Question 1

Solve the formula for the indicated variable.
-$\mathrm { I } =$ Prt, for $\mathrm { P }$

Accepted Answer

A)  $P = \frac { I } { r t }$ 
B)  $P = r - I t$ 
C)  $P = \frac { r - I } { 1 + t }$ 
D)  $P = \frac { r - 1 } { \text { It } }$ 
A)  $P = \frac { I } { r t }$ 
B)  $P = r - I t$ 
C)  $P = \frac { r - I } { 1 + t }$ 
D)  $P = \frac { r - 1 } { \text { It } }$

Question 2

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { x } { x - 3 } + \frac { 1 } { x + 9 } = \frac { 12 } { x ^ { 2 } + 6 x - 27 }$$

Accepted Answer

A)  $- 9,3$ 
B)  $- 3,0,9$ 
C)  $- 3,9 , - 27$ 
D)  $- 9,0,3$ 
A)  $- 9,3$ 
B)  $- 3,0,9$ 
C)  $- 3,9 , - 27$ 
D)  $- 9,0,3$

Question 3

Solve the equation.
-Only one of the following equations is set up so that the values of a, b, and c can be determined immediately. Which one is it?

Accepted Answer

A)  $2 x ^ { 2 } + 5 x + 1 = 0$ 
B)  $( 2 x + 5 ) ( x + 1 ) = 0$ 
C)  $( 2 x + 5 ) ^ { 2 } = 1$ 
D)  $x ^ { 2 } + x = 1$ 
A)  $2 x ^ { 2 } + 5 x + 1 = 0$ 
B)  $( 2 x + 5 ) ( x + 1 ) = 0$ 
C)  $( 2 x + 5 ) ^ { 2 } = 1$ 
D)  $x ^ { 2 } + x = 1$

Question 4

Decide whether the statement is true or false.
--7 is a solution of -7x - 7x = -5.

Accepted Answer

A) True 
 B)False

Question 5

Solve the equation by completing the square.
-$$x ^ { 2 } = 7 - 4 x$$

Accepted Answer

A)  $\{ 2 + \sqrt { 11 } \}$ 
B)  $\{ - 1 \pm \sqrt { 11 } \}$ 
C)  $\{ - 2 \pm 2 \sqrt { 11 } \}$ 
D)  $\{ - 2 \pm \sqrt { 11 } \}$ 
A)  $\{ 2 + \sqrt { 11 } \}$ 
B)  $\{ - 1 \pm \sqrt { 11 } \}$ 
C)  $\{ - 2 \pm 2 \sqrt { 11 } \}$ 
D)  $\{ - 2 \pm \sqrt { 11 } \}$

Question 6

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 2 } ( x + 64 ) ^ { 2 } \geq 0$$

Accepted Answer

A)  $\varnothing$ 
B)  $( - \infty , \infty )$ 
C)  $[ - 8,0 ] \cup [ 8 , \infty )$ 
D)  $( - \infty , - 8 ] \cup [ 0,8 ]$ 
A)  $\varnothing$ 
B)  $( - \infty , \infty )$ 
C)  $[ - 8,0 ] \cup [ 8 , \infty )$ 
D)  $( - \infty , - 8 ] \cup [ 0,8 ]$

Question 7

Find the product. Write the answer in standard form.
-$$( 5 + i ) ( 5 - i ) ( 4 + 6 i )$$

Accepted Answer

A)  $100 - 6 i ^ { 3 }$ 
B)  $96 + 144 \mathrm { i }$ 
C)  $104 + 156 \mathrm { i }$ 
D)  $104 + 6 i$ 
A)  $100 - 6 i ^ { 3 }$ 
B)  $96 + 144 \mathrm { i }$ 
C)  $104 + 156 \mathrm { i }$ 
D)  $104 + 6 i$

Question 8

Solve the equation by the square root property.
-$$x ^ { 2 } = - 25$$

Accepted Answer

A)  $\{ \pm 5 i \}$ 
B)  $\{ \pm 5 \}$ 
C)  $\{ 5 \}$ 
D)  $\{ 12.5 \}$ 
A)  $\{ \pm 5 i \}$ 
B)  $\{ \pm 5 \}$ 
C)  $\{ 5 \}$ 
D)  $\{ 12.5 \}$

Question 9

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.
-$4 i , - 4 i$

Accepted Answer

A)  $x ^ { 2 } - 8 - 16 = 0$ 
B)  $x ^ { 2 } - 16 = 0$ 
C)  $x ^ { 2 } + 8 + 16 = 0$ 
D)  $x ^ { 2 } + 16 = 0$ 
A)  $x ^ { 2 } - 8 - 16 = 0$ 
B)  $x ^ { 2 } - 16 = 0$ 
C)  $x ^ { 2 } + 8 + 16 = 0$ 
D)  $x ^ { 2 } + 16 = 0$

Question 10

Solve the problem.
-It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 50 liters of 20% solution. How many liters of this should be drained and replaced with 100%
Antifreeze to get the desired strength?

Accepted Answer

A)  12.5 L 
B)  25 L 
C)  16.7 L 
D)  20 L 
A)  12.5 L 
B)  25 L 
C)  16.7 L 
D)  20 L

Question 11

Solve the equation.
-$$- 3.6 x + 1.0 = - 16 - 1.9 x$$

Accepted Answer

A)  $\{ 4.7 \}$ 
B)  $\{ 10 \}$ 
C)  $\{ - 19 \}$ 
D)  $\{ 5.3 \}$ 
A)  $\{ 4.7 \}$ 
B)  $\{ 10 \}$ 
C)  $\{ - 19 \}$ 
D)  $\{ 5.3 \}$

Question 12

Solve for y.
-Levi borrowed $5007 at 6% simple interest for 5 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 5 months? Round answers to
The nearest cent if necessary.

Accepted Answer

A)  $126.23; $5133.23 
B)  $125.18; $5132.18 
C)  $150.21; $5157.21 
D)  $100.14; $5107.14 
A)  $126.23; $5133.23 
B)  $125.18; $5132.18 
C)  $150.21; $5157.21 
D)  $100.14; $5107.14

Question 13

Simplify the power of i.
-$\frac { 1 } { i ^ { - 9 } }$

Accepted Answer

A)  i 
B)  -1 
C)  1 
D)  -i 
A)  i 
B)  -1 
C)  1 
D)  -i

Question 14

Solve the equation using the quadratic formula.
-$$x ^ { 2 } - 4 x + 20 = 0$$

Accepted Answer

A)  $\{ 6 , - 2 \}$ 
B)  $\{ 4 \pm 8 i \}$ 
C)  $\{ - 2 \pm 4 i \}$ 
D)  $\{ 2 \pm 4 i \}$ 
A)  $\{ 6 , - 2 \}$ 
B)  $\{ 4 \pm 8 i \}$ 
C)  $\{ - 2 \pm 4 i \}$ 
D)  $\{ 2 \pm 4 i \}$

Question 15

Simplify the power of i.
-Which one of the following equations is set up for direct use of the zero-factor property?

Accepted Answer

A)  $( 4 x - 5 ) ^ { 2 } = 6$ 
B)  $x ^ { 2 } - x = 6$ 
C)  $( 4 x - 5 ) ( x - 6 ) = 0$ 
D)  $4 x ^ { 2 } - 5 x - 6 = 0$ 
A)  $( 4 x - 5 ) ^ { 2 } = 6$ 
B)  $x ^ { 2 } - x = 6$ 
C)  $( 4 x - 5 ) ( x - 6 ) = 0$ 
D)  $4 x ^ { 2 } - 5 x - 6 = 0$

Question 16

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { x } { x - 7 } = \frac { 7 } { x - 7 } + 7$$

Accepted Answer

A)  $\{ 7 \}$ 
B)  $\{ - 7 \}$ 
C)  $\varnothing$ 
D)  $\{ 0 \}$ 
A)  $\{ 7 \}$ 
B)  $\{ - 7 \}$ 
C)  $\varnothing$ 
D)  $\{ 0 \}$

Question 17

Decide what values of the variable cannot possibly be solutions for the equation.
-$$4 \sqrt { x } = \sqrt { 9 x + 9 }$$

Accepted Answer

A)  $\left\{ \frac { 9 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 9 } { 8 } \right\}$ 
C)  $\left\{ \frac { 9 } { 25 } \right\}$ 
D)  $\left\{ - \frac { 9 } { 5 } \right\}$ 
A)  $\left\{ \frac { 9 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 9 } { 8 } \right\}$ 
C)  $\left\{ \frac { 9 } { 25 } \right\}$ 
D)  $\left\{ - \frac { 9 } { 5 } \right\}$

Question 18

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

Accepted Answer

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

Question 19

Solve the rational inequality. Write the solution set in interval notation.
-A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of $208 \mathrm { ft } / \mathrm { sec }$, and the gorge is $672 \mathrm { ft }$ deep, during what interval can the flare be seen? $\left( h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \right)$

Accepted Answer

A)  $6 < t < 7$ 
B)  $0 < t < 6$ 
C)  $12 < t < 13$ 
D)  $18 < \mathrm { t } < 19$ 
A)  $6 < t < 7$ 
B)  $0 < t < 6$ 
C)  $12 < t < 13$ 
D)  $18 < \mathrm { t } < 19$

Question 20

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

Accepted Answer

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

Solve the formula for the indicated variable. - $\mathrm { I } =$ Prt, for $\mathrm { P }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x } { x - 3 } + \frac { 1 } { x + 9 } = \frac { 12 } { x ^ { 2 } + 6 x - 27 }$

Solve the equation. -Only one of the following equations is set up so that the values of a, b, and c can be determined immediately. Which one is it?

Decide whether the statement is true or false. --7 is a solution of -7x - 7x = -5.

Solve the equation by completing the square. - $x ^ { 2 } = 7 - 4 x$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } ( x + 64 ) ^ { 2 } \geq 0$

Find the product. Write the answer in standard form. - $( 5 + i ) ( 5 - i ) ( 4 + 6 i )$

Solve the equation by the square root property. - $x ^ { 2 } = - 25$

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. - $4 i , - 4 i$

Solve the problem. -It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 50 liters of 20% solution. How many liters of this should be drained and replaced with 100% Antifreeze to get the desired strength?

Solve the equation. - $- 3.6 x + 1.0 = - 16 - 1.9 x$

Solve for y. -Levi borrowed $5007 at 6% simple interest for 5 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 5 months? Round answers to The nearest cent if necessary.

Simplify the power of i. - $\frac { 1 } { i ^ { - 9 } }$

Solve the equation using the quadratic formula. - $x ^ { 2 } - 4 x + 20 = 0$

Simplify the power of i. -Which one of the following equations is set up for direct use of the zero-factor property?

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x } { x - 7 } = \frac { 7 } { x - 7 } + 7$

Decide what values of the variable cannot possibly be solutions for the equation. - $4 \sqrt { x } = \sqrt { 9 x + 9 }$

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

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

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 formula for the indicated variable. - I=\mathrm { I } =I= Prt, for P\mathrm { P }P

Decide what values of the variable cannot possibly be solutions for the equation. - xx−3+1x+9=12x2+6x−27\frac { x } { x - 3 } + \frac { 1 } { x + 9 } = \frac { 12 } { x ^ { 2 } + 6 x - 27 }x−3x​+x+91​=x2+6x−2712​