Question 1

Perform the indicated operation and simplify. $$\frac { p ^ { 3 } r ^ { 2 } } { c d } \cdot c ^ { - 4 } d ^ { 3 }$$

Accepted Answer

A)  $\frac { p ^ { 3 } r ^ { 2 } d } { c ^ { 5 } }$ 
B)  $\frac { p ^ { 3 } r ^ { 2 } d ^ { 2 } } { c ^ { 5 } }$ 
C)  $\frac { c r ^ { 2 } d } { p ^ { 5 } }$ 
D)  $\frac { p ^ { 2 } r d ^ { 5 } } { d ^ { 2 } }$ 
E)  $\frac { p r ^ { 2 } d ^ { 2 } } { c ^ { 5 } }$ 
A)  $\frac { p ^ { 3 } r ^ { 2 } d } { c ^ { 5 } }$ 
B)  $\frac { p ^ { 3 } r ^ { 2 } d ^ { 2 } } { c ^ { 5 } }$ 
C)  $\frac { c r ^ { 2 } d } { p ^ { 5 } }$ 
D)  $\frac { p ^ { 2 } r d ^ { 5 } } { d ^ { 2 } }$ 
E)  $\frac { p r ^ { 2 } d ^ { 2 } } { c ^ { 5 } }$ B

Question 2

A dealer bought some cell phones for a total of $1,066. He gave away 1 cell phone as a gift, sold the rest for $15 more then he paid for each cell phone, and earned $98. How many cell phones did he buy?

Accepted Answer

A) 14 
B) 12 
C) 15 
D) 13 
E) 11 
A) 14 
B) 12 
C) 15 
D) 13 
E) 11 D

Question 3

Solve $d = \frac { 4 c b } { c - b }$ for c .

Accepted Answer

A)  $c = \frac { b d } { 4 b - 1 }$ 
B)  $c = \frac { 1 } { 4 }$ 
C)  $c = \frac { d ( c - b ) } { 4 b }$ 
D)  $c = - \frac { b d } { 4 b - d }$ 
A)  $c = \frac { b d } { 4 b - 1 }$ 
B)  $c = \frac { 1 } { 4 }$ 
C)  $c = \frac { d ( c - b ) } { 4 b }$ 
D)  $c = - \frac { b d } { 4 b - d }$ D

Question 4

Perform the indicated operation and simplify. $$\frac { 6 } { z } \cdot z ^ { 3 }$$

Accepted Answer

A)  $\frac { z ^ { 1 } } { 6 }$ 
B)  $\frac { 6 } { z ^ { 4 } }$ 
C)  $6 z ^ { 2 }$ 
D)  $6 z ^ { 4 }$ 
A)  $\frac { z ^ { 1 } } { 6 }$ 
B)  $\frac { 6 } { z ^ { 4 } }$ 
C)  $6 z ^ { 2 }$ 
D)  $6 z ^ { 4 }$

Question 5

A model railroad engine is 2 inches long. If the scale is 168 feet to 1 foot, how long is the real engine?

Accepted Answer

A) 31 
B) 29 
C) 26 
D) 34 
E) 28 
A) 31 
B) 29 
C) 26 
D) 34 
E) 28

Question 6

A man roller-blades at a rate 5 miles per hour faster than he jogs. In the same time it takes him to roller-blade 6 miles he can jog 3 miles. How fast does he jog?

Accepted Answer

A) 4 mph 
B) 3 mph 
C) 5 mph 
D) 1 mph 
E) 2 mph 
A) 4 mph 
B) 3 mph 
C) 5 mph 
D) 1 mph 
E) 2 mph

Question 7

Evaluate the following expression for the given value of the variable. $\frac { x - 8 } { 4 }$ for $x = 28$

Accepted Answer

A)  $-$ 20 
B) 13 
C) 20 
D) 5 
E)  $-$ 5 
A)  $-$ 20 
B) 13 
C) 20 
D) 5 
E)  $-$ 5

Question 8

Perform the indicated operation. Simplify the answer if possible. $$\frac { t + 6 } { t - 3 } - \frac { t + 10 } { 3 - t }$$

Accepted Answer

A)  $\frac { 2 t + 16 } { t - 3 }$ 
B)  $\frac { 2 t + 16 } { t + 3 }$ 
C)  $\frac { 2 t - 16 } { t + 3 }$ 
D)  $\frac { 2 t - 16 } { t - 3 }$ 
E) none of these 
A)  $\frac { 2 t + 16 } { t - 3 }$ 
B)  $\frac { 2 t + 16 } { t + 3 }$ 
C)  $\frac { 2 t - 16 } { t + 3 }$ 
D)  $\frac { 2 t - 16 } { t - 3 }$ 
E) none of these

Question 9

Write the ratio 27 feet to 12 yards as a fraction in simplest form. ( Hint : 3 feet = 1 yard.)

Accepted Answer

A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 4 } { 3 }$ 
C)  $4$ 
D)  $\frac { 1 } { 3 }$ 
E)  $3$ 
A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 4 } { 3 }$ 
C)  $4$ 
D)  $\frac { 1 } { 3 }$ 
E)  $3$

Question 10

Perform the indicated operation. $$\frac { 8 a } { y } - \frac { 6 a } { y }$$

Accepted Answer

The answer of Perform the indicated operation. \[\frac { 8...

Question 11

Perform the indicated division and express your answer in simplest form. $$\frac { 4 s ^ { 2 } + 3 s r - r ^ { 2 } } { s ^ { 2 } r } \div \frac { 5 s ^ { 2 } + 4 s r - r ^ { 2 } } { r }$$

Accepted Answer

A)  $\frac { 5 s + r } { s ^ { 2 } ( 4 s + r ) }$ 
B)  $\frac { 4 s + r } { s ^ { 2 } ( 5 s - r ) }$ 
C)  $\frac { 5 s - r } { s ^ { 2 } ( 4 s - r ) }$ 
D)  $\frac { 4 s - r } { s ^ { 2 } ( 5 s - r ) }$ 
E)  $\frac { 4 s - r } { s ^ { 2 } ( 5 s + r ) }$ 
A)  $\frac { 5 s + r } { s ^ { 2 } ( 4 s + r ) }$ 
B)  $\frac { 4 s + r } { s ^ { 2 } ( 5 s - r ) }$ 
C)  $\frac { 5 s - r } { s ^ { 2 } ( 4 s - r ) }$ 
D)  $\frac { 4 s - r } { s ^ { 2 } ( 5 s - r ) }$ 
E)  $\frac { 4 s - r } { s ^ { 2 } ( 5 s + r ) }$

Question 12

Express the sentence as a formula. Assume that $k$ is a constant of variation. The distance $S$ that a body falls varies directly with the square of the time $z$ .

Accepted Answer

A)  $s = \frac { k } { z ^ { 2 } }$ 
B)  $s = k + z ^ { 2 }$ 
C)  $s = k z ^ { 2 }$ 
D)  $s = k - z ^ { 2 }$ 
E)  $s = \frac { z ^ { 2 } } { k }$ 
A)  $s = \frac { k } { z ^ { 2 } }$ 
B)  $s = k + z ^ { 2 }$ 
C)  $s = k z ^ { 2 }$ 
D)  $s = k - z ^ { 2 }$ 
E)  $s = \frac { z ^ { 2 } } { k }$

Question 13

Solve for the variable in the proportion. $$\frac { 3 } { 5 } = \frac { x } { 15 }$$

Accepted Answer

A)  $x = 7$ 
B)  $x = 9$ 
C)  $x = 10$ 
D)  $x = 12$ 
E)  $x = 6$ 
A)  $x = 7$ 
B)  $x = 9$ 
C)  $x = 10$ 
D)  $x = 12$ 
E)  $x = 6$

Question 14

Evaluate: $\frac { - x - 8 } { x ^ { 2 } - 4 x - 12 } \text { for } x = - 4$

Accepted Answer

A)  $- \frac { 3 } { 5 }$ 
B)  $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $- \frac { 1 } { 2 }$ 
A)  $- \frac { 3 } { 5 }$ 
B)  $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $- \frac { 1 } { 2 }$

Question 15

Solve the formula for t : $$\frac { 5 } { y } + \frac { 2 } { t } = 7$$

Accepted Answer

The answer of Solve the formula for t : \[\frac...

Question 16

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.)Round your answer to the nearest integer.

Accepted Answer

A) x = 870 ft 
B) x = 813 ft 
C) x = 845 ft 
D) x = 885 ft 
E) x = 833 ft 
A) x = 870 ft 
B) x = 813 ft 
C) x = 845 ft 
D) x = 885 ft 
E) x = 833 ft

Question 17

Write the ratio as a fraction in simplest form. $3$ inches to $12$ inches

Accepted Answer

A)  $\frac { 4 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $4$ 
D)  $\frac { 4 } { 3 }$ 
E)  $\frac { 3 } { 4 }$ 
A)  $\frac { 4 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $4$ 
D)  $\frac { 4 } { 3 }$ 
E)  $\frac { 3 } { 4 }$

Question 18

Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree.

Accepted Answer

A) h = 27 ft 
B) h = 42 ft 
C) h = 30 ft 
D) h = 35 ft 
E) h = 22 ft 
A) h = 27 ft 
B) h = 42 ft 
C) h = 30 ft 
D) h = 35 ft 
E) h = 22 ft

Question 19

Perform the indicated operation. Simplify the answer if possible. $$\frac { 5 } { a + 9 } - \frac { 2 } { - 9 - a }$$

Accepted Answer

A)  $\frac { 7 } { a - 9 }$ 
B)  $\frac { 7 } { a + 9 }$ 
C)  $\frac { - 7 } { a + 9 }$ 
D)  $\frac { 7 a } { a - 9 }$ 
E) none of these 
A)  $\frac { 7 } { a - 9 }$ 
B)  $\frac { 7 } { a + 9 }$ 
C)  $\frac { - 7 } { a + 9 }$ 
D)  $\frac { 7 a } { a - 9 }$ 
E) none of these

Question 20

A school board has determined that there should be 3 teachers for every 50 students. How many teachers are needed for an enrollment of 2,750 students?

Accepted Answer

A) 190 teachers 
B) 176 teachers 
C) 165 teachers 
D) 181 teachers 
E) 222 teachers 
A) 190 teachers 
B) 176 teachers 
C) 165 teachers 
D) 181 teachers 
E) 222 teachers

Perform the indicated operation and simplify. $\frac { p ^ { 3 } r ^ { 2 } } { c d } \cdot c ^ { - 4 } d ^ { 3 }$

A dealer bought some cell phones for a total of $1,066. He gave away 1 cell phone as a gift, sold the rest for $15 more then he paid for each cell phone, and earned $98. How many cell phones did he buy?

Solve $d = \frac { 4 c b } { c - b }$ for c .

Perform the indicated operation and simplify. $\frac { 6 } { z } \cdot z ^ { 3 }$

A model railroad engine is 2 inches long. If the scale is 168 feet to 1 foot, how long is the real engine?

A man roller-blades at a rate 5 miles per hour faster than he jogs. In the same time it takes him to roller-blade 6 miles he can jog 3 miles. How fast does he jog?

Evaluate the following expression for the given value of the variable. $\frac { x - 8 } { 4 }$ for $x = 28$

Perform the indicated operation. Simplify the answer if possible. $\frac { t + 6 } { t - 3 } - \frac { t + 10 } { 3 - t }$

Write the ratio 27 feet to 12 yards as a fraction in simplest form. ( Hint : 3 feet = 1 yard.)

Perform the indicated operation. $\frac { 8 a } { y } - \frac { 6 a } { y }$

Perform the indicated division and express your answer in simplest form. $\frac { 4 s ^ { 2 } + 3 s r - r ^ { 2 } } { s ^ { 2 } r } \div \frac { 5 s ^ { 2 } + 4 s r - r ^ { 2 } } { r }$

Express the sentence as a formula. Assume that $k$ is a constant of variation. The distance $S$ that a body falls varies directly with the square of the time $z$ .

Solve for the variable in the proportion. $\frac { 3 } { 5 } = \frac { x } { 15 }$

Evaluate: $\frac { - x - 8 } { x ^ { 2 } - 4 x - 12 } \text { for } x = - 4$

Solve the formula for t : $\frac { 5 } { y } + \frac { 2 } { t } = 7$

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.)Round your answer to the nearest integer.

Write the ratio as a fraction in simplest form. $3$ inches to $12$ inches

Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree.

Perform the indicated operation. Simplify the answer if possible. $\frac { 5 } { a + 9 } - \frac { 2 } { - 9 - a }$

A school board has determined that there should be 3 teachers for every 50 students. How many teachers are needed for an enrollment of 2,750 students?

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Factoring and Quadratic Equations

Roots and Radicals

Quadratic Equations

Filters

Exam 7: Rational Expressions and Equations

Perform the indicated operation and simplify. p3r2cd⋅c−4d3\frac { p ^ { 3 } r ^ { 2 } } { c d } \cdot c ^ { - 4 } d ^ { 3 }cdp3r2​⋅c−4d3

A dealer bought some cell phones for a total of $1,066. He gave away 1 cell phone as a gift, sold the rest for $15 more then he paid for each cell phone, and earned $98. How many cell phones did he buy?

Solve d=4cbc−bd = \frac { 4 c b } { c - b }d=c−b4cb​ for c .

Perform the indicated operation and simplify. 6z⋅z3\frac { 6 } { z } \cdot z ^ { 3 }z6​⋅z3

A model railroad engine is 2 inches long. If the scale is 168 feet to 1 foot, how long is the real engine?

A man roller-blades at a rate 5 miles per hour faster than he jogs. In the same time it takes him to roller-blade 6 miles he can jog 3 miles. How fast does he jog?

Evaluate the following expression for the given value of the variable. x−84\frac { x - 8 } { 4 }4x−8​ for x=28x = 28x=28

Perform the indicated operation. Simplify the answer if possible. t+6t−3−t+103−t\frac { t + 6 } { t - 3 } - \frac { t + 10 } { 3 - t }t−3t+6​−3−tt+10​

Write the ratio 27 feet to 12 yards as a fraction in simplest form. ( Hint : 3 feet = 1 yard.)

Perform the indicated operation. 8ay−6ay\frac { 8 a } { y } - \frac { 6 a } { y }y8a​−y6a​

Perform the indicated division and express your answer in simplest form. 4s2+3sr−r2s2r÷5s2+4sr−r2r\frac { 4 s ^ { 2 } + 3 s r - r ^ { 2 } } { s ^ { 2 } r } \div \frac { 5 s ^ { 2 } + 4 s r - r ^ { 2 } } { r }s2r4s2+3sr−r2​÷r5s2+4sr−r2​

Express the sentence as a formula. Assume that kkk is a constant of variation. The distance SSS that a body falls varies directly with the square of the time zzz .

Solve for the variable in the proportion. 35=x15\frac { 3 } { 5 } = \frac { x } { 15 }53​=15x​

Evaluate: −x−8x2−4x−12 for x=−4\frac { - x - 8 } { x ^ { 2 } - 4 x - 12 } \text { for } x = - 4x2−4x−12−x−8​ for x=−4

Solve the formula for t : 5y+2t=7\frac { 5 } { y } + \frac { 2 } { t } = 7y5​+t2​=7

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.)Round your answer to the nearest integer.

Write the ratio as a fraction in simplest form. 333 inches to 121212 inches

Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree.

Perform the indicated operation. Simplify the answer if possible. 5a+9−2−9−a\frac { 5 } { a + 9 } - \frac { 2 } { - 9 - a }a+95​−−9−a2​

A school board has determined that there should be 3 teachers for every 50 students. How many teachers are needed for an enrollment of 2,750 students?

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Factoring and Quadratic Equations

Roots and Radicals

Quadratic Equations

Filters

Perform the indicated operation and simplify. $\frac { p ^ { 3 } r ^ { 2 } } { c d } \cdot c ^ { - 4 } d ^ { 3 }$

Solve $d = \frac { 4 c b } { c - b }$ for c .

Perform the indicated operation and simplify. $\frac { 6 } { z } \cdot z ^ { 3 }$

Evaluate the following expression for the given value of the variable. $\frac { x - 8 } { 4 }$ for $x = 28$

Perform the indicated operation. Simplify the answer if possible. $\frac { t + 6 } { t - 3 } - \frac { t + 10 } { 3 - t }$

Perform the indicated operation. $\frac { 8 a } { y } - \frac { 6 a } { y }$

Perform the indicated division and express your answer in simplest form. $\frac { 4 s ^ { 2 } + 3 s r - r ^ { 2 } } { s ^ { 2 } r } \div \frac { 5 s ^ { 2 } + 4 s r - r ^ { 2 } } { r }$

Express the sentence as a formula. Assume that $k$ is a constant of variation. The distance $S$ that a body falls varies directly with the square of the time $z$ .

Solve for the variable in the proportion. $\frac { 3 } { 5 } = \frac { x } { 15 }$

Evaluate: $\frac { - x - 8 } { x ^ { 2 } - 4 x - 12 } \text { for } x = - 4$

Solve the formula for t : $\frac { 5 } { y } + \frac { 2 } { t } = 7$

Write the ratio as a fraction in simplest form. $3$ inches to $12$ inches

Perform the indicated operation. Simplify the answer if possible. $\frac { 5 } { a + 9 } - \frac { 2 } { - 9 - a }$