Question 1

How can you tell when an equation has a solution set of all real numbers?

Accepted Answer

An equation has a solution set of all re

Question 2

Decide whether the proportion is true or false.
-$\frac { 25 } { 90 } = \frac { 100 } { 450 }$

Accepted Answer

A) True 
 B)False

Question 3

True or false? This pair of equations is equivalent. 8x - 3 = 37 and 6x + 3 = 33

Accepted Answer

A) True 
 B)False

Question 4

Solve the problem.
-If four times a number is added to 3, the result is three times the number added to 6. Find the number.

Accepted Answer

A) -9 
B) 9 
C) 3 
D) -3 
A) -9 
B) 9 
C) 3 
D) -3

Question 5

An equilateral triangle has perimeter 33 inches. What would be the perimeter of a square whose sides each measure the same length as the side of the triangle?

Accepted Answer

A) 121 inches 
B) 11 inches 
C) 22 inches 
D) 44 inches 
A) 121 inches 
B) 11 inches 
C) 22 inches 
D) 44 inches

Question 6

Evaluate.
-$\frac { 0 ^ { 7 } } { ( - 7 ) ^ { 0 } }$

Accepted Answer

A)  $- 7$ 
B)  1 
C)  $- 1$ 
D)  0 
A)  $- 7$ 
B)  1 
C)  $- 1$ 
D)  0

Question 7

Let x represent the unknown, and write an equation for the sentence. Do not solve.
-When $\frac { 1 } { 4 }$ of a number is added to 16 , the result is 26 .

Accepted Answer

A)  $\frac { 1 } { 4 } x - 16 = 26$ 
B)  $\frac { 1 } { 4 } x + 26$ 
C)  $\frac { 1 } { 4 } + x = 26$ 
D)  $\frac { 1 } { 4 } x + 16 = 26$ 
A)  $\frac { 1 } { 4 } x - 16 = 26$ 
B)  $\frac { 1 } { 4 } x + 26$ 
C)  $\frac { 1 } { 4 } + x = 26$ 
D)  $\frac { 1 } { 4 } x + 16 = 26$

Question 8

What amount of money is found in a coin purse containing 12 dimes and 9 quarters?

Accepted Answer

A) $345.00 
B) $3.45 
C) $3.90 
D) $0.21 
A) $345.00 
B) $3.45 
C) $3.90 
D) $0.21

Question 9

Solve the inequality. Give the solution set in interval form and graph the interval.
-$2 ( 6 x - 7 ) - 3 x < 9 x + 5$

Accepted Answer

A)  $\varnothing$
  
B)  $( \infty , \infty )$
  
C)  $( - \infty , 0 )$
  
D)  $( 0 , \infty )$
  
A)  $\varnothing$
  
B)  $( \infty , \infty )$
  
C)  $( - \infty , 0 )$
  
D)  $( 0 , \infty )$

Question 10

Solve and graph.
-$- 16 r - 28 \leq - 4 ( 3 r + 10 )$

Accepted Answer

A)  $( 3 , \infty )$
  
B)  $( - \infty , 3 )$
  
C)  $( - \infty , 3 ]$
  
D)  $[ 3 , \infty )$
  
A)  $( 3 , \infty )$
  
B)  $( - \infty , 3 )$
  
C)  $( - \infty , 3 ]$
  
D)  $[ 3 , \infty )$

Question 11

Determine the ratio and write it in lowest terms.
-21 people to 15 people

Accepted Answer

A)  $\frac { 8 } { 11 }$ 
B)  $\frac { 11 } { 8 }$ 
C)  $\frac { 7 } { 5 }$ 
D)  $\frac { 5 } { 7 }$ 
A)  $\frac { 8 } { 11 }$ 
B)  $\frac { 11 } { 8 }$ 
C)  $\frac { 7 } { 5 }$ 
D)  $\frac { 5 } { 7 }$

Question 12

Let x represent the unknown, and write an equation for the sentence. Do not solve.
-At a garage sale, the most expensive item was marked $23.00 more than the cheapest item. The sum of the two items was $26.70.

Accepted Answer

A) x + 23.00 = 26.70 
B) x(x + 23.00)= 26.70 
C) 26.70 - x = 23.00 
D) x + (x + 23.00)= 26.70 
A) x + 23.00 = 26.70 
B) x(x + 23.00)= 26.70 
C) 26.70 - x = 23.00 
D) x + (x + 23.00)= 26.70

Question 13

Let x represent the unknown, and write an equation for the sentence. Do not solve.
-If the quotient of a number and 8 is added to twice the number, the result is 5 more than the number.

Accepted Answer

A)  $\frac { x } { 8 } + 2 = x + 5$ 
B)  $\frac { x } { 8 } + 2 x = x + 5$ 
C)  $\frac { x } { 8 } + 2 x = 5 x$ 
D)  $8 x + 2 x = 5 x$ 
A)  $\frac { x } { 8 } + 2 = x + 5$ 
B)  $\frac { x } { 8 } + 2 x = x + 5$ 
C)  $\frac { x } { 8 } + 2 x = 5 x$ 
D)  $8 x + 2 x = 5 x$

Question 14

Answer the question based on the given graph.
-

There were a total of 13,126 earthquakes reported. In which month(s) did the number of earthquakes exceed 1272?

Accepted Answer

A)  August, September, and November 
B)  August and November 
C)  August and September 
D)  September and November 
A)  August, September, and November 
B)  August and November 
C)  August and September 
D)  September and November

Question 15

Solve the inequality. Give the solution set in interval form and graph the interval.
-$6 x + 4 ( x - 2 ) < 10 x - 5$

Accepted Answer

A)  $\varnothing$
  
B)  $( 0 , \infty )$
  
C)  $( \infty , \infty )$
  
D)  $( - \infty , 0 )$
  
A)  $\varnothing$
  
B)  $( 0 , \infty )$
  
C)  $( \infty , \infty )$
  
D)  $( - \infty , 0 )$

Question 16

Solve the problem.
-A salesperson has two job offers. Company A offers a weekly salary of $540 plus commission of 18% of sales. Company B offers a weekly salary of $1080 plus commission of 9% of sales. What is The amount of sales above which Company A's offer is the better of the two?

Accepted Answer

A) $6000 
B) $3000 
C) $6100 
D) $12,000 
A) $6000 
B) $3000 
C) $6100 
D) $12,000

Question 17

Body mass index, or BMI, is used by physicians to assess a person's level of fatness. BMI varies directly as an individual's weight in pounds and inversely as the square of their height in inches. A person who weighs $179 \mathrm { lb }$ and is $72 \mathrm { in }$. tall has a BMI of 24 (rounded to the nearest whole number). Find the BMI of a person who weighs $155 \mathrm { lb }$ and who is 63 in tall. Round your answer to the nearest whole number.

Accepted Answer

A)  28 
B)  25 
C)  27 
D)  26 
A)  28 
B)  25 
C)  27 
D)  26

Question 18

Solve the equation.
-$( \mathrm { y } - 8 ) - ( \mathrm { y } + 6 ) = 9 \mathrm { y }$

Accepted Answer

A)  $\left\{ - \frac { 7 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 14 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 3 } \right\}$ 
A)  $\left\{ - \frac { 7 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 14 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 3 } \right\}$

Question 19

Solve the equation.
-$3 ( 4 x + 1 ) = 9 - 5 ( 4 x - 3 )$

Accepted Answer

A)  $\{ 21 \}$ 
B)  $\left\{ \frac { 9 } { 32 } \right\}$ 
C)  $\left\{ - \frac { 9 } { 32 } \right\}$ 
D)  $\left\{ \frac { 21 } { 32 } \right\}$ 
A)  $\{ 21 \}$ 
B)  $\left\{ \frac { 9 } { 32 } \right\}$ 
C)  $\left\{ - \frac { 9 } { 32 } \right\}$ 
D)  $\left\{ \frac { 21 } { 32 } \right\}$

Question 20

Solve the formula for the specified variable.
-$A = 4 x h + 2 x ^ { 2 }$; for $h$ (surface area of a rectangular solid with a square base)

Accepted Answer

A)  $h = \frac { A } { 2 x ^ { 2 } + 4 x }$ 
B)  $h = \frac { A } { 4 x } - 2 x ^ { 2 }$ 
C)  $h = \frac { A - 2 x ^ { 2 } } { 4 x }$ 
D)  $h = A - 2 x ^ { 2 } - 4 x$ 
A)  $h = \frac { A } { 2 x ^ { 2 } + 4 x }$ 
B)  $h = \frac { A } { 4 x } - 2 x ^ { 2 }$ 
C)  $h = \frac { A - 2 x ^ { 2 } } { 4 x }$ 
D)  $h = A - 2 x ^ { 2 } - 4 x$

How can you tell when an equation has a solution set of all real numbers?

Decide whether the proportion is true or false. - $\frac { 25 } { 90 } = \frac { 100 } { 450 }$

True or false? This pair of equations is equivalent. 8x - 3 = 37 and 6x + 3 = 33

Solve the problem. -If four times a number is added to 3, the result is three times the number added to 6. Find the number.

An equilateral triangle has perimeter 33 inches. What would be the perimeter of a square whose sides each measure the same length as the side of the triangle?

Evaluate. - $\frac { 0 ^ { 7 } } { ( - 7 ) ^ { 0 } }$

Let x represent the unknown, and write an equation for the sentence. Do not solve. -When $\frac { 1 } { 4 }$ of a number is added to 16 , the result is 26 .

What amount of money is found in a coin purse containing 12 dimes and 9 quarters?

Solve the inequality. Give the solution set in interval form and graph the interval. - $2 ( 6 x - 7 ) - 3 x < 9 x + 5$

Solve and graph. - $- 16 r - 28 \leq - 4 ( 3 r + 10 )$ $Solve and graph. - - 16 r - 28 \leq - 4 ( 3 r + 10 )$

Determine the ratio and write it in lowest terms. -21 people to 15 people

Let x represent the unknown, and write an equation for the sentence. Do not solve. -At a garage sale, the most expensive item was marked $23.00 more than the cheapest item. The sum of the two items was $26.70.

Let x represent the unknown, and write an equation for the sentence. Do not solve. -If the quotient of a number and 8 is added to twice the number, the result is 5 more than the number.

Answer the question based on the given graph. - There were a total of 13,126 earthquakes reported. In which month(s) did the number of earthquakes exceed 1272?

Solve the inequality. Give the solution set in interval form and graph the interval. - $6 x + 4 ( x - 2 ) < 10 x - 5$

Solve the problem. -A salesperson has two job offers. Company A offers a weekly salary of $540 plus commission of 18% of sales. Company B offers a weekly salary of $1080 plus commission of 9% of sales. What is The amount of sales above which Company A's offer is the better of the two?

Solve the equation. - $( \mathrm { y } - 8 ) - ( \mathrm { y } + 6 ) = 9 \mathrm { y }$

Solve the equation. - $3 ( 4 x + 1 ) = 9 - 5 ( 4 x - 3 )$

Solve the formula for the specified variable. - $A = 4 x h + 2 x ^ { 2 }$ ; for $h$ (surface area of a rectangular solid with a square base)

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

How can you tell when an equation has a solution set of all real numbers?

Decide whether the proportion is true or false. - 2590=100450\frac { 25 } { 90 } = \frac { 100 } { 450 }9025​=450100​

True or false? This pair of equations is equivalent. 8x - 3 = 37 and 6x + 3 = 33

Solve the problem. -If four times a number is added to 3, the result is three times the number added to 6. Find the number.

An equilateral triangle has perimeter 33 inches. What would be the perimeter of a square whose sides each measure the same length as the side of the triangle?

Evaluate. - 07(−7)0\frac { 0 ^ { 7 } } { ( - 7 ) ^ { 0 } }(−7)007​

Let x represent the unknown, and write an equation for the sentence. Do not solve. -When 14\frac { 1 } { 4 }41​ of a number is added to 16 , the result is 26 .

What amount of money is found in a coin purse containing 12 dimes and 9 quarters?

Solve the inequality. Give the solution set in interval form and graph the interval. - 2(6x−7)−3x<9x+52 ( 6 x - 7 ) - 3 x < 9 x + 52(6x−7)−3x<9x+5

Solve and graph. - −16r−28≤−4(3r+10)- 16 r - 28 \leq - 4 ( 3 r + 10 )−16r−28≤−4(3r+10)

Determine the ratio and write it in lowest terms. -21 people to 15 people

Let x represent the unknown, and write an equation for the sentence. Do not solve. -At a garage sale, the most expensive item was marked $23.00 more than the cheapest item. The sum of the two items was $26.70.

Let x represent the unknown, and write an equation for the sentence. Do not solve. -If the quotient of a number and 8 is added to twice the number, the result is 5 more than the number.

Answer the question based on the given graph. - There were a total of 13,126 earthquakes reported. In which month(s) did the number of earthquakes exceed 1272?

Solve the inequality. Give the solution set in interval form and graph the interval. - 6x+4(x−2)<10x−56 x + 4 ( x - 2 ) < 10 x - 56x+4(x−2)<10x−5

Solve the problem. -A salesperson has two job offers. Company A offers a weekly salary of $540 plus commission of 18% of sales. Company B offers a weekly salary of $1080 plus commission of 9% of sales. What is The amount of sales above which Company A's offer is the better of the two?

Solve the equation. - (y−8)−(y+6)=9y( \mathrm { y } - 8 ) - ( \mathrm { y } + 6 ) = 9 \mathrm { y }(y−8)−(y+6)=9y

Solve the equation. - 3(4x+1)=9−5(4x−3)3 ( 4 x + 1 ) = 9 - 5 ( 4 x - 3 )3(4x+1)=9−5(4x−3)

Solve the formula for the specified variable. - A=4xh+2x2A = 4 x h + 2 x ^ { 2 }A=4xh+2x2 ; for hhh (surface area of a rectangular solid with a square base)

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

Decide whether the proportion is true or false. - $\frac { 25 } { 90 } = \frac { 100 } { 450 }$

Evaluate. - $\frac { 0 ^ { 7 } } { ( - 7 ) ^ { 0 } }$

Let x represent the unknown, and write an equation for the sentence. Do not solve. -When $\frac { 1 } { 4 }$ of a number is added to 16 , the result is 26 .

Solve the inequality. Give the solution set in interval form and graph the interval. - $2 ( 6 x - 7 ) - 3 x < 9 x + 5$

Solve and graph. - $- 16 r - 28 \leq - 4 ( 3 r + 10 )$ $Solve and graph. - - 16 r - 28 \leq - 4 ( 3 r + 10 )$

Solve the inequality. Give the solution set in interval form and graph the interval. - $6 x + 4 ( x - 2 ) < 10 x - 5$

Solve the equation. - $( \mathrm { y } - 8 ) - ( \mathrm { y } + 6 ) = 9 \mathrm { y }$

Solve the equation. - $3 ( 4 x + 1 ) = 9 - 5 ( 4 x - 3 )$

Solve the formula for the specified variable. - $A = 4 x h + 2 x ^ { 2 }$ ; for $h$ (surface area of a rectangular solid with a square base)