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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
=
2/9/2016 Chapter 7 Review Homework-Virginia Davis
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Simplify the complex fraction.
53 − x
+6
x − 35x+
2x − 3
53 − x
+6
x − 35x+
2x − 3
=
Simplify the complex fraction.
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.)
2/9/2016 Chapter 7 Review Homework-Virginia Davis
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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°
2/9/2016 Chapter 7 Review Homework-Virginia Davis
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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=
Perform the indicated operation.
+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.)=
B. There is no solution.
2/9/2016 Chapter 7 Review Homework-Virginia Davis
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Simplify the expression.
x + 7
x2 − x − 56
Select the correct choice below and fill in any answer boxes in your choice.
A. (Simplify your answer.)x + 7
x2 − x − 56=
B. The expression cannot be simplified.
Simplify the expression.
x3 + 9x2
x2 + 2x − 63
Select the correct choice below and fill in any answer boxes in your choice.
A. (Simplify your answer.)x3 + 9x2
x2 + 2x − 63=
B. The expression cannot be simplified.
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.)
2/9/2016 Chapter 7 Review Homework-Virginia Davis
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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.)
Simplify the complex fraction.
93x36x
93x36x
=
Simplify the complex fraction.
3 +23
1 +23
3 +23
1 +23
=
2/9/2016 Chapter 7 Review Homework-Virginia Davis
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Solve the equation and check the proposed solution.
9 + =72a − 9
8aa − 9
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. a = (Simplify your answer. Use a comma to separate answers as needed.)
B. There is no solution.
Solve the equation.
=a
a − 9− 8a − 7
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. a = (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There is no solution.
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.)=
2/9/2016 Chapter 7 Review Homework-Virginia Davis
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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=
Perform the indicated operation.
+4
x
5
8x2
(Simplify your answer.)+ =4
x
5
8x2
3 ft y
10 ft 6 ft
2/9/2016 Chapter 7 Review Homework-Virginia Davis
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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.)
2/9/2016 Chapter 7 Review Homework-Virginia Davis
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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
2/9/2016 Chapter 7 Review Homework-Virginia Davis
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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
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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