Question 1

Solve the equation by the zero-factor property.
-$$6 x ^ { 2 } + 23 x + 21 = 0$$

Accepted Answer

A)  $\left\{ \frac { 3 } { 2 } , \frac { 7 } { 3 } \right\}$ 
B)  $\left\{ \frac { 2 } { 3 } , \frac { 3 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 2 } { 3 } , - \frac { 7 } { 3 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 2 } , - \frac { 7 } { 3 } \right\}$ 
A)  $\left\{ \frac { 3 } { 2 } , \frac { 7 } { 3 } \right\}$ 
B)  $\left\{ \frac { 2 } { 3 } , \frac { 3 } { 7 } \right\}$ 
C)  $\left\{ - \frac { 2 } { 3 } , - \frac { 7 } { 3 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 2 } , - \frac { 7 } { 3 } \right\}$

Question 2

Solve for y.
-$$3 = 4 x - 9 y$$

Accepted Answer

A)  $y = \frac { 4 x + 3 } { 9 }$ 
B)  $y = \frac { 4 x - 3 } { 9 }$ 
C)  $y = 12 + 4 x$ 
D)  $y = 12 - 4 x$ 
A)  $y = \frac { 4 x + 3 } { 9 }$ 
B)  $y = \frac { 4 x - 3 } { 9 }$ 
C)  $y = 12 + 4 x$ 
D)  $y = 12 - 4 x$

Question 3

Solve the problem
-Find two consecutive even integers whose product is 1520.

Accepted Answer

A)  $38 , - 40$ 
B)  38,40 
C)  38,40 or $- 38 , - 40$ 
D)  $- 38 , - 40$ 
A)  $38 , - 40$ 
B)  38,40 
C)  38,40 or $- 38 , - 40$ 
D)  $- 38 , - 40$

Question 4

Solve the problem.
-Your company uses the quadratic model y $y = - 4.5 x ^ { 2 } + 150 x$ 150x to represent the average number of new customers who will be signed on (x) weeks after the release of your new service. How many new
Customers can you expect to gain in week 16?

Accepted Answer

A)  2328 customers 
B)  624 customers 
C)  48 customers 
D)  1248 customers 
A)  2328 customers 
B)  624 customers 
C)  48 customers 
D)  1248 customers

Question 5

Solve for the indicated variable.
-$A = 2 \pi a ^ { 2 }$, for $a$

Accepted Answer

A)  $\mathrm { a } = \frac { \pm \mathrm { A } \sqrt { 2 \pi } } { 2 \pi }$ 
B)  $\mathrm { a } = \frac { \pm \sqrt { \mathrm { A } \pi } } { 2 }$ 
C)  $a = \frac { \pm \sqrt { 2 \pi \mathrm { A } } } { 2 \pi }$ 
D)  $a = \sqrt { 2 \pi \mathrm { A } }$ 
A)  $\mathrm { a } = \frac { \pm \mathrm { A } \sqrt { 2 \pi } } { 2 \pi }$ 
B)  $\mathrm { a } = \frac { \pm \sqrt { \mathrm { A } \pi } } { 2 }$ 
C)  $a = \frac { \pm \sqrt { 2 \pi \mathrm { A } } } { 2 \pi }$ 
D)  $a = \sqrt { 2 \pi \mathrm { A } }$

Question 6

Solve and graph the inequality. Give answer in interval notation.
-$$- 2 > 5 x + 3 \geq - 22$$

Accepted Answer

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

Question 7

Solve the equation.
-$$| 2 x + 3 | + 9 = 13$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 3 } , - \frac { 7 } { 3 } \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } , - \frac { 7 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } , \frac { 7 } { 2 } \right\}$ 
D)  $\varnothing$ 
A)  $\left\{ \frac { 1 } { 3 } , - \frac { 7 } { 3 } \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } , - \frac { 7 } { 2 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 2 } , \frac { 7 } { 2 } \right\}$ 
D)  $\varnothing$

Question 8

Solve the equation.
-$$\left| x ^ { 2 } + 6 x - 27 \right| = 0$$

Accepted Answer

A)  $\{ - 9,3 \}$ 
B)  $\{ - 3,9 \}$ 
C)  $\{ 3,9 \}$ 
D)  $\{ - 9 , - 3 \}$ 
A)  $\{ - 9,3 \}$ 
B)  $\{ - 3,9 \}$ 
C)  $\{ 3,9 \}$ 
D)  $\{ - 9 , - 3 \}$

Question 9

Solve the problem.
-The position of an object moving in a straight line is given by s $\mathrm { s } = 2 \mathrm { t } ^ { 2 } - 3 \mathrm { t }$ where s is in meters and t 281) is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the
Object to move 20 meters?

Accepted Answer

A)  21.0 sec 
B)  3.8 sec 
C)  74.0 sec 
D)  4.0 sec 
A)  21.0 sec 
B)  3.8 sec 
C)  74.0 sec 
D)  4.0 sec

Question 10

Solve the equation.
-$$| 6 x + 6 | = 5$$

Accepted Answer

A)  $\left\{ \frac { 11 } { 6 } , \frac { 1 } { 6 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 6 } , \frac { 1 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 6 } , - \frac { 11 } { 6 } \right\}$ 
A)  $\left\{ \frac { 11 } { 6 } , \frac { 1 } { 6 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 6 } , \frac { 1 } { 6 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
D)  $\left\{ - \frac { 1 } { 6 } , - \frac { 11 } { 6 } \right\}$

Question 11

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$16 i , - 16 i$

Accepted Answer

A)  $x ^ { 2 } + 256 = 0$ 
B)  $x ^ { 2 } + 32 + 256 = 0$ 
C)  $x ^ { 2 } - 256 = 0$ 
D)  $x ^ { 2 } - 32 - 256 = 0$ 
A)  $x ^ { 2 } + 256 = 0$ 
B)  $x ^ { 2 } + 32 + 256 = 0$ 
C)  $x ^ { 2 } - 256 = 0$ 
D)  $x ^ { 2 } - 32 - 256 = 0$

Question 12

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { - 5 x ^ { 2 } - 6 } { x - 4 } = \frac { - 15 x } { x - 4 } + 6$$

Accepted Answer

A)  $\left\{ - \frac { 6 } { 5 } , 3 \right\}$ 
B)  $\left\{ \frac { 6 } { 5 } , - 3 \right\}$ 
C)  $\{ 3 \}$ 
D)  $\left\{ \frac { - 5 \pm \sqrt { 105 } } { 3 } \right\}$ 
A)  $\left\{ - \frac { 6 } { 5 } , 3 \right\}$ 
B)  $\left\{ \frac { 6 } { 5 } , - 3 \right\}$ 
C)  $\{ 3 \}$ 
D)  $\left\{ \frac { - 5 \pm \sqrt { 105 } } { 3 } \right\}$

Question 13

Solve the equation.
-$$- 7 x + 1 = x - 6$$

Accepted Answer

A)  $\left\{ \frac { 5 } { 8 } \right\}$ 
B)  $\left\{ \frac { 7 } { 8 } \right\}$ 
C)  $\left\{ \frac { 5 } { 7 } \right\}$ 
D)  $\{ 1 \}$ 
A)  $\left\{ \frac { 5 } { 8 } \right\}$ 
B)  $\left\{ \frac { 7 } { 8 } \right\}$ 
C)  $\left\{ \frac { 5 } { 7 } \right\}$ 
D)  $\{ 1 \}$

Question 14

Solve the equation for the indicated variable. Assume no denominator is 0.
-$$2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1 , \text { for } x$$

Accepted Answer

A)  $x = \frac { 2 y \pm \sqrt { 2 - 2 y ^ { 2 } } } { 2 }$ 
B)  $x = y \pm ( 1 - y )$ 
C)  $x = - y \pm \sqrt { 1 - y ^ { 2 } }$ 
D)  $x = - y \pm 2 \sqrt { 1 - y ^ { 2 } }$ 
A)  $x = \frac { 2 y \pm \sqrt { 2 - 2 y ^ { 2 } } } { 2 }$ 
B)  $x = y \pm ( 1 - y )$ 
C)  $x = - y \pm \sqrt { 1 - y ^ { 2 } }$ 
D)  $x = - y \pm 2 \sqrt { 1 - y ^ { 2 } }$

Question 15

Indicate whether the statement is true always, sometimes, or never.
-The product of a pair of complex conjugates is a real number.

Accepted Answer

A)  Sometimes 
B)  Never 
C)  Always 
A)  Sometimes 
B)  Never 
C)  Always

Question 16

Solve the formula for the indicated variable.
-$V = \frac { 1 } { 3 } B h$, for $B$

Accepted Answer

A)  $B = \frac { h } { 3 V }$ 
B)  $B = \frac { V } { 3 h }$ 
C)  $B = \frac { 3 V } { h }$ 
D)  $B = \frac { 3 h } { V }$ 
A)  $B = \frac { h } { 3 V }$ 
B)  $B = \frac { V } { 3 h }$ 
C)  $B = \frac { 3 V } { h }$ 
D)  $B = \frac { 3 h } { V }$

Question 17

Decide whether or not the equations are equivalent.
-$\begin{array} { l } 
\frac { x + 1 } { 5 } = \frac { 4 } { 5 } \
x + 2 = 5
\end{array}$

Accepted Answer

A)  Equivalent 
B)  Not equivalent 
A)  Equivalent 
B)  Not equivalent

Question 18

Solve the problem.
-Find the length of a rectangular lot with a perimeter of 148 m if the length is 6 m more than the width.

Accepted Answer

A)  40 m 
B)  74 m 
C)  80 m 
D)  34 m 
A)  40 m 
B)  74 m 
C)  80 m 
D)  34 m

Question 19

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

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , \frac { 14 } { 9 } \right)$ 
C)  $\left( - \frac { 4 } { 9 } , \frac { 14 } { 9 } \right)$ 
D)  $\varnothing$ 
A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , \frac { 14 } { 9 } \right)$ 
C)  $\left( - \frac { 4 } { 9 } , \frac { 14 } { 9 } \right)$ 
D)  $\varnothing$

Question 20

Graph the solution set.
-$$| x | \leq 9$$

Accepted Answer

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

Solve the equation by the zero-factor property. - $6 x ^ { 2 } + 23 x + 21 = 0$

Solve for y. - $3 = 4 x - 9 y$

Solve the problem -Find two consecutive even integers whose product is 1520.

Solve the problem. -Your company uses the quadratic model y $y = - 4.5 x ^ { 2 } + 150 x$ 150x to represent the average number of new customers who will be signed on (x) weeks after the release of your new service. How many new Customers can you expect to gain in week 16?

Solve for the indicated variable. - $A = 2 \pi a ^ { 2 }$ , for $a$

Solve and graph the inequality. Give answer in interval notation. - $- 2 > 5 x + 3 \geq - 22$ $Solve and graph the inequality. Give answer in interval notation. - - 2 > 5 x + 3 \geq - 22$

Solve the equation. - $| 2 x + 3 | + 9 = 13$

Solve the equation. - $\left| x ^ { 2 } + 6 x - 27 \right| = 0$

Solve the equation. - $| 6 x + 6 | = 5$

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $16 i , - 16 i$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { - 5 x ^ { 2 } - 6 } { x - 4 } = \frac { - 15 x } { x - 4 } + 6$

Solve the equation. - $- 7 x + 1 = x - 6$

Solve the equation for the indicated variable. Assume no denominator is 0. - $2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1 , \text { for } x$

Indicate whether the statement is true always, sometimes, or never. -The product of a pair of complex conjugates is a real number.

Solve the formula for the indicated variable. - $V = \frac { 1 } { 3 } B h$ , for $B$

Decide whether or not the equations are equivalent. - = x+2=5

Solve the problem. -Find the length of a rectangular lot with a perimeter of 148 m if the length is 6 m more than the width.

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

Graph the solution set. - $| x | \leq 9$ $Graph the solution set. - | x | \leq 9$

Review of Basic Concepts

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

Filters

Exam 2: Equations and Inequalities

Solve the equation by the zero-factor property. - 6x2+23x+21=06 x ^ { 2 } + 23 x + 21 = 06x2+23x+21=0

Solve for y. - 3=4x−9y3 = 4 x - 9 y3=4x−9y