Question 1

Simplify the complex fraction by using Method II. $$\frac { t + 3 t ^ { 2 } } { 5 - 2 t ^ { - 1 } }$$

Accepted Answer

A)  $\frac { 5 - 2 t ^ { 2 } } { 4 t }$ 
B)  $\frac { 4 t } { 5 - 2 t ^ { 2 } }$ 
C)  $\frac { t ^ { 3 } + 3 } { 5 t ^ { 2 } - 2 t }$ 
D)  $\frac { t ^ { 3 } + 3 } { 5 t ^ { 3 } - 2 t ^ { 2 } }$

Question 2

Write the domain of the rational function in interval notation. $$g ( t ) = \frac { 5 - t } { t ^ { 2 } + 4 }$$

Accepted Answer

A)  $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
B)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( - 2,2 ) \cup ( 2 , \infty )$ 
D)  $( - \infty , \infty )$

Question 3

Solve the proportion. $$\frac { 5 } { z + 5 } = \frac { - 3 } { 5 z }$$

Accepted Answer

A)  $\left\{ - \frac { 14 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 15 } { 28 } \right\}$ 
C)  $\{ 0 , - 5 \}$ 
D)  $\{ - 5,5 \}$

Question 4

Solve the rational equation. $$\frac { 1 } { x - 4 } - \frac { 5 } { x + 1 } = \frac { 1 } { x ^ { 2 } - 3 x - 4 }$$

Accepted Answer

The answer of Solve the rational equation. \[\frac { 1...

Question 5

Q varies inversely as the square of p, and Q = 36 when p = 7. Find Q when p = 6 .

Accepted Answer

A)  Q = 1764 
B)  Q = 42 
C)  Q = 49 
D)  Q = 6

Question 6

Write a variation model. Use k as the constant of variation. Q is directly proportional to the square of x and inversely proportional to the cube of y.

Accepted Answer

A)  $Q = \frac { k x ^ { 2 } } { y ^ { 3 } }$ 
B)  $Q = \frac { k x ^ { 2 } } { \sqrt [ 3 ] { y } }$ 
C)  $Q = k x ^ { 2 } y ^ { 3 }$ 
D)  $Q = k x ^ { 2 } + \frac { k } { y ^ { 3 } }$

Question 7

A bus driver follows a morning route and an afternoon route each day. Because there are more cities on the morning route, the average speed is 12 miles per hour less than the afternoon route.
She covers 70 miles on the morning route in the same amount of time as she covers 100 miles on the Afternoon route. Find her average speed on the afternoon route.

Accepted Answer

A)  51 miles per hour 
B)  40 miles per hour 
C)  36 miles per hour 
D)  28 miles per hour

Question 8

Evaluate the rational function, if possible. $$f ( x ) = \frac { 8 } { 8 x - 1 } ; f ( 3 ) , f ( - 2 )$$

Accepted Answer

The answer of Evaluate the rational function, if possible. \[f...

Question 9

B varies directly as m and inversely as n, and B = 44 when m = 11 and n = 3. Find B when m = 15 and n = 16.

Accepted Answer

A)  $B = \frac { 3 } { 4 }$ 
B)  $B = \frac { 15 } { 16 }$ 
C)  $B = \frac { 45 } { 4 }$ 
D)  $B = 12$

Question 10

Write the domain of the function in interval notation and use that information to graph the function. $$n ( x ) = \frac { 1 } { x + 3 }$$

Accepted Answer

A)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$
 
B)  $( - \infty , 3 ) \cup ( 3 , \infty )$
 
C)  $( - \infty , 1 ) \cup ( 1 , \infty )$
 
D)  $( - \infty , - 1 ) \cup ( - 1 , \infty )$

Question 11

A bottle of liquid pool chlorine has a recommended daily dosage of 12 ounces per 10,000 gallons of water. At this rate, how many ounces would be needed in a 22,000 gallon pool?

Accepted Answer

A)  26.4 oz 
B)  31.5 oz 
C)  22 oz 
D)  16 oz

Question 12

Multiply the rational expressions. $$\frac { 6 t ^ { 2 } - 4 t - 2 } { 3 } \cdot \frac { 9 t ^ { 2 } + 45 t } { 3 t ^ { 3 } + t ^ { 2 } }$$

Accepted Answer

A)  $6 ( t - 2 ) ( t + 15 )$ 
B)  $\frac { 54 t ( t + 9 ) } { t + 1 }$ 
C)  $\frac { 3 ( t + 5 ) } { t ^ { 2 } ( t + 1 ) }$ 
D)  $\frac { 6 ( t - 1 ) ( t + 5 ) } { t }$

Question 13

Solve the rational equation. $$\frac { 15 } { p - 40 } = \frac { 3 p - 21 } { p - 40 } - \frac { 3 } { p }$$

Accepted Answer

The answer of Solve the rational equation. \[\frac { 15...

Question 14

Solve for $d _ { 1 }$.
$$\frac { 1 } { f } = \frac { 1 } { d _ { 1 } } + \frac { 1 } { d _ { 2 } }$$

Accepted Answer

A)  $d _ { 1 } = \frac { d _ { 2 } f - d _ { 1 } f } { d _ { 2 } }$ 
B)  $d _ { 1 } = \frac { 1 } { f - d _ { 2 } }$ 
C)  $d _ { 1 } = f - d _ { 2 }$ 
D)  $d _ { 1 } = \frac { f d _ { 2 } } { d _ { 2 } - f }$

Question 15

In the equation $v = \frac { 1 } { 10 } w$ does v vary directly or inversely with w?

Accepted Answer

A)  Directly 
B)  Inversely

Question 16

On August 19, 2002, the ratio of stocks gaining value on the New York Stock Exchange to stocks losing value was about 43 to 20. If 869 stocks lost value, how many gained? Round to the nearest Whole number.

Accepted Answer

A)  1797 stocks 
B)  892 stocks 
C)  1953 stocks 
D)  1868 stocks

Question 17

Solve the rational equation. $$\frac { 3 } { x } + \frac { 3 } { x - 4 } = \frac { 3 x - 9 } { x - 4 }$$

Accepted Answer

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

Question 18

Simplify the complex fraction by using Method II. $$\frac { 2 - \frac { 5 } { 3 } + \frac { 13 } { 2 } } { \frac { 15 } { 2 } + 6 }$$

Accepted Answer

A)  $\frac { 41 } { 81 }$ 
B)  $\frac { 81 } { 41 }$ 
C)  $\frac { 20 } { 73 }$ 
D)  $\frac { 73 } { 20 }$

Question 19

It takes Terrell 74 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 54 minutes. How long would it take them working together? Round to the nearest tenth of a minute.

Accepted Answer

The answer of It takes Terrell 74 minutes to weed...

Question 20

Solve the rational equation. $$\frac { 15 } { 2 } y + \frac { 1 } { 3 } = \frac { 5 } { 4 } y$$

Accepted Answer

A)  $\left\{ - \frac { 4 } { 75 } \right\}$ 
B)  $\{ - 4 \}$ 
C)  $\left\{ - \frac { 1 } { 10 } \right\}$ 
D)  $\left\{ \frac { 4 } { 105 } \right\}$

Exam 5: Rational Expressions and Rational Equations

Simplify the complex fraction by using Method II. $\frac { t + 3 t ^ { 2 } } { 5 - 2 t ^ { - 1 } }$

Write the domain of the rational function in interval notation. $g ( t ) = \frac { 5 - t } { t ^ { 2 } + 4 }$

Solve the proportion. $\frac { 5 } { z + 5 } = \frac { - 3 } { 5 z }$

Solve the rational equation. $\frac { 1 } { x - 4 } - \frac { 5 } { x + 1 } = \frac { 1 } { x ^ { 2 } - 3 x - 4 }$

Q varies inversely as the square of p, and Q = 36 when p = 7. Find Q when p = 6 .

Write a variation model. Use k as the constant of variation. Q is directly proportional to the square of x and inversely proportional to the cube of y.

Evaluate the rational function, if possible. $f ( x ) = \frac { 8 } { 8 x - 1 } ; f ( 3 ) , f ( - 2 )$

B varies directly as m and inversely as n, and B = 44 when m = 11 and n = 3. Find B when m = 15 and n = 16.

Write the domain of the function in interval notation and use that information to graph the function. $n ( x ) = \frac { 1 } { x + 3 }$

A bottle of liquid pool chlorine has a recommended daily dosage of 12 ounces per 10,000 gallons of water. At this rate, how many ounces would be needed in a 22,000 gallon pool?

Multiply the rational expressions. $\frac { 6 t ^ { 2 } - 4 t - 2 } { 3 } \cdot \frac { 9 t ^ { 2 } + 45 t } { 3 t ^ { 3 } + t ^ { 2 } }$

Solve the rational equation. $\frac { 15 } { p - 40 } = \frac { 3 p - 21 } { p - 40 } - \frac { 3 } { p }$

Solve for $d _ { 1 }$ . $\frac { 1 } { f } = \frac { 1 } { d _ { 1 } } + \frac { 1 } { d _ { 2 } }$

In the equation $v = \frac { 1 } { 10 } w$ does v vary directly or inversely with w?

On August 19, 2002, the ratio of stocks gaining value on the New York Stock Exchange to stocks losing value was about 43 to 20. If 869 stocks lost value, how many gained? Round to the nearest Whole number.

Solve the rational equation. $\frac { 3 } { x } + \frac { 3 } { x - 4 } = \frac { 3 x - 9 } { x - 4 }$

Simplify the complex fraction by using Method II. $\frac { 2 - \frac { 5 } { 3 } + \frac { 13 } { 2 } } { \frac { 15 } { 2 } + 6 }$

It takes Terrell 74 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 54 minutes. How long would it take them working together? Round to the nearest tenth of a minute.

Solve the rational equation. $\frac { 15 } { 2 } y + \frac { 1 } { 3 } = \frac { 5 } { 4 } y$

Exam 5: Rational Expressions and Rational Equations

Simplify the complex fraction by using Method II. t+3t25−2t−1\frac { t + 3 t ^ { 2 } } { 5 - 2 t ^ { - 1 } }5−2t−1t+3t2​

Write the domain of the rational function in interval notation. g(t) =5−tt2+4g ( t ) = \frac { 5 - t } { t ^ { 2 } + 4 }g(t) =t2+45−t​

Solve the proportion. 5z+5=−35z\frac { 5 } { z + 5 } = \frac { - 3 } { 5 z }z+55​=5z−3​

Solve the rational equation. 1x−4−5x+1=1x2−3x−4\frac { 1 } { x - 4 } - \frac { 5 } { x + 1 } = \frac { 1 } { x ^ { 2 } - 3 x - 4 }x−41​−x+15​=x2−3x−41​

Q varies inversely as the square of p, and Q = 36 when p = 7. Find Q when p = 6 .

Write a variation model. Use k as the constant of variation. Q is directly proportional to the square of x and inversely proportional to the cube of y.

Evaluate the rational function, if possible. f(x)=88x−1;f(3),f(−2)f ( x ) = \frac { 8 } { 8 x - 1 } ; f ( 3 ) , f ( - 2 )f(x)=8x−18​;f(3),f(−2)

B varies directly as m and inversely as n, and B = 44 when m = 11 and n = 3. Find B when m = 15 and n = 16.

Write the domain of the function in interval notation and use that information to graph the function. n(x) =1x+3n ( x ) = \frac { 1 } { x + 3 }n(x) =x+31​

A bottle of liquid pool chlorine has a recommended daily dosage of 12 ounces per 10,000 gallons of water. At this rate, how many ounces would be needed in a 22,000 gallon pool?

Multiply the rational expressions. 6t2−4t−23⋅9t2+45t3t3+t2\frac { 6 t ^ { 2 } - 4 t - 2 } { 3 } \cdot \frac { 9 t ^ { 2 } + 45 t } { 3 t ^ { 3 } + t ^ { 2 } }36t2−4t−2​⋅3t3+t29t2+45t​

Solve the rational equation. 15p−40=3p−21p−40−3p\frac { 15 } { p - 40 } = \frac { 3 p - 21 } { p - 40 } - \frac { 3 } { p }p−4015​=p−403p−21​−p3​

Solve for d1d _ { 1 }d1​ . 1f=1d1+1d2\frac { 1 } { f } = \frac { 1 } { d _ { 1 } } + \frac { 1 } { d _ { 2 } }f1​=d1​1​+d2​1​

In the equation v=110wv = \frac { 1 } { 10 } wv=101​w does v vary directly or inversely with w?

On August 19, 2002, the ratio of stocks gaining value on the New York Stock Exchange to stocks losing value was about 43 to 20. If 869 stocks lost value, how many gained? Round to the nearest Whole number.

Solve the rational equation. 3x+3x−4=3x−9x−4\frac { 3 } { x } + \frac { 3 } { x - 4 } = \frac { 3 x - 9 } { x - 4 }x3​+x−43​=x−43x−9​

Simplify the complex fraction by using Method II. 2−53+132152+6\frac { 2 - \frac { 5 } { 3 } + \frac { 13 } { 2 } } { \frac { 15 } { 2 } + 6 }215​+62−35​+213​​

It takes Terrell 74 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 54 minutes. How long would it take them working together? Round to the nearest tenth of a minute.

Solve the rational equation. 152y+13=54y\frac { 15 } { 2 } y + \frac { 1 } { 3 } = \frac { 5 } { 4 } y215​y+31​=45​y

Simplify the complex fraction by using Method II. $\frac { t + 3 t ^ { 2 } } { 5 - 2 t ^ { - 1 } }$

Write the domain of the rational function in interval notation. $g ( t ) = \frac { 5 - t } { t ^ { 2 } + 4 }$

Solve the proportion. $\frac { 5 } { z + 5 } = \frac { - 3 } { 5 z }$

Solve the rational equation. $\frac { 1 } { x - 4 } - \frac { 5 } { x + 1 } = \frac { 1 } { x ^ { 2 } - 3 x - 4 }$

Evaluate the rational function, if possible. $f ( x ) = \frac { 8 } { 8 x - 1 } ; f ( 3 ) , f ( - 2 )$

Write the domain of the function in interval notation and use that information to graph the function. $n ( x ) = \frac { 1 } { x + 3 }$

Multiply the rational expressions. $\frac { 6 t ^ { 2 } - 4 t - 2 } { 3 } \cdot \frac { 9 t ^ { 2 } + 45 t } { 3 t ^ { 3 } + t ^ { 2 } }$

Solve the rational equation. $\frac { 15 } { p - 40 } = \frac { 3 p - 21 } { p - 40 } - \frac { 3 } { p }$

Solve for $d _ { 1 }$ . $\frac { 1 } { f } = \frac { 1 } { d _ { 1 } } + \frac { 1 } { d _ { 2 } }$

In the equation $v = \frac { 1 } { 10 } w$ does v vary directly or inversely with w?

Solve the rational equation. $\frac { 3 } { x } + \frac { 3 } { x - 4 } = \frac { 3 x - 9 } { x - 4 }$

Simplify the complex fraction by using Method II. $\frac { 2 - \frac { 5 } { 3 } + \frac { 13 } { 2 } } { \frac { 15 } { 2 } + 6 }$

Solve the rational equation. $\frac { 15 } { 2 } y + \frac { 1 } { 3 } = \frac { 5 } { 4 } y$