Question 1

Solve the inequality.
-$0 \leq 4 t + 1 < 7$

Accepted Answer

A)  $ = \frac { 1 } { 4 } \leq t < \frac { 7 } { 4 }$ 
B)  $- \frac { 1 } { 4 } \leq t < \frac { 3 } { 2 }$ 
C)  $- 2 \leq t < \frac { 3 } { 2 }$ 
D)  $- \frac { 1 } { 4 } < t \leq \frac { 3 } { 2 }$ 
A)  $ = \frac { 1 } { 4 } \leq t < \frac { 7 } { 4 }$ 
B)  $- \frac { 1 } { 4 } \leq t < \frac { 3 } { 2 }$ 
C)  $- 2 \leq t < \frac { 3 } { 2 }$ 
D)  $- \frac { 1 } { 4 } < t \leq \frac { 3 } { 2 }$

Question 2

Convert to inequality notation. Find the endpoints and state whether the interval is bounded or unbounded, and its type.
-$$( - \infty , 10 )$$

Accepted Answer

The answer of Convert to inequality notation. Find the endpoints...

Question 3

Write the expression in the form bi, where b is a real number.
-$- \sqrt { - 272 }$

Accepted Answer

A)  $4 \sqrt { 17 }$ 
B)  $4 \mathrm { i } \sqrt { 17 }$ 
C)  $- 4 \sqrt { 17 }$ 
D)  $- 4 i \sqrt { 17 }$ 
A)  $4 \sqrt { 17 }$ 
B)  $4 \mathrm { i } \sqrt { 17 }$ 
C)  $- 4 \sqrt { 17 }$ 
D)  $- 4 i \sqrt { 17 }$

Question 4

Solve the equation using the quadratic formula.
-$$x ( x + 5 ) = 2$$

Accepted Answer

A)  $x = \frac { - \sqrt { 33 } } { 2 }$ or $x = \frac { \sqrt { 33 } } { 2 }$ 
B)  $x = \frac { - 5 - \sqrt { 33 } } { 2 }$ or $x = \frac { - 5 + \sqrt { 33 } } { 2 }$ 
C)  $x = - 5$ or $x = 0$ 
D)  $x = - 5$ or $x = 5$ 
A)  $x = \frac { - \sqrt { 33 } } { 2 }$ or $x = \frac { \sqrt { 33 } } { 2 }$ 
B)  $x = \frac { - 5 - \sqrt { 33 } } { 2 }$ or $x = \frac { - 5 + \sqrt { 33 } } { 2 }$ 
C)  $x = - 5$ or $x = 0$ 
D)  $x = - 5$ or $x = 5$

Question 5

Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
-Through $( - 7 , - 5 )$, perpendicular to $6 x + 5 y = - 67$

Accepted Answer

A)  $y = - \frac { 5 } { 6 } x - \frac { 5 } { 6 }$ 
B)  $y = \frac { 5 } { 6 } x + \frac { 5 } { 6 }$ 
C)  $y = \frac { 5 } { 6 } x$ 
D)  $y = \frac { 6 } { 5 } x - 5$ 
A)  $y = - \frac { 5 } { 6 } x - \frac { 5 } { 6 }$ 
B)  $y = \frac { 5 } { 6 } x + \frac { 5 } { 6 }$ 
C)  $y = \frac { 5 } { 6 } x$ 
D)  $y = \frac { 6 } { 5 } x - 5$

Question 6

Find the real numbers x and y that make the equation true.
-$$( x + 2 i ) = ( 4 - i ) + ( - 4 - 6 y i )$$

Accepted Answer

A)  $x = 0 , y = - \frac { 1 } { 2 }$ 
B)  $x = 8 , y = 3$ 
C)  $x = 8 , y = \frac { 1 } { 2 }$ 
D)  $x = 0 , y = 3$ 
A)  $x = 0 , y = - \frac { 1 } { 2 }$ 
B)  $x = 8 , y = 3$ 
C)  $x = 8 , y = \frac { 1 } { 2 }$ 
D)  $x = 0 , y = 3$

Question 7

Find the decimal form for the rational number. If it repeats, then so indicate with a bar.
-$- \frac { 3 } { 8 }$

Accepted Answer

A)  $- 0.3 \overline { 75 }$  . 
B)  $- 0.37 \overline { 5 }$ . 
C)  $- 0.375$   . 
D)  $- 0 . \overline { 375 }$. 
A)  $- 0.3 \overline { 75 }$  . 
B)  $- 0.37 \overline { 5 }$ . 
C)  $- 0.375$   . 
D)  $- 0 . \overline { 375 }$.

Question 8

Write the product in standard form.
-(6 - 8i)(3 - 8i)

Accepted Answer

A)  -46 - 72i 
B)  64i2 - 72i + 18 
C)  -46 + 72i 
D)  82 + 24i 
A)  -46 - 72i 
B)  64i2 - 72i + 18 
C)  -46 + 72i 
D)  82 + 24i

Question 9

Solve the inequality and draw a number line graph of the solution.
-$4 x-1>2 x+3$

Accepted Answer

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

Question 10

Find the real numbers x and y that make the equation true.
-$$( - 4 - 2 i ) - 5 = x - ( - 7 + y i )$$

Accepted Answer

A)  $x = - 16 , y = 2$ 
B)  $x = - 6 , y = - 2$ 
C)  $x = - 6 , y = 2$ 
D)  $x = 8 , y = 2$ 
A)  $x = - 16 , y = 2$ 
B)  $x = - 6 , y = - 2$ 
C)  $x = - 6 , y = 2$ 
D)  $x = 8 , y = 2$

Question 11

Use interval notation to describe the interval of real numbers.
-

Accepted Answer

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

Question 12

Use a method of your choice to solve the equation.
-$$x + 1 - 2 \sqrt { x + 7 } = 0$$

Accepted Answer

A)  $x = - 1 + 2 \sqrt { 7 }$ 
B)  $x = - 2 \sqrt { 7 }$ or $x = 2 \sqrt { 7 }$ 
C)  $x = 1 + 2 \sqrt { 7 }$ 
D)  $x = - 13$ or $x = 15$ 
A)  $x = - 1 + 2 \sqrt { 7 }$ 
B)  $x = - 2 \sqrt { 7 }$ or $x = 2 \sqrt { 7 }$ 
C)  $x = 1 + 2 \sqrt { 7 }$ 
D)  $x = - 13$ or $x = 15$

Question 13

Solve the inequality algebraically. Write the solution in interval notation.
-$$| 5 + 3 x | - 2 > 5$$

Accepted Answer

A)  $\left( - 4 , \frac { 2 } { 3 } \right)$ 
B)  $( - \infty , - 4 )$ 
C)  $( - \infty , - 4 ) \cup \left( \frac { 2 } { 3 } , \infty \right)$ 
D)  $\left( - \infty , \frac { 2 } { 3 } \right)$ 
A)  $\left( - 4 , \frac { 2 } { 3 } \right)$ 
B)  $( - \infty , - 4 )$ 
C)  $( - \infty , - 4 ) \cup \left( \frac { 2 } { 3 } , \infty \right)$ 
D)  $\left( - \infty , \frac { 2 } { 3 } \right)$

Question 14

Perform the indicated operation. Write the result in standard form.
-$$( - 1 - 4 i ) ^ { 3 }$$

Accepted Answer

A)  $47 - 12 i + i ^ { 3 }$ 
B)  $47 + 52 \mathrm { i }$ 
C)  $47 - 37 i$ 
D)  $1 - 48 \mathrm { i } ^ { 2 } - 12 \mathrm { i } + \mathrm { i } ^ { 3 }$ 
A)  $47 - 12 i + i ^ { 3 }$ 
B)  $47 + 52 \mathrm { i }$ 
C)  $47 - 37 i$ 
D)  $1 - 48 \mathrm { i } ^ { 2 } - 12 \mathrm { i } + \mathrm { i } ^ { 3 }$

Question 15

Use interval notation to describe the set of numbers.
-The cost of a computer is more than $917 and less than $5532.

Accepted Answer

A)  [917, 5532) 
B)  [5532, 917] 
C)  [917, 5532] 
D)  (917, 5532) 
A)  [917, 5532) 
B)  [5532, 917] 
C)  [917, 5532] 
D)  (917, 5532)

Question 16

Find the product of the complex number and its conjugate.
-$3 + \sqrt { 11 } i$

Accepted Answer

A)  $- 2$ 
B)  $- 112$ 
C)  20 
D)  130 
A)  $- 2$ 
B)  $- 112$ 
C)  20 
D)  130

Question 17

Write the statement using absolute value notation.
-The distance between $\mathrm { z }$ and $\mathrm { c }$ is greater than 13 units.

Accepted Answer

A) $| z - c | > 13$ B) $| \mathrm { z } + \mathrm { c } | > 13$ C) $| \mathrm { z } + 13 | \geq \mathrm { C }$ D) $| \mathrm { z } - 13 | < \mathrm { C }$ A) $| z - c | > 13$ B) $| \mathrm { z } + \mathrm { c } | > 13$ C) $| \mathrm { z } + 13 | \geq \mathrm { C }$ D) $| \mathrm { z } - 13 | < \mathrm { C }$

Question 18

Find the real numbers x and y that make the equation true.
-$( - 2 - 5 i ) + 6 = x - ( 7 + y i )$

Accepted Answer

A)  $x = - 1 , y = 5$ 
B)  $x = 11 , y = 5$ 
C)  $x = - 15 , y = 5$ 
D)  $x = - 1 , y = - 5$ 
A)  $x = - 1 , y = 5$ 
B)  $x = 11 , y = 5$ 
C)  $x = - 15 , y = 5$ 
D)  $x = - 1 , y = - 5$

Question 19

Determine whether the equation is linear in x.
-$$9 x + 7 = 0.9$$

Accepted Answer

A) True 
 B)False

Question 20

Simplify the expression. Assume that the variables in the denominator are nonzero.
-$\left( \frac { 4 } { y ^ { 8 } } \right) ^ { 3 }$

Accepted Answer

A)  $\frac { \mathrm { y } ^ { 12 } } { 64 }$ 
B)  $\frac { 64 } { y ^ { 24 } }$ 
C)  $\frac { 64 } { y ^ { 8 } }$ 
D)  $\frac { 4 } { \mathrm { y } ^ { 24 } }$ 
A)  $\frac { \mathrm { y } ^ { 12 } } { 64 }$ 
B)  $\frac { 64 } { y ^ { 24 } }$ 
C)  $\frac { 64 } { y ^ { 8 } }$ 
D)  $\frac { 4 } { \mathrm { y } ^ { 24 } }$

Solve the inequality. - $0 \leq 4 t + 1 < 7$

Convert to inequality notation. Find the endpoints and state whether the interval is bounded or unbounded, and its type. - $( - \infty , 10 )$

Write the expression in the form bi, where b is a real number. - $- \sqrt { - 272 }$

Solve the equation using the quadratic formula. - $x ( x + 5 ) = 2$

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through $( - 7 , - 5 )$ , perpendicular to $6 x + 5 y = - 67$

Find the real numbers x and y that make the equation true. - $( x + 2 i ) = ( 4 - i ) + ( - 4 - 6 y i )$

Find the decimal form for the rational number. If it repeats, then so indicate with a bar. - $- \frac { 3 } { 8 }$

Write the product in standard form. -(6 - 8i)(3 - 8i)

Solve the inequality and draw a number line graph of the solution. - $4 x-1>2 x+3$

Find the real numbers x and y that make the equation true. - $( - 4 - 2 i ) - 5 = x - ( - 7 + y i )$

Use interval notation to describe the interval of real numbers. -

Use a method of your choice to solve the equation. - $x + 1 - 2 \sqrt { x + 7 } = 0$

Solve the inequality algebraically. Write the solution in interval notation. - $| 5 + 3 x | - 2 > 5$

Perform the indicated operation. Write the result in standard form. - $( - 1 - 4 i ) ^ { 3 }$

Use interval notation to describe the set of numbers. -The cost of a computer is more than $917 and less than $5532.

Find the product of the complex number and its conjugate. - $3 + \sqrt { 11 } i$

Write the statement using absolute value notation. -The distance between $\mathrm { z }$ and $\mathrm { c }$ is greater than 13 units.

Find the real numbers x and y that make the equation true. - $( - 2 - 5 i ) + 6 = x - ( 7 + y i )$

Determine whether the equation is linear in x. - $9 x + 7 = 0.9$

Simplify the expression. Assume that the variables in the denominator are nonzero. - $\left( \frac { 4 } { y ^ { 8 } } \right) ^ { 3 }$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 12: Prerequisites

Solve the inequality. - 0≤4t+1<70 \leq 4 t + 1 < 70≤4t+1<7

Convert to inequality notation. Find the endpoints and state whether the interval is bounded or unbounded, and its type. - (−∞,10)( - \infty , 10 )(−∞,10)

Write the expression in the form bi, where b is a real number. - −−272- \sqrt { - 272 }−−272​

Solve the equation using the quadratic formula. - x(x+5)=2x ( x + 5 ) = 2x(x+5)=2

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through (−7,−5)( - 7 , - 5 )(−7,−5) , perpendicular to 6x+5y=−676 x + 5 y = - 676x+5y=−67

Find the real numbers x and y that make the equation true. - (x+2i)=(4−i)+(−4−6yi)( x + 2 i ) = ( 4 - i ) + ( - 4 - 6 y i )(x+2i)=(4−i)+(−4−6yi)

Find the decimal form for the rational number. If it repeats, then so indicate with a bar. - −38- \frac { 3 } { 8 }−83​