Question 1

Solve the equation.
-$$\frac { 2 } { t } = \frac { t } { 7 t - 24 }$$

Accepted Answer

A)  7,12 
B)  2,7 
C)  8,6 
D)  0,7 
A)  7,12 
B)  2,7 
C)  8,6 
D)  0,7

Question 2

Multiply and, if possible, simplify.
-$\frac { 3 z ^ { 3 } } { 5 } \cdot \frac { 30 } { z ^ { 2 } }$

Accepted Answer

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

Question 3

Subtract. Simplify, if possible.
-$$\frac { 2 x } { x ^ { 2 } - 5 x + 6 } - \frac { 8 } { x ^ { 2 } - 6 x + 8 }$$

Accepted Answer

A)  $\frac { 2 x - 8 } { ( x - 2 ) ( x - 3 ) ( x - 4 ) }$ 
B)  $\frac { 2 ( x - 6 ) } { ( x - 3 ) ( x - 4 ) }$ 
C)  $\frac { x - 6 } { ( x - 3 ) ( x - 4 ) }$ 
D)  $\frac { 2 } { ( x - 2 ) ( x - 3 ) }$ 
A)  $\frac { 2 x - 8 } { ( x - 2 ) ( x - 3 ) ( x - 4 ) }$ 
B)  $\frac { 2 ( x - 6 ) } { ( x - 3 ) ( x - 4 ) }$ 
C)  $\frac { x - 6 } { ( x - 3 ) ( x - 4 ) }$ 
D)  $\frac { 2 } { ( x - 2 ) ( x - 3 ) }$

Question 4

Simplify.
-$$\frac { 4 x ^ { 2 } - 8 x } { 6 x ^ { 2 } - 12 x }$$

Accepted Answer

A)  2 
B)  $\frac { 3 } { 2 }$ 
C)  $\frac { x - 2 } { 3 x - 6 }$ 
D)  $\frac { 2 } { 3 }$ 
A)  2 
B)  $\frac { 3 } { 2 }$ 
C)  $\frac { x - 2 } { 3 x - 6 }$ 
D)  $\frac { 2 } { 3 }$

Question 5

Solve the equation.
-$$\frac { - 2 x } { 3 x + 3 } = \frac { 7 x } { 6 x + 6 } + \frac { 2 x - 1 } { x + 1 }$$

Accepted Answer

A)  6 
B)  $\frac { 6 } { 23 }$ 
C)  $\frac { 1 } { 23 }$ 
D)  $- \frac { 6 } { 23 }$ 
A)  6 
B)  $\frac { 6 } { 23 }$ 
C)  $\frac { 1 } { 23 }$ 
D)  $- \frac { 6 } { 23 }$

Question 6

Find the ratio. Simplify, if possible.
-David's paycheck for a week at the video store was $135.43. If he worked 29 hours that week, what was his pay rate?

Accepted Answer

A) $4.63/hour 
B) $4.38/hour 
C) $4.84/hour 
D) $4.67/hour 
A) $4.63/hour 
B) $4.38/hour 
C) $4.84/hour 
D) $4.67/hour

Question 7

Solve.
-The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 394 vibrations per second and a wavelength of 11.4 ft. Find the wavelength of another tone that has a pitch of 430 vibrations per
Second. Round to the nearest hundredths when necessary.

Accepted Answer

A) 0.1 ft 
B) 10.45 ft 
C) 14,861.4 ft 
D) 1.05 ft 
A) 0.1 ft 
B) 10.45 ft 
C) 14,861.4 ft 
D) 1.05 ft

Question 8

Find an equation of variation in which y varies inversely as x and the following is true.
-$y = 0.5$, when $x = 24$

Accepted Answer

A)  $y = 12 x$ 
B)  $y = \frac { 15 } { x }$ 
C)  $y = \frac { 13 } { x }$ 
D)  $y = \frac { 12 } { x }$ 
A)  $y = 12 x$ 
B)  $y = \frac { 15 } { x }$ 
C)  $y = \frac { 13 } { x }$ 
D)  $y = \frac { 12 } { x }$

Question 9

Find an equation of variation in which the following are true.
-$y$ varies jointly as $x$ and $p$ and inversely as the square of $s$, and $y = \frac { 9 } { 2 }$ when $x = 1 , p = 9$, and $s = 4$.

Accepted Answer

A)  $y = \frac { 12x p ^ { 2 } } { s }$ 
B)  $y = \frac { 32 x ^ { 2 } p } { s ^ { 2 } }$ 
C)  $y = \frac { 8 x p } { s ^ { 2 } }$ 
D)  $\mathrm { y } = 9 \mathrm { xps } ^ { 2 }$ 
A)  $y = \frac { 12x p ^ { 2 } } { s }$ 
B)  $y = \frac { 32 x ^ { 2 } p } { s ^ { 2 } }$ 
C)  $y = \frac { 8 x p } { s ^ { 2 } }$ 
D)  $\mathrm { y } = 9 \mathrm { xps } ^ { 2 }$

Question 10

Add. Simplify, if possible.
-$$\frac { 4 } { r } + \frac { 9 } { r - 7 }$$

Accepted Answer

A)  $\frac { 13 r - 28 } { r ( 7 - r ) }$ 
B)  $\frac { 28 r - 13 } { r ( r - 7 ) }$ 
C)  $\frac { 13 r - 28 } { r ( r - 7 ) }$ 
D)  $\frac { 28 r - 13 } { r ( 7 - r ) }$ 
A)  $\frac { 13 r - 28 } { r ( 7 - r ) }$ 
B)  $\frac { 28 r - 13 } { r ( r - 7 ) }$ 
C)  $\frac { 13 r - 28 } { r ( r - 7 ) }$ 
D)  $\frac { 28 r - 13 } { r ( 7 - r ) }$

Question 11

Add. Simplify, if possible.
-$$\frac { 2 } { 2 x - 5 } + \frac { 8 } { 5 - 2 x }$$

Accepted Answer

A)  $\frac { - 6 } { 2 x - 5 }$ 
B)  $\frac { - 10 } { 2 x - 5 }$ 
C)  $\frac { 10 } { 2 x - 5 }$ 
D)  $\frac { 6 } { 2 x - 5 }$ 
A)  $\frac { - 6 } { 2 x - 5 }$ 
B)  $\frac { - 10 } { 2 x - 5 }$ 
C)  $\frac { 10 } { 2 x - 5 }$ 
D)  $\frac { 6 } { 2 x - 5 }$

Question 12

Find an equation of variation in which the following are true.
-f varies jointly as $q ^ { 2 }$ and $h$, and $f = 96$ when $q = 4$ and $h = 3$.

Accepted Answer

A)  $f = 2 q ^ { 2 } h$ 
B)  $f = \frac { 1 } { 4608 } q ^ { 2 } h$ 
C)  $f = 4608 q ^ { 2 } h$ 
D)  $f = \frac { 1 } { 2 } q ^ { 2 } h$ 
A)  $f = 2 q ^ { 2 } h$ 
B)  $f = \frac { 1 } { 4608 } q ^ { 2 } h$ 
C)  $f = 4608 q ^ { 2 } h$ 
D)  $f = \frac { 1 } { 2 } q ^ { 2 } h$

Question 13

Solve.
-The number of miles per gallon of gasoline that a car averages varies inversely as the average speed the car travels. A car gets 20 miles per gallon at 60 mph. How many miles per gallon will it get at 66 mph?

Accepted Answer

A) 22 miles per gallon 
B) 0.05 miles per gallon 
C) 18.2 miles per gallon 
D) 0.06 miles per gallon 
A) 22 miles per gallon 
B) 0.05 miles per gallon 
C) 18.2 miles per gallon 
D) 0.06 miles per gallon

Question 14

Solve.
-The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 60 miles per hour in 20 minutes, how fast must it travel to cover the same distance in 30 Minutes?

Accepted Answer

A) 40 miles per hour 
B) 10 miles per hour 
C) 90 miles per hour 
D) $\frac{1}{90} \text { miles per hour }$ 
A) 40 miles per hour 
B) 10 miles per hour 
C) 90 miles per hour 
D) $\frac{1}{90} \text { miles per hour }$

Question 15

Solve.
-The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the car's speed, and inversely as the radius of the curve. If a force of 3600 pounds is needed to keep an1800 pound car traveling at 20 mph from skidding on a curve of radius 600 feet, what force would be required To keep the same car from skidding on a curve of radius 550 feet at 60 mph? Round your answer to the nearest Pound of force?

Accepted Answer

A) 35,213 pounds 
B) 35,345 pounds 
C) 35,377 pounds 
D) 35,915 pounds 
A) 35,213 pounds 
B) 35,345 pounds 
C) 35,377 pounds 
D) 35,915 pounds

Question 16

Solve.
-It takes 11 hours for 6 people to paint a house. How long will it take 2 people to do the job?

Accepted Answer

A) 3.5 hr 
B) 29.7 hr 
C) 33 hr 
D) 3.7 hr 
A) 3.5 hr 
B) 29.7 hr 
C) 33 hr 
D) 3.7 hr

Question 17

Solve the equation.
-$$\frac { - 2 } { m - 3 } - \frac { 2 } { m + 3 } = \frac { 12 } { m ^ { 2 } - 9 }$$

Accepted Answer

A)  $- 3$ 
B)  3 
C)  12 
D)  $\sqrt { 7 }$ 
A)  $- 3$ 
B)  3 
C)  12 
D)  $\sqrt { 7 }$

Question 18

Find the equation of variation if the following is true.
-Suppose $r$ varies directly as $\mathrm { s }$ and $\mathrm { r } = 0.0714$ when $\mathrm { s } = 1$.

Accepted Answer

A)  $r = 14 \mathrm {~s}$ 
B)  $r = 0.0714 \mathrm {~s}$ 
C)  $\mathrm { r } = 15 \mathrm {~s}$ 
D)  $r = 13 s$ 
A)  $r = 14 \mathrm {~s}$ 
B)  $r = 0.0714 \mathrm {~s}$ 
C)  $\mathrm { r } = 15 \mathrm {~s}$ 
D)  $r = 13 s$

Question 19

Subtract. Simplify, if possible.
-$$\frac { 7 } { 1 - y } - \frac { 5 } { y - 1 }$$

Accepted Answer

A)  $\frac { 35 } { 1 - y }$ 
B)  $\frac { 2 } { 1 - y }$ 
C)  $\frac { 12 } { 1 - y }$ 
D)  $\frac { - 2 } { 1 - y }$ 
A)  $\frac { 35 } { 1 - y }$ 
B)  $\frac { 2 } { 1 - y }$ 
C)  $\frac { 12 } { 1 - y }$ 
D)  $\frac { - 2 } { 1 - y }$

Question 20

Simplify.
-$$\frac { y ^ { 2 } + 6 y - 16 } { y ^ { 2 } + 13 y + 40 }$$

Accepted Answer

A)  $\frac { 6 y - 16 } { 13 y + 40 }$ 
B)  $\frac { y - 2 } { y + 5 }$ 
C)  $- \frac { y ^ { 2 } + 6 y - 16 } { y ^ { 2 } + 13 y + 40 }$ 
D)  $\frac { 6 y + 16 } { 13 y - 13 }$ 
A)  $\frac { 6 y - 16 } { 13 y + 40 }$ 
B)  $\frac { y - 2 } { y + 5 }$ 
C)  $- \frac { y ^ { 2 } + 6 y - 16 } { y ^ { 2 } + 13 y + 40 }$ 
D)  $\frac { 6 y + 16 } { 13 y - 13 }$

Solve the equation. - $\frac { 2 } { t } = \frac { t } { 7 t - 24 }$

Multiply and, if possible, simplify. - $\frac { 3 z ^ { 3 } } { 5 } \cdot \frac { 30 } { z ^ { 2 } }$

Subtract. Simplify, if possible. - $\frac { 2 x } { x ^ { 2 } - 5 x + 6 } - \frac { 8 } { x ^ { 2 } - 6 x + 8 }$

Simplify. - $\frac { 4 x ^ { 2 } - 8 x } { 6 x ^ { 2 } - 12 x }$

Solve the equation. - $\frac { - 2 x } { 3 x + 3 } = \frac { 7 x } { 6 x + 6 } + \frac { 2 x - 1 } { x + 1 }$

Find the ratio. Simplify, if possible. -David's paycheck for a week at the video store was $135.43. If he worked 29 hours that week, what was his pay rate?

Solve. -The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 394 vibrations per second and a wavelength of 11.4 ft. Find the wavelength of another tone that has a pitch of 430 vibrations per Second. Round to the nearest hundredths when necessary.

Find an equation of variation in which y varies inversely as x and the following is true. - $y = 0.5$ , when $x = 24$

Find an equation of variation in which the following are true. - $y$ varies jointly as $x$ and $p$ and inversely as the square of $s$ , and $y = \frac { 9 } { 2 }$ when $x = 1 , p = 9$ , and $s = 4$ .

Add. Simplify, if possible. - $\frac { 4 } { r } + \frac { 9 } { r - 7 }$

Add. Simplify, if possible. - $\frac { 2 } { 2 x - 5 } + \frac { 8 } { 5 - 2 x }$

Find an equation of variation in which the following are true. -f varies jointly as $q ^ { 2 }$ and $h$ , and $f = 96$ when $q = 4$ and $h = 3$ .

Solve. -The number of miles per gallon of gasoline that a car averages varies inversely as the average speed the car travels. A car gets 20 miles per gallon at 60 mph. How many miles per gallon will it get at 66 mph?

Solve. -The speed of a vehicle is inversely proportional to the time it takes to travel a fixed distance. If a vehicle travels a fixed distance at 60 miles per hour in 20 minutes, how fast must it travel to cover the same distance in 30 Minutes?

Solve. -It takes 11 hours for 6 people to paint a house. How long will it take 2 people to do the job?

Solve the equation. - $\frac { - 2 } { m - 3 } - \frac { 2 } { m + 3 } = \frac { 12 } { m ^ { 2 } - 9 }$

Find the equation of variation if the following is true. -Suppose $r$ varies directly as $\mathrm { s }$ and $\mathrm { r } = 0.0714$ when $\mathrm { s } = 1$ .

Subtract. Simplify, if possible. - $\frac { 7 } { 1 - y } - \frac { 5 } { y - 1 }$

Simplify. - $\frac { y ^ { 2 } + 6 y - 16 } { y ^ { 2 } + 13 y + 40 }$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Filters

Exam 6: Rational Expressions and Equations

Solve the equation. - 2t=t7t−24\frac { 2 } { t } = \frac { t } { 7 t - 24 }t2​=7t−24t​

Multiply and, if possible, simplify. - 3z35⋅30z2\frac { 3 z ^ { 3 } } { 5 } \cdot \frac { 30 } { z ^ { 2 } }53z3​⋅z230​

Subtract. Simplify, if possible. - 2xx2−5x+6−8x2−6x+8\frac { 2 x } { x ^ { 2 } - 5 x + 6 } - \frac { 8 } { x ^ { 2 } - 6 x + 8 }x2−5x+62x​−x2−6x+88​

Simplify. - 4x2−8x6x2−12x\frac { 4 x ^ { 2 } - 8 x } { 6 x ^ { 2 } - 12 x }6x2−12x4x2−8x​

Solve the equation. - −2x3x+3=7x6x+6+2x−1x+1\frac { - 2 x } { 3 x + 3 } = \frac { 7 x } { 6 x + 6 } + \frac { 2 x - 1 } { x + 1 }3x+3−2x​=6x+67x​+x+12x−1​