Instructor: Virginia Davis...

2/9/2016 Chapter 7 Review Homework-Virginia Davis

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Student: _____________________Date: _____________________

Instructor: Virginia DavisCourse: Foundations for College Math(1)

Assignment: Chapter 7 ReviewHomework

Simplify the expression.

7x + 28

x2+ 4x

Select the correct choice below and fill in any answer boxes in your choice.

A. (Simplify your answer.)7x + 28

x2+ 4x

=

B. The expression cannot be simplified.

Multiply.

•4x − 8

3x2+ x

3x2+ 7x + 2

x2− 4

(Type your answer in factored form.)•4x − 8

3x2+ x

3x2+ 7x + 2

x2− 4

=

Add the rational expressions.

+5m

2n

9m

2n

(Simplify your answer.)+5m

2n

9m

2n=

Simplify the complex fraction.

1

x

+1

x2

x +1

x2

1

x

+1

x2

x +1

x2

=



5.

6.

7.

8.

9.


53 − x

+6

x − 35x+

2x − 3

53 − x

+6

x − 35x+

2x − 3

=


x + 4x

−6

x − 1x + 1x

+x + 1x − 1

x + 4x

−6

x − 1x + 1x

+x + 1x − 1

=

Simplify.

3a − 1 + 4b − 2

a − 1 − b − 1

3a − 1 + 4b − 2

a − 1 − b − 1=

If a number, added to is divided by the number plus , the result is Find the number.three times 2 8 five halves.

The number is .

Smith Engineering is in the process of reviewing the salaries of their surveyors. During this review, the company found that an experienced surveyor can survey a roadbed in hours. An apprentice surveyor needs hours to survey the same stretch of road. If the two work together, find how long it takes them to complete the job.

4 10

The answer is hr. (Type an integer or a simplified fraction.)



10.

11.

12.

13.

14.

In minutes, a conveyor belt moves pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in minutes. If both belts are used, find how long it takes to move the cans to the storage area.

5 2007

The conveyor belts can move the pounds of recyclable aluminum from the delivery truck to a storage area in minutes.

200

(Simplify your answer. Type an integer, fraction, or a mixed number.)

A jogger begins her workout by jogging to the park, a distance of miles. She then jogs home at the same speed, but along a different route. This return trip is miles, and her time is one hour longer. Find her jogging speed. Complete the accompanying chart, and use it to find her jogging speed. Let x the jogging speed.

610

=

Distance = Rate • Time

Trip to Park 6

Return Trip 10

(Type an expression using x as the variable.)

The jogger's speed is mph.

Perform the indicated operation.

+15

x2 + 8x + 16

2

x + 4

(Simplify your answer.)+15

x2 + 8x + 16

2

x + 4=

A board of length inches was cut into two pieces.

If one piece is inches, express the length of the

other piece as a rational expression.

8x + 3

5x − 3

?

in.

in.

The other piece of the board has length inches. (Simplify your answer.)

Two angles are said to be complementary if the sum of their measures is 90 . If one angle measures

degrees, find the measure of its complement.

°58x

?

The measure of its complement is degrees. (Simplify your answer.)

8x+3

5x−3

58x°



15.

16.

17.

18.

19.

20.

Solve the equation.

+ =b − 73

b − 54

23

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution is . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

B. There is no solution.

The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs pounds on Planet A, find the elephant's weight on Planet B.4600

The elephant's weight on Planet B is lb.

There are 110 calories per 28.4 grams of Cereal X. Find how many calories are in grams of this cereal.36.92

There are calories in grams of this cereal.36.92

Perform the indicated operation. Simplify if possible.

−5

x + 4

4x

x2 − 16

(Simplify your answer.)−5

x + 4

4x

x2 − 16=


+3

d − 83

8 − d

(Simplify your answer.)+3

d − 83

8 − d=

Solve the equation.

+ 2 =8y

y − 106y

y − 10

Select the correct answer below and, if necessary, fill in the answer box to complete your choice.

A. y (Use a comma to separate answers as needed.)=




21.

22.

23.

24.


x + 7

x2 − x − 56


A. (Simplify your answer.)x + 7

x2 − x − 56=



x3 + 9x2

x2 + 2x − 63


A. (Simplify your answer.)x3 + 9x2

x2 + 2x − 63=


Multiply. Simplify if possible.

•36x

4

x9

9x6

•36x

4

x9

9x6=

Find the product and simplify if possible.

•(p − t)4

5p + 5t

5p

p2 − pt

•(p − t)4

5p + 5t

5p

p2 − pt=

(Simplify your answer. Type your answer in factored form.)



25.

26.

27.

28.

Find the quotient and simplify the result.

÷5x9

3x525x2

6x4

÷5x9

3x525x2

6x4=

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

Multiply.

•x2 + 5x

715

3x + 15

•x2 + 5x

715

3x + 15=

(Simplify your answer. Use integers or fractions for any numbers in the expression.)


93x36x

93x36x

=


3 +23

1 +23

3 +23

1 +23

=



29.

30.

31.

32.

33.

34.

Solve the equation and check the proposed solution.

9 + =72a − 9

8aa − 9


A. a = (Simplify your answer. Use a comma to separate answers as needed.)


Solve the equation.

=a

a − 9− 8a − 7


A. a = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)


Solve the equation for the indicated variable.

for I =6AT + B

B

(Simplify your answer.)B =

Solve the equation for the indicated variable.

for L = P +AN

N

N =

Solve the proportion.

47=

x14

(Simplify your answer.)x =

Solve the following proportion.

=x + 22x + 9

47

x (Simplify your answer.)=



35.

36.

37.

38.

39.

40.

Solve the proportion.

=32

99x + 5

x (Simplify your answer. Type an integer or a fraction.)=

Find the unknown length y in the following pair of similar triangles.

15

2731

3.75

6.75

y =

Find the unknown length y in the pair of similar triangles.

ft y = (Simplify your answer. Type an integer, fraction, or a mixed number.)

times the reciprocal of a number equals times the reciprocal of . Find the number.Nine 3 6

The number is .

Subtract the rational expressions and simplify if possible.

−4x

2x − 714

2x − 7

(Simplify your answer.)−4x

2x − 714

2x − 7=


+4

x

5

8x2

(Simplify your answer.)+ =4

x

5

8x2

3 ft y

10 ft 6 ft



41.

42.

43.

A pilot can travel miles with the wind in the same amount of time as miles against the wind. Find the speed of the wind if the pilot's speed in still air is miles per hour.

600 400250

The speed of the wind is miles per hour.

Find the quotient and simplify.

÷a2 − b2

a − b

a

a2 − ba

(Simplify your answer.)÷a2 − b2

a − b

a

a2 − ba=

Divide.

5x − 2027

÷9x − 3618

5x − 2027

÷9x − 3618

=

(Type an integer or a simplified fraction.)



1.

A. (Simplify your answer.)7x + 28

x2 + 4x=

7x

2. 4x

3. 7mn

4.

1x2 − x + 1

5. x

7x − 15

6. x − 4

2x − 1

7. 3b2 + 4ab(b − a)

8. 36

9. 2 67

10. 2 1112

11. x

6x

x

10x

4

12.

2x + 23(x + 4)2



13. 3x − 39

(x + 3)(x − 3)

14. 90x − 58

x

15.

A. The solution is . 517

(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

16. 138

17. 143

18. x − 20

(x + 4)(x − 4)

19. 0

20. A. y (Use a comma to separate answers as needed.)= 5

21.

A. (Simplify your answer.)x + 7

x2 − x − 56=

1x − 8

22.

A. (Simplify your answer.)x3 + 9x2

x2 + 2x − 63=

x2

x − 7

23. x4

24. (p − t)3

p + t

25. 2x6

5

26. x57

27. 6



28. 115

29. B. There is no solution.

30. A. a = 8, − 9 (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

31. 6A − TI

I

32. A

L − P

33. 8

34. − 22

35. 19

36. 7.75

37. 1 45

38. 18

39. 2

40.

32x + 58x2

41. 50

42. a − b2 2

43. 1027

Instructor: Virginia Davis...

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