearea of the square minus the area of the circle. The areaof the square is 6 3 6, or 36 units2. The area of the circleis about 3.14 3 32, or about 28 units2. The area of theshaded area equals 36 2 28, or about 8 units2. Thecorrect choice is G. 13. The number 10,550 written inscientific notation is 1.055 3 104. The correct choice is B.14. To seat 5 out of 8 people in 5 chairs there are 8 ? 7 ? 6 ? 5 ? 4, or 6,270 different ways. The correct choiceis G. 15. A circle is 360º, so the angle of a sector thatmakes up 24% of the whole is equal to 24% of 360º,0.24 ? 360, or 86.4º. The correct choice is D. 16. Bylooking at a box-and-whisker plot the range, median,and upper quartile can all be determined. Therefore, themode cannot be determined; the correct choice is G.17. Since the triangles are similar their proportions areequal.

5

10h 5 6 ? 155

h 5 9 ft; the correct choice is B.18. Jim started with $500 and took out $200, then tookout another $400. His account balance is $500 2 $200 2$400, or 2 $100. The correct choice is F. 19. Examples ofa prism are a shoe box, a domino, and a file cabinet. Asoup can is a cylinder, not a prism; the correct choice is D.20. The relationship in the scatter plot is a positive trendbecause as one set of values increases, the other set ofvalues increases; the correct choice is G. 21. The totalnumber of students is 15 1 12 1 8 1 3 1 5, or 43students; grid 43. 22. The number of students thatstudied 1 hour or less is 15 1 12, or 27 students; grid 27.23. The percent of students that studied more than 2 hours is 5 , or 18.6 %; grid 18.6. 24. The medianis the middle number of the data set when written innumerical order; 82, 82, 82, 83, 85, 86, 87, 90, 95, 95;

5 85.5; grid 85.5. 25. When x 5 24 and y 5

28, 23 1 x 2 y 5 23 1 (24) 2 (28) 5 23 2 4 1 8 527 1 8 5 1; grid 1. 26. With an equilateral triangle allthree sides are equal, so if the perimeter is 5 cm, the length of one side is 5 cm 4 3, or 1.75 cm; grid 1.75.27. To find the area of the figure, separate the figure intotwo rectangles and add their areas. 7 mm 3 5 mm 5 35mm2; 3 mm 3 2 mm 5 6 mm2; 35 mm2 1 6 mm2 5 41mm2; grid 41. 28. If a person dives down 10 feet

14

14

85 1 862

843

3 1 543

6 ? 1510

10h10

h15

610

29

m



40a-b. [4] The surface areaequals the surfacearea of the 2 circlesplus the surfacearea of therectangle. d 5 4 yd;r 5 2 yd; h 5 7 ydS.A. 5 2(pr2) 12prh 5 2(p ? 22) +2p(2)(7) 5 8π 1

28π 5 36π 5

113.098; the surfacearea is 113 yd2 [3] appropriate methods with onecomputational error; [2] correct net OR correct surfacearea; [1] correct solution without work shown41a-b. [4] The amount of money Boise will have savedafter x weeks will be 34 1 15x. To find out how manyweeks Boise must save the equation 34 1 15x 5 349must be solved for x.

34 1 15x 5 34934 1 15x 2 34 5 349 2 34

15x 5 3155

x 5 21Boise must save for 21 weeks to be able to buy the scanner. [3] appropriate equation with onecomputational error; [2] correct equation solvedincorrectly; [1] correct solution without work shown42a-b. [4] In the diagram, the scale is 1 in. 5 20 ft; so todetermine how long 2.5 in. will be in the real building 2.5should be multiplied by 20. 2.5 3 20 5 50. The 2.5 in.side will be 50 ft in the real building. The diagram for thekitchen floor is 0.5 in. by 0.5 in.; 0.5 3 20 5 10; whichmeans in the real building it is 10 ft by 10 ft. 10 3 10 5100. The area of the actual floor is 100 ft2. [3]appropriate methods with one computational error; [2]correct lengths of sides but incorrect area; [1] correctsolution without work shown43a-b. [4] The percent markup is the markup divided bythe store’s cost. The markup is $6.00 2 $3.50, or $2.50.The percent markup is 5 0.714, or 71.4%. To find thenumber of bottles you can buy divide the amount ofmoney you have by the price per water bottle. 5

2.5. You can buy 2 water bottles because youmust buy water bottles in whole numbers. [3] correctprocedure with one computational error; [2] correctpercent of markup OR correct number of bottles; [1]correct answers without work shown


1a. 5.79 3 103 mm 5 5.79 m 1b. 1 t 5 2 3 103 lb, so (7.5 3 1024) ? (2 3 103) 5 15 3 1021 5 1.5 lb. 1c. 1 mi 55.28 3 103 ft and 1 decade 5 10 3 365 3 24 58.76 3 104 h, so 1 mi/h 5 3 1023 ? 3 1024 <2.16 3 1029. So the rabbit’s speed is (5.55 3 109) ? (2.16 3 1029) 5 5.55 ? 2.16 5 11.988 <12 mi/h. 2–3. Check students’ work.

B18.76AB1

5.28A

$ 15.00$ 6.00

2.503.50

31515

15x15

12.57 yd

7 yd

4 yd

4 ydvertically off a diving board 4 feet above the water theywill dive 10 2 4, or 6 feet below the surface of the water;grid 6. 29. To make 250 copies at $0.08 a copy it will cost$0.08 ? 250, or $20; grid 20. 30. The volume of a pyramidis times the base times the height. So the volume is

? 126 cm2 ? 23 cm, or 966 cm3; grid 966. 31. [2] Thelateral area is the area of the surface area of the fourtriangular sides; 4 ? ? 12 ? 8, or 192 ft2. The surface areaincludes the square base; 12 ? 12 1 192 5 144 1 192, or336 ft2 [1] only one answer correct 32. [2] The percentmarkup is the markup divided by the store’s cost. Themarkup is $15.95 2 $4.87, or $11.08. The percent markupis = 2.275, or 227.5%. [1] appropriate method withone computational error OR correct answer withoutwork shown33a-b. [2] When y 5 11,

y 5 23x 2 111 5 23x 2 111 1 1 5 23x 2 1 1 112 5 23x

5

24 5 x[1] correct graph OR correct value of x

34. [2] The stock fund earned the most at about 1.8 yearsbecause that is the peak or highest point on the graph.[1] correct answer without explanation 35. [2] The conewith height 2 cm and radius 6 cm has the greater volume,since p ? 62 ? 2 . p ? 22 ? 6. [1] correct answer withinadequate explanation 36a-b. [2] In the sequence 4, 12,36, 108, … the next term is 3 times the previous term.The next term will be 108 ? 3, or 324. The common ratiois 3 because each term is multiplied by 3. [1] correct termOR correct ratio. 37.[2] The circumference of a circle isfound by pd 5 p ? 14, or 44.0 cm. The area of a circle ispr2 5 p( ) 5 p ? 72, or 153.9 cm2. [1] only one answercorrect 38.[2] On the first day she swam 30 minutes andby the fourth day she increased her time, she wasswimming 60 minutes. This can be written as an equationwith 30 1 4m 5 60, where m is the number of minutesshe increases her workout by each day.

30 1 4m 5 60 She increased her daily 30 1 4m 2 30 5 60 2 30 workout by 7.5 minutes.

4m 5 30 [1] inappropriate procedure5 with one computational

m 5 7.5 error OR correct answerwithout work shown

39a-c. [4] C 5 3.99 1 3.99x, where x is the number ofminutes and C is the total cost. C 5 3.99 1 3.99(10) 543.89

[3] appropriate methodswith one error;[2] correct functionevaluated correctly ORcorrect functiongraphed correctly butevaluated incorrectly;[1] correct solutionwithout work shown

x

C

2 4 6 8O

36

24

12

Co

st (

do

llars

)

304

4m4

d2

13

13

23x23

1223

1Ox

y

11.084.87

12

13

13


Course 3 Solution Key • Extra Practice, page 154

48. Let c 5 the cost of one lunch.

The cost of one lunch is $4.49. Let m 5 the amount of money that goes to eachcharity.

Each charity gets $48.

Chapter 2 pages 606–607

1. 9 5 32; 33 5 3 ? 11; GCF 5 3 2. 7 5 7; 15 5 3 ? 5;GCF 5 1 3. 6 5 3 ? 2; 24 5 3 ? 23; GCF 5 3 ? 2 5 64. 4 5 22; 18 5 2 ? 32; GCF 5 2 5. 22 5 2 ? 11; 121 5 112;GCF 5 11 6. 17 5 17 ? 1, 51 5 17 ? 3, GCF 5 17 7. 42 53 ? 2 ? 7, 165 5 3 ? 5 ? 11, GCF 5 3 8. 18 5 32 ? 2, 60 5 3 ?22 ? 5, GCF 5 6 9. 5 10. 5 11. 5

12. 2 5 2 13. 2 5 2 14. 5 15. 5

16. 5 17. 0.45 5 5 18. 12.2 5 5

12 19. 8.6 5 5 8 20. 0. 5 21. 5 0.69

22. 2.7 , 23. 24.3 , 24.2 24. 2 . 215.9

25. 2 1 5 5 26. 2 1 A2 B 5 2 5 2

27. 12 2 6 5 5 28. 3 2 A2 B 5 3 5 4

29. 2 ? 5 2 5 2 30. 24 ? 26 5 2 ? 26 5

5 25 31. 22 4 6 5 2 ? 5 2 32. 225 4 5

225 ? 5 2 5 235

33. 34.

35. 36.

37. 232 2 (28) 5 29 1 8 5 21 38. (22)3 1 4 4 2 2 3 528 1 2 2 3 5 29 39. (3 2 4)5 2 17 1 112 5

(21)5 2 17 1 1 5 21 2 16 5 217 40. 2r2 1 6r 1 3 52(26)2 1 6(26) 1 3 5 72 2 36 1 3 5 39 41. 2c3 1 2c2

2 c 1 8 5 2(3)3 1 2(3)2 2 3 1 8 5 227 1 18 2 3 1 85 24 42. 400,000,000 5 4 3 108 43. 8,750,000 5 8.75 3106 44. 40,000 5 4 3 104 45. 19,000,000 5 1.9 3 107

46. Find the multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104,117, 130, 143; find the multiples of 11: 11, 22, 33, 44, 55,66, 77, 88, 99, 110, 121, 132, 143; the LCM is 143.143 4 60 5 2 R 23. They will meet up again after going

Ec2 5 m c 2 44a 5 b

1c2 ? E 5 mc2 ? 1

c2 c 2 44a 5 44a 1 b 2 44a

E 5 mc2c 5 44a 1 b

Ipt 5 r 3VB 5 h

Ipt 5prtpt 3B ? V 5 3

B ? 13Bh

I 5 prt V 5 13Bh

1755

75

57

512

16

52

12

14

60624

10124

524

521

1563

59

37

27

1814

1114

12

2311

43 2 6

23 52

313

49

818

16

518

12

48

78

38

175

103

42536

8983

58.61 5 86

1015

12.21 5 122

10920

45100

23

3451

225226

6547

3663

314

942

37

1535

56

4048

111

777

45

2025

m 5 48

3m3 5 144

3

3m 5 144

c 5 4

15c15 5 60

15

15c 5 60

3(5c) 5 60Chapter 1 pages 604–605

1. 3t 2 4n 5 3(5) 2 4(2) 5 15 2 8 5 7 2. 13 2 (m 1 n) 513 2 (3 1 2) 5 13 2 5 5 8 3. 5 5 5 4

4. 4.7 1 mt 5 4.7 1 (3)(5) 5 4.7 1 15 5 19.7 5. 27 , 76. 32 5 232 7. 29 . 23 8. 28 . 26 9. 26 14 5 22 10. 24 1 (25) 5 29 11. 22 2 6 5 2812. 28 2 (25) 5 23 13. 15 2 (28) 5 23 14. 99 1(2101) 5 22 15. 23 ? 4 5 212 16. 215 ? (25) 5 7517. 2 ? (27) ? 5 5 214 ? 5 5 270 18. 5 22

19. 5 5 20. 5 22 21. Distributive Property22. Associative Property of Addition 23. CommutativeProperty of Addition 24. Distributive Property25. Associative Property of Multiplication 26. IdentityProperty of Addition27. 28.

29. 30.

31. 32.

33. 34.

35. 1,605 ft 2 855 ft 5 750 ft 36. $240 1 $230 1 $220 1$210 1 $200 5 $1,100 37. The estimate of 1 is off by 7 2 1, or 6. The estimate of 12 is off by 12 2 7, or 5. Thestudent who answered 1 was off by the most.38. $34 2 $15 5 $19 39. 128 ft 1 47 ft 5 175 ft 40. 20s 2 5c 5 20(12) 2 5(7) 5 240 2 35, or $205 41. 7,200 4 3 5 2,400; 2,400 passengers per hour 42. 3(1.99) 5 3(2 2 0.01) 5 3(2) 2 3(0.01) 56 2 0.03 5 5.97, or $5.97 43. 6(0.97) 5 6(1 2 0.03) 56(1) 2 6(0.03) 5 6 2 0.18 5 5.82, or $5.82 44. 4(1.98) 54(2 2 0.02) 5 4(2) 2 4(0.02) 5 8 2 0.08 5 7.92, or $7.9245. 5(2.95) 5 5(2 2 0.05) 5 5(2) 2 5(0.05) 510 2 0.25 5 14.75, or $14.7546. Let s 5 the number of students in school at 7:30 A.M.

47. Let m 5 the run time of the movie Antz.

m 5 87; 87 minutes

m 1 33 2 33 5 120 2 33

m 1 33 5 120

s 5 79; 79 students

s 1 73 2 73 5 152 2 73

s 1 73 5 152

2200 5 k 24 5 k

(210) ? 20 5 (210) ? h210 144

6 5 6k6

20 5 h210 144 5 6k

w 5 2120 b 5 63

23w23 5 360

23 (7) ? b7 5 (7) ? 9

23w 5 360 b7 5 9

x 5 0 4.7 5 m x 1 10 2 10 5 10 2 10 1.5 1 3.2 5 m 2 3.2 1 3.2

x 1 10 5 101.5 5 m 2 3.2

220 5 m x 5 29

212 2 8 5 m 1 8 2 8 x 2 6 1 6 5 215 1 6

212 5 m 1 8 x 2 6 5 215

1628

280216

2126

uuuuuuuu

82

3 1 52

m 1 tn

Extra Practice pages 604–627

phm07c3_sk_em_ep_sh natl.qxd 8/23/06 11:15 AM Page 154

around the track twice and ending up 23 inches from thestart. 47. 5 ? 6 5 30; there are 16 oz per lb, so the total weight is 30 4 16, or 1.875 lbs. 48. < 0.59; 0.59 , 0.60,so the second liquid has a larger fraction of water.49. P 5 4s 5 4(4 ) 5 19.5; 19.5 inches 50. 48.75 2 4 5

48 2 4 5 44 ft2

51. of a pound is 0.75 lb.

52. 2 ? 3 5 ? 5 5 7 ; 7 oz 53. There are 25 ? 24,or 600 hours, in a 25-day period. 4 million 4 600 56,666 ; 6,666 eggs per hour 54. A 5 s2 5 122 5 144;

144 cm2 55. 60 ? 60 ? 24 ? 50 days 5

4,320,000 5 4.32 3 106


1. Irrational; the decimal does not repeat. 2. Rational;25 is a perfect square. 3. Irrational; 26 is not a perfectsquare. 4. Rational; the decimal repeats.5. 6.

7. 8.

9. 10.

11. 12.

13.

b 5 24

"b2 5 !576

b2 5 576

49 1 b2 2 49 5 625 2 49

49 1 b2 5 625

72 1 b2 5 252 a2 1 b2 5 c2

!1,130 5 c !925 5 c

!1,130 5 "c2 !925 5 "c2

1,130 5 c2 925 5 c2 169 1 961 5 c2 441 1 484 5 c2 132 1 312 5 c2 212 1 222 5 c2

a2 1 b2 5 c2 a2 1 b2 5 c2 2 5 c 3 5 c

!4 5 "c2 !9 5 "c2

4 5 c2 9 5 c2 1.44 1 2.56 5 c2 2 1 7 5 c2 1.22 1 1.62 5 c2 (!2)2 1 (!7)2 5 c2

a2 1 b2 5 c2 a2 1 b2 5 c2 !157 5 c !218 5 c

!157 5 "c2 !218 5 "c2

157 5 c2 218 5 c2 36 1 121 5 c2 49 1 169 5 c2 62 1 112 5 c2 72 1 132 5 c2 a2 1 b2 5 c2 a2 1 b2 5 c2

26 5 c 5 5 c

!676 5 "c2 !25 5 "c2

676 5 c2 25 5 c2 100 1 576 5 c2 9 1 16 5 c2 102 1 242 5 c2 32 1 42 5 c2

a2 1 b2 5 c2 a2 1 b2 5 c2

hday

minh

smin

23

23

78

78

638

72

94

12

14

x 5 1.125; 1.125 lbs

4x4 5 4.5

4

4x 5 4.5

0.754 5 x

6

34

112

812

912

23

78

1017

14.

15.

16.

17. (23, 1) 18. (2, 1) 19. (3, 22) 20. (24, 22)21. Slope: 3; y-intercept: 3

22. Slope: 22; 23. Slope: ;y-intercept: 23 y-intercept: ;

24. Slope: ; y-intercept: 1

O

2

2 4�2�4

�2

4

x

y23

4

O1�1

�1

1

x

y

O

2

2�2

4

x

y22

3

13

O

2

2�2�4 4

�2

4

6

x

y

b 5 !3,276

"b2 5 !3,276

b2 5 3,276

2,500 1 b2 2 2,500 5 5,776 2 2,500

2,500 1 b2 5 5,776

502 1 b2 5 762 a2 1 b2 5 c2

b 5 !1,407

"b2 5 !1,407

b2 5 1,407

529 1 b2 2 529 5 1,936 2 529

529 1 b2 5 1,936

232 1 b2 5 442 a2 1 b2 5 c2

b 5 10

"b2 5 !100

b2 5 100

56.25 1 b2 2 56.25 5 156.25 2 56.25

56.25 1 b2 5 156.25

7.52 1 b2 5 12.52 a2 1 b2 5 c2



25.

26. 27.

28. Answers may vary. Sample:29.

30.

31.

32. (4, 8), (6, 8), (9, 8), (13, 8), (17, 8), (20, 8), (22, 8);these coordinates all share the same y-coordinate.

33.

about 42.8 million people34. (x 2 4 5 4, y 1 11 5 211); (8 2 4 5 4, 222 1 11 5211); (8, 22)

O4

8

16

24

32

40

8 12 16 20y

p

b 5 !135; !135 ft

b2 5 135

9 2 9 1 b2 5 144 2 9

9 1 b2 5 144

32 1 b2 5 122 a2 1 b2 5 c2

a < 3.5; about 3.5 cm

"a2 5 #252

a2 5 252

2a2

2 5 252

2a2 5 25

a2 1 a2 5 52 a2 1 b2 5 c2

s 5 15.5; 15.5 in.

!240.25 5 "s2 240.25 5 s2

A 5 s2

12

2 4Ox

y

2

2 4Ox

y4

2

2 8Ox

y6

4

2

35. The coordinates aftera reflection over the y-axis are Rr(0, 4),Sr(0, 0), Tr(4, 0).36. The coordinates of point Q are (6, 5).After a 908 rotationclockwise about theorigin, the coordinatesof point Qr are (5, 26).37. 3608 4 728 5

5; 5 sides


1. 240 4 8 5 30 mi/gal 2. 3.50 4 10 5 $.35/oz3. 450 4 9 5 50 mph 4. $18 4 12 5 $1.50/can5. 3.5 mi ? 5,280 5 18,480 ft 6. 7.2 km ? 1,000 5 7,200 m7. 80 oz 4 16 5 5 lb 8. 120 fl oz 4 128 5 0.9375 gal9. 10.

11. 12.

13. 14.

15.

16. 17.

18. 3 in. 3 5 90 mi. 19. 2 in. 3 5 3 5

80 mi 20. in. 3 5 7.5 mi 21. 5 in. 3 5

150 mi 22. 6 in. 3 5 3 5 195 mi

23.

24. $3.99 4 12 oz < $.33 per oz; $7.49 4 25.4 oz < $.29per oz; the 25.4-oz bottle is a better buy. 25. There are5,280 feet per mile and 60 ? 60, or 3,600 seconds perhour. 37.6 ? 5,280 4 3,600 5 198, 528 4 3,600 5 55.14 ;55.14 ft/s6

6

n 5 10.4 ft

12n 5 125

512 5 n25

301

132

30 mi1 in.

12

30 mi1 in.

30 mi1 in.

14

301

83

30 mi1 in.

23

30 mi1 in.

A

A�

B� C�B C

x

y

1

1

2

�2

2�2

�12 4Ox

y6

4

B C

A

y 5 1.5

2y 5 3 z 5 4

21 5 3y 21 5

z2

y 5 6.75 x 5 10.5

4y 5 27 2x 5 21

9y 5 43 27 5 3

x

x 5 313 x 5 51

3

3x 5 10 15x 5 80

35 5 2x x10 5 8

15

x 5 112 x 5 12

18x 5 27 7x 5 84

3x 5 189 47 5 x

21

x

y

S

R

T (0,0)

(0,4)(0,4)

(4,0)(-4,0) (0,0)



14 lb 1 oz 5 14 3 16 1 1 5 225 oz; < 0.372 5

37.2% 29. 20 2 16 5 4; 5 0.25 5 25%

30. 57.19 2 43 5 14.19; 5 0.33 5 33%

31. 34.79 2 24.50 5 10.29; 5 0.42 5 42%

32. 100 2 6 5 94; 0.94 ? 14.49 5 $13.62 33. 100 2 11 589; 0.89 ? 28 5 $24.92 34. 100 2 18 5 82; 0.82 ? 61.25 5

$50.23 35. I 5 prt 5 165 ? 0.045 ? 2 5 14.85; 165 1 14.855 $179.85 36. I 5 prt 5 350 ? 0.0525 ? 3 5 55.125;350 1 55.125 5 405.125 < $405.13 37. 38. 39.40. There are 3 1 35 1 42 1 8, or 88 students, taking thesurvey. < 47.7%41. Let c 5 the original cost of the appetizers before thediscount.

15% of $25 is 0.15 ? 25, or $3.7542. 123.3% of 55,869 is 1.233 ? 55,869, or about 68,886 square miles. 43. 3 % of $34,285 is 0.035 ? 34,285, or

about $1,200. 44. 5 5 1.5 ; the percent of increase is 152.2%. 45. A 50% markup is 150% of theoriginal price. 150% of $18.00 is 1.5 ? 18, or $27.00; 22.954 27.00 5 0.85; the discount price is 85% of the originalprice so it's a 15% discount. 46. 2.3% of $250 for 9 months out of 12 months per year is ? 0.023 ? 250, or

about $4.31; $250 1 $4.31 is $254.31. 47. <0.00025 5 0.025%


1. 3x 2 4 5 2 2. 5 2 4x 5 213. 4.

5. 6.

7. 8.

9. 10.

x 5 2 12

4x4 5 10

4 3 5 k

4x 5 10 23 5 2k

4x 2 2 1 2 5 8 1 2 15 2 18 5 2k 1 18 2 18

4x 2 2 5 8 15 5 2k 1 18

d 5 3 22 5 w 5d5 5 15

5 2126 5 6w

6

5d 5 15 212 5 6w 5d 1 10 2 10 5 25 2 10 210 2 2 5 2 1 6w 2 2

5d 1 10 5 25 210 5 2 1 6w g 5 2

7g7 5 14

7 b 5 212

7g 5 14 2b 5 2212

7g 2 4 1 4 5 10 1 4 2b 1 2 2 2 5 212 2 2

7g 2 4 5 10 2b 1 2 5 212

40 5 m n 5 3

(5) ? 8 5 (5) ? m5 6n

6 5 186

8 5 m5 6n 5 18

10 2 2 5 m5 1 2 2 2 6n 1 3 2 3 5 21 2 3

10 5 m5 1 2 6n 1 3 5 21

14,001

912

21.370.9

2.27 2 0.90.9

12

c 5 25.88

32 ? 23c 5 3

2 ? 17.25

23c 5 17.25

4288

34

12

14

10.2924.50

14.1943

416

225 2 164164

26. Let t 5 the time it will take her to knit 10 scarves.

It will take her 23 days to knit 10 scarves.27. Let < 5 the length of the airplane model.

The length of the airplane model is 21.38 cm.28. Let < 5 the wingspan of the model.

29. Let w 5 the width of the photo.

The width of the photo is 27.75 inches.30. 5 ; 1 in. : 36 ft

31. Let h 5 the height of the flagpole.

The height of the flagpole is about 413 ft.


1. 0.3 5 30% 5 2. 21% 5 0.21 5 3. 3.47 5 3 5

347% 4. 0.004 5 0.4% 5 5 5. 5 0.15 5 15%

6. 5 0. 5 33 % 7. 0.62% 5 0.0062 5 5

8. 2 5 2.5 5 250% 9–12. Answers may vary. Sample:9. 28% of 99 < 0.28 ? 100 5 28 10. 7% of 93 <0.07 ? 100 5 7 11. 48% of 32 < 0.5 ? 32 5 16 12. 125% of 84 < 1.25 ? 84 5 105 13. 15% of $16 5 $2.40 14. 15%of $30 5 $4.50 15. 15% of $35 5 $5.25 16. 15% of $50 5$7.50 17. 6% of 51 5 0.06 ? 51 5 3.06 18. 117% of 22 51.17 ? 22 5 25.74 19. 2.5% of 78 5 0.025 ? 78 5 1.95 20. 145 4 15% 5 145 4 0.15 5 966. 21. 0.4 4 5 50.08 5 8% 22. 215% of 20 5 2.15 ? 20 5 43 23. 20 2 16 5 4; 4 4 16 5 0.25 5 25% increase24. 542 2 320 5 222 4 320 5 0.69375 5 69.4% increase25. 4 2 1 5 3; 3 4 1 5 3 5 300% increase 26. 13 ft 5 in. 5 13 3 12 1 5 5 161 in.; 17 ft 4 in. 5

17 3 12 1 4 5 208 in.; < 0.292 5 29.2% 27. 8 qt 3 pt 5 8 3 2 1 3 5 19 pt; 6 qt 6 pt 56 3 2 1 6 5 18 pt; < 20.053 5 25.3% 28. 10 lb 4 oz 5 10 3 16 1 4 5 164 oz;

18 2 1919

208 2 161161

6

12

315,000

6210,000

1331

3

320

1250

41,000

47100

21100

310

h 5 412.95

8h8 5

3,303.68

8h 5 3,303.6

550.6h 5 8

6

1 in.36 ft

2 in.72 ft

w 5 27.75

4w4 5 111

4

4w 5 111

46

5181

2w

/ 5 2.45

36/36 5 88.4

36

36/ 5 88.4

136 5 /88.4

/ < 21.38

88.4/88.4 5

1,89088.4

88.4/ 5 1,890

22.588.4 5 /

84

13

t 5 2313

3t3 5 70

3

3t 5 70

37 5 10t




11. 6x 1 4 2 3x 5 3x 1 4 12. 7(h 2 5) 5 7h 2 3513. 2(x 1 1) 1 5 5 2x 1 2 1 5 5 2x 1 714. 25 1 3p 2 p 5 25 1 2p 15. 13q 1 91 2 13q 5 91 16. 2(8z 1 2z 2 1) 5 28z 2 2z 1 1 5 210z 1 117. 47 2 11r 2 7r 5 47 2 18r 18. 215h 2 (23 2 9h) 5215h 2 23 1 9h 5 26h 2 23

19.

20.

21.

22.

23.

24.

25.

2 5 w 4020 5 20w

20

40 5 20w 14 1 26 5 20w 2 26 1 26

14 5 20w 2 26

14 2 2w 1 2w 5 18w 2 26 1 2w 14 2 2w 5 18w 2 26

5 5 p

8016 5

16p16

80 5 16p

80 2 5p 1 5p 5 11p 1 5p

80 2 5p 5 11p

30 2 5p 1 50 5 11p

30 2 5(p 2 10) 5 11p

27 5 y

2284 5

4y4

228 5 4y

29 2 19 5 19 1 4y 2 19

29 5 19 1 4y

29 2 3y 1 3y 5 19 1 y 1 3y

29 2 3y 5 19 1 y

5912 5 y

1192 5

2y2

119 5 2y

123 2 4 5 2y 1 4 2 4

123 5 2y 1 4

123 5 9y 1 4 2 7y

12 5 a

4080 5 80a

80

40 5 80a

224a 1 40 1 24a 5 56a 1 24a

224a 1 40 5 56a

28(3a 2 5) 5 56a

k 5 4.2

2.5k2.5 5 10.5

2.5

2.5k 5 10.5

k 1 1.5k 5 10.5 2 1.5k 1 1.5k

k 5 10.5 2 1.5k

k 5 1.5(7 2 k)

9 5 b

182 5 2b

2

18 5 2b

16 1 2 5 22 1 2b 1 2

16 5 22 1 2b

16 5 2(2 2 2b)

26.

27.

28.

29.

30.

31.

32.

33.

34. x 1 35. x . 036. 37.

38. 39.

x , 0 q . 218.6

x3 ? 3 , 0 ? 3 q

26 ? 26 , 3.1 ? 26

x3 , 0 q

26 , 3.1

y . 27 p # 25

24y24 , 28

24 7p7 # 235

7

24y , 28 7p # 235

#

9 10 11 12 13 14

m , 12

m 1 4 2 4 , 16 2 4

m 1 4 , 16

�13 �12 �11 �10 �9 �8

210 $ y

212 1 2 $ 22 1 y 1 2

212 $ 22 1 y

�12 �11 �10 �9 �8 �7

a $ 210

5 1 a 2 5 $ 25 2 5

5 1 a $ 25

2 1 0 1 2 3

p . 0

p 2 1 1 1 . 21 1 1

p 2 1 . 21

�12 �11 �10 �9 �8 �7

f # 29

f 1 21 2 21 # 12 2 21

f 1 21 # 12

9 10 11 12 13 14

x # 12

x 2 2 1 2 # 10 1 2

x 2 2 # 10

x 5 25.2

2x21

55.221

2x 5 5.2

2x 1 1.4 2 1.4 5 6.6 2 1.4

2x 1 1.4 5 6.6

4.1x 1 1.4 2 5.1x 5 6.6

d 5 338

8d8 5 27

8

8d 5 27

8d 2 4 1 4 5 23 1 4

8d 2 4 5 23

8.8d 2 4 2 0.8d 5 23

4(2.2d 2 1) 2 0.8d 5 23


40. 41.

42. Let m 5 the cost of each movie ticket.

Each movie ticket costs $9.50.43. Let s 5 the number of pairs of socks.

You bought 6 pairs of socks.44. b 5 breakfast cost; < 5 lunch cost;(3< 1 2b) 1 (4< 1 b) 5 7< 1 3b45. Let a 5 the amount of Bosc pears.

Seth bought about 4 lbs of Bosc pears.46. Let < 5 the length of the boat

The length of the boat is 28 feet.47. Let w 5 the number of weeks it will take him to savethe money.

It will take him 18 weeks to save the money.48. Let m 5 the amount of money you have left afterbuying gas and groceries.

No, he will not have enough money to get an oil change.49. 47 4 6 5 7 ; 8 vans are needed to transport all the children. 50. $1,250 4 $7 < 178.6; 179 tickets must be sold.


1. 908 2 538 5 378 2. Answers may vary. Sample:/LPM and /KPN 3. /LPM and /NPK are verticalangles; m/LPM 5 1158; /LPM and /MPN aresupplementary; 1808 2 1158 5 658 4. Answers may vary.Sample: /3 and /6 5. 1808 2 1088 5 728; /2 5 728;/3 5 728; /4 5 1088; /5 5 1088; /6 5 728; /7 5 728;/8 5 1088 6. nRST > nMNQ by SAS 7. nABC >nDEF by ASA 8. nKLM > nGKH by SSS 9. rhombus 10. trapezoid 11. parallelogram12. rectangle 13. (n 2 2)1808 5 (4 2 2)1808 5

56

m # 4.01

95.99 1 m # 100

39.85 1 56.14 1 m # 100

w 5 18

20w 5 360

100 1 20w 5 460

/ 5 28

15/ 5 420

175 1 15/ 5 595

12

a < 4.5

a(1.09) 5 4.91

5(1.09) 1 a(1.09) 5 10.36

s 5 6

4.99s4.99 5 29.94

4.99

4.99s 5 29.94

4.99s 1 29.99 2 29.99 5 59.93 2 29.99

4.99s 1 29.99 5 59.93

m 5 9.50

3m3 5 28.50

3

3m 5 28.50

3m 1 4.99 2 4.99 5 33.49 2 4.99

3m 1 4.99 5 33.49

210.4 # t z , 11

2622.5 $ 22.5t

22.5 z

21 ? 21 . 211 ? 21

26 $ 22.5t z

21 . 211


2 ? 1808 5 3608 14. (n 2 2)1808 5 (6 2 2)1808 5

4 ? 1808 5 7208 15. (n 2 2)1808 5 (3 2 2)1808 5

1 ? 1808 5 1808 16. (n 2 2)1808 5 (5 2 2)1808 5

3 ? 1808 5 5408 17. (n 2 2)1808 5 (4 2 2)1808 5

2 ? 1808 5 3608 18. A 5 bh 5 6 ? 12 5 72 m2 19. A 5

pr2 5 p ? 2.752 5 23.8 in.2 20. Check students’ work.21. 1808 2 88.58 5 91.58 22. none 23. none 24. a and b25. > because they are both four units long.nMNP is the exact image of nABC after a 908 rotationabout point C and a translation of 6 units to the rightand 5 units up. The coordinates of point P are (5, 3).26. A shape with exactly two parallel sides is atrapezoid. 27. (n 2 2)1808 5 (8 2 2)1808 5 6 ? 1808 5

10808; 10808 4 8 5 1358 28. A 5 ? h; ? 8 5? 8 5

9.25 ? 8 5 74; 74 ? 2 5 148 ft2 29. She walked 3 times thecircumference of the arena, so she walked 3pd = 3p(710) = 2130p, or about 6,691.6 ft. 30. Checkstudents’ work.


1. circle; cone; diameter 2. circle; cylinder; diameter3. triangle; triangular prism; edge

4. 5.

6. 7. cone 8a. S.A. 5

L.A. 1 2B 5 ph 1 2s2 5

4.8 ? 1.2 1 2 ? 1.22 5 8.64 <9 m2 8b. V 5 /wh 5

1.2 ? 1.2 ? 1.2 5 1.728 < 2 m3

9a. S.A. 5 L.A. 1 2B 5 ph 1 2/w 5 50 ? 18 1 2 ? 10 ? 15 51,200 cm2 9b. V 5 /wh 5 10 ? 15 ? 18 5 2,700 cm3

10a. S.A. 5 L.A. 1 2B 5 2prh 1 2pr2 5

2p ? 1 ? 8 1 2p ? 12 5 56.54 < 57 ft2 10b. V 5 Bh 5

pr2h 5 p ? 12 ? 8 5 25.13 < 25 ft3 11a. S.A. 5

L.A. 1 2B 5 2prh 1 2pr2 5 2p ? 3 ? 4 1 2p ? 32 5

131.94 < 132 in.2 11b. V 5 Bh 5 pr2h 5 p ? 32 ? 4 5113.09 < 113 in.3 12a. S.A. 5 L.A. 1 B 5 2bh 1 36 5

2 ? 6 ? 5 1 36 5 96 in.2 12b. V 5 Bh 5 ? 36 ? 4 5 48 in.3

13a. S.A. 5 L.A. 1 B 5 pr/ 1 pr2 5 p ? 6 ? 10 1 p ? 62 5

301.59 < 302 cm2 13b. V 5 Bh 5 pr2h 5 ? p ? 62 ? 8 5

301.59 < 302 cm3 14. S.A. 5 4pr2 5 4p( )2 5

4p(82.81) < 1,041 cm2; V 5 pr3 5 p( )3 5

p(753.571) < 3,157 cm3 15. 5 ; ( )3 5 ; 5

; 8x 5 3,570; x 5 446.25 m3 16. The common solids thatmake up the structure are a rectangular prism, atriangular prism, a cylinder, and a cone. 17. Answersmay vary. Sample: A base plan would be more useful ifyou were going to use the plan to construct something,such as the set of a school play.

81

3,570x

81

21

21

147

43

18.22

43

43

18.22

13

13

13

13

13

Top Front Right

Top Front RightTop Front Right

18.52

10 1 8.52

b1

1 b2

2

MNAB

0154_3PHM07_sk_em_ep_sh.qxd 8/22/08 4:16 PM Page 159

4.

5. pear 6. The line break does not show all of the dataproportionally. 7. mode: 71 ,median: 68

8.

9. no trend 10. negative trend 11. positive trend 12. The total enrollment is 14,664; 4,152 4 14,664 50.283 ? 3608 5 1028; 4,297 4 14,664 5 0.293 ? 3608 5

1058;4,365 4 14,664 5 0.298 ? 3608 5 1078; 919 4 14,664 50.063 ? 3608 5 238; 931 4 14,664 5 0.063 ? 3608 5 238

13. Circle graph; it shows parts of the whole budget.14. Double bar graph; it shows the comparison of twosets of data. 15. The outlier is $15. This outlier lowersthe mean by (45 1 51 1 66 1 39 1 49 1 78) 4 6 2 (151 45 1 51 1 66 1 39 1 49 1 78) 4 7 < 54.66 2 49.00, orabout $5.66.

U.S. ServiceAcademy Enrollment

MerchantMarine 6%

Army

CoastGuard 6%

28%

Air Force30%

Navy29%

Source: 2003 College Board Handbook

67646158 70 73 76

mihr

mihr

Blueshapes

8

Circles3 2

1.2 1.3 1.4 1.5 1.6Time (minutes)

Waiting Time

1.7 1.8 1.9

1.2–1.3

Fre

qu

ency

1.4–1.51.6–1.7

1.8–1.9

7654321


18. 19. Donniewill needenoughparchmentpaper tocover thearea of thebase of thepan and theside of thepan, which is

equal to the circumference of the base of the panmultiplied by its height. A 5 pr2 + 2prh 5 p(4.5)2 1

2p(4.5)(2) 5 20.25p1 18p5 38.25p < 120; about 120 in.2

20. V 5 pr2h 5 p(4.5)2(2) 5 p(20.25)(2) 5 40.5p < 127;about 127 in.3 21. L.A. 5 pr< 5 p( )(3.25) 5

4.0625p < 12.7; 12.7 in.2 22. V 5 bh 5 (pr2)(3) <

(p1.252)(3) < 5; 5 in.3 23. S.A. 5 4pr2 5 4p(2,440)2 <

74,815,144 km2; V 5 (pr3) 5 p(2,4403) <

60,849,650,530 km3

24. Let v 5 the volume of the similar can.

The volume of the similar can is about 423 mL.25. Let s 5 the surface area of the similar cone.

The surface area of the similar cone is about 459 ft2.


1. 1 1 1 1 1 1 2 1 2 1 2 1 4 1 4 5 17; 174 8 < 2.13;The mean is 2.13, the median is 5 2, the modes are1 and 2, and the range is 4 2 1 5 3. 2. 22 1 23 1 2 1

5 1 0 1 3 1 7 5 12; 12 4 7 < 1.71; The mean is 1.71,the median is 2, there is no mode and the range is 7 2 (23) 5 10.

3.

Minutes TallyWaiting Time

Frequency2472

1.2–1.31.4–1.51.6–1.71.8–1.9

2 1 22

s < 459

16s16 5

7,35016

16s 5 7,350

16s 5 49(150)

42s 5 72(150)

42

72 5 150s

v < 423

125v125 5

52,920125

125v 5 52,920

125v 5 216(245)

53v 5 63(245)

53

63 5 245v

43

43

13

13

13

2.52

24 in

.

18 in

.

18 in.


16.

17. The total of Spanish and French is 14 1 10 5 24;Subtract the number of students in both classes: 24 2 5 519; Subtract this number from the number of students inthe class. 21 2 19 5 2; There are 2 students who do nottake either language.

18. The graph with the break shows the data moreclearly; check students’ graphs.

19.

20.5.5

54.5

43.5

32.5

20

Min

imum

Wag

e(in

Do

llars

)

197519

8019

8519

9019

9520

0020

05

2 3 4 5 6 7 8 9 10

2 7

5 4

6 3 6 9

7 2 5

8 3

9 1

10 0

French10

Both5

Spanish14

Ages

Freq

uenc

y

543210

13–1415–16

17–18

Age of Ski Team Members

Ages

13

15

Tally Frequency

5

3–16

–14

17 2–18

21.

22. A bar graph is appropriate because it shows thecomparison of sets of data.


1. 5 2. 5 3. 4. 5. South and West

6. 7.

about 161 students about 107 students8.

about 402 students9. Unbiased; the question does not favor an answer.10. Biased; the question assumes that the personinterviewed does homework and that homework is done every night. 11. ? 5 12. ? 5 13. ? 5

14. ? 5 15. 4! 5 4 ? 3 ? 2 ? 1 5 24 16. 8! 5

8 ? 7 ? 6 ? 5 ? 4 ? 3 ? 2 ? 1 5 40,320 17. 6P3 5 6 ? 5 ? 4 5 12018. 17P2 5 17 ? 16 5 272 19. 24P4 5 24 ? 23 ? 22 ? 21 5255,024 20. 18P5 5 18 ? 17 ? 16 ? 15 ? 14 5 1,028,160

21. 7C4 5 5 35 22. 16C2 5 5 120

23. 19C7 5 5 50,388

24. 24C2 5 5 276 25. 15C5 5 5

3,003 ways 26. Total number of marbles: 33 1 25 5 58,green marbles: 33; P(green marble) 5 27. Totalnumber of marbles: 33 1 25 5 58, blue marbles: 25;P(green marble) 5 28. Total number of occurrences:41 1 35 5 76, blue marbles: 35; green marbles: 41;P(blue marble) 5 ; P(green marble) 5

29.

335 customers 335 5 x

33,500

100 5 100x100

33,500 5 100x

500 ? 67 5 100 ? x

x500 5 67

100

4176

3576

2558

3358

15 ? 14 ? 13 ? 12 ? 115!

24 ? 232!

19 ? 18 ? 17 ? 16 ? 15 ? 14 ? 137!

16 ? 152!

7 ? 6 ? 53!

752

16

2126

552

36

526

152

12

126

1156

16

126

x 5 402

50x50 5

20,10050

50x 5 20,100

3050 5 x

670

7 1 2350 5 x

670

x 5 107.2 x 5 160.8

50x5 5

5,36050 50x

50 58,040

50

50x 5 5,360 50x 5 8,040

850 5 x670 12

50 5 x670

14

1320

25

820

14

520

English30

Math15

Science23

SocialStudies

57



30. hybrid bicycles: 100 2 67 2 11 5 22

165 bikers31. Not random; the gas station customers may notrepresent all those who use public transportation.32. Total sandwiches: 5 1 2 1 2 1 1 5 10; roast beef sandwiches: 2; P(roast beef) 5 5 33. Total sandwiches: 5 1 2 1 2 1 1 21 5 9; tuna sandwiches: 2;P(tuna) 5 34. There are 3 officers and 144 choices foreach officer, so 144 3 144 3 144 5 2,924,064; 2,924,064

ways. 35. One officer per office so, . 36. 5

5 5 220; 220 combinations


1. The common ratio is 4; start with 4 and multiply by 4 repeatedly; 64 ? 4 5 256; 256 ? 4 5 1,024; 1,024 ? 4 54,096 2. The common difference is 2; start with 25 and add 2 repeatedly; 21 1 2 5 1; 1 1 2 5 3; 3 1 2 5 53. The common difference is 2 ; start with 1 and add 2

repeatedly; 2 5 ; 2 5 ; 2 5 0 4. The

common ratio is ; start with 12 and multiply by

repeatedly; 3 ? 5 ; ? 5 ; ? 5 5. $2 6. $5 7. $8 8. 2x 2 1 5 2(1) 2 1 5 2 2 1 5 1 9. 2x 2 1 52(0) 2 1 5 0 2 1 5 21 10. 2x 2 1 5 2(23) 2 1 526 2 1 5 27 11. 2x 2 1 5 2A B 2 1 5 1 2 1 5 012. 2,

13. ,

4Ox

y

4

232

2 4Ox

y

8

6

4

2

12

38

12

34

34

12

32

32

12

12

12

16

16

16

16

13

13

16

12

16

16

1,3206

12 ? 11 ? 103 ? 2 ? 1

12C

33!

12,924,064

29

15

210

165 5 x

16,500

100 5 100x100

16,500 5 100x

750 ? 22 5 100 ? x

x750 5 22

100

14. ,

15-18. Answers may vary. Samples are given.

15. 16.

17.

18.

31 5O x

y4

2

xy

0

1

5

4

1Ox

y

2

xy

0

3

1

1

2Ox

y6

4

2

xy

0

0

1

3

2

6

4 8Ox

y

12

8

4

53



19. yes; When x 5 0, y 5 8; As each x increases by 1,each y increases by 22; y 5 22x 1 8 20. yes; When x 5 0, y 5 ; As each x increases by 1, each y increases

by ; y 5 x 1 21. The data is not linear.

22.

23.

24.

2 4Ox

y50

40

30

20

10

xy

0

0

1

3

2

12

3

27

4

48

2 4O x

y

xy

0

0

2 4Ox

f(x)24

16

8

xy

0

2

1

3

2

6

3

11

4

18

32

12

12

32

25.

26. arithmetic; each term in the sequence differs fromthe previous term by a fixed number. 27. neither; eachterm in the sequence does not differ from the previousterm by a fixed number, and each term is not found bymultiplying the previous term by a fixed number.

28.

29. Potatoes cost $.99 per pound so the function is f(x) 50.99x; f(6) 5 0.99(6) 5 $5.94 30. The length of the rampis 15 3 2 5 30; 30 ft.

31.

32. A plumber charges $60 for a house call, plus $75 foreach hour of work, the function is y 5 75x 1 60.

12010080604020

Hei

ght

(in

inch

es)

10 2 3 4 5Days

0 1 2 3 4Days

Height 23 39 55 71 87

5

103

Am

ou

nt

Ch

arg

ed(d

olla

rs)

4Days Overdue

8x

y4

3

2

1

0

4O x

y4

xy

0

3

1

2




33.


1. 3x 2 5 1 23x 2 9 5 26x 2 14 2. 2x2 1 2x2 2 6x 1

3 2 2 5 x2 2 6x 1 1 3. x2 2 5x 1 3x 1 4 5 x2 2 2x 1 44. 24 1 x 2 13x 1 10 2 5 1 20x 5 8x 1 1 5. 2x 1

4x2 1 3 1 x 2 5 5 4x2 1 3x 2 2 6. (2x2 2 x 1 1) 2

2402101801501209060300

30 60 9012015

018

021

024

0

Number of Workers

Num

ber

of

Day

s

x

y

11

225

3

75

5

45

15

15

45

5

75

31

225

1

(4x2 2 3) 5 22x2 2 x 1 4 7. (3x 1 2) 1 (2x2 1 5x 2 7) 5

2x2 1 8x 2 5 8. (5x2 1 2x 2 10) 1 (23x2 2 2) 52x2 1 2x 2 12 9. (x2 1 6x 1 4) 2 (4x 2 9) 5x2 1 2x 1 13 10. 48 ? 410 5 418 11. (29)2 ? (29)4 5

(29)6 12. 3.28 ? 3.23 5 3.211 13. 7t ? 73t 5 74t

14. (3 3 104)(2 3 1012) 5 6 3 1016 15. (5 3 109)(7 3 103) 5 35 3 1012 5 3.5 3 1013 16. (1 3 103)(2.6 3 108) 5 2.6 3 1011 17. (7 3 102)(8 3 1010) 556 3 1012 5 5.6 3 1013 18. (24x2)(3x4) 5 212x6

19. (6x)(22x) 5 212x2 20. 4x2(2x 2 7) 5 8x3 2 28x2

21. 26x(x2 2 5) 5 26x3 1 30x 22. (x2 1 2x)(3x 1 2) 5

3x3 1 2x2 1 6x2 1 4x 5 3x3 1 8x2 1 4x 23. 5 42

24. 5 8.13 25. 5 (2654)9 26. 5 22x

27. (2142)0 5 1 28. (4c)21 5 29. 72w 5

30. (23)25 5 5 2 31. x2 1 2x 1 2x 1 2x 1

2x 1 x2 5 2x2 1 8x 32. (2x 1 2) 1 (3x 1 15) 1 (x 1 7) 1 (3x 1 14) 1 (2x) 1 (x 1 9) 5 12x 1 47 33. 500 ? (5 3 1010) 5 2,500 3 1010 5 2.5 3 1013

34. 31 ? (2.65 3 1032) 5 82.15 3 1032 5 8.215 3 1033

35. 8x ? ( 3x 1 5) 5 (24x2 1 40x) ft2 36. 0.0000076 5 7.6 3 1026

1243

1

(23)5

17

w14c

23x

2x

(2654)10

(2654)1

8.115

8.112

47

45

0154_3PHM07_sk_em_ep_sh.qxd 8/22/08 4:17 PM Page 164

Course 3 Solution Key • Skills Handbook, page 165

Decimals and Place Value page 628

1. The digit 9 is in the hundred-thousandths place. So itsvalue is 9 hundred-thousandths. 2. The digit 7 is in thetenths place. So its value is 7 tenths. 3. The digit 5 is inthe hundredths place. So its value is 5 hundredths.4. The digit 6 is in the ten thousands place. So its value is6 ten thousands. 5. The digit 4 is in the hundred millionsplace. So its value is 4 hundred millions. 6. The digit 3 is in the tens place. So its value is 3 tens. 7. Ten-thousandths is 4 places to the right of the decimal point.So the decimal will have 4 places after the decimal point.The answer is 0.0041. 8. Thousandths is 3 places to the right of the decimal point. So the decimal will have 3 places after the decimal point. The answer is 18.504.9. Millionths is 6 places to the right of the decimal point.So the decimal will have 6 places after the decimal point.The answer is 0.000008. 10. Hundred-thousandths is 5 places to the right of the decimal point. So the decimalwill have 5 places after the decimal point. The answer is7.00063. 11. Thousandths is 3 places to the right of thedecimal point. So the decimal will have 3 places after thedecimal point. The answer is 0.012. 12. Thousandths is 3 places to the right of the decimal point. So the decimalwill have 3 places after the decimal point. The answer is65.201. 13. The digit 6 is in the hundredths place. Theanswer is six hundredths. 14. The digit 7 is in the tenthsplace. The answer is four and seven tenths. 15. The digit1 is in the hundred-thousandths place. The answer iseleven hundred-thousandths. 16. The digit 9 is in thetenths place. The answer is nine tenths. 17. The digit 2 is in the thousandths place. The answer is twelvethousandths. 18. The digit 9 is in the millionths place.The answer is fifty-nine millionths. 19. The digit 2 is inthe ten-thousandths place. The answer is forty-two tenthousandths. 20. The digit 6 is in the millionths place.The answer is six and twenty-nine thousand onehundred eight-six millionths.

Comparing and Ordering Decimalspage 629

1. 0 hundredths , 2 hundredth, so 0.003 , 0.02.2. 0 hundreds , 8 hundreds, so 84.2 , 842.3. 6 hundredths . 0 hundredths, so 0.162 . 0.106.4. 0 tenths , 6 tenths, so 0.0659 , 0.6059. 5. 1 tenth ,9 tenths, so 2.13 , 2.99. 6. 3 hundredths . 2 hundredths,so 3.53 . 3.529. 7. The digits in each place are the same,so 2.01 5 02.010. 8. 0 hundredths , 7 hundredths,so 0.00072 , 0.07002. 9. 0 ten-thousandths , 9 ten-thousandths, so 0.458 , 0.4589. 10. 2 hundredths ,4 hundredths, so 8.627 , 8.649. 11. 1 thousandth .0 thousandths, so 0.0019 . 0.0002. 12. 3 thousandths .

2 thousandths, so 0.19321 . 0.19231. 13. 0.23, 0.231,2.31, 3.21, 23.1 14. 1.002, 1.02, 1.021, 1.11, 1.2 15. 0.002,0.02, 0.22, 0.222, 2.22 16. 5.5555, 55.5, 55.555, 555.517. 7, 7.0324, 7.3, 7.3246, 7.3264 18. 0.00019, 0.0099,0.0101, 0.011 19. 0.08, 0.082, 0.083, 0.8, 083 20. 4.6,4.6002, 4.601, 4.602, 4.61, 4.62

Rounding page 630

1. The digit to the right of the thousands place is 0, so105,099 rounds down to 105,000. 2. The digit to the rightof the thousands place is 4, so 10,400 rounds down to10,000. 3. The digit to the right of the thousands place is8, so 79,527,826 rounds up to 79,528,000. 4. The digit tothe right of the thousands place is 9, so 79,932 rounds upto 80,000. 5. The digit to the right of the thousands placeis 3, so 4,312,349 rounds down to 4,312,000. 6. The digitto the right of the units place is 9, so 135.91 rounds up to136. 7. The digit to the right of the units place is 0, so3.001095 rounds down to 3. 8. The digit to the right ofthe units place is 9, so 96.912 rounds up to 97. 9. Thedigit to the right of the units place is 1, so 101.167 roundsdown to 101. 10. The digit to the right of the units placeis 9, so 299.9 rounds up to 300. 11. The digit to the rightof the tenths place is 1, so 82.01 rounds down to 82.0.12. The digit to the right of the tenths place is 7, so4.67522 rounds up to 4.7. 13. The digit to the right of thetenths place is 9, so 20.397 rounds up to 20.4. 14. Thedigit to the right of the tenths place is 5, so 399.95 roundsup to 400.0. 15. The digit to the right of the tenths placeis 8, so 129.98 rounds up to 130.0. 16. The digit to theright of the hundredths place is 8, so 13.458 rounds up to13.46. 17. The digit to the right of the hundredths placeis 4, so 96.4045 rounds down to 96.40. 18. The digit tothe right of the hundredths place is 9, so 0.699 rounds upto 0.70. 19. The digit to the right of the hundredthsplace is 4, so 4.234 rounds down to 4.23. 20. The digit tothe right of the hundredths place is 5, so 12.09531 roundsup to 12.10. 21. The digit to the right of the underlineddigit is 1, so 7.0615 rounds down to 7.06. 22. The digit tothe right of the underlined digit is 7, so 5.77125 roundsup to 6. 23. The digit to the right of the underlined digitis 2, so 1,522 rounds down to 1,520. 24. The digit to theright of the underlined digit is 2, so 0.91952 rounds up to0.9195. 25. The digit to the right of the underlined digitis 4, so 4.243 rounds down to 4.2. 26. The digit to theright of the underlined digit is 6, so 236.001 rounds up to240. 27. The digit to the right of the underlined digit is5, so 352 rounds up to 400. 28. The digit to the right ofthe underlined digit is 6, so 3.495366 rounds up to3.49537. 29. The digit to the right of the underlined digitis 7, so 8.97092 rounds up to 8.1. 30. The digit to theright of the underlined digit is 6, so 0.6008 rounds up to 1.

Skills Handbook pages 628-642



31. The digit to the right of the underlined digit is 1, so918 rounds down to 900. 32. The digit to the right of theunderlined digit is 3, so 7,735 rounds down to 7,700.33. The digit to the right of the underlined digit is 4, so25.66047 rounds down to 25.660. 34. The digit to theright of the underlined digit is 3, so 983,240,631 roundsdown to 980,000,000. 35. The digit to the right of theunderlined digit is 7, so 27 rounds up to 30.

Adding and Subtracting Decimalspage 631

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

22. 23. 24.

25. 26. 27.

28. 29. 30.

31. 32. 33.

34. 35. 36.

37. 38. 39. 4.27

6.18

1 0.91

11.36

0.045

16.320

1 8.600

24.965

741.0000

6.0800

1 0.0309

747.1109

57.0000

0.6327

1 189.0070

246.6397

4.521

1.800

1 3.070

9.391

9.50

12.32

1 6.40

28.22

8.30

2.99

1 17.52

28.81

0.50

2 0.18

0.32

0.230

1 0.091

0.321

6.80

1 3.57

10.37

5.002

2 3.450

1.552

7.060

2 4.235

2.825

8.29

1 4.30

12.59

3.450

1 4.061

7.511

11.90

2 2.06

9.84

14.81

2 8.60

6.21

3.90

1 6.57

10.47

1.245

1 5.800

7.045

8.90

2 4.45

4.45

20.50

1 11.45

31.95

32.403

1 12.060

44.463

8.70

1 17.03

25.73

76.39

2 8.47

67.92

12.22

9.80

12.375

24.395

3.70

20.06

1 16.19

39.95

15.220

7.400

1 8.125

30.745

9.420

3.600

1 21.003

34.023

12.20

3.06

1 0.50

15.76

0.10

58.21

1 1.90

60.21

2.600

1 23.107

25.707

1.05

112.90

13.95

8.23

2 3.10

5.13

2.1

2 0.5

1.6

8.634

1 1.409

10.043

13.020

1 23.107

36.127

5.01

2 0.87

4.14

6.784

1 0.528

7.312

1.08

2 0.90

0.18

39.70

2 36.03

3.67

40. 41.

Multiplying Decimals page 632

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

22.

Zeros in a Product page 633

1. 2. 3.

4. 5. 6.

7. 8. 9. 0.27

3 0.033

81

810

0.00891

0.03

3 0.2

0.006

0.031

3 0.08

0.00248

0.016

3 0.12

32

160

0.00192

0.05

3 0.05

0.0025

7

3 0.01

0.07

2.4

3 0.03

0.072

0.06

3 0.5

0.030

0.03

3 0.9

0.027

11.8

3 0.05

0.590

30.02

3 6

18.012

42.2

3 0.9

37.98

8.003

3 0.6

4.8018

76

3 3.3

228

2280

250.8

45

3 0.028

360

900

1.260

6.3

3 8.5

315

5040

535.5

0.42

3 98

336

3780

41.16

0.74

3 0.23

222

1480

0.1702

3.2

3 0.15

160

320

0.480

0.12

3 61

12

720

7.32

2.07

3 1.004

828

207000

2.07828

3

3 0.5

0.15

0.136

3 8.4

544

10880

1.1424

0.04

3 7

0.28

0.512

3 0.76

3072

35840

0.38912

6.23

3 0.21

623

12460

1.3083

1.36

3 3.8

1088

4080

5.168

0.27

3 5

1.35

0.05

3 43

15

200

2.15

191.1

3 3.4

7644

57330

649.74

1.48

3 3.6

888

4440

5.328

11.450

3.790

1 23.861

39.101

3.856

14.010

1 1.720

19.586



10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

22. 23. 24.

25. 26. 27.0.019

7q0.133

7

63

63

0

0.305

32q9.760

9 6

160

160

0

0.0756

5q0.3780

35

28

25

30

30

0

0.4

8q3.2

3 2

0

7.23

11q79.53

77

2 5

2 2

33

33

0

3.227

53q171.031

159

12 0

10 6

1 43

1 06

371

371

0

0.0014

48q0.0672

48

192

192

0

6.123

13q79.599

78

1 5

1 3

29

26

39

39

0

2.551

18q45.918

36

9 9

9 0

91

90

18

18

0

0.315

36q11.340

10 8

54

36

180

180

0

0.868

26q22.568

20 8

1 76

1 56

208

208

0

0.931

32q29.792

28 8

99

96

32

32

0

0.561

22q12.342

11 0

1 34

1 32

22

22

0

0.1447

6q0.8682

6

26

24

28

24

42

42

0

0.0147

6q0.0882

6

28

24

42

42

0

0.0036

9q0.0324

27

54

54

0

0.0169

8q0.1352

8

55

48

72

72

0

6.19

6q37.14

36

1 1

6

54

54

0

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

22. 23. 24.

25. 26. 27.

28.

Dividing Decimals by Whole Numbers page 634

1. 2. 3.

4. 5. 6.

7. 8. 9.8.76

2q17.52

15

1 5

1 4

12

12

0

66.3

26q1723.8

156

163

156

7 8

7 8

0

0.11

22q2.42

2 2

22

22

0

0.158

56q8.848

5 6

3 42

2 80

448

448

0

8.79

4q35.16

32

3 1

2 8

36

36

0

15.24

6q91.44

6

31

30

1 4

1 2

24

24

0

0.776

9q6.984

6 3

68

63

54

54

0

3.3

5q16.5

15

1 5

1 5

0

2.56

7q17.92

14

3 9

3 5

42

42

0

0.07

3 0.85

35

560

0.0595

0.14

3 0.05

0.0070

0.31

3 0.08

0.0248

3.02

3 0.006

0.01812

0.67

3 0.09

0.0603

0.3

3 0.24

12

60

0.072

0.06

3 0.7

0.042

0.5

3 0.08

0.040

4.003

3 0.02

0.08006

0.03

3 0.03

0.0009

0.43

3 0.2

0.086

0.018

3 0.04

0.00072

0.19

3 0.05

0.0095

0.3

3 0.27

21

60

0.081

0.76

3 0.1

0.076

0.47

3 0.08

0.0376

0.01

3 0.74

4

70

0.0074

0.003

3 0.55

15

150

0.00165

0.014

3 0.25

70

280

0.0035



7. Multiply by 10.

10. Multiply by 10.

13. Multiply by 100.

16. Multiply by 10.


22. Multiply by 10.

\

8. Multiply by 10.

11. Multiplyby 100.


17. Multiply by 10.


23. Multiply by 10.

9. Multiply by 10.

12. Multiplyby 100.

15. Multiply by 10.

18. Multiply by 10.



90.6

5q453.0

45

3 0

3 0

0

3.6

69q248.4

207

41 4

41 4

0

56

29q1624

145

174

174

0

16

39q624

39

234

234

0

26

346q8996

692

2076

2076

0

3.1

78q241.8

234

7 8

7 8

0

1.24

8q9.92

8

1 9

1 6

32

32

0

7.5

43q322.5

301

21 5

21 5

0

44

72q3168

288

288

288

0

17

627q10659

627

4389

4389

0

26

517q13442

1034

3102

3102

0

5.2

31q161.2

155

6 2

6 2

0

93

55q5115

495

165

165

0

2.8

54q151.2

108

43 2

43 2

0

31

84q2604

252

84

84

0

31

518q16058

1554

518

518

0

2.3

63q144.9

126

18 9

18 9

0

31.1

23q715.3

69

25

23

2 3

2 3

0

28.

Multiplying and Dividing by Powersof Ten page 635

1. Move the decimal point 4 places to the right.The answer is 560. 2. Move the decimal point 3 places to theleft.The answer is 0.00009. 3. Move the decimal point 1place to the right.The answer is 52. 4. Move the decimalpoint 3 places to the right.The answer is 30. 5. Move thedecimal point 1 place to the right.The answer is 2,367.6. Move the decimal point 1 place to the left.The answer is4.528. 7. Move the decimal point 3 places to the left.Theanswer is 0.0009. 8. Move the decimal point 2 places tothe right.The answer is 107. 9. Move the decimal point 2places to the right.The answer is 8. 10. Move the decimalpoint 4 places to the right.The answer is 10,300. 11. Movethe decimal point 3 places to the left.The answer is0.001803. 12. Move the decimal point 2 places to the right.The answer is 410. 13. Move the decimal point 3 placesto the right. The answer is 13,700. 14. Move the decimalpoint 2 places to the right. The answer is 20,305.15. Move the decimal point 1 place to the left. Theanswer is 0.47. 16. Move the decimal point 2 places tothe left. The answer is 0.0005.

Dividing Decimals by Decimal page 636

1.769

35q61.915

35

26 9

24 5

2 41

2 10

315

315

0

1. Multiplyby 10.

4. Multiplyby 10.

2. Multiply by 10.

5. Multiply by 10.

3. Multiplyby 10.

6. Multiply by 10.

1.8

57q102.6

57

45 6

45 6

0

452

3q1356

12

15

15

6

6

0

32

79q2528

237

158

158

0

65

19q1235

114

95

95

0

74

23q1702

161

92

92

0

84

32q2688

256

12 8

12 8

0




28. Multiply by 10.

31. Multiply by 10.

34. Multiply by 10.

37. Multiply by 10.

26. Multiply by 10.

29. Multiply by 10.



38. Multiply by 10.



33. Multiply by 10.


39. Multiply by 10.

0.243

18q4.374

3 6

77

72

54

54

0

12.5

9q112.5

9

22

18

4 5

4 5

0

9.5

75q712.5

675

37 5

37 5

0

659

4q2636

24

23

20

36

36

0

31.4

7q219.8

21

9

7

2 8

2 8

0

0.16

91q14.56

9 1

5 46

5 46

0

1.6

52q83.2

52

31 2

31 2

0

24

98q2352

196

392

392

0

3.96

5q19.80

15

4 8

4 5

30

30

0

74

8q592

56

32

32

0

3.58

27q96.66

81

15 6

13 5

2 16

2 16

0

31

37q1147

111

37

37

0

0.53

74q39.22

37 0

2 22

2 22

0

20.4

7q142.8

14

2 8

2 8

0

58.3

6q349.8

30

49

48

1 8

1 8

0

Zeros in Decimal Division page 637

1. Multiply by 100.

4. Multiply by 10.

7. Multiply by 100.

10. Multiply by 10.


16. Multiply by 10.

2. Multiply by 100.

5. Multiply by 10.

8. Multiply by 100.

11. Multiply by 10.

14. Multiply by 10.


3. Multiply by 100.

6. Multiply by 10.

9. Multiply by 100.


15. Multiply by 10.

18. Multiply by 10.

0.092

63q5.796

567

126

126

0

0.07

31q2.17

2 17

0

0.68

5q3.40

3 0

40

40

0

0.085

2q0.170

16

10

10

0

1.125

8q9.000

8

1 0

8

20

20

0

0.075

12q0.900

84

60

60

0

0.0021

44q0.0924

88

44

44

0

0.0085

72q0.6120

576

360

360

0

0.015

7q0.105

7

35

35

0

3.55

4q14.20

12

2 2

2 0

20

20

0

0.0095

2q0.0190

18

10

10

0

0.0081

2q0.0162

16

2

2

0

0.065

8q0.520

48

40

40

0

0.0035

16q0.0560

48

80

80

0

0.005

6q0.030

30

0

0.0025

7q0.0175

14

35

35

0

0.0084

25q0.2100

200

100

100

0

0.046

5q0.230

20

30

30

0


1 5 33. 1 5 1 5 34. 5 5 1 5

35. 4 5 1 5 36. 9 5 1 5 37. 2 5

1 5 38. 7 5 1 5 39. 1 5 1 5

40. 3 5 1 5 41. 6 5 1 5 42. 3 5

1 5 43. 4 5 1 5 44. 8 5 1 5

45. 6 5 1 5

Adding and Subtracting Fractionswith Like Denominators page 639

1.–4. Answers may vary. Samples are given. 1. 1 5

5 1 2. 2 5 3. 1 5 4. 1 5 5 1

5. 1 2 5 1 6. 2 5 5 7. 2 5 8. 1 5

5 9. 2 5 10. 1 5 5 1 5 1 11. 9 2

8 5 1 12. 8 2 4 5 4 13. 3 1 1 5 4 5 4

14. 2 1 3 5 5 5 5 15. 4 2 3 5 1 5 1 16. 9 1

6 5 15 5 16 5 16 17. 5 1 2 5 7 5 8 5 8

18. 4 2 2 5 2 19. 9 1 1 5 10 5 11 5 11

20. 8 2 4 5 4 21. 8 1 2 5 10 5 11 22. 1 1

3 5 4 5 5 23. 7 2 2 5 6 2 2 5 4 24. 4 2 1 5

3 2 1 5 2 25. 4 2 3 5 3 2 3 5 5 26. 5 2

2 5 4 2 2 5 2 5 2

Measuring Angles page 640

1–4. Measures may vary. Samples are given. 1. 1108;obtuse 2. 908; right 3. 608; acute 4. 1608; obtuse5. acute 6. acute 7. obtuse 8. straight 9. obtuse10. obtuseBar Graphs page 6411.

2.

Nu

mb

er o

fS

tud

ents

Pets in Students’ Homes

Number of Pets

16

8

00 1 2 3 More

than 3

Turk

eyPork

ChickenBeefP

oun

ds

per

Per

son

per

Yea

r

Meat Consumption

60

40

20

0

12

612

712

1312

712

112

34

68

58

118

58

38

23

23

43

23

13

35

35

65

35

15

25

75

35

45

1010

310

710

13

13

23

12

24

64

34

34

37

17

47

14

28

108

38

78

13

39

129

79

59

13

412

112

512

23

69

49

29

25

410

310

110

47

27

67

13

13

13

39

129

79

59

35

15

45

13

39

19

29

38

38

68

13

26

16

36

15

15

25

18

98

28

78

47

27

27

16

16

26

25

75

35

45

193

13

183

13

658

18

648

18

347

67

287

67

3110

110

3010

110

132

12

122

12

247

37

217

37

1712

512

1212

512

638

78

568

78

198

38

168

38

374

14

364

14

439

79

369

79

265

15

255

15

119

29

99

29

238

78

168

19. Multiply by 10.

22. Multiply by 10.


28. Multiply by 10.




21. Multiply by 10.


27. Multiply by 10.

0.033

93q3.069

2 79

279

279

0

2.08

5q10.40

10

40

40

0

0.006

14q0.084

84

0

0.044

25q1.100

1 00

100

100

0

0.009

52q0.468

468

0

1.06

9q9.54

9

54

54

0

0.0015

3q0.0045

3

15

15

0

0.0035

18q0.0630

54

90

90

0

0.074

35q2.590

2 45

140

140

0

0.00015

82q0.01230

82

410

410

0

Mixed Numbers and Improper Fractions page 638

1. 7 4 5 5 1 R2; 5 1 2. 9 4 2 5 4 R1; 5 4 3. 13 4

4 5 3 R1; 5 3 4. 21 4 5 5 4 R1; 5 4 5. 13 4 10 5

1 R3; 5 1 6. 49 4 5 5 9 R4; 5 9 7. 21 4 8 5

2 R5; 5 2 8. 13 4 7 5 1 R6; 5 1 9. 17 4 5 5 3 R2;

5 3 10. 49 4 6 5 8 R1; 5 8 11. 17 4 4 5 4 R1;

5 4 12. 5 4 2 5 2 R1; 5 2 13. 27 4 5 5 5 R2;

5 5 14. 12 4 9 5 1 R3; 5 1 5 1 15. 30 4 8 5

3 R6; 5 3 5 3 16. 37 4 12 5 3 R1; 5 3

17. 8 4 6 5 1 R2; 5 1 5 1 18. 19 4 12 5 1 R7; 5

1 19. 45 4 10 5 4 R5; 5 4 5 4 20. 15 4 12 5

1 R3; 5 1 5 1 21. 11 4 2 5 5 R1; 5 5

22. 20 4 6 5 3 R2; 5 3 5 3 23. 34 4 8 5 4 R2; 5

4 5 4 24. 21 4 9 5 2 R3; 5 2 5 2 25. 42 4 4 5

10 R2; 5 10 5 10 26. 1 5 1 5 27. 2 5

1 5 28. 1 5 1 5 29. 3 5 1 5

30. 2 5 1 5 31. 4 5 1 5 32. 2 578

92

12

82

12

167

27

147

27

165

15

155

15

1312

112

1212

112

83

23

63

23

32

12

22

12

12

24

424

13

39

219

14

28

348

13

26

206

12

112

14

312

1512

12

510

4510

712

1912

13

26

86

112

3712

34

68

308

13

39

129

25

275

12

52

14

174

16

496

25

175

67

137

58

218

45

495

310

1310

15

215

14

134

12

92

25

75




3.

4.

Line Graphs page 642

1.

2001200019991998

Average Baseballand Hockey Salaries

Sal

ary

(Mill

ion

s o

f D

olla

rs)

2.5

2.0

1.5

1.0

0.5

0

BaseballHockey

Year

Average SAT Mathand Verbal Scores

1

600

400

200

Sco

re

2Year

3

Math Verbal

Weekly Leisure Time

Sports

12

8

4

0

Ho

urs

Reading Working

Anna Tobi

2.

3.

4.

1 2 3 4 5

Space Launches

Year

Nu

mb

er o

f L

aun

ches

50

40

30

20

10

0

USARussia

1 2 3 4 5

Movies Rented Per Household

Year

Mo

vies

50

40

30

20

10

CassettesDVDS

2001 2002 2003 2004

U.S. NewspaperCirculation

Year

Cir

cula

tio

n (m

illio

ns) 60

50

40

30

20

10

0

MorningEvening


Algebra Readiness (Pre-Algebra) Answer Key · Mathematics: Course 3 CC-2 Pythagorean Proofs (...

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Transcript of Algebra Readiness (Pre-Algebra) Answer Key · Mathematics: Course 3 CC-2 Pythagorean Proofs (...