Question 1

Evaluate the expression.
-$\frac { 1 } { - 7 ^ { - 4 } }$

Accepted Answer

A)  343 
B)  $- 2401$ 
C)  2401 
D)  $- 343$ 
A)  343 
B)  $- 2401$ 
C)  2401 
D)  $- 343$

Question 2

Match the inequality with its correct representation.
-$\{ x \mid - 5 \leq x \leq 9 \}$

Accepted Answer

A)  $( - 5,9 )$ 
B)  $[ - 5,9 )$ 
C)  $( - 5,9 ]$ 
D)  $[ - 5,9 ]$ 
A)  $( - 5,9 )$ 
B)  $[ - 5,9 )$ 
C)  $( - 5,9 ]$ 
D)  $[ - 5,9 ]$

Question 3

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.
-427 divided by some number

Accepted Answer

A)  $427 + x$ 
B)  $427 x$ 
C)  $\frac { 427 } { x }$ 
D)  $427 - x$ 
A)  $427 + x$ 
B)  $427 x$ 
C)  $\frac { 427 } { x }$ 
D)  $427 - x$

Question 4

Solve the equation.
-$26 \mathrm {~s} + 14 = 10 \mathrm {~s}$

Accepted Answer

A)  $\left\{ - \frac { 7 } { 8 } \right\}$ 
B)  $\left\{ \frac { 7 } { 8 } \right\}$ 
C)  $\left\{ \frac { 7 } { 18 } \right\}$ 
D)  $\left\{ \frac { 8 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 7 } { 8 } \right\}$ 
B)  $\left\{ \frac { 7 } { 8 } \right\}$ 
C)  $\left\{ \frac { 7 } { 18 } \right\}$ 
D)  $\left\{ \frac { 8 } { 7 } \right\}$

Question 5

Decide whether the proportion is true or false.
-$\frac { 2 } { 6 } = \frac { 8 } { 24 }$

Accepted Answer

A) True 
 B)False

Question 6

Match the inequality with its correct representation.
-$\{ \mathrm { x } \mid - 4 < \mathrm { x } < 8 \}$

Accepted Answer

A)  $[ - 4,8 ]$ 
B)  $[ - 4,8 )$ 
C)  $( - 4,8 ]$ 
D)  $( - 4,8 )$ 
A)  $[ - 4,8 ]$ 
B)  $[ - 4,8 )$ 
C)  $( - 4,8 ]$ 
D)  $( - 4,8 )$

Question 7

The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 90 seconds are required to make a 3-by-5 enlargement, find the time required
For a 5-by-6 enlargement.

Accepted Answer

A) 210 sec 
B) 150 sec 
C) 240 sec 
D) 180 sec 
A) 210 sec 
B) 150 sec 
C) 240 sec 
D) 180 sec

Question 8

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set.
-$12 \mathrm { k } + 70 = 4 ( 3 \mathrm { k } + 17 )$

Accepted Answer

A)  Identity;{all real numbers} 
B)  Identity; $\varnothing$ 
C)  Contradiction; $\varnothing$ 
D)  Conditional; {all real numbers} 
A)  Identity;{all real numbers} 
B)  Identity; $\varnothing$ 
C)  Contradiction; $\varnothing$ 
D)  Conditional; {all real numbers}

Question 9

Solve the equation.
-$\frac { - 5 x + 9 } { 7 } + \frac { 2 } { 7 } = - \frac { 3 x } { 4 }$

Accepted Answer

A)  $\{ - 28 \}$ 
B)  $\{ 28 \}$ 
C)  $\left\{ \frac { 44 } { 41 } \right\}$ 
D)  $\{ - 44 \}$ 
A)  $\{ - 28 \}$ 
B)  $\{ 28 \}$ 
C)  $\left\{ \frac { 44 } { 41 } \right\}$ 
D)  $\{ - 44 \}$

Question 10

Tell which brand or which size is the better buy.
-Brand $X : 25 \mathrm { oz }$ for $\$ 7.50$
Brand Y: 20 oz for $\$ 5.80$

Accepted Answer

A) Not enough information 
B) Equal value 
C) Brand X 
D) Brand Y 
A) Not enough information 
B) Equal value 
C) Brand X 
D) Brand Y

Question 11

If x varies inversely as v, and x = 42 when v = 5, find x when v = 35.

Accepted Answer

A) x = 30 
B) x = 7 
C) x = 6 
D) x = 25 
A) x = 30 
B) x = 7 
C) x = 6 
D) x = 25

Question 12

Decide whether the proportion is true or false.
-$\frac { \frac { 1 } { 5 } } { 10 } = \frac { 1 } { 51 }$

Accepted Answer

A) True 
 B)False

Question 13

Tell which brand or which size is the better buy.
-Brand X: 4 oz for $0.44 Brand Y: 6 oz for $0.72

Accepted Answer

A) Not enough information 
B) Brand X 
C) Equal value 
D) Brand Y 
A) Not enough information 
B) Brand X 
C) Equal value 
D) Brand Y

Question 14

Evaluate the expression.
-$- 3 ^ { 2 }$

Accepted Answer

A)  9 
B)  $- 9$ 
C)  $- 6$ 
D)  6 
A)  9 
B)  $- 9$ 
C)  $- 6$ 
D)  6

Question 15

Over a specified distance, speed varies inversely with time. If Joe can drive from his house to his office in 40 minutes at an average speed of 40 miles per hour, what average speed is needed to
Drive the same distance in half an hour? If necessary, round your answer to the nearest tenth.

Accepted Answer

A) 50 miles per hour 
B) 60 miles per hour 
C) 30 miles per hour 
D) 53.3 miles per hour 
A) 50 miles per hour 
B) 60 miles per hour 
C) 30 miles per hour 
D) 53.3 miles per hour

Question 16

On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up 2%. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $
1224?

Accepted Answer

A) $1248 
B) $1174 
C) $1250 
D) $1200 
A) $1248 
B) $1174 
C) $1250 
D) $1200

Question 17

Solve the equation.
-$\frac { 8 x } { 9 } - 7 = x$

Accepted Answer

A)  $\left\{ \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 63 } \right\}$ 
C)  $\{ - 63 \}$ 
D)  $\left\{ \frac { 9 } { 8 } \right\}$ 
A)  $\left\{ \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 63 } \right\}$ 
C)  $\{ - 63 \}$ 
D)  $\left\{ \frac { 9 } { 8 } \right\}$

Question 18

Solve the problem.
-Find the missing length in the similar triangles.

Accepted Answer

A)  $x = 12$ 
B)  $x = 6$ 
C)  $x = 9$ 
D)  $x = 3$ 
A)  $x = 12$ 
B)  $x = 6$ 
C)  $x = 9$ 
D)  $x = 3$

Question 19

If s varies directly as t2, and s = 125 when t = 5, find s when t is 7.

Accepted Answer

A) s = 25 
B) s = 35 
C) s = 175 
D) s = 245 
A) s = 25 
B) s = 35 
C) s = 175 
D) s = 245

Question 20

Solve the problem.
-On a map of the Thunderbird Country Club golf course, 2.5 inches equals 60 yards. How long is the 10th hole if the map shows 14 inches?

Accepted Answer

A) 10.7 yd 
B) 336 yd 
C) 840 yd 
D) 2100 yd 
A) 10.7 yd 
B) 336 yd 
C) 840 yd 
D) 2100 yd

Evaluate the expression. - $\frac { 1 } { - 7 ^ { - 4 } }$

Match the inequality with its correct representation. - $\{ x \mid - 5 \leq x \leq 9 \}$

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -427 divided by some number

Solve the equation. - $26 \mathrm {~s} + 14 = 10 \mathrm {~s}$

Decide whether the proportion is true or false. - $\frac { 2 } { 6 } = \frac { 8 } { 24 }$

Match the inequality with its correct representation. - $\{ \mathrm { x } \mid - 4 < \mathrm { x } < 8 \}$

The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 90 seconds are required to make a 3-by-5 enlargement, find the time required For a 5-by-6 enlargement.

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $12 \mathrm { k } + 70 = 4 ( 3 \mathrm { k } + 17 )$

Solve the equation. - $\frac { - 5 x + 9 } { 7 } + \frac { 2 } { 7 } = - \frac { 3 x } { 4 }$

Tell which brand or which size is the better buy. -Brand $X : 25 \mathrm { oz }$ for $\$ 7.50$ Brand Y: 20 oz for $\$ 5.80$

If x varies inversely as v, and x = 42 when v = 5, find x when v = 35.

Decide whether the proportion is true or false. - $\frac { \frac { 1 } { 5 } } { 10 } = \frac { 1 } { 51 }$

Tell which brand or which size is the better buy. -Brand X: 4 oz for $0.44 Brand Y: 6 oz for $0.72

Evaluate the expression. - $- 3 ^ { 2 }$

Over a specified distance, speed varies inversely with time. If Joe can drive from his house to his office in 40 minutes at an average speed of 40 miles per hour, what average speed is needed to Drive the same distance in half an hour? If necessary, round your answer to the nearest tenth.

On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up 2%. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $ 1224?

Solve the equation. - $\frac { 8 x } { 9 } - 7 = x$

Solve the problem. -Find the missing length in the similar triangles.

If s varies directly as t2, and s = 125 when t = 5, find s when t is 7.

Solve the problem. -On a map of the Thunderbird Country Club golf course, 2.5 inches equals 60 yards. How long is the 10th hole if the map shows 14 inches?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Exam 7: The Basic Concepts of Algebra

Evaluate the expression. - 1−7−4\frac { 1 } { - 7 ^ { - 4 } }−7−41​

Match the inequality with its correct representation. - {x∣−5≤x≤9}\{ x \mid - 5 \leq x \leq 9 \}{x∣−5≤x≤9}

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -427 divided by some number

Solve the equation. - 26 s+14=10 s26 \mathrm {~s} + 14 = 10 \mathrm {~s}26 s+14=10 s

Decide whether the proportion is true or false. - 26=824\frac { 2 } { 6 } = \frac { 8 } { 24 }62​=248​

Match the inequality with its correct representation. - {x∣−4<x<8}\{ \mathrm { x } \mid - 4 < \mathrm { x } < 8 \}{x∣−4<x<8}

The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 90 seconds are required to make a 3-by-5 enlargement, find the time required For a 5-by-6 enlargement.

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - 12k+70=4(3k+17)12 \mathrm { k } + 70 = 4 ( 3 \mathrm { k } + 17 )12k+70=4(3k+17)

Solve the equation. - −5x+97+27=−3x4\frac { - 5 x + 9 } { 7 } + \frac { 2 } { 7 } = - \frac { 3 x } { 4 }7−5x+9​+72​=−43x​

Tell which brand or which size is the better buy. -Brand X:25ozX : 25 \mathrm { oz }X:25oz for $7.50\$ 7.50$7.50 Brand Y: 20 oz for $5.80\$ 5.80$5.80

If x varies inversely as v, and x = 42 when v = 5, find x when v = 35.

Decide whether the proportion is true or false. - 1510=151\frac { \frac { 1 } { 5 } } { 10 } = \frac { 1 } { 51 }1051​​=511​

Tell which brand or which size is the better buy. -Brand X: 4 oz for $0.44 Brand Y: 6 oz for $0.72

Evaluate the expression. - −32- 3 ^ { 2 }−32

Over a specified distance, speed varies inversely with time. If Joe can drive from his house to his office in 40 minutes at an average speed of 40 miles per hour, what average speed is needed to Drive the same distance in half an hour? If necessary, round your answer to the nearest tenth.

On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up 2%. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $ 1224?

Solve the equation. - 8x9−7=x\frac { 8 x } { 9 } - 7 = x98x​−7=x

Solve the problem. -Find the missing length in the similar triangles.

If s varies directly as t2, and s = 125 when t = 5, find s when t is 7.

Solve the problem. -On a map of the Thunderbird Country Club golf course, 2.5 inches equals 60 yards. How long is the 10th hole if the map shows 14 inches?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Evaluate the expression. - $\frac { 1 } { - 7 ^ { - 4 } }$

Match the inequality with its correct representation. - $\{ x \mid - 5 \leq x \leq 9 \}$

Solve the equation. - $26 \mathrm {~s} + 14 = 10 \mathrm {~s}$

Decide whether the proportion is true or false. - $\frac { 2 } { 6 } = \frac { 8 } { 24 }$

Match the inequality with its correct representation. - $\{ \mathrm { x } \mid - 4 < \mathrm { x } < 8 \}$

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $12 \mathrm { k } + 70 = 4 ( 3 \mathrm { k } + 17 )$

Solve the equation. - $\frac { - 5 x + 9 } { 7 } + \frac { 2 } { 7 } = - \frac { 3 x } { 4 }$

Tell which brand or which size is the better buy. -Brand $X : 25 \mathrm { oz }$ for $\$ 7.50$ Brand Y: 20 oz for $\$ 5.80$

Decide whether the proportion is true or false. - $\frac { \frac { 1 } { 5 } } { 10 } = \frac { 1 } { 51 }$

Evaluate the expression. - $- 3 ^ { 2 }$

Solve the equation. - $\frac { 8 x } { 9 } - 7 = x$