Deck 14: Rational Expressions

Question 1

Simplify the expression.

- $\frac { 24 \mathrm { k } ^ { 3 } } { 6 \mathrm { k } }$

A) $18 \mathrm { k } ^ { 2 }$
B)4k
C) $4 \mathrm { k } ^ { 2 }$
D)18

Answer 1

$4 \mathrm { k } ^ { 2 }$

Question 2

Simplify the expression.

- $\frac { 8 - \mathrm { m } } { \mathrm { m } - 8 }$

A)already in lowest terms
B)-m
C)-1
D)1

Answer 2

-1

Question 3

Simplify the expression.

- $\frac { ( y + 3 ) ( y - 7 ) } { ( y - 7 ) ( y + 9 ) }$

A) $\frac { y - 3 } { y - 9 }$
B) $\frac { y + 7 } { y + 2 }$
C) $\frac { 2 y - 7 } { 2 y + 2 }$
D) $\frac { y + 3 } { y + 9 }$

Answer 3

$\frac { y + 3 } { y + 9 }$

Question 4

Solve the problem.

-A formula for the focal length of a lens is $f = \frac { a b } { b + a }$ Calculate f (the focal length)for a = 8 cm and b = 11 cm. Round to the nearest tenth of a centimeter when necessary.

A)4.0 cm
B)5.5 cm
C)3.4 cm
D)4.6 cm

Question 5

Find any numbers for which the rational expression is undefined.

- $\frac { m - 6 } { 4 - m }$

A)m = -4
B)m = 4, m = 6
C)m = 4
D)none

Question 6

Find the value of the expression for the given replacement value.

- $\frac { x + 9 } { x - 8 };$ ; x= 7

A)- 16
B) $- \frac { 1 } { 16 }$
C) $- \frac { 2 } { 15 }$
D) $- \frac { 15 } { 2 }$

Question 7

Find any numbers for which the rational expression is undefined.

- $\frac { 9 x ^ { 2 } - 4 } { 8 x - 32 }$

A)x = 4
B) $x = \frac { 2 } { 3 } , x = - \frac { 2 } { 3 }$
C)x = 32
D)none

Question 8

Find the value of the expression for the given replacement value.

- $\frac { x - 7 } { - 3 x - 1 } ; x = 4$

A) $\frac { 3 } { 13 }$
B) $\frac { 7 } { 4 }$
C) $\frac { 13 } { 3 }$
D) $\frac { 3 } { 4 }$

Question 9

Simplify the expression.

- $\frac { - 2 x - 2 y } { x + y }$

A)2
B)-2
C) $\frac { 1 } { 2 }$
D) $- \frac { 1 } { 2 }$

Question 10

Find the value of the expression for the given replacement value.

- $\frac { a ^ { 2 } } { 1 - a ^ { 2 } } ; a = 9$

A) $\frac { 81 } { 82 }$
B) $- \frac { 81 } { 80 }$
C) $- \frac { 80 } { 81 }$
D) $\frac { 81 } { 80 }$

Question 11

Find any numbers for which the rational expression is undefined.

- $\frac { x ^ { 2 } - 100 } { x ^ { 2 } + 12 x + 27 }$

A)x = 10, x = -10
B)x = 3, x = -9
C)x = -3, x = -9
D)x = 0

Question 12

Find any numbers for which the rational expression is undefined.

- $\frac { 3 } { r + 8 }$

A)r = 0
B)r = 8
C)r = -8
D)none

Question 13

Find any numbers for which the rational expression is undefined.

- $\frac { 4 } { z - 7 }$

A)z = 7
B)z = 0
C)z = -7
D)none

Question 14

Find any numbers for which the rational expression is undefined.

- $\frac { x ^ { 3 } + 16 x } { 2 x - 20 }$

A)x = -4, x = 0, x = 4
B)x = 0
C)x = 10
D)x = -10

Question 15

Find the value of the expression for the given replacement value.

- $\frac { x ^ { 2 } - 10 x + 5 } { x ^ { 2 } + 2 x - 1 } ; x = 3$

A)- 1
B) $\frac { 22 } { 7 }$
C) $\frac { 8 } { 7 }$
D) $- \frac { 8 } { 7 }$

Question 16

Solve the problem.

-A gas law in chemistry says that $\frac { P V } { T } = \frac { p v } { t }$ . . If T = 210, t = 290, V = 7, P = 90, and v = 6, find the value of p. Round to the nearest thousandth when necessary.

A)14.5
B)145
C)0.5
D)840

Question 17

Find any numbers for which the rational expression is undefined.

- $\frac { 3 y - 2 } { y ^ { 2 } - 64 }$

A) $y = \frac { 2 } { 3 }$
B)y = 64
C)y = 8, y = -8
D)y = 8

Question 18

Find any numbers for which the rational expression is undefined.

- $\frac { x ^ { 2 } - 9 } { x ^ { 2 } - 9 x + 18 }$

A)x = -6, x = -3
B)x = 3, x = -3
C)x = 6, x = 3
D)x = 0

Question 19

Find any numbers for which the rational expression is undefined.

- $\frac { z - 5 } { 7 }$

A)z = 5
B)z = -5
C)z = 0
D)none

Question 20

Find any numbers for which the rational expression is undefined.

- $\frac { x ^ { 3 } + 4 x ^ { 4 } } { x ^ { 2 } + 9 }$

A)x = 0, x = $- \frac { 1 } { 4 }$
B)x = -3
C)x = -9
D)none

Question 21

Find the product and simplify.

- $\frac { 3 z ^ { 3 } } { 4 } \cdot \frac { 24 } { z ^ { 2 } }$

A) $\frac { \mathrm { Z } } { 18 }$
B) $\frac { 18 z ^ { 2 } } { z ^ { 3 } }$
C)18z
D) $\frac { 18 } { \mathrm { z } }$

Question 22

Simplify the expression.

- $\frac { 3 k - 9 } { 6 - 2 k }$

A) $- \frac { 3 } { 2 }$
B)1
C) $\frac { 3 } { 2 }$
D)-1

Question 23

Find the product and simplify.

- $\frac { 3 x ^ { 3 } y ^ { 10 } } { - 27 x y ^ { 13 } } \cdot y ^ { 3 }$

A) $\frac { x ^ { 3 } } { - 9 y }$
B) $\frac { x ^ { 2 } y } { - 9 }$
C) $\frac { x ^ { 3 } } { - 9 }$
D) $\frac { x ^ { 2 } } { - 9 }$

Question 24

List four equivalent forms for the rational expression.

- $- \frac { x - 2 } { x + 7 }$

A) $\frac { - ( x - 2 ) } { x + 7 } , \frac { - x + 2 } { x - 7 } , \frac { x - 2 } { - ( x - 7 ) } , \frac { x - 2 } { - x - 7 }$
B) $\frac { - ( x + 2 ) } { x + 7 } , \frac { - x + 2 } { x + 7 } , \frac { x + 2 } { - ( x + 7 ) } , \frac { x - 2 } { - x - 7 }$
C) $\frac { - ( x - 2 ) } { x - 7 } , \frac { - x + 2 } { x + 7 } , \frac { x - 2 } { - ( x - 7 ) } , \frac { x - 2 } { - x - 7 }$
D) $\frac { - ( x - 2 ) } { x + 7 } , \frac { - x + 2 } { x + 7 } , \frac { x - 2 } { - ( x + 7 ) } , \frac { x - 2 } { - x - 7 }$

Question 25

List four equivalent forms for the rational expression.

- $- \frac { 7 y - 2 } { y - 16 }$

A) $\frac { - ( 7 y - 2 ) } { y - 16 } , \frac { - 7 y - 2 } { y - 16 } , \frac { 7 y - 2 } { - ( y - 16 ) } , \frac { 7 y - 2 } { - y - 16 }$
B) $\frac { - ( 7 y - 2 ) } { y - 16 } , \frac { - 7 y + 2 } { y - 16 } , \frac { 7 y - 2 } { - ( y - 16 ) } , \frac { 7 y - 2 } { - y - 16 }$
C) $\frac { - ( 7 y - 2 ) } { y - 16 } , \frac { - 7 y + 2 } { y - 16 } , \frac { 7 y - 2 } { - ( y - 16 ) } , \frac { 7 y - 2 } { - y + 16 }$
D) $\frac { - ( 7 y - 2 ) } { y - 16 } , \frac { - 7 y - 2 } { y - 16 } , \frac { 7 y - 2 } { - ( y - 16 ) } , \frac { 7 y - 2 } { - y + 16 }$

Question 26

Simplify the expression.

- $\frac { a ^ { 2 } - a b + 9 a - 9 b } { a + 9 }$

A) $\frac { 1 } { a + 9 }$
B) $\frac { a ^ { 2 } - a b + 9 a - 9 b } { a + 9 }$
C)a - 2b + 1
D)a - b

Question 27

Find the product and simplify.

- $\frac { 5 p - 5 } { p } \cdot \frac { 2 p ^ { 2 } } { 8 p - 8 }$

A) $\frac { 5 p } { 4 }$
B) $\frac { 10 p ^ { 3 } - 10 p ^ { 2 } } { 8 p ^ { 2 } - 8 p }$
C) $\frac { 40 p ^ { 2 } + 80 p + 40 } { 2 p ^ { 3 } }$
D) $\frac { 4 } { 5 p }$

Question 28

Find the product and simplify.

- $\frac { 7 } { x + 7 } \cdot \frac { x } { 8 }$

A) $\frac { x } { ( x + 8 ) }$
B) $\frac { 7 } { 8 }$
C) $\frac { 7 x } { 8 ( x + 7 ) }$
D) $\frac { 1 } { 8 }$

Question 29

Find the product and simplify.

- $\frac { 3 y } { 6 y + 3 } \cdot \frac { 14 y + 7 } { 6 }$

A) $\frac { 7 } { 6 }$
B) $\frac { 7 y } { 6 }$
C) $\frac { 7 y } { 18 }$
D) $\frac { y } { 6 }$

Question 30

Simplify the expression.

- $\frac { 5 x ^ { 2 } + 15 x ^ { 3 } } { 12 x + 36 x ^ { 2 } }$

A) $\frac { 5 + 15 x ^ { 3 } } { 12 x + 36 }$
B) $\frac { 5 x ^ { 2 } + 15 x ^ { 3 } } { 12 x + 36 x ^ { 2 } }$
C) $\frac { 5 x } { 12 }$
D) $\frac { 5 } { 12 }$

Question 31

Find the product and simplify.

- $\frac { 4 x ^ { 8 } y } { 24 x ^ { 8 } y } \cdot y ^ { 10 }$

A) $\frac { y ^ { 4 } } { 6 }$
B) $\frac { x ^ { 16 } y ^ { 3 } } { 6 }$
C) $\frac { x ^ { 16 } y ^ { 4 } } { 6 }$
D) $\frac { y ^ { 3 } } { 6 }$

Question 32

Simplify the expression.

- $\frac { - 12 x + 12 y } { - 12 y + 12 x }$

A)-1
B)-12
C)12
D)1

Question 33

Find the product and simplify.

- $8 x ^ { 4 } \cdot \frac { x ^ { 2 } y } { 80 x ^ { 3 } y ^ { 2 } }$

A) $\frac { x ^ { 6 } y } { 10 x ^ { 3 } y ^ { 2 } }$
B) $\frac { 1 } { 80 x y }$
C) $\frac { x ^ { 5 } } { 10 y }$
D) $\frac { x ^ { 3 } } { 10 y }$

Question 34

Simplify the expression.

- $\frac { 4 x ^ { 2 } - 21 x + 27 } { x - 3 }$

A) $4 x ^ { 2 } - 30$
B) $\frac { 4 x ^ { 2 } - 21 x + 27 } { x - 3 }$
C) $\frac { 1 } { x - 3 }$
D)4x - 9

Question 35

Find the product and simplify.

- $\frac { 3 x ^ { 2 } } { 4 } \cdot \frac { 16 } { x ^ { 3 } }$

A) $\frac { x } { 12 }$
B) $\frac { 48 x ^ { 2 } } { 4 x ^ { 3 } }$
C) $\frac { 12 x ^ { 2 } } { x ^ { 3 } }$
D) $\frac { 12 } { x }$

Question 36

Find the product and simplify.

- $\frac { x ^ { 2 } + x } { 3 } \cdot \frac { 24 } { x + 1 }$

A) $8 x ^ { 2 }$
B)8x
C) $\frac { x } { 8 }$
D) $\frac { 8 x ^ { 2 } + 8 x } { x + 1 }$

Question 37

Simplify the expression.

- $\frac { y ^ { 2 } + 10 y + 16 } { y ^ { 2 } + 17 y + 72 }$

A) $- \frac { y ^ { 2 } + 10 y + 16 } { y ^ { 2 } + 17 y + 72 }$
B) $\frac { 10 y + 2 } { 17 y + 9 }$
C) $\frac { 10 y + 16 } { 17 y + 72 }$
D) $\frac { y + 2 } { y + 9 }$

Question 38

Simplify the expression.

- $\frac { 3 x + 2 } { 12 x ^ { 2 } + 17 x + 6 }$

A) $\frac { 1 } { 4 x + 3 }$
B) $\frac { 3 x } { 4 x + 3 }$
C) $\frac { 3 x + 2 } { 12 x ^ { 2 } + 17 x + 6 }$
D) $\frac { 3 x + 4 } { 4 x + 17 }$

Question 39

Find the product and simplify.

- $\frac { z ^ { 3 } } { 25 z } \cdot \frac { 5 } { 2 z ^ { 2 } }$

A) $\frac { 1 } { 10 }$
B) $\frac { \mathrm { z } ^ { 3 } } { 10 \mathrm { z } ^ { 2 } }$
C) $\frac { Z } { 10 }$
D) $\frac { 1 } { 10 z }$

Question 40

Find the product and simplify.

- $\frac { 2 p - 2 } { 3 } \cdot \frac { 5 p ^ { 2 } } { p ^ { 2 } - p }$

A) $\frac { 10 p } { 3 }$
B) $\frac { 10 p - 10 } { - 3 p }$
C) $\frac { 10 p ^ { 3 } - 10 p ^ { 2 } } { 3 p ^ { 2 } - 3 p }$
D) $\frac { 3 } { 10 \mathrm { p } }$

Question 41

Find the quotient and simplify.

- $\frac { b ^ { 2 } - m ^ { 2 } } { b + m } \div \frac { b } { b ^ { 2 } + b m }$

A) $- \frac { 1 } { b }$
B) $b ^ { 2 } - m ^ { 2 }$
C)b
D)b - m

Question 42

Find the quotient and simplify.

- $\frac { 6 y ^ { 3 } } { z ^ { 5 } } + \frac { 9 y ^ { 3 } z ^ { 5 } } { 8 }$

A) $\frac { 27 y ^ { 6 } } { 4 }$
B) $\frac { 16 y ^ { 6 } } { 3 z ^ { 10 } }$
C) $\frac { 16 } { 3 z ^ { 10 } }$
D) $\frac { 16 } { 3 }$

Question 43

Find the quotient and simplify.

- $\frac { ( r - x ) ^ { 2 } } { r + x } \div \frac { r ^ { 2 } - r x } { r }$

A) $\frac { r - x } { r + x }$
B) $\frac { x } { r + x }$
C) $\frac { r + x } { r - x }$
D) $\frac { ( r - x ) ^ { 3 } } { r + x }$

Question 44

Find the quotient and simplify.

- $\frac { ( x - 7 ) ( x + 6 ) } { 5 x } \div \frac { 4 x - 28 } { 20 x ^ { 7 } }$

A) $4 x ^ { 6 } ( x + 6 )$
B) $\frac { x ^ { 6 } ( x + 6 ) } { 4 }$
C) $x ^ { 7 } ( x + 6 )$
D) $x ^ { 6 } ( x + 6 )$

Question 45

Find the product and simplify.

- $\frac { x ^ { 2 } + 10 x + 24 } { x ^ { 2 } + 8 x + 12 } \cdot \frac { x ^ { 2 } + 10 x + 16 } { x ^ { 2 } + 12 x + 32 }$

A) $\frac { x + 2 } { x + 8 }$
B)1
C) $\frac { x + 4 } { x + 2 }$
D) $\frac { 1 } { x + 8 }$

Question 46

Find the quotient and simplify.

- $\frac { x + 9 } { 1 - x } \div \frac { x ^ { 2 } - 12 x + 27 } { x ^ { 2 } - 10 x + 9 }$

A) $- \frac { ( x + 9 ) ( x - 9 ) } { ( x - 1 ) ^ { 2 } }$
B) $- \frac { x - 9 } { x - 3 }$
C) $\frac { x - 9 } { x - 3 }$
D) $- \frac { x + 9 } { x - 3 }$

Question 47

Find the product and simplify.

- $\frac { t ^ { 2 } - r ^ { 2 } } { t + r } \cdot \frac { t } { t ^ { 2 } - t r }$

A)-t
B)t
C)1
D) $- \frac { 1 } { t }$

Question 48

Find the quotient and simplify.

- $\frac { 60 x ^ { 5 } } { x ^ { 2 } - 1 } \div \frac { x ^ { 12 } } { ( x + 1 ) ^ { 2 } }$

A) $\frac { 60 x ^ { 7 } ( x + 1 ) } { ( x - 1 ) }$
B) $\frac { 60 ( x + 1 ) } { x ^ { 7 } ( x - 1 ) }$
C) $\frac { 60 x ^ { 60 } } { ( x - 1 ) ( x + 1 ) ^ { 3 } }$
D) $\frac { 5 ( x + 1 ) } { x ^ { 7 } ( x - 1 ) }$

Question 49

Find the quotient and simplify.

- $( x + 6 ) \div \frac { x ^ { 2 } - 7 x + 6 } { 1 - x }$

A) $- \frac { x + 6 } { x - 6 }$
B)-1
C) $- ( x - 6 ) ( x + 6 )$
D) $- \frac { x - 6 } { x + 6 }$

Question 50

Find the quotient and simplify.

- $\frac { ( y - 2 ) ^ { 2 } } { 3 } \div \frac { 3 y - 6 } { 9 }$

A) $\frac { 3 ( y - 2 ) ^ { 2 } } { 3 y - 6 }$
B) $\frac { 1 } { y - 2 }$
C)y - 2
D) $\frac { ( y - 2 ) ^ { 3 } } { 9 }$

Question 51

Find the product and simplify.

- $\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 3 x } { - 33 x - 33 }$

A) $- \frac { x ^ { 2 } + 1 } { 11 }$
B) $\frac { x + 1 } { 11 ( - x - 1 ) }$
C) $- \frac { x ^ { 3 } + 1 } { 11 ( x + 1 ) }$
D) $- \frac { 1 } { 11 }$

Question 52

Find the product and simplify.

- $\frac { x ^ { 2 } - 19 x + 84 } { x ^ { 2 } - 16 x + 55 } \cdot \frac { x ^ { 2 } - 11 x + 30 } { x ^ { 2 } - 17 x + 70 }$

A) $\frac { ( x - 12 ) } { ( x - 10 ) }$
B) $\frac { \left( x ^ { 2 } - 19 x + 84 \right) \left( x ^ { 2 } - 11 x + 30 \right) } { \left( x ^ { 2 } - 16 x + 55 \right) \left( x ^ { 2 } - 17 x + 70 \right) }$
C) $\frac { ( x + 12 ) ( x + 6 ) } { ( x + 11 ) ( x + 10 ) }$
D) $\frac { ( x - 12 ) ( x - 6 ) } { ( x - 11 ) ( x - 10 ) }$

Question 53

Find the quotient and simplify.

- $\frac { 7 x ^ { 11 } } { 9 x ^ { 6 } } \div \frac { 14 x } { 18 x ^ { 4 } }$

A) $\frac { 7 x ^ { 8 } } { 9 }$
B) $x ^ { 8 }$
C) $\frac { 98 x ^ { 2 } } { 162 }$
D) $\frac { 49 x ^ { 2 } } { 81 }$

Question 54

Find the quotient and simplify.

- $\frac { 8 m ^ { 2 } a } { 7 m a ^ { 2 } } \div \frac { 56 m ^ { 2 } a ^ { 2 } } { 40 m a }$

A) $\frac { 8 m ^ { 2 } } { 5 }$
B) $\frac { 8 } { 5 \mathrm { a } ^ { 2 } }$
C) $\frac { 8 \mathrm { ma } } { 5 }$
D) $\frac { 40 } { 49 a ^ { 2 } }$

Question 55

Solve the problem.

-Find the area of the rectangle.

A) $\frac { 7 } { 3 x ^ { 2 } ( x + 11 ) } \text { sq. ft }$
B) $\frac { 7 } { 3 x ^ { 2 } ( x - 11 ) } \text { sq. ft }$
C) $\frac { 7 x ^ { 2 } } { 3 ( x - 11 ) } \text { sq. } f t$
D) $\frac { 11 } { 3 x ^ { 3 } - 33 } \text { sq. ft }$

Question 56

Find the quotient and simplify.

- $\frac { 9 x - 9 } { 5 } \div \frac { 3 x - 3 } { 35 }$

A) $\frac { 27 ( x - 1 ) ^ { 2 } } { 175 }$
B) $\frac { 1 } { 21 }$
C) $\frac { 7 ( 9 x - 9 ) } { 3 x - 3 }$
D)21

Question 57

Find the quotient and simplify.

- $\frac { 2 x ^ { 2 } } { 5 } \div \frac { x ^ { 3 } } { 15 }$

A) $\frac { 30 x ^ { 2 } } { 5 x ^ { 3 } }$
B) $\frac { x } { 6 }$
C) $\frac { 6 x ^ { 2 } } { x ^ { 3 } }$
D) $\frac { 6 } { x }$

Question 58

Find the product and simplify.

- $\frac { x ^ { 2 } + 13 x + 40 } { x ^ { 2 } + 14 x + 48 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } - 3 x - 40 }$

A) $\frac { x } { x - 8 }$
B) $\frac { x ( x + 6 ) } { x - 8 }$
C) $\frac { 1 } { x - 8 }$
D) $\frac { x } { x ^ { 2 } + 14 x + 48 }$

Question 59

Find the product and simplify.

- $\frac { ( a - z ) ^ { 2 } } { a + z } \cdot \frac { a } { a ^ { 2 } - a z }$

A) $\frac { a - z } { a + z }$
B)1
C) $\frac { a + z } { a - z }$
D) $\frac { z } { a + z }$

Question 60

Find the product and simplify.

- $\frac { 9 x ^ { 4 } - 72 x } { 3 x ^ { 2 } - 12 } \cdot \frac { x ^ { 2 } + x - 2 } { 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x }$

A) $\frac { 3 x ( x - 1 ) ( x - 2 ) ^ { 2 } } { 4 ( x + 2 ) ^ { 2 } }$
B) $\frac { 3 x ( x - 1 ) } { 4 }$
C) $\frac { 3 ( x - 1 ) } { 4 }$
D) $\frac { 3 x ( x + 1 ) } { 4 }$

Question 61

Perform the indicated operation. Simplify if possible.

- $\frac { x + 2 } { 15 } + \frac { 2 } { 15 }$

A) $\frac { 4 x } { 30 }$
B) $\frac { x + 4 } { 15 }$
C) $\frac { 4 x } { 15 }$
D) $\frac { x + 4 } { 30 }$

Question 62

Multiply or divide as indicated.

- $\frac { x ^ { 2 } - 36 } { 6 y } \div \frac { 6 - x } { 12 x y }$

A)-2x(x - 6)
B)-2x(x + 6)
C)2x(x + 6)
D)2x(x - 6)

Question 63

Perform the indicated operation. Simplify if possible.

- $\frac { x } { 15 } + \frac { 7 } { 15 }$

A) $\frac { x + 7 } { 30 }$
B) $\frac { 7 x } { 15 }$
C) $\frac { 7 x } { 30 }$
D) $\frac { x + 7 } { 15 }$

Question 64

Find the quotient and simplify.

- $\frac { 30 x ^ { 2 } - 49 x y + 20 y ^ { 2 } } { 35 x ^ { 2 } - 48 x y + 16 y ^ { 2 } } + \frac { 30 x ^ { 2 } - 13 x y - 10 y ^ { 2 } } { 20 x ^ { 2 } - 17 x y - 10 y ^ { 2 } }$

A) $\frac { ( 6 x - 5 y ) ^ { 2 } } { ( 4 x - 5 y ) ( 7 x - 4 y ) }$
B) $\frac { ( 6 x + 5 y ) ^ { 2 } } { ( 4 x + 5 y ) ( 7 x + 4 y ) }$
C) $\frac { ( 7 x + 4 y ) } { ( 4 x + 5 y ) }$
D) $\frac { 4 x - 5 y } { 7 x - 4 y }$

Question 65

Convert as indicated.

-In a physics lab, Shelly recorded the speed of an object at 110 feet per second. Convert this speed to miles per hour. (Round to the nearest whole, if necessary.)

A)1 mph
B)396,000 mph
C) $\frac { 1 } { 48 }$ mph
D)75 mph

Question 66

Convert as indicated.
The meeting hall in the student union has 7200 square feet of floor space. Convert this to square yards.

A)21,600 square yards
B)2400 square yards
C)800 square yards
D)64,800 square yards

Question 67

Convert as indicated.
1008 square inches = ______ square feet

A)84
B)12,096
C)7
D)145,152

Question 68

Convert as indicated.

-The field behind one of the dormitories at State College contains approximately 400 square yards of grass. Convert this to square feet.

A)1200 square feet
B) $44 \frac { 4 } { 9 }$ square fee square feet
C)3600 square feet
D) $133 \frac { 1 } { 3 }$ square feet square fee

Question 69

Multiply or divide as indicated.

- $\frac { ( x + 4 ) ^ { 2 } } { x - 4 } \div \frac { x ^ { 2 } - 16 } { 4 x - 16 }$

A) $\frac { 4 ( x + 4 ) } { x - 4 }$
B) $\frac { ( x + 4 ) ^ { 3 } } { 4 ( x - 4 ) }$
C) $\frac { ( x + 4 ) ^ { 2 } } { ( x - 4 ) ^ { 2 } }$
D) $\frac { 8 \left( x ^ { 2 } + 16 \right) } { x ^ { 2 } - 16 }$

Question 70

Find the quotient and simplify.

- $\frac { x ^ { 2 } - 4 x + 4 } { 4 x - 8 } \div \frac { 9 x - 18 } { 36 }$

A) $\frac { ( x - 2 ) ^ { 2 } } { 16 }$
B) $\frac { x ^ { 2 } - 4 x + 4 } { ( x - 2 ) ^ { 2 } }$
C)36
D)1

Question 71

Perform the indicated operation. Simplify if possible.

- $\frac { 8 } { 15 + x } + \frac { x + 5 } { 15 + x }$

A) $\frac { x + 13 } { 15 + x }$
B) $\frac { 13 } { 15 }$
C) $\frac { x + 13 } { 30 + x }$
D) $\frac { 13 } { 30 }$

Question 72

Convert as indicated.

-13 square feet = ______ square inches

A)156
B)1872
C)169
D) $\frac { 13 } { 144 }$

Question 73

Multiply or divide as indicated.

- $\frac { x ^ { 2 } + 8 x } { 7 } \cdot \frac { 81 } { 9 x + 72 }$

A) $\frac { 81 x ^ { 2 } + 648 x } { 63 x + 504 }$
B) $\frac { x + 8 } { x + 9 }$
C) $\frac { x ^ { 2 } + 16 x + 72 } { 567 }$
D) $\frac { 9 x } { 7 }$

Question 74

Find the quotient and simplify.

- $\frac { p ^ { 2 } - 3 p + p q - 3 q } { 12 p ^ { 2 } - 12 q ^ { 2 } } \div \frac { p - 3 } { 7 p - 7 q }$

A) $\frac { ( p - 3 ) ^ { 2 } } { 84 ( p - q ) ^ { 2 } }$
B) $\frac { 7 \left( p ^ { 2 } - 3 p + p q - 3 q \right) } { 12 ( p + q ) ( p - 3 ) }$
C) $\frac { 7 } { 12 }$
D)1

Question 75

Find the quotient and simplify.

- $\frac { z ^ { 2 } + 11 z + 30 } { z ^ { 2 } + 13 z + 42 } \div \frac { z ^ { 2 } + 5 z } { z ^ { 2 } + 15 z + 56 }$

A) $\frac { z + 8 } { z }$
B) $\frac { z } { z ^ { 2 } + 13 z + 42 }$
C) $\frac { z + 8 } { z ^ { 2 } + 7 z }$
D)z + 8

Question 76

Multiply or divide as indicated.

- $\frac { x ^ { 2 } + 13 x + 36 } { x ^ { 2 } + 7 x + 12 } \cdot \frac { x ^ { 2 } + 10 x + 24 } { x ^ { 2 } + 16 x + 63 }$

A) $\frac { 1666 } { 1501 }$
B) $\frac { ( x + 6 ) ( x + 4 ) } { ( x + 7 ) ( x + 3 ) }$
C) $\frac { ( x + 7 ) ( x + 3 ) } { ( x + 6 ) ( x + 4 ) }$
D) $\frac { ( x + 9 ) ^ { 2 } ( x + 7 ) } { ( x + 6 ) ( x + 4 ) ( x + 3 ) }$

Question 77

Multiply or divide as indicated.

- $\frac { 4 x + 20 } { 6 } \div \frac { 3 x + 15 } { 15 }$

A) $\frac { 10 } { 3 }$
B) $\frac { 7 x + 35 } { 21 }$
C) $\frac { 2 } { 15 }$
D) $\frac { 4 x + 20 } { 18 x }$

Question 78

Find the quotient and simplify.

- $\frac { ( x + 7 ) } { ( x + 7 ) ( 4 x + 3 ) } \div \frac { 4 } { 4 x + 3 }$

A)4
B)1
C) $\frac { 1 } { 4 }$
D) $\frac { 4 } { ( 4 x + 3 ) ^ { 2 } }$

Question 79

Multiply or divide as indicated.

- $\frac { 5 x + 4 y } { x ^ { 2 } + 4 x y + 4 y ^ { 2 } } \cdot \frac { x + 2 y } { 2 }$

A) $\frac { 5 x ^ { 2 } + 8 x y + 8 y ^ { 2 } } { 2 x ^ { 2 } + 8 x y + 8 y ^ { 2 } }$
B) $\frac { 5 x ^ { 2 } + 8 x y } { 2 x ^ { 2 } + 8 x y + 8 y ^ { 2 } }$
C) $\frac { 5 x + 4 y } { 2 ( x + 2 y ) }$
D) $\frac { 7 } { 8 x y }$

Question 80

Convert as indicated.

-50 miles per hour = ______ feet per second (Round to the nearest whole, if necessary.)

A)264,000
B)4400
C) $\frac { 1 } { 72 }$
D)73