Question 1

Solve the equation.
-$$\left| x ^ { 2 } + 2 x - 15 \right| = 0$$

Accepted Answer

A)  $\{ - 5 , - 3 \}$ 
B)  $\{ 3,5 \}$ 
C)  $\{ - 3,5 \}$ 
D)  $\{ - 5,3 \}$ 
A)  $\{ - 5 , - 3 \}$ 
B)  $\{ 3,5 \}$ 
C)  $\{ - 3,5 \}$ 
D)  $\{ - 5,3 \}$

Question 2

Write the number as the product of a real number and i.
-$\sqrt { - 3 }$

Accepted Answer

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

Question 3

Graph the solution set.
-$$| x | < 9$$

Accepted Answer

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

Question 4

Solve the problem.
-Only one of the following equations does not require Step 1 of the method for completing the square. Which one is it?

Accepted Answer

A)  $( 4 x + 7 ) ( x - 7 ) = 0$ 
B)  $x ^ { 2 } + x = 7$ 
C)  $4 x ^ { 2 } + 7 x - 7 = 0$ 
D)  $( 4 x + 7 ) ^ { 2 } = 7$ 
A)  $( 4 x + 7 ) ( x - 7 ) = 0$ 
B)  $x ^ { 2 } + x = 7$ 
C)  $4 x ^ { 2 } + 7 x - 7 = 0$ 
D)  $( 4 x + 7 ) ^ { 2 } = 7$

Question 5

Solve the inequality. Write the solution set in interval notation.
-$$( x - 6 ) ( x - 7 ) ( x + 1 ) < 0$$

Accepted Answer

A)  $( - 7 , - 6 ) \cup ( 1 , \infty )$ 
B)  $( - 6 , - 1 ) \cup ( 7 , \infty )$ 
C)  $( - \infty , - 1 ) \cup ( 6,7 )$ 
D)  $( - \infty , - 6 ) \cup ( 1,7 )$ 
A)  $( - 7 , - 6 ) \cup ( 1 , \infty )$ 
B)  $( - 6 , - 1 ) \cup ( 7 , \infty )$ 
C)  $( - \infty , - 1 ) \cup ( 6,7 )$ 
D)  $( - \infty , - 6 ) \cup ( 1,7 )$

Question 6

Solve the problem.
-A lot is in the shape of a right triangle. The shorter leg measures 120 m. The hypotenuse is 40 m longer than the length of the longer leg. How long is the longer leg?

Accepted Answer

A)  160 m 
B)  200 m 
C)  240 m 
D)  120 m 
A)  160 m 
B)  200 m 
C)  240 m 
D)  120 m

Question 7

Solve the problem.
-If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 117.6 \mathrm { t }$. During what interval of time will the rocket be higher than $343 \mathrm {~m}$ ?

Accepted Answer

A)  $10 < t < 12$ 
B)  $0 < \mathrm { t } < 5$ 
C)  $5 < \mathrm { t } < 7$ 
D)  $7 < \mathrm { t } < 10$ 
A)  $10 < t < 12$ 
B)  $0 < \mathrm { t } < 5$ 
C)  $5 < \mathrm { t } < 7$ 
D)  $7 < \mathrm { t } < 10$

Question 8

Solve the problem.
-A can has a surface area of 939 square inches. Its height is 6.64 inches. What is the radius of the circular top? Round to the nearest hundredth.

Accepted Answer

A)  9.35 in. 
B)  11.88 in. 
C)  4.42 in. 
D)  22.51 in. 
A)  9.35 in. 
B)  11.88 in. 
C)  4.42 in. 
D)  22.51 in.

Question 9

Find the quotient. Write the answer in standard form.
-$\frac { - 11 } { - \mathrm { i } }$

Accepted Answer

A)  $- 11 \mathrm { i }$ 
B)  $- 11$ 
C)  11 
D)  $11 \mathrm { i }$ 
A)  $- 11 \mathrm { i }$ 
B)  $- 11$ 
C)  11 
D)  $11 \mathrm { i }$

Question 10

Simplify the power of i.
-$\mathrm { i } ^ { 71 }$

Accepted Answer

A)  $- \mathrm { i }$ 
B)  -1 
C)  $\mathrm { i }$ 
D)  1 
A)  $- \mathrm { i }$ 
B)  -1 
C)  $\mathrm { i }$ 
D)  1

Question 11

Solve the equation.
-$$x ^ { 2 } = 28$$

Accepted Answer

A)  $\pm 2 \sqrt { 7 }$ 
B)  $\pm 4 \mathrm { i } \sqrt { 7 }$ 
C)  $\pm 4 \sqrt { 7 }$ 
D)  $\pm 2 \mathrm { i } \sqrt { 7 }$ 
A)  $\pm 2 \sqrt { 7 }$ 
B)  $\pm 4 \mathrm { i } \sqrt { 7 }$ 
C)  $\pm 4 \sqrt { 7 }$ 
D)  $\pm 2 \mathrm { i } \sqrt { 7 }$

Question 12

Solve the equation.
-$$\frac { 2 } { 17 x } + 7 = \frac { 3 } { 23 x }$$

Accepted Answer

A)  $\left\{ \frac { 3 } { 7 } \right\}$ 
B)  $\varnothing$ 
C)  $\left\{ \frac { 5 } { 7 } \right\}$ 
D)  $\left\{ \frac { 5 } { 2737 } \right\}$ 
A)  $\left\{ \frac { 3 } { 7 } \right\}$ 
B)  $\varnothing$ 
C)  $\left\{ \frac { 5 } { 7 } \right\}$ 
D)  $\left\{ \frac { 5 } { 2737 } \right\}$

Question 13

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 14

Solve the equation by the square root property.
-$$( 6 x + 9 ) ^ { 2 } = 16$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 6 } , - \frac { 13 } { 6 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 6 } , 0 \right\}$ 
C)  $\left\{ \frac { 5 } { 6 } , \frac { 13 } { 6 } \right\}$ 
D)  $\left\{ \frac { 7 } { 6 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 6 } , - \frac { 13 } { 6 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 6 } , 0 \right\}$ 
C)  $\left\{ \frac { 5 } { 6 } , \frac { 13 } { 6 } \right\}$ 
D)  $\left\{ \frac { 7 } { 6 } \right\}$

Question 15

Solve the formula for the indicated variable.
-$I =$ Prt, for $t$

Accepted Answer

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

Question 16

Solve the equation by the square root property.
-$$x ^ { 2 } = - 225$$

Accepted Answer

A)  $\{ 112.5 \}$ 
B)  $\{ 15 \}$ 
C)  $\{ \pm 15 i \}$ 
D)  $\{ \pm 15 \}$ 
A)  $\{ 112.5 \}$ 
B)  $\{ 15 \}$ 
C)  $\{ \pm 15 i \}$ 
D)  $\{ \pm 15 \}$

Question 17

Solve the equation.
-$$4 x - 6 + 7 ( x + 1 ) = - 3 x - 4$$

Accepted Answer

A)  $\left\{ - \frac { 17 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 17 } { 14 } \right\}$ 
D)  $\left\{ - \frac { 5 } { 14 } \right\}$ 
A)  $\left\{ - \frac { 17 } { 4 } \right\}$ 
B)  $\left\{ - \frac { 5 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 17 } { 14 } \right\}$ 
D)  $\left\{ - \frac { 5 } { 14 } \right\}$

Question 18

Solve the problem.
-Sophia borrowed $\$ 16,007$ at $5 \%$ simple interest for 9 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 9 months? Round answers to the nearest cent if necessary.

Accepted Answer

A)  $\$ 533.57 ; \$ 16,540.57$ 
B)  $\$ 605.31 ; \$ 16,612.31$ 
C)  $\$ 600.26 ; \$ 16,607.26$ 
D)  $\$ 666.96 ; \$ 16,673.96$ 
A)  $\$ 533.57 ; \$ 16,540.57$ 
B)  $\$ 605.31 ; \$ 16,612.31$ 
C)  $\$ 600.26 ; \$ 16,607.26$ 
D)  $\$ 666.96 ; \$ 16,673.96$

Question 19

Solve the equation by the square root property.
-$$( x + 9 ) ^ { 2 } = - 5$$

Accepted Answer

A)  $\{ - 3 - \sqrt { 5 } \}$ 
B)  $\{ - 9 \pm \sqrt { 5 } \}$ 
C)  $\{ - 9 \pm i \sqrt { 5 } \}$ 
D)  $\{ - 4,14 \}$ 
A)  $\{ - 3 - \sqrt { 5 } \}$ 
B)  $\{ - 9 \pm \sqrt { 5 } \}$ 
C)  $\{ - 9 \pm i \sqrt { 5 } \}$ 
D)  $\{ - 4,14 \}$

Question 20

Solve the equation.
-$$( 2 x + 5 ) ^ { 1 / 2 } - ( x - 2 ) ^ { 1 / 2 } = 3$$

Accepted Answer

A)  $\{ 2 \}$ 
B)  $\{ 3,8 \}$ 
C)  $\{ 2,38 \}$ 
D)  $\{ - 2 \}$ 
A)  $\{ 2 \}$ 
B)  $\{ 3,8 \}$ 
C)  $\{ 2,38 \}$ 
D)  $\{ - 2 \}$

Solve the equation. - $\left| x ^ { 2 } + 2 x - 15 \right| = 0$

Write the number as the product of a real number and i. - $\sqrt { - 3 }$

Graph the solution set. - $| x | < 9$

Solve the problem. -Only one of the following equations does not require Step 1 of the method for completing the square. Which one is it?

Solve the inequality. Write the solution set in interval notation. - $( x - 6 ) ( x - 7 ) ( x + 1 ) < 0$

Solve the problem. -A lot is in the shape of a right triangle. The shorter leg measures 120 m. The hypotenuse is 40 m longer than the length of the longer leg. How long is the longer leg?

Solve the problem. -If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 117.6 \mathrm { t }$ . During what interval of time will the rocket be higher than $343 \mathrm {~m}$ ?

Solve the problem. -A can has a surface area of 939 square inches. Its height is 6.64 inches. What is the radius of the circular top? Round to the nearest hundredth.

Find the quotient. Write the answer in standard form. - $\frac { - 11 } { - \mathrm { i } }$

Simplify the power of i. - $\mathrm { i } ^ { 71 }$

Solve the equation. - $x ^ { 2 } = 28$

Solve the equation. - $\frac { 2 } { 17 x } + 7 = \frac { 3 } { 23 x }$

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 by the square root property. - $( 6 x + 9 ) ^ { 2 } = 16$

Solve the formula for the indicated variable. - $I =$ Prt, for $t$

Solve the equation by the square root property. - $x ^ { 2 } = - 225$

Solve the equation. - $4 x - 6 + 7 ( x + 1 ) = - 3 x - 4$

Solve the problem. -Sophia borrowed $\$ 16,007$ at $5 \%$ simple interest for 9 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 9 months? Round answers to the nearest cent if necessary.

Solve the equation by the square root property. - $( x + 9 ) ^ { 2 } = - 5$

Solve the equation. - $( 2 x + 5 ) ^ { 1 / 2 } - ( x - 2 ) ^ { 1 / 2 } = 3$

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. - ∣x2+2x−15∣=0\left| x ^ { 2 } + 2 x - 15 \right| = 0​x2+2x−15​=0

Write the number as the product of a real number and i. - −3\sqrt { - 3 }−3​

Graph the solution set. - ∣x∣<9| x | < 9∣x∣<9