Question 1

Solve the equation.
-$$37 b + 20 = - 8 b$$

Accepted Answer

A)  $b = - \frac { 4 } { 9 }$ 
B)  $\mathrm { b } = \frac { 4 } { 9 }$ 
C)  $b = \frac { 20 } { 29 }$ 
D)  $b = - \frac { 9 } { 4 }$ 
A)  $b = - \frac { 4 } { 9 }$ 
B)  $\mathrm { b } = \frac { 4 } { 9 }$ 
C)  $b = \frac { 20 } { 29 }$ 
D)  $b = - \frac { 9 } { 4 }$

Question 2

Solve the inequality. Use algebra to solve the corresponding equation.
-$$x ^ { 2 } - 8 x + 15 \geq 0$$

Accepted Answer

A)  $[ 3,5 ]$ 
B)  $[ 5 , \infty )$ 
C)  $( - \infty , 3 ]$ 
D)  $( - \infty , 3 ] \cup [ 5 , \infty )$ 
A)  $[ 3,5 ]$ 
B)  $[ 5 , \infty )$ 
C)  $( - \infty , 3 ]$ 
D)  $( - \infty , 3 ] \cup [ 5 , \infty )$

Question 3

Find a slope-intercept form equation for the line.
-Through $( 0,3 )$, with slope $- \frac { 4 } { 9 }$

Accepted Answer

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

Question 4

Simplify the expression. Assume that the variables in the denominator are nonzero.
-$$\frac { \left( x ^ { - 3 } y ^ { 4 } \right) ^ { - 3 } } { \left( y ^ { 4 } x ^ { - 5 } \right) ^ { - 4 } }$$

Accepted Answer

A)  $\frac { x ^ { 11 } } { y ^ { 4 } }$ 
B)  $\frac { y ^ { 4 } } { x ^ { 11 } }$ 
C)  $\frac { y ^ { 4 } } { x ^ { 6 } }$ 
D)  $\frac { x ^ { 6 } } { y ^ { 4 } }$ 
A)  $\frac { x ^ { 11 } } { y ^ { 4 } }$ 
B)  $\frac { y ^ { 4 } } { x ^ { 11 } }$ 
C)  $\frac { y ^ { 4 } } { x ^ { 6 } }$ 
D)  $\frac { x ^ { 6 } } { y ^ { 4 } }$

Question 5

Solve the inequality. Use algebra to solve the corresponding equation.
-$$x ^ { 2 } + 4 > 0$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( 4 , \infty )$ 
C)  $( - \infty , 4 )$ 
D)  No solution 
A)  $( - \infty , \infty )$ 
B)  $( 4 , \infty )$ 
C)  $( - \infty , 4 )$ 
D)  No solution

Question 6

Solve the problem.
-Assume that the situation described can be modeled by a straight line graph. Use the given information to find the y = mx + b form of the equation of the line. The number of births in County A has been increasing in recent
Years. Use the information given on the bar graph for the years 1960 and 1990. Let x = 0 represent the year 1960
And y represent the number of births.

Accepted Answer

A)  $y = \frac { 30 } { 497 } x + \frac { 930,140 } { 497 }$ 
B)  $y = \frac { 1990 } { 497 } x - 2190$ 
C)  $y = \frac { 497 } { 1990 } x + 1693$ 
D)  $y = \frac { 497 } { 30 } x + 1693$ 
A)  $y = \frac { 30 } { 497 } x + \frac { 930,140 } { 497 }$ 
B)  $y = \frac { 1990 } { 497 } x - 2190$ 
C)  $y = \frac { 497 } { 1990 } x + 1693$ 
D)  $y = \frac { 497 } { 30 } x + 1693$

Question 7

Find a slope-intercept form equation for the line.
-Through $( 5,5 )$, with slope $- \frac { 2 } { 5 }$

Accepted Answer

A)  $y = \frac { 2 } { 5 } x - \frac { 35 } { 5 }$ 
B)  $y = - \frac { 2 } { 5 } x + \frac { 10 } { 5 }$ 
C)  $y = - \frac { 2 } { 5 } x + \frac { 35 } { 5 }$ 
D)  $y = \frac { 2 } { 5 } x + \frac { 10 } { 5 }$ 
A)  $y = \frac { 2 } { 5 } x - \frac { 35 } { 5 }$ 
B)  $y = - \frac { 2 } { 5 } x + \frac { 10 } { 5 }$ 
C)  $y = - \frac { 2 } { 5 } x + \frac { 35 } { 5 }$ 
D)  $y = \frac { 2 } { 5 } x + \frac { 10 } { 5 }$

Question 8

Write the expression in standard form.
-$$\frac { 1 + 5 i } { ( 1 - 5 i ) ^ { 2 } }$$

Accepted Answer

A)  $- \frac { 37 } { 338 } + \frac { 35 } { 169 } i$ 
B)  $\frac { 1 } { 676 } + \frac { 15 } { 676 } \mathrm { i }$ 
C)  $- \frac { 37 } { 338 } - \frac { 61 } { 338 } \mathrm { i }$ 
D)  $- \frac { 37 } { 338 } - \frac { 55 } { 338 } i$ 
A)  $- \frac { 37 } { 338 } + \frac { 35 } { 169 } i$ 
B)  $\frac { 1 } { 676 } + \frac { 15 } { 676 } \mathrm { i }$ 
C)  $- \frac { 37 } { 338 } - \frac { 61 } { 338 } \mathrm { i }$ 
D)  $- \frac { 37 } { 338 } - \frac { 55 } { 338 } i$

Question 9

Find the center and radius of the circle.
-$$x ^ { 2 } + y ^ { 2 } = 7$$

Accepted Answer

A)  $( 0,0 ) , r = 7$ 
B)  $( 1,1 ) , r = \sqrt { 7 }$ 
C)  $( 1,1 ) , r = 7$ 
D)  $( 0,0 ) , r = \sqrt { 7 }$ 
A)  $( 0,0 ) , r = 7$ 
B)  $( 1,1 ) , r = \sqrt { 7 }$ 
C)  $( 1,1 ) , r = 7$ 
D)  $( 0,0 ) , r = \sqrt { 7 }$

Question 10

Find the decimal form for the rational number. If it repeats, then so indicate with a bar.
-$\frac { 11 } { 4 }$

Accepted Answer

A)  $2.76$ 
B)  $2 . \overline { 75 }$ 
C)  $2.75$ 
D)  $2.7 \overline { 5 }$ 
A)  $2.76$ 
B)  $2 . \overline { 75 }$ 
C)  $2.75$ 
D)  $2.7 \overline { 5 }$

Question 11

Solve by completing the square.
-$$9 x ^ { 2 } + 5 = 18 x$$

Accepted Answer

A)  $\frac { - 5 } { 3 } , \frac { - 1 } { 3 }$ 
B)  $\frac { 1 } { 9 } , \frac { 4 } { 9 }$ 
C)  $\frac { 5 } { 3 } , \frac { 1 } { 3 }$ 
D)  $\frac { 5 } { 9 } , \frac { 1 } { 9 }$ 
A)  $\frac { - 5 } { 3 } , \frac { - 1 } { 3 }$ 
B)  $\frac { 1 } { 9 } , \frac { 4 } { 9 }$ 
C)  $\frac { 5 } { 3 } , \frac { 1 } { 3 }$ 
D)  $\frac { 5 } { 9 } , \frac { 1 } { 9 }$

Question 12

Solve the inequality algebraically. Write the solution in interval notation.
-$$| x - 4 | > 3.7$$

Accepted Answer

A)  $( - \infty , 0.3 ] \cup [ 7.7 , \infty )$ 
B)  $( - \infty , 0.3 ) \cup ( 7.7 , \infty )$ 
C)  $( 7.7 , \infty )$ 
D)  $( - \infty , 0.3 )$ 
A)  $( - \infty , 0.3 ] \cup [ 7.7 , \infty )$ 
B)  $( - \infty , 0.3 ) \cup ( 7.7 , \infty )$ 
C)  $( 7.7 , \infty )$ 
D)  $( - \infty , 0.3 )$

Question 13

Solve the inequality algebraically. Write the solution in interval notation.
-$$| x + 3 | \leq 7$$

Accepted Answer

A)  $[ - 10,4 ]$ 
B)  $[ - 10,4 )$ 
C)  $( - 10,4 ]$ 
D)  $( - 10,4 )$ 
A)  $[ - 10,4 ]$ 
B)  $[ - 10,4 )$ 
C)  $( - 10,4 ]$ 
D)  $( - 10,4 )$

Question 14

Convert to inequality notation. Find the endpoints and state whether the interval is bounded or unbounded, and its type.
-$$( - 4 , - 1 )$$

Accepted Answer

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

Question 15

Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
-Through $( 1,4 )$, perpendicular to $x = 5$

Accepted Answer

A)  $y = 5$ 
B)  $y = - 4$ 
C)  $y = 4$ 
D)  $x = 5$ 
A)  $y = 5$ 
B)  $y = - 4$ 
C)  $y = 4$ 
D)  $x = 5$

Question 16

Write the statement using absolute value notation.
-The distance between $x$ and 3 is 7 .

Accepted Answer

A)  $| x + 3 | = 7$ 
B)  $| x - 7 | = 3$ 
C)  $| x + 7 | = 3$ 
D)  $| x - 3 | = 7$ 
A)  $| x + 3 | = 7$ 
B)  $| x - 7 | = 3$ 
C)  $| x + 7 | = 3$ 
D)  $| x - 3 | = 7$

Question 17

Solve the inequality algebraically. Write the solution in interval notation.
-$$\left| \frac { x + 3 } { 2 } \right| \geq 1$$

Accepted Answer

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

Question 18

Write the expression in the form bi, where b is a real number.
-$\sqrt { - 25 }$

Accepted Answer

A)  $\pm 5$ 
B)  $- i \sqrt { 5 }$ 
C)  $- 5 \mathrm { i }$ 
D)  $5 \mathrm { i }$ 
A)  $\pm 5$ 
B)  $- i \sqrt { 5 }$ 
C)  $- 5 \mathrm { i }$ 
D)  $5 \mathrm { i }$

Question 19

Find the real numbers x and y that make the equation true.
-5 + yi = x + 7i

Accepted Answer

A)  x = 7, y = 5 
B)  x = 5, y = 7 
C)  x = -5, y = 7 
D)  x = 5, y = -7 
A)  x = 7, y = 5 
B)  x = 5, y = 7 
C)  x = -5, y = 7 
D)  x = 5, y = -7

Question 20

Evaluate the expression.
-$$| ( - 3 ) 8 |$$
$$| ( - 3 ) 8 |$$

Accepted Answer

A)  8 
B)  24 
C)  $- 3$ 
D)  $- 24$ 
A)  8 
B)  24 
C)  $- 3$ 
D)  $- 24$

Solve the equation. - $37 b + 20 = - 8 b$

Solve the inequality. Use algebra to solve the corresponding equation. - $x ^ { 2 } - 8 x + 15 \geq 0$

Find a slope-intercept form equation for the line. -Through $( 0,3 )$ , with slope $- \frac { 4 } { 9 }$

Simplify the expression. Assume that the variables in the denominator are nonzero. - $\frac { \left( x ^ { - 3 } y ^ { 4 } \right) ^ { - 3 } } { \left( y ^ { 4 } x ^ { - 5 } \right) ^ { - 4 } }$

Solve the inequality. Use algebra to solve the corresponding equation. - $x ^ { 2 } + 4 > 0$

Find a slope-intercept form equation for the line. -Through $( 5,5 )$ , with slope $- \frac { 2 } { 5 }$

Write the expression in standard form. - $\frac { 1 + 5 i } { ( 1 - 5 i ) ^ { 2 } }$

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } = 7$

Find the decimal form for the rational number. If it repeats, then so indicate with a bar. - $\frac { 11 } { 4 }$

Solve by completing the square. - $9 x ^ { 2 } + 5 = 18 x$

Solve the inequality algebraically. Write the solution in interval notation. - $| x - 4 | > 3.7$

Solve the inequality algebraically. Write the solution in interval notation. - $| x + 3 | \leq 7$

Convert to inequality notation. Find the endpoints and state whether the interval is bounded or unbounded, and its type. - $( - 4 , - 1 )$

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through $( 1,4 )$ , perpendicular to $x = 5$

Write the statement using absolute value notation. -The distance between $x$ and 3 is 7 .

Solve the inequality algebraically. Write the solution in interval notation. - $\left| \frac { x + 3 } { 2 } \right| \geq 1$

Write the expression in the form bi, where b is a real number. - $\sqrt { - 25 }$

Find the real numbers x and y that make the equation true. -5 + yi = x + 7i

Evaluate the expression. - $| ( - 3 ) 8 |$ $| ( - 3 ) 8 |$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

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Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

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An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 12: Prerequisites

Solve the equation. - 37b+20=−8b37 b + 20 = - 8 b37b+20=−8b

Solve the inequality. Use algebra to solve the corresponding equation. - x2−8x+15≥0x ^ { 2 } - 8 x + 15 \geq 0x2−8x+15≥0

Find a slope-intercept form equation for the line. -Through (0,3)( 0,3 )(0,3) , with slope −49- \frac { 4 } { 9 }−94​

Simplify the expression. Assume that the variables in the denominator are nonzero. - (x−3y4)−3(y4x−5)−4\frac { \left( x ^ { - 3 } y ^ { 4 } \right) ^ { - 3 } } { \left( y ^ { 4 } x ^ { - 5 } \right) ^ { - 4 } }(y4x−5)−4(x−3y4)−3​

Solve the inequality. Use algebra to solve the corresponding equation. - x2+4>0x ^ { 2 } + 4 > 0x2+4>0

Find a slope-intercept form equation for the line. -Through (5,5)( 5,5 )(5,5) , with slope −25- \frac { 2 } { 5 }−52​

Write the expression in standard form. - 1+5i(1−5i)2\frac { 1 + 5 i } { ( 1 - 5 i ) ^ { 2 } }(1−5i)21+5i​

Find the center and radius of the circle. - x2+y2=7x ^ { 2 } + y ^ { 2 } = 7x2+y2=7

Find the decimal form for the rational number. If it repeats, then so indicate with a bar. - 114\frac { 11 } { 4 }411​

Solve by completing the square. - 9x2+5=18x9 x ^ { 2 } + 5 = 18 x9x2+5=18x

Solve the inequality algebraically. Write the solution in interval notation. - ∣x−4∣>3.7| x - 4 | > 3.7∣x−4∣>3.7

Solve the inequality algebraically. Write the solution in interval notation. - ∣x+3∣≤7| x + 3 | \leq 7∣x+3∣≤7

Convert to inequality notation. Find the endpoints and state whether the interval is bounded or unbounded, and its type. - (−4,−1)( - 4 , - 1 )(−4,−1)

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through (1,4)( 1,4 )(1,4) , perpendicular to x=5x = 5x=5

Write the statement using absolute value notation. -The distance between xxx and 3 is 7 .

Solve the inequality algebraically. Write the solution in interval notation. - ∣x+32∣≥1\left| \frac { x + 3 } { 2 } \right| \geq 1​2x+3​​≥1

Write the expression in the form bi, where b is a real number. - −25\sqrt { - 25 }−25​