Question 1

Solve the rational equation. $$\frac { t - 2 } { t - 1 } = \frac { t + 17 } { t ^ { 2 } - 1 } - \frac { 1 } { t + 1 }$$

Accepted Answer

A)  $\{ - 4,5 \}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ 7 , \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ - 3 , - \frac { 5 } { 2 } \right\}$ 
A)  $\{ - 4,5 \}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ 7 , \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ - 3 , - \frac { 5 } { 2 } \right\}$

Question 2

b is inversely proportional to c. If b is 5 when c is 12, find b when c = 20.

Accepted Answer

A)  b = 4 
B)  b = 15 
C)  b = 60 
D)  b = 3 
A)  b = 4 
B)  b = 15 
C)  b = 60 
D)  b = 3

Question 3

The two triangles pictured below are similar triangles. Find the missing length.

Accepted Answer

A)  10 feet 
B)  19 feet 
C)  17.5 feet 
D)  20 feet 
A)  10 feet 
B)  19 feet 
C)  17.5 feet 
D)  20 feet

Question 4

If a baseball player has a batting average of 0.350, his ratio of hits to at-bats 350 to 1000. How many base hits would a player with a batting average of 0.350 have if he had 520 at-bats?

Accepted Answer

A)  350 hits 
B)  338 hits 
C)  182 hits 
D)  162 hits 
A)  350 hits 
B)  338 hits 
C)  182 hits 
D)  162 hits

Question 5

Find the slope of the line that passes through the given points. $$\left( \frac { 2 } { 7 } , \frac { 3 } { 4 } \right) , ( 0 , - 1 )$$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 49 } { 8 }$ 
C)  $\frac { 2 } { 7 }$ 
D)  $\frac { 7 } { 2 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 49 } { 8 }$ 
C)  $\frac { 2 } { 7 }$ 
D)  $\frac { 7 } { 2 }$

Question 6

The stopping distance of a car is directly proportional to the square of the speed of the car. If a car traveling 40 mph has a stopping distance of 109 ft, find the stopping distance of a car traveling 25 Mph) (Round your answer to one decimal place.)

Accepted Answer

A)  42.6 ft 
B)  55.4 ft 
C)  68.1 ft 
D)  49.0 ft 
A)  42.6 ft 
B)  55.4 ft 
C)  68.1 ft 
D)  49.0 ft

Question 7

Solve for h. $$a + b = \frac { 2 A } { h }$$

Accepted Answer

A)  $h = \frac { a } { 2 A } - b$ 
B)  $h = \frac { a + b } { 2 A }$ 
C)  $h = \frac { 2 A } { a } - b$ 
D)  $h = \frac { 2 A } { a + b }$ 
A)  $h = \frac { a } { 2 A } - b$ 
B)  $h = \frac { a + b } { 2 A }$ 
C)  $h = \frac { 2 A } { a } - b$ 
D)  $h = \frac { 2 A } { a + b }$

Question 8

The recipe for a sheet cake calls for 7 cups of flour and 3 cups of sugar. Suppose you want to make as much cake batter as you can using all of the flour you have, which is 23 cups. How many cups of Sugar would you need? Round to the nearest tenth of a cup.

Accepted Answer

A)  16.4 cups 
B)  53.7 cups 
C)  9.9 cups 
D)  6.6 cups 
A)  16.4 cups 
B)  53.7 cups 
C)  9.9 cups 
D)  6.6 cups

Question 9

The ratio of men to women at one college is 4 to 5. If there are 1000 more women than men, how many women are there?

Accepted Answer

A)  4000 women 
B)  444 women 
C)  5000 women 
D)  4500 women 
A)  4000 women 
B)  444 women 
C)  5000 women 
D)  4500 women

Question 10

The number of hours it takes to paint a house is inversely proportional to the number of people painting. If it takes 4 workers 12.5 hours to paint a certain house, how long would it take 6 Workers? Round to one tenth of an hour.

Accepted Answer

A)  10.5 hours 
B)  25.0 hours 
C)  14.5 hours 
D)  8.3 hours 
A)  10.5 hours 
B)  25.0 hours 
C)  14.5 hours 
D)  8.3 hours

Question 11

Simplify the rational expression. $$\frac { 6 t ^ { 2 } + 10 t } { - 5 t ^ { 2 } }$$

Accepted Answer

The answer of Simplify the rational expression. \[\frac { 6...

Question 12

z varies directly as the square of t and z = 75 when t = 5. Find z when t = 3.

Accepted Answer

The answer of z varies directly as the square of...

Question 13

Find the constant of variation k.
T is inversely proportional to x and when x = 5, T = 15.

Accepted Answer

The answer of Find the constant of variation k.
T is...

Question 14

Perform the indicated operations. $$\frac { 5 x ^ { 2 } } { y } \cdot \frac { x } { 15 y ^ { 3 } } \div \frac { 10 y ^ { 7 } } { 25 x }$$

Accepted Answer

A)  $\frac { 6 y ^ { 11 } } { 5 x ^ { 4 } }$ 
B)  $\frac { 15 } { 2 x ^ { 2 } y ^ { 3 } }$ 
C)  $\frac { 5 x ^ { 4 } } { 6 y ^ { 11 } }$ 
D)  $\frac { 2 x ^ { 2 } y ^ { 3 } } { 15 }$ 
A)  $\frac { 6 y ^ { 11 } } { 5 x ^ { 4 } }$ 
B)  $\frac { 15 } { 2 x ^ { 2 } y ^ { 3 } }$ 
C)  $\frac { 5 x ^ { 4 } } { 6 y ^ { 11 } }$ 
D)  $\frac { 2 x ^ { 2 } y ^ { 3 } } { 15 }$

Question 15

Write the domain of the rational function in set-builder notation. $$f ( x ) = \frac { 3 } { x - 10 }$$

Accepted Answer

A)  $\{ x \mid x \neq 10 \}$ 
B)  $\{ x \mid x \neq - 10 \}$ 
C)  $\{ x \mid x \neq 10 , x \neq - 3 \}$ 
D)  $\{ x \mid x = 10 \}$ 
A)  $\{ x \mid x \neq 10 \}$ 
B)  $\{ x \mid x \neq - 10 \}$ 
C)  $\{ x \mid x \neq 10 , x \neq - 3 \}$ 
D)  $\{ x \mid x = 10 \}$

Question 16

Divide the rational expressions. $$\frac { 7 y - 1 } { y ^ { 2 } - 36 } \div \frac { 1 - 7 y } { y + 6 }$$

Accepted Answer

A)  $\frac { 1 } { 6 - y }$ 
B)  $\frac { 49 y ^ { 2 } - 1 } { y - 6 }$ 
C)  $\frac { ( 7 y - 1 ) ( 1 - 7 y ) } { ( y - 6 ) ( y + 6 ) ^ { 2 } }$ 
D)  $\frac { 1 } { y - 6 }$ 
A)  $\frac { 1 } { 6 - y }$ 
B)  $\frac { 49 y ^ { 2 } - 1 } { y - 6 }$ 
C)  $\frac { ( 7 y - 1 ) ( 1 - 7 y ) } { ( y - 6 ) ( y + 6 ) ^ { 2 } }$ 
D)  $\frac { 1 } { y - 6 }$

Question 17

In an average year, the ratio of days with rain to dry days in Fort Lauderdale is 26 to 47. How many rainy days are there in an average year?

Accepted Answer

The answer of In an average year, the ratio of...

Question 18

The recipe for a holiday punch calls for 7 cups of fruit drink and 3 cups of ginger ale. Suppose you want to make as much punch as you can using all of the fruit drink you have, which is 22 cups. How many cups of ginger ale would you need? Round to the nearest tenth of a cup.

Accepted Answer

A)  15.7 cups 
B)  51.3 cups 
C)  6.3 cups 
D)  9.4 cups 
A)  15.7 cups 
B)  51.3 cups 
C)  6.3 cups 
D)  9.4 cups

Question 19

Simplify the rational expression. $$\frac { x ^ { 3 } - 4 x ^ { 2 } + 2 x - 8 } { 3 x ^ { 2 } - 48 }$$

Accepted Answer

A)  $\frac { x ^ { 2 } + 2 } { 3 ( x + 4 ) } \quad ($ Provided $x \neq 4 )$ 
B)  $\frac { x ^ { 3 } + 2 x - 6 } { - 9 }$ (Provided $\left. x \neq - 4 \right)$ 
C)  $\frac { x ^ { 2 } + 2 } { 3 x - 12 }$ (Provided $x \neq - 4$ ) 
D)  $\frac { x ^ { 3 } - 4 x ^ { 2 } + 2 x - 8 } { 3 x ^ { 2 } - 48 }$; cannot be simplified 
A)  $\frac { x ^ { 2 } + 2 } { 3 ( x + 4 ) } \quad ($ Provided $x \neq 4 )$ 
B)  $\frac { x ^ { 3 } + 2 x - 6 } { - 9 }$ (Provided $\left. x \neq - 4 \right)$ 
C)  $\frac { x ^ { 2 } + 2 } { 3 x - 12 }$ (Provided $x \neq - 4$ ) 
D)  $\frac { x ^ { 3 } - 4 x ^ { 2 } + 2 x - 8 } { 3 x ^ { 2 } - 48 }$; cannot be simplified

Question 20

Fill in the blank to make an equivalent fraction with the given denominator. $$\frac { 3 } { y - 2 } = \frac { } { y ^ { 3 } + y ^ { 2 } - 6 y }$$

Accepted Answer

A)  $3 y ^ { 3 } + 3 y ^ { 2 } - 18 y$ 
B)  $3 y ^ { 2 } - 3$ 
C)  $3 y ^ { 2 } + 9 y$ 
D)  $y ^ { 2 } + 3 y$ 
A)  $3 y ^ { 3 } + 3 y ^ { 2 } - 18 y$ 
B)  $3 y ^ { 2 } - 3$ 
C)  $3 y ^ { 2 } + 9 y$ 
D)  $y ^ { 2 } + 3 y$

Solve the rational equation. $\frac { t - 2 } { t - 1 } = \frac { t + 17 } { t ^ { 2 } - 1 } - \frac { 1 } { t + 1 }$

b is inversely proportional to c. If b is 5 when c is 12, find b when c = 20.

The two triangles pictured below are similar triangles. Find the missing length.

If a baseball player has a batting average of 0.350, his ratio of hits to at-bats 350 to 1000. How many base hits would a player with a batting average of 0.350 have if he had 520 at-bats?

Find the slope of the line that passes through the given points. $\left( \frac { 2 } { 7 } , \frac { 3 } { 4 } \right) , ( 0 , - 1 )$

The stopping distance of a car is directly proportional to the square of the speed of the car. If a car traveling 40 mph has a stopping distance of 109 ft, find the stopping distance of a car traveling 25 Mph) (Round your answer to one decimal place.)

Solve for h. $a + b = \frac { 2 A } { h }$

The recipe for a sheet cake calls for 7 cups of flour and 3 cups of sugar. Suppose you want to make as much cake batter as you can using all of the flour you have, which is 23 cups. How many cups of Sugar would you need? Round to the nearest tenth of a cup.

The ratio of men to women at one college is 4 to 5. If there are 1000 more women than men, how many women are there?

The number of hours it takes to paint a house is inversely proportional to the number of people painting. If it takes 4 workers 12.5 hours to paint a certain house, how long would it take 6 Workers? Round to one tenth of an hour.

Simplify the rational expression. $\frac { 6 t ^ { 2 } + 10 t } { - 5 t ^ { 2 } }$

z varies directly as the square of t and z = 75 when t = 5. Find z when t = 3.

Find the constant of variation k. T is inversely proportional to x and when x = 5, T = 15.

Perform the indicated operations. $\frac { 5 x ^ { 2 } } { y } \cdot \frac { x } { 15 y ^ { 3 } } \div \frac { 10 y ^ { 7 } } { 25 x }$

Write the domain of the rational function in set-builder notation. $f ( x ) = \frac { 3 } { x - 10 }$

Divide the rational expressions. $\frac { 7 y - 1 } { y ^ { 2 } - 36 } \div \frac { 1 - 7 y } { y + 6 }$

In an average year, the ratio of days with rain to dry days in Fort Lauderdale is 26 to 47. How many rainy days are there in an average year?

The recipe for a holiday punch calls for 7 cups of fruit drink and 3 cups of ginger ale. Suppose you want to make as much punch as you can using all of the fruit drink you have, which is 22 cups. How many cups of ginger ale would you need? Round to the nearest tenth of a cup.

Simplify the rational expression. $\frac { x ^ { 3 } - 4 x ^ { 2 } + 2 x - 8 } { 3 x ^ { 2 } - 48 }$

Fill in the blank to make an equivalent fraction with the given denominator. $\frac { 3 } { y - 2 } = \frac { } { y ^ { 3 } + y ^ { 2 } - 6 y }$

Linear Equations and Inequalities in One Variable

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Exam 5: Rational Expressions and Rational Equations

Solve the rational equation. t−2t−1=t+17t2−1−1t+1\frac { t - 2 } { t - 1 } = \frac { t + 17 } { t ^ { 2 } - 1 } - \frac { 1 } { t + 1 }t−1t−2​=t2−1t+17​−t+11​

b is inversely proportional to c. If b is 5 when c is 12, find b when c = 20.

The two triangles pictured below are similar triangles. Find the missing length.

If a baseball player has a batting average of 0.350, his ratio of hits to at-bats 350 to 1000. How many base hits would a player with a batting average of 0.350 have if he had 520 at-bats?

Find the slope of the line that passes through the given points. (27,34),(0,−1)\left( \frac { 2 } { 7 } , \frac { 3 } { 4 } \right) , ( 0 , - 1 )(72​,43​),(0,−1)

The stopping distance of a car is directly proportional to the square of the speed of the car. If a car traveling 40 mph has a stopping distance of 109 ft, find the stopping distance of a car traveling 25 Mph) (Round your answer to one decimal place.)

Solve for h. a+b=2Aha + b = \frac { 2 A } { h }a+b=h2A​

The recipe for a sheet cake calls for 7 cups of flour and 3 cups of sugar. Suppose you want to make as much cake batter as you can using all of the flour you have, which is 23 cups. How many cups of Sugar would you need? Round to the nearest tenth of a cup.

The ratio of men to women at one college is 4 to 5. If there are 1000 more women than men, how many women are there?

The number of hours it takes to paint a house is inversely proportional to the number of people painting. If it takes 4 workers 12.5 hours to paint a certain house, how long would it take 6 Workers? Round to one tenth of an hour.

Simplify the rational expression. 6t2+10t−5t2\frac { 6 t ^ { 2 } + 10 t } { - 5 t ^ { 2 } }−5t26t2+10t​

z varies directly as the square of t and z = 75 when t = 5. Find z when t = 3.

Find the constant of variation k. T is inversely proportional to x and when x = 5, T = 15.

Perform the indicated operations. 5x2y⋅x15y3÷10y725x\frac { 5 x ^ { 2 } } { y } \cdot \frac { x } { 15 y ^ { 3 } } \div \frac { 10 y ^ { 7 } } { 25 x }y5x2​⋅15y3x​÷25x10y7​

Write the domain of the rational function in set-builder notation. f(x)=3x−10f ( x ) = \frac { 3 } { x - 10 }f(x)=x−103​

Divide the rational expressions. 7y−1y2−36÷1−7yy+6\frac { 7 y - 1 } { y ^ { 2 } - 36 } \div \frac { 1 - 7 y } { y + 6 }y2−367y−1​÷y+61−7y​

In an average year, the ratio of days with rain to dry days in Fort Lauderdale is 26 to 47. How many rainy days are there in an average year?

The recipe for a holiday punch calls for 7 cups of fruit drink and 3 cups of ginger ale. Suppose you want to make as much punch as you can using all of the fruit drink you have, which is 22 cups. How many cups of ginger ale would you need? Round to the nearest tenth of a cup.

Simplify the rational expression. x3−4x2+2x−83x2−48\frac { x ^ { 3 } - 4 x ^ { 2 } + 2 x - 8 } { 3 x ^ { 2 } - 48 }3x2−48x3−4x2+2x−8​

Fill in the blank to make an equivalent fraction with the given denominator. 3y−2=y3+y2−6y\frac { 3 } { y - 2 } = \frac { } { y ^ { 3 } + y ^ { 2 } - 6 y }y−23​=y3+y2−6y​

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

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Solve the rational equation. $\frac { t - 2 } { t - 1 } = \frac { t + 17 } { t ^ { 2 } - 1 } - \frac { 1 } { t + 1 }$

Find the slope of the line that passes through the given points. $\left( \frac { 2 } { 7 } , \frac { 3 } { 4 } \right) , ( 0 , - 1 )$

Solve for h. $a + b = \frac { 2 A } { h }$

Simplify the rational expression. $\frac { 6 t ^ { 2 } + 10 t } { - 5 t ^ { 2 } }$

Perform the indicated operations. $\frac { 5 x ^ { 2 } } { y } \cdot \frac { x } { 15 y ^ { 3 } } \div \frac { 10 y ^ { 7 } } { 25 x }$

Write the domain of the rational function in set-builder notation. $f ( x ) = \frac { 3 } { x - 10 }$

Divide the rational expressions. $\frac { 7 y - 1 } { y ^ { 2 } - 36 } \div \frac { 1 - 7 y } { y + 6 }$

Simplify the rational expression. $\frac { x ^ { 3 } - 4 x ^ { 2 } + 2 x - 8 } { 3 x ^ { 2 } - 48 }$

Fill in the blank to make an equivalent fraction with the given denominator. $\frac { 3 } { y - 2 } = \frac { } { y ^ { 3 } + y ^ { 2 } - 6 y }$