Question 1

Solve the equation by the zero-factor property.
-$$x ^ { 2 } + 14 x + 40 = 0$$

Accepted Answer

A)  $\{ 2 \sqrt { 10 } , - 2 \sqrt { 10 } \}$ 
B)  $\{ 4,10 \}$ 
C)  $\{ - 20 , - 8 \}$ 
D)  $\{ - 10 , - 4 \}$ 
A)  $\{ 2 \sqrt { 10 } , - 2 \sqrt { 10 } \}$ 
B)  $\{ 4,10 \}$ 
C)  $\{ - 20 , - 8 \}$ 
D)  $\{ - 10 , - 4 \}$

Question 2

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

Accepted Answer

A)  $\left[ - \frac { 4 } { 3 } , 0 \right]$ 
B)  $( - \infty , \infty )$ 
C)  $\varnothing$ 
D)  $\left( - \infty , - \frac { 4 } { 3 } \right) \cup ( 0 , \infty )$ 
A)  $\left[ - \frac { 4 } { 3 } , 0 \right]$ 
B)  $( - \infty , \infty )$ 
C)  $\varnothing$ 
D)  $\left( - \infty , - \frac { 4 } { 3 } \right) \cup ( 0 , \infty )$

Question 3

Solve and graph the inequality. Give answer in interval notation.
-$$12 < - 5 x + 2 \leq 32$$

Accepted Answer

A)  $( 2,6 ]$
  
B)  $( - 6 , - 2 ]$
  
C)  $[ 2,6 )$
  
D)  $[ - 6 , - 2 )$
  
A)  $( 2,6 ]$
  
B)  $( - 6 , - 2 ]$
  
C)  $[ 2,6 )$
  
D)  $[ - 6 , - 2 )$

Question 4

Solve for the indicated variable.
-$\frac { 1 } { \mathrm { Q } } = \frac { 1 } { \mathrm {~T} _ { 1 } } + \frac { 1 } { \mathrm {~T} _ { 2 } }$, for $\mathrm { T } _ { 2 }$

Accepted Answer

A)  $\mathrm { T } _ { 2 } = \frac { \mathrm { QT } _ { 1 } } { \mathrm {~T} _ { 1 } - \mathrm { Q } }$ 
B)  $\mathrm { T } _ { 2 } = \frac { \mathrm { Q } - \mathrm { T } _ { 1 } } { \mathrm {~T} _ { 1 } \mathrm { Q } }$ 
C)  $\mathrm { T } _ { 2 } = \frac { \mathrm { QT } _ { 1 } } { \mathrm {~T} _ { 1 } + 4 \mathrm { Q } }$ 
D)  $\mathrm { T } _ { 2 } = \frac { \mathrm { T } _ { 1 } - \mathrm { Q } } { \mathrm { T } _ { 1 } \mathrm { Q } }$ 
A)  $\mathrm { T } _ { 2 } = \frac { \mathrm { QT } _ { 1 } } { \mathrm {~T} _ { 1 } - \mathrm { Q } }$ 
B)  $\mathrm { T } _ { 2 } = \frac { \mathrm { Q } - \mathrm { T } _ { 1 } } { \mathrm {~T} _ { 1 } \mathrm { Q } }$ 
C)  $\mathrm { T } _ { 2 } = \frac { \mathrm { QT } _ { 1 } } { \mathrm {~T} _ { 1 } + 4 \mathrm { Q } }$ 
D)  $\mathrm { T } _ { 2 } = \frac { \mathrm { T } _ { 1 } - \mathrm { Q } } { \mathrm { T } _ { 1 } \mathrm { Q } }$

Question 5

Solve the equation.
-$$( x + 2 ) ^ { 2 / 5 } = ( 9 x ) ^ { 1 / 5 }$$

Accepted Answer

A)  $\{ 4 , - 1 \}$ 
B)  $\left\{ - \frac { 8 } { 23 } \right\}$ 
C)  $\{ 4,1 \}$ 
D)  $\{ - 4,1 \}$ 
A)  $\{ 4 , - 1 \}$ 
B)  $\left\{ - \frac { 8 } { 23 } \right\}$ 
C)  $\{ 4,1 \}$ 
D)  $\{ - 4,1 \}$

Question 6

Solve the equation.
-$\sqrt { 3 x + 10 } = 5 - 2 x$

Accepted Answer

A)  $\left\{ \frac { 3 } { 4 } , 5 \right\}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ \frac { 5 } { 4 } , 9 \right\}$ 
D)  $\left\{ \frac { 3 } { 4 } \right\}$ 
A)  $\left\{ \frac { 3 } { 4 } , 5 \right\}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ \frac { 5 } { 4 } , 9 \right\}$ 
D)  $\left\{ \frac { 3 } { 4 } \right\}$

Question 7

Find the sum or difference. Write the answer in standard form.
-$$( 2 - 9 \mathrm { i } ) - ( - 1 - 2 \mathrm { i } ) - ( - 2 - 3 \mathrm { i } )$$

Accepted Answer

A)  $5 - 14 \mathrm { i }$ 
B)  $1 - 10 \mathrm { i }$ 
C)  $- 1 - 14 \mathrm { i }$ 
D)  $5 - 4 \mathrm { i }$ 
A)  $5 - 14 \mathrm { i }$ 
B)  $1 - 10 \mathrm { i }$ 
C)  $- 1 - 14 \mathrm { i }$ 
D)  $5 - 4 \mathrm { i }$

Question 8

Solve the problem.
-Helen Weller invested $11,000 in an account that pays 1.5% simple interest. How much additional money must be invested in an account that pays 3% simple interest so that the average return on
The two investments amounts to 2%?

Accepted Answer

A)  $7000 
B)  $11,000 
C)  $5500 
D)  $8000 
A)  $7000 
B)  $11,000 
C)  $5500 
D)  $8000

Question 9

Indicate whether the statement is true always, sometimes, or never.
-The product of two imaginary numbers is a real number.

Accepted Answer

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

Question 10

Solve the equation.
-$$x ^ { 1 / 2 } = 3 x ^ { 1 / 4 }$$

Accepted Answer

A)  $\{ 0,3 \}$ 
B)  $\{ 0,81 \}$ 
C)  $\varnothing$ 
D)  $\{ 0,9 \}$ 
A)  $\{ 0,3 \}$ 
B)  $\{ 0,81 \}$ 
C)  $\varnothing$ 
D)  $\{ 0,9 \}$

Question 11

Find the product. Write the answer in standard form.
-$$( \sqrt { 5 } + 3 i ) ( \sqrt { 5 } - 3 i )$$

Accepted Answer

A)  14 
B)  2 
C)  $5 - 9 \mathrm { i }$ 
D)  $5 + 9 \mathrm { i }$ 
A)  14 
B)  2 
C)  $5 - 9 \mathrm { i }$ 
D)  $5 + 9 \mathrm { i }$

Question 12

Solve the equation.
-$$| 9 x + 8 | = | 8 x + 5 |$$

Accepted Answer

A)  $\{ 13,1 \}$ 
B)  $\{ - 13,1 \}$ 
C)  $\left\{ - \frac { 3 } { 17 } , - 13 \right\}$ 
D)  $\left\{ - 3 , - \frac { 13 } { 17 } \right\}$ 
A)  $\{ 13,1 \}$ 
B)  $\{ - 13,1 \}$ 
C)  $\left\{ - \frac { 3 } { 17 } , - 13 \right\}$ 
D)  $\left\{ - 3 , - \frac { 13 } { 17 } \right\}$

Question 13

Solve the equation by completing the square.
-$$x ^ { 2 } - 4 x - 45 = 0$$

Accepted Answer

A)  $\{ \pm 3 i \sqrt { 5 } \}$ 
B)  $\{ - 40 , - 5 \}$ 
C)  $\{ 9 , - 5 \}$ 
D)  $\{ - 9,5 \}$ 
A)  $\{ \pm 3 i \sqrt { 5 } \}$ 
B)  $\{ - 40 , - 5 \}$ 
C)  $\{ 9 , - 5 \}$ 
D)  $\{ - 9,5 \}$

Question 14

Solve the equation.
-$$- 5 [ - 4 x + 5 - 2 ( x + 1 ) ] = 3 x - 4$$

Accepted Answer

A)  $\left\{ - \frac { 13 } { 9 } \right\}$ 
B)  $\left\{ \frac { 11 } { 27 } \right\}$ 
C)  $\left\{ - \frac { 11 } { 4 } \right\}$ 
D)  $\left\{ \frac { 39 } { 4 } \right\}$ 
A)  $\left\{ - \frac { 13 } { 9 } \right\}$ 
B)  $\left\{ \frac { 11 } { 27 } \right\}$ 
C)  $\left\{ - \frac { 11 } { 4 } \right\}$ 
D)  $\left\{ \frac { 39 } { 4 } \right\}$

Question 15

Graph the solution set.
-$$| x | > 5$$

Accepted Answer

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

Question 16

Solve the inequality. Write the solution set in interval notation.
-$| - 3 - 4 x | > 2$

Accepted Answer

A)  $\left( - \infty , \frac { 3 } { 4 } \right) \cup \left( - \frac { 1 } { 4 } , \infty \right)$ 
B)  $\left( \frac { 5 } { 4 } , \frac { 1 } { 4 } \right)$ 
C)  $\left( \frac { 1 } { 4 } , - \frac { 5 } { 4 } \right)$ 
D)  $\left( - \infty , - \frac { 5 } { 4 } \right) \cup \left( - \frac { 1 } { 4 } , \infty \right)$ 
A)  $\left( - \infty , \frac { 3 } { 4 } \right) \cup \left( - \frac { 1 } { 4 } , \infty \right)$ 
B)  $\left( \frac { 5 } { 4 } , \frac { 1 } { 4 } \right)$ 
C)  $\left( \frac { 1 } { 4 } , - \frac { 5 } { 4 } \right)$ 
D)  $\left( - \infty , - \frac { 5 } { 4 } \right) \cup \left( - \frac { 1 } { 4 } , \infty \right)$

Question 17

Solve the equation.
-$$x = \sqrt { 4 x + 12 }$$

Accepted Answer

A)  $\{ 6 \}$ 
B)  $\{ 4 \}$ 
C)  $\varnothing$ 
D)  $\{ 6 , - 2 \}$ 
A)  $\{ 6 \}$ 
B)  $\{ 4 \}$ 
C)  $\varnothing$ 
D)  $\{ 6 , - 2 \}$

Question 18

Solve the equation.
-$$x ^ { 2 } = - 49$$

Accepted Answer

A)  $\pm 7$ 
B)  $\pm \mathrm { i } \sqrt { 7 }$ 
C)  $\pm \sqrt { 7 }$ 
D)  $\pm 7 \mathrm { i }$ 
A)  $\pm 7$ 
B)  $\pm \mathrm { i } \sqrt { 7 }$ 
C)  $\pm \sqrt { 7 }$ 
D)  $\pm 7 \mathrm { i }$

Question 19

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 3 } + 4 x ^ { 2 } - 4 x - 16 \geq 0$$

Accepted Answer

A)  $[ - 4 , - 2 ] \cup [ 2 , \infty )$ 
B)  $[ - 4,2 ]$ 
C)  $[ - 4 , \infty )$ 
D)  $[ - 2,2 ] \cup [ 4 , \infty )$ 
A)  $[ - 4 , - 2 ] \cup [ 2 , \infty )$ 
B)  $[ - 4,2 ]$ 
C)  $[ - 4 , \infty )$ 
D)  $[ - 2,2 ] \cup [ 4 , \infty )$

Question 20

Solve the equation.
-$$4 x = \sqrt { 1 - 6 x }$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 } { 4 } \right\}$ 
D)  $\left\{ \frac { 1 } { 8 } \right\}$ 
A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 } { 4 } \right\}$ 
D)  $\left\{ \frac { 1 } { 8 } \right\}$

Solve the equation by the zero-factor property. - $x ^ { 2 } + 14 x + 40 = 0$

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

Solve and graph the inequality. Give answer in interval notation. - $12 < - 5 x + 2 \leq 32$ $Solve and graph the inequality. Give answer in interval notation. - 12 < - 5 x + 2 \leq 32$

Solve for the indicated variable. - $\frac { 1 } { \mathrm { Q } } = \frac { 1 } { \mathrm {~T} _ { 1 } } + \frac { 1 } { \mathrm {~T} _ { 2 } }$ , for $\mathrm { T } _ { 2 }$

Solve the equation. - $( x + 2 ) ^ { 2 / 5 } = ( 9 x ) ^ { 1 / 5 }$

Solve the equation. - $\sqrt { 3 x + 10 } = 5 - 2 x$

Find the sum or difference. Write the answer in standard form. - $( 2 - 9 \mathrm { i } ) - ( - 1 - 2 \mathrm { i } ) - ( - 2 - 3 \mathrm { i } )$

Solve the problem. -Helen Weller invested $11,000 in an account that pays 1.5% simple interest. How much additional money must be invested in an account that pays 3% simple interest so that the average return on The two investments amounts to 2%?

Indicate whether the statement is true always, sometimes, or never. -The product of two imaginary numbers is a real number.

Solve the equation. - $x ^ { 1 / 2 } = 3 x ^ { 1 / 4 }$

Find the product. Write the answer in standard form. - $( \sqrt { 5 } + 3 i ) ( \sqrt { 5 } - 3 i )$

Solve the equation. - $| 9 x + 8 | = | 8 x + 5 |$

Solve the equation by completing the square. - $x ^ { 2 } - 4 x - 45 = 0$

Solve the equation. - $- 5 [ - 4 x + 5 - 2 ( x + 1 ) ] = 3 x - 4$

Graph the solution set. - $| x | > 5$

Solve the inequality. Write the solution set in interval notation. - $| - 3 - 4 x | > 2$

Solve the equation. - $x = \sqrt { 4 x + 12 }$

Solve the equation. - $x ^ { 2 } = - 49$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } + 4 x ^ { 2 } - 4 x - 16 \geq 0$

Solve the equation. - $4 x = \sqrt { 1 - 6 x }$

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 equation by the zero-factor property. - x2+14x+40=0x ^ { 2 } + 14 x + 40 = 0x2+14x+40=0

Solve the quadratic inequality. Write the solution set in interval notation. - (2+3x)2≤−4( 2 + 3 x ) ^ { 2 } \leq - 4(2+3x)2≤−4

Solve and graph the inequality. Give answer in interval notation. - 12<−5x+2≤3212 < - 5 x + 2 \leq 3212<−5x+2≤32

Solve for the indicated variable. - 1Q=1 T1+1 T2\frac { 1 } { \mathrm { Q } } = \frac { 1 } { \mathrm {~T} _ { 1 } } + \frac { 1 } { \mathrm {~T} _ { 2 } }Q1​= T1​1​+ T2​1​ , for T2\mathrm { T } _ { 2 }T2​

Solve the equation. - (x+2)2/5=(9x)1/5( x + 2 ) ^ { 2 / 5 } = ( 9 x ) ^ { 1 / 5 }(x+2)2/5=(9x)1/5

Solve the equation. - 3x+10=5−2x\sqrt { 3 x + 10 } = 5 - 2 x3x+10​=5−2x

Find the sum or difference. Write the answer in standard form. - (2−9i)−(−1−2i)−(−2−3i)( 2 - 9 \mathrm { i } ) - ( - 1 - 2 \mathrm { i } ) - ( - 2 - 3 \mathrm { i } )(2−9i)−(−1−2i)−(−2−3i)