Algebra Connections 28

Chapter 5

Lesson 5.1.1

5-1. b. x + 4 and x + 2 c. x2 + 6x + 8 = (x + 2)(x + 4)

5-2. a. (x +1)(x + 2) b. 3(2x + 5) c . (2x + 3)(x + 2)

d. (x +1)(3x +1) e. (2x + 6)(x + 2) or (2x + 4)(x + 3)

f. 2y(y + 3) g. (y + x)(y + 2) h. (x +1)(y +1)

i. (x + y +1)(x + y + 2) j. (2y +1)(x + 2)

5-4. 77 + 56 + 33+ 24 = 190 5-5. y = 7x + 5

5-6. (2x + 4)(x + 2) = 2x2 + 8x + 8 5-7. Answers vary.

5-8. No, he is not correct. Parallel lines do not have a point of intersection. 5-9. 62,000 votes

Lesson 5.1.2

5-10. a. (2x + 3)(x + 2) = 2x2 + 7x + 6 b. (y + x + 2)(x + 4) = xy + x2 + 6x + 4y + 8

5-11. a. 8x2 b. 2x2 + 7x + 3 c. 2x2 +10x

d. 4x2 + 4x +1 e. 2x2 + xy

f. 2x2 + 2xy + 9x + 5y +10 g. 6x +10 h. 2xy + y2 + 3y

5-13. a. 12x2 +10x b. 24x + 6 c. 12xy + 9y d. 70xy + 77y2

5-15. a. (x +1)(x + 3) = x2 + 4x + 3 b. (2x +1)(x + 2) = 2x2 + 5x + 2

5-16. a. 238 b. 112 5-17. a. Multiply by 6 b. x = 15 c. x = 4

5-18. a. m = 3 b. (0, –2) c. y = 3x ! 2

5-19. 10,000 + 1,500x = 18,000 + 1,300x, x = 40 months 5-20. x-intercepts are (1.5, 0) and (–1, 0), y-intercept is (0, –3).

Answer Key 29

Lesson 5.1.3

5-21. a. !18x +12 b. 4x2 ! 2x

c. 50t !15t2 d. !32 + 24k ! 4y

5-22. (4x + 5)(2x + 3) = 8x2 + 22x +15

5-23. The area inside each smaller rectangle of the generic rectangle corresponds to the tiles in the same portions of the rectangle in problem 5-22.

5-24. a. (3)(y + 5) = 3y +15 b. (x)(2x) = 2x2

c. (x + 5)(2x ! 3) = 2x2 + 7x !15 d. (4y ! 7)(6y !1) = 24y2 ! 46y + 7

5-25. a. 3x2 +17x +10 b. 10y2 !11y ! 35

c. 18xy ! 33x d. 15w2 ! wp ! 2p2 ! 20w + 8p

5-26. a. y(x + 3) = xy + 3y b. (x +12)(x + 5) = x2 +17x + 60

c. (x ! 2)(2x ! 3y + 5) = 2x2 ! 3xy + x + 6y !10

d. Multiple answers possible

5-27. a. 2x2 +17x + 30 b. 3m2 ! 4m !15

c. 12x2 ! 59x ! 5 d. 6 ! 7y ! 5y2

5-28. a. 6 b. 16 c. 1.5 d. 8

5-29. a. –4, 0 b. –16, 6 c. 2, 14 d. 20, –1 5-30. a. y = !2x +1 b. x: (0.5, 0), y: (0, 1) c. y = !2x

5-31. 30 ounces 5-32. These expressions are equivalent because of the Commutative Properties of Addition

and Multiplication.

Algebra Connections 30

Lesson 5.1.4

5-33. a. 12x2 + 8x ! 55 b. !30x2 + 6x

c. !y2 + 4y +12 d. 48 !16m2

5-34. This can be built with 3 rows, each containing 2 x-tiles and 1 unit tile

a. 4

b. 3(2·4 + 1) = 8·4 – 5 5-35. A and C are correct. 5-36. x = !2 5-37. a. x = 9 b. x = 0 c. y = 6

d. x = !3.5 e. x = 2 f. x = !10

3

5-38. a. –1 b. 5 c. –2.5 d. 8 5-39. The equation in part (b) has no solution. Possible reason: There are the same number

of x-terms on each side of the equation, so if you try to solve, you end up with an equation such as 11 = 14 , which is impossible.

5-40. Rena is correct.

5-41. y = !2x +13

5-42. a. After 3 hours b. 8

5-43. (–2, –1)

5-44. No, on average he will make about 375 baskets.

Answer Key 31

Lesson 5.1.5

5-45. a. 5 feet, the y-intercept is the constant

b. 4 feet per year, the rate is the coefficient of the x. 5-46. b. y = 3x + 5

c. y-intercept is (0, 5); growth factor is 3. 5-47. See table below.

y =mx + b form Growth factor y-intercept

a. y = x ! 7 1 (0, –7)

b. y = x + 2 1 (0, 2)

c. y = !5x ! 2 –5 (0, –2)

d. y = x 1 (0, 0)

e. y = 0 0 (0, 0)

f. y = !3x ! 4 –3 (0, –4)

5-48. a. y = 5 b. x = 5 ! 5

2y c. y = 6x !11

d. x can be any number e. x = !1

3y + 2 f. p = m

2+ 4

g. y = x ! 3 h. q = !37

3

5-50. a. 4x2 +17x +15 b. !6x2 ! 20x !16

c. !3xy + 3y2 + 8x ! 8y d. 3xy + 5y2 ! 22y !12x + 8

5-51. a. x =y+5

2 b. w =

p!9

!3 c. m = 2n + 5 d. y = !3x

5-52. y = 3+ 2x

5-53. b. no solution

c. there is no solution to the system of equations because the two lines do not intersect

5-54. 100 ÷ 4 = 25, 3,000 ÷ 25 = 120 gallons

Algebra Connections 32

Lesson 5.1.6

5-55. a. x = 3 b. y = 1

2x ! 2 c. x = 3 d. y = !

1

2x + 4 e. x = –2

f. y = !x + 3 g. x =y!4

!3 h. x = 2 i. w = 3! 2v j. no solution

5-57. a. x = 5 b. x = 2 c. y = 0 d. x = 38

5-58. (x + 3)(x ! 5) = x2 ! 2x !15

5-59. See graph at right.

5-60. The numbers are 55 and 60. 5-61. a. 6x +10 = 10x , after 2.5 hours b. 25 problems 5-62. ! 1222

Lesson 5.2.1

5-63. a. 18 b. 12 c. 4.5 d. 127

5-64. a. 34 people b. Yes c. 238,085 votes 5-65. a. Ratios vary b. No c. When ratios are of corresponding parts, the ratios are equal

d. The ratios used will vary. One example: 68100

=x

527. Therefore,

x = 358.36 , so Mr. Mears would probably receive roughly 358 votes from

Carina’s neighborhood.

5-66. a. 217

=x

85, x = 10 minutes b. 8

29=

x

1490, x ! 411 students

5-67. 19.9 minutes 5-68. 9.6 weeks; 179.2 pounds 5-69. answers vary

5-70. a. x2 + 9x + 20 b. 2y2 + 6y

5-71. a. 3x2 + 5x +13 b. 5x2 +16x + 5 c. !x2 + 4x + 6

d. 5x e. 4x2 !11x ! 2

3–3

4

y

x

Answer Key 33

Lesson 5.2.2

5-72. a. 30 b. 16 c. 32 d. .3

5-73. See table below:

# of Cans Weight (kg)

50 0.77

1,240 x

b. 50

1240=0.77

x, x ! 19.1 kg c. ! 31.9 kg

5-74. a. $8 b. $74.95 c. 10 days (rounded up to nearest whole day)

5-75. 15 units

5-76. 74

184=

x

4, x ! 1.6 inches

5-77. a. x = !5 b. y = 2x ! 3 c. no solution d. y = !3x + 5

5-78. ! 574 times at bat

5-79. a. 132

=8

x, x = 256 miles b.

g

118=1

32, g ! 3.7 gallons

5-80. a. (3, 5) 5-81. a. Yes, because the sum of two even numbers is always an even number. If one even

number is written as 2m and the other as 2n , then the sum is 2m + 2n = 2(m + n) ,

which is even.

b. Yes, because the product of two even numbers is always even. If one even number is written as 2m and the other as 2n , then the product is (2m)(2n) = 2(2mn) , which is even.

5-82. a. 2x(x + 5) = 2x2 +10x b. (2x + 5)(x + 3) = 2x2 +13x +15

Lesson 5.2.3

5-85. a. x2 +10x +16 b. 2m2 + 70m + 600

c. xy +10x d. 6x2 +17x +12

5-86. a. 0.08 feet or about 1 inch b. ! 42 feet

5-87. a. 11.2 b. 7.5 c. 3.75 d. –0.25

5-88. (2, -5)

5-89. a. y = 4x ! 3 b. y = x + 3 c. y = !3

2x + 6 d. y = !

2

3x + 2