Question 1

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { ( x - 3 ) ( x + 7 ) } { x - 4 } \leq 0$$

Accepted Answer

A)  $( - \infty , - 7 ) \cup ( 3,4 )$ 
B)  $[ - 7,3 ] \cup ( 4 , \infty )$ 
C)  $( - \infty , - 7 ] \cup [ 3,4 )$ 
D)  $[ 3,4 )$ 
A)  $( - \infty , - 7 ) \cup ( 3,4 )$ 
B)  $[ - 7,3 ] \cup ( 4 , \infty )$ 
C)  $( - \infty , - 7 ] \cup [ 3,4 )$ 
D)  $[ 3,4 )$

Question 2

Solve the problem.
-Find the corresponding Fahrenheit temperature for a temperature of $73 ^ { \circ } \mathrm { C }$. Round to the nearest tenth, if necessary.

Accepted Answer

A)  $22.8 ^ { \circ } \mathrm { F }$ 
B)  $189 ^ { \circ } \mathrm { F }$ 
C)  $163.4 ^ { \circ } \mathrm { F }$ 
D)  $58.3 ^ { \circ } \mathrm { F }$ 
A)  $22.8 ^ { \circ } \mathrm { F }$ 
B)  $189 ^ { \circ } \mathrm { F }$ 
C)  $163.4 ^ { \circ } \mathrm { F }$ 
D)  $58.3 ^ { \circ } \mathrm { F }$

Question 3

Solve the equation.
-$$x ^ { 2 } = - 8$$

Accepted Answer

A)  $\pm 2 \sqrt { 2 }$ 
B)  $\pm 4 \sqrt { 2 }$ 
C)  $\pm 2 \mathrm { i } \sqrt { 2 }$ 
D)  $\pm 4 \mathrm { i } \sqrt { 2 }$ 
A)  $\pm 2 \sqrt { 2 }$ 
B)  $\pm 4 \sqrt { 2 }$ 
C)  $\pm 2 \mathrm { i } \sqrt { 2 }$ 
D)  $\pm 4 \mathrm { i } \sqrt { 2 }$

Question 4

Solve for y.
-$$9 x - 3 ( x + y ) = y - x$$

Accepted Answer

A)  $y = 7 x - 4$ 
B)  $y = \frac { 7 } { 4 } x$ 
C)  $y = 7 x + 4$ 
D)  $\mathrm { y } = 7 \mathrm { x }$ 
A)  $y = 7 x - 4$ 
B)  $y = \frac { 7 } { 4 } x$ 
C)  $y = 7 x + 4$ 
D)  $\mathrm { y } = 7 \mathrm { x }$

Question 5

Solve and graph the inequality. Give answer in interval notation.
-$$- 1 \leq \frac { x + 1 } { 2 } \leq 3$$

Accepted Answer

A)  $[ - 1,7 ]$
  
B)  $[ - 5,3 ]$
  
C)  $[ - 3,5 ]$
  
D)  $( - 7,1 )$
  
A)  $[ - 1,7 ]$
  
B)  $[ - 5,3 ]$
  
C)  $[ - 3,5 ]$
  
D)  $( - 7,1 )$

Question 6

Solve the equation for the indicated variable. Assume no denominator is 0.
-$A = 3 \pi a ^ { 2 }$, for $a$

Accepted Answer

A)  $\mathrm { a } = \sqrt { 3 \pi \mathrm { A } }$ 
B)  $\mathrm { a } = \frac { \pm \sqrt { 3 \pi \mathrm { A } } } { 3 \pi }$ 
C)  $\mathrm { a } = \frac { \pm \sqrt { \mathrm { A } \pi } } { 3 }$ 
D)  $\mathrm { a } = \frac { \pm \mathrm { A } \sqrt { 3 \pi } } { 3 \pi }$ 
A)  $\mathrm { a } = \sqrt { 3 \pi \mathrm { A } }$ 
B)  $\mathrm { a } = \frac { \pm \sqrt { 3 \pi \mathrm { A } } } { 3 \pi }$ 
C)  $\mathrm { a } = \frac { \pm \sqrt { \mathrm { A } \pi } } { 3 }$ 
D)  $\mathrm { a } = \frac { \pm \mathrm { A } \sqrt { 3 \pi } } { 3 \pi }$

Question 7

Solve the problem.
-A triangular shaped lake-front lot has a perimeter of 1300 ft. One side is 100 ft longer than the shortest side, while the third side is 300 ft longer than the shortest side. Find the lengths of all three
Sides.

Accepted Answer

A)  400 ft, 400 ft, 400 ft 
B)  400 ft, 500 ft, 700 ft 
C)  300 ft, 400 ft, 600 ft 
D)  100 ft, 200 ft, 300 ft 
A)  400 ft, 400 ft, 400 ft 
B)  400 ft, 500 ft, 700 ft 
C)  300 ft, 400 ft, 600 ft 
D)  100 ft, 200 ft, 300 ft

Question 8

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { x - 7 } { x + 8 } \leq 0$$

Accepted Answer

A)  $( - 7,8 ]$ 
B)  $[ - 8,7 ]$ 
C)  $[ - 7,8 ]$ 
D)  $( - 8,7 ]$ 
A)  $( - 7,8 ]$ 
B)  $[ - 8,7 ]$ 
C)  $[ - 7,8 ]$ 
D)  $( - 8,7 ]$

Question 9

Graph the solution set.
-$$| x | \geq 1$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 10

Solve the equation.
-$$\frac { x + 9 } { 3 } = \frac { x - 8 } { 2 }$$

Accepted Answer

A)  $\{ 33 \}$ 
B)  $\left\{ - \frac { 42 } { 5 } \right\}$ 
C)  $\{ 6 \}$ 
D)  $\{ 42 \}$ 
A)  $\{ 33 \}$ 
B)  $\left\{ - \frac { 42 } { 5 } \right\}$ 
C)  $\{ 6 \}$ 
D)  $\{ 42 \}$

Question 11

Solve the problem.
-Roberto invested some money at 2.5%, and then invested $4000 more than twice this amount at 4%. His total annual income from the two investments was $1735.00. How much was invested at
4%?

Accepted Answer

A)  $30,000 
B)  $3400 
C)  $12,000 
D)  $34,000 
A)  $30,000 
B)  $3400 
C)  $12,000 
D)  $34,000

Question 12

Solve the inequality. Write the solution set in interval notation.
-$| 5 x - 9 | \leq - 8$

Accepted Answer

A)  $\left( - \infty , \frac { 1 } { 5 } \right) \cup ( - 3 , \infty )$ 
B)  $\left( - \infty , \frac { 17 } { 5 } \right) \cup \left( \frac { 1 } { 5 } , \infty \right)$ 
C)  $\left( \frac { 17 } { 5 } , \frac { 1 } { 5 } \right)$ 
D)  $\varnothing$ 
A)  $\left( - \infty , \frac { 1 } { 5 } \right) \cup ( - 3 , \infty )$ 
B)  $\left( - \infty , \frac { 17 } { 5 } \right) \cup \left( \frac { 1 } { 5 } , \infty \right)$ 
C)  $\left( \frac { 17 } { 5 } , \frac { 1 } { 5 } \right)$ 
D)  $\varnothing$

Question 13

Solve for y.
-$$9 = 5 x - 2 y$$

Accepted Answer

A)  $y = 11 + 5 x$ 
B)  $y = \frac { 5 x + 9 } { 2 }$ 
C)  $y = \frac { 5 x - 9 } { 2 }$ 
D)  $y = 11 - 5 x$ 
A)  $y = 11 + 5 x$ 
B)  $y = \frac { 5 x + 9 } { 2 }$ 
C)  $y = \frac { 5 x - 9 } { 2 }$ 
D)  $y = 11 - 5 x$

Question 14

Solve the problem.
-A computer company uses the linear model y = -22x + 50,787 to predict the decline in sales of a computer after it has been on the market more than one year. If x is the number of months after
The first year and y is the number of computers sold during that month, how many computers will
Be sold 15 months after the first year?

Accepted Answer

A)  50,457 computers 
B)  50,193 computers 
C)  51,117 computers 
D)  2308 computers 
A)  50,457 computers 
B)  50,193 computers 
C)  51,117 computers 
D)  2308 computers

Question 15

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } - 1 = 0$$

Accepted Answer

A)  $\{ 1,1 \pm i \sqrt { 3 } \}$ 
B)  $\{ 1 , \pm i \}$ 
C)  $\{ 1 , - 1 \pm i \sqrt { 3 } \}$ 
D)  $\left\{ 1 , - \frac { 1 } { 2 } \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$ 
A)  $\{ 1,1 \pm i \sqrt { 3 } \}$ 
B)  $\{ 1 , \pm i \}$ 
C)  $\{ 1 , - 1 \pm i \sqrt { 3 } \}$ 
D)  $\left\{ 1 , - \frac { 1 } { 2 } \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$

Question 16

Solve the equation.
-$$| - 8 x + 7 | = 4$$

Accepted Answer

A)  $\left\{ \frac { 3 } { 8 } , \frac { 11 } { 8 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 8 } , - \frac { 3 } { 8 } \right\}$ 
C)  $\left\{ \frac { 3 } { 8 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 8 } , \frac { 3 } { 8 } \right\}$ 
A)  $\left\{ \frac { 3 } { 8 } , \frac { 11 } { 8 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 8 } , - \frac { 3 } { 8 } \right\}$ 
C)  $\left\{ \frac { 3 } { 8 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 8 } , \frac { 3 } { 8 } \right\}$

Question 17

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 3 } + 4 x ^ { 2 } - 16 x \leq 64$$

Accepted Answer

A)  $[ 4 , \infty )$ 
B)  $( - \infty , - 4 ] \cup [ 4 , \infty )$ 
C)  $( - \infty , 4 ]$ 
D)  $[ - 4,4 ]$ 
A)  $[ 4 , \infty )$ 
B)  $( - \infty , - 4 ] \cup [ 4 , \infty )$ 
C)  $( - \infty , 4 ]$ 
D)  $[ - 4,4 ]$

Question 18

Solve and graph the inequality. Give answer in interval notation.
-$$- 4 x + 3 \geq - 5 x + 8$$

Accepted Answer

A)  $[ 5 , \infty )$
  
B)  $( - \infty , 5 ]$
  
C)  $( - \infty , - 4 )$
  
D)  $( - 4 , \infty )$
  
A)  $[ 5 , \infty )$
  
B)  $( - \infty , 5 ]$
  
C)  $( - \infty , - 4 )$
  
D)  $( - 4 , \infty )$

Question 19

Solve the equation.
-$$6 x + 3 + 2 ( x + 1 ) = - ( 4 x - 4 )$$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 4 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 12 } \right\}$ 
A)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 4 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 12 } \right\}$

Question 20

Write the number as the product of a real number and i.
-$- \sqrt { - 9 }$

Accepted Answer

A)  3 
B)  $- 3 \mathrm { i }$ 
C)  $3 \mathrm { i }$ 
D)  i $\sqrt { 9 }$ 
A)  3 
B)  $- 3 \mathrm { i }$ 
C)  $3 \mathrm { i }$ 
D)  i $\sqrt { 9 }$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { ( x - 3 ) ( x + 7 ) } { x - 4 } \leq 0$

Solve the problem. -Find the corresponding Fahrenheit temperature for a temperature of $73 ^ { \circ } \mathrm { C }$ . Round to the nearest tenth, if necessary.

Solve the equation. - $x ^ { 2 } = - 8$

Solve for y. - $9 x - 3 ( x + y ) = y - x$

Solve and graph the inequality. Give answer in interval notation. - $- 1 \leq \frac { x + 1 } { 2 } \leq 3$ $Solve and graph the inequality. Give answer in interval notation. - - 1 \leq \frac { x + 1 } { 2 } \leq 3$

Solve the equation for the indicated variable. Assume no denominator is 0. - $A = 3 \pi a ^ { 2 }$ , for $a$

Solve the problem. -A triangular shaped lake-front lot has a perimeter of 1300 ft. One side is 100 ft longer than the shortest side, while the third side is 300 ft longer than the shortest side. Find the lengths of all three Sides.

Solve the rational inequality. Write the solution set in interval notation. - $\frac { x - 7 } { x + 8 } \leq 0$

Graph the solution set. - $| x | \geq 1$ $Graph the solution set. - | x | \geq 1$

Solve the equation. - $\frac { x + 9 } { 3 } = \frac { x - 8 } { 2 }$

Solve the problem. -Roberto invested some money at 2.5%, and then invested $4000 more than twice this amount at 4%. His total annual income from the two investments was $1735.00. How much was invested at 4%?

Solve the inequality. Write the solution set in interval notation. - $| 5 x - 9 | \leq - 8$

Solve for y. - $9 = 5 x - 2 y$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } - 1 = 0$

Solve the equation. - $| - 8 x + 7 | = 4$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } + 4 x ^ { 2 } - 16 x \leq 64$

Solve and graph the inequality. Give answer in interval notation. - $- 4 x + 3 \geq - 5 x + 8$ $Solve and graph the inequality. Give answer in interval notation. - - 4 x + 3 \geq - 5 x + 8$

Solve the equation. - $6 x + 3 + 2 ( x + 1 ) = - ( 4 x - 4 )$

Write the number as the product of a real number and i. - $- \sqrt { - 9 }$

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 1: Equations and Inequalities

Solve the rational inequality. Write the solution set in interval notation. - (x−3)(x+7)x−4≤0\frac { ( x - 3 ) ( x + 7 ) } { x - 4 } \leq 0x−4(x−3)(x+7)​≤0

Solve the problem. -Find the corresponding Fahrenheit temperature for a temperature of 73∘C73 ^ { \circ } \mathrm { C }73∘C . Round to the nearest tenth, if necessary.

Solve the equation. - x2=−8x ^ { 2 } = - 8x2=−8

Solve for y. - 9x−3(x+y)=y−x9 x - 3 ( x + y ) = y - x9x−3(x+y)=y−x

Solve and graph the inequality. Give answer in interval notation. - −1≤x+12≤3- 1 \leq \frac { x + 1 } { 2 } \leq 3−1≤2x+1​≤3

Solve the equation for the indicated variable. Assume no denominator is 0. - A=3πa2A = 3 \pi a ^ { 2 }A=3πa2 , for aaa