Question 1

Find all real solutions of the equation. $| 7 x + 1 | = 7$

Accepted Answer

A)  $x = - 8$ ,
$x = 8$ 
B)  $x = - \frac { 8 } { 7 }$ ,
$x = \frac { 6 } { 7 }$ 
C)  $x = - \frac {8 } { 7 }$ ,
$x = - 1$ 
D)  $x = - \frac { 7 } { 8 }$ ,
$x = \frac { 7 } { 6 }$ 
E)  no solution 
A)  $x = - 8$ ,
$x = 8$ 
B)  $x = - \frac { 8 } { 7 }$ ,
$x = \frac { 6 } { 7 }$ 
C)  $x = - \frac {8 } { 7 }$ ,
$x = - 1$ 
D)  $x = - \frac { 7 } { 8 }$ ,
$x = \frac { 7 } { 6 }$ 
E)  no solution

Question 2

Use a graphing calculator or computer to determine which of the viewing rectangles produces the most appropriate graph of the equation $y = - | x + 2 | - 3$ .

Accepted Answer

A)  $[ - 1,1 ]$ by
$[ - 1,1 ]$ 
B)  $[ - 6,1 ]$ by
$[ - 8,0 ]$ 
C)  $[ 6,1 ]$ by
$[ - 8,8 ]$ 
D)  $[ - 6,8 ]$ by
$[ 8,0 ]$ 
E)  $[ - 15,2 ]$ by
$[ - 1,1 ]$ 
A)  $[ - 1,1 ]$ by
$[ - 1,1 ]$ 
B)  $[ - 6,1 ]$ by
$[ - 8,0 ]$ 
C)  $[ 6,1 ]$ by
$[ - 8,8 ]$ 
D)  $[ - 6,8 ]$ by
$[ 8,0 ]$ 
E)  $[ - 15,2 ]$ by
$[ - 1,1 ]$

Question 3

Determine an appropriate viewing rectangle for the equation $y = \sqrt { 5 x + 1 }$ and use it to draw the graph.

Accepted Answer

The answer of Determine an appropriate viewing rectangle for the...

Question 4

Factor the expression. $x ^ { 2 } + 7 x - 8$

Accepted Answer

A)  $( x - 4 ) ( x + 2 )$ 
B)  $( x + 4 ) ( x + 2 )$ 
C)  $( x - 8 ) ( x - 1 )$ 
D)  $( x + 8 ) ( x - 1 )$ 
E)  $( x + 4 ) ( x - 2 )$ 
A)  $( x - 4 ) ( x + 2 )$ 
B)  $( x + 4 ) ( x + 2 )$ 
C)  $( x - 8 ) ( x - 1 )$ 
D)  $( x + 8 ) ( x - 1 )$ 
E)  $( x + 4 ) ( x - 2 )$

Question 5

Factor the expression. $64 s ^ { 2 } - y ^ { 2 }$

Accepted Answer

The answer of Factor the expression. \(64 s ^ {...

Question 6

Evaluate the expression. $\left| \frac { 25 - 52 } { 52 - 25 } \right|$

Accepted Answer

The answer of Evaluate the expression. \(\left| \frac { 25...

Question 7

A prescription label for a certain type of medicine indicates that the medicine needs to be stored in the refrigerator at a temperature between $5 ^ { \circ }$ C and $10 ^ { \circ }$ C. What range of temperatures does this correspond to on the Fahrenheit scale?

Accepted Answer

The answer of A prescription label for a certain type...

Question 8

Factor the expression completely. $x ^ { 2 } \left( x ^ { 2 } - 4 \right) - 16 \left( x ^ { 2 } - 4 \right)$

Accepted Answer

The answer of Factor the expression completely. \(x ^ {...

Question 9

Let $S = \left\{ - 1,0 , \frac { 1 } { 2 } , \sqrt { 2 } , 2 \right\}$ . Use substitution to determine which of the elements of $S$ satisfy the inequality $x - 1 \leq 0$ .

Accepted Answer

A)  $\{ - 1,0 \}$ 
B)  $\left\{ - 1,0 , \frac { 1 } { 2 } \right\}$ 
C)  $\left\{ 0 , \frac { 1 } { 2 } , \sqrt { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } , \sqrt { 2 } , 2 \right\}$ 
E)  $\{ \sqrt { 2 } , 2 \}$ 
A)  $\{ - 1,0 \}$ 
B)  $\left\{ - 1,0 , \frac { 1 } { 2 } \right\}$ 
C)  $\left\{ 0 , \frac { 1 } { 2 } , \sqrt { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } , \sqrt { 2 } , 2 \right\}$ 
E)  $\{ \sqrt { 2 } , 2 \}$

Question 10

Use a Factoring Formula to factor the expression. $16 x ^ { 2 } - 56 x + 49$

Accepted Answer

The answer of Use a Factoring Formula to factor the...

Question 11

Factor the expression. $6 x ^ { 2 } + 13 x + 6$

Accepted Answer

A)  $( 2 x + 3 ) ^ { 2 }$ 
B)  $( x + 3 ) ( 6 x + 2 )$ 
C)  $( 2 x + 1 ) ( 3 x + 6 )$ 
D)  $( 6 x + 1 ) ( x + 6 )$ 
E)  $( 2 x + 3 ) ( 3 x + 2 )$ 
A)  $( 2 x + 3 ) ^ { 2 }$ 
B)  $( x + 3 ) ( 6 x + 2 )$ 
C)  $( 2 x + 1 ) ( 3 x + 6 )$ 
D)  $( 6 x + 1 ) ( x + 6 )$ 
E)  $( 2 x + 3 ) ( 3 x + 2 )$

Question 12

Solve the equation $A = 2 l w + 2 l h + 2 w$ for $h$ .

Accepted Answer

The answer of Solve the equation \(A = 2 l...

Question 13

Find the slope of the line through $P ( 5,1 )$ and $Q ( 7,6 )$ .

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 5 }$ 
E)  $\frac { 11 } { 2 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 5 }$ 
E)  $\frac { 11 } { 2 }$

Question 14

Find the slope and $y$ - intercept of the line $- 2 x + 2 y + 15 = 0$ and draw its graph.

Accepted Answer

The answer of Find the slope and $y$ - intercept...

Question 15

A particular mountain highway has a $5 \%$ grade. While making your accent to the top of the mountain, you notice that an elevation sign indicates that you are at an elevation of $2342$ ft. (assume this means a vertical distance from the base where you started and not from sea level). Find the change in your horizontal distance in miles. Round to two significant digits.

Accepted Answer

Slope of t

Question 16

Evaluate the expression. $- | | ( - 2 ) | - | ( - 2 ) | |$

Accepted Answer

The answer of Evaluate the expression. \(- | | (...

Question 17

Simplify the expression. $\frac { 6 x ^ { 2 } - x y - y ^ { 2 } } { 3 x ^ { 2 } - 5 y x - 2 y ^ { 2 } } \cdot \frac { x ^ { 2 } - 3 x y + 2 y ^ { 2 } } { x ^ { 2 } + x y - 2 y ^ { 2 } }$

Accepted Answer

A)  $\frac { 2 x + y } { x - 2 y }$ 
B)  $\frac { x + 2 y } { 2 x - y }$ 
C)  $\frac { 2 x - y } { x + 2 y }$ 
D)  $\frac { 2 - x y } { 2 x + y }$ 
E)  $\frac { x + y + 2 } { x - 2 y - 2 }$ 
A)  $\frac { 2 x + y } { x - 2 y }$ 
B)  $\frac { x + 2 y } { 2 x - y }$ 
C)  $\frac { 2 x - y } { x + 2 y }$ 
D)  $\frac { 2 - x y } { 2 x + y }$ 
E)  $\frac { x + y + 2 } { x - 2 y - 2 }$

Question 18

Simplify $\frac { x ^ { 1 / 3 } y ^ { 1 / 3 } } { ( x y ) ^ { - 2 / 3 } }$ and eliminate any negative exponents.

Accepted Answer

A)  $x y$ 
B)  $( x y ) ^ { -2 / 3 }$ 
C)  $( x y ) ^ { 1 / 3 }$ 
D)  $y$ 
E)  $x ^ { 1 / 3 } y$ 
A)  $x y$ 
B)  $( x y ) ^ { -2 / 3 }$ 
C)  $( x y ) ^ { 1 / 3 }$ 
D)  $y$ 
E)  $x ^ { 1 / 3 } y$

Question 19

State the property of real numbers being used. $$3 x y = y x 3$$

Accepted Answer

A)  Commutative Property for addition 
B)  Commutative Property for multiplication 
C)  Associative Property for addition 
D)  Associative Property for multiplication 
E)  Distributive Property 
A)  Commutative Property for addition 
B)  Commutative Property for multiplication 
C)  Associative Property for addition 
D)  Associative Property for multiplication 
E)  Distributive Property

Question 20

Suppose that Alyson scores $67$ , $87$ , $93$ , $95$ on her algebra tests, and the only test left to take is the final exam. Her final exam however, accounts for one-half of her overall course average. What range of scores on the final exam would she need in order to achieve an overall course grade of between $80$ and $85$ ?

Accepted Answer

The answer of Suppose that Alyson scores $67$ , $87$...

Find all real solutions of the equation. $| 7 x + 1 | = 7$

Use a graphing calculator or computer to determine which of the viewing rectangles produces the most appropriate graph of the equation $y = - | x + 2 | - 3$ .

Determine an appropriate viewing rectangle for the equation $y = \sqrt { 5 x + 1 }$ and use it to draw the graph.

Factor the expression. $x ^ { 2 } + 7 x - 8$

Factor the expression. $64 s ^ { 2 } - y ^ { 2 }$

Evaluate the expression. $\left| \frac { 25 - 52 } { 52 - 25 } \right|$

A prescription label for a certain type of medicine indicates that the medicine needs to be stored in the refrigerator at a temperature between $5 ^ { \circ }$ C and $10 ^ { \circ }$ C. What range of temperatures does this correspond to on the Fahrenheit scale?

Factor the expression completely. $x ^ { 2 } \left( x ^ { 2 } - 4 \right) - 16 \left( x ^ { 2 } - 4 \right)$

Let $S = \left\{ - 1,0 , \frac { 1 } { 2 } , \sqrt { 2 } , 2 \right\}$ . Use substitution to determine which of the elements of $S$ satisfy the inequality $x - 1 \leq 0$ .

Use a Factoring Formula to factor the expression. $16 x ^ { 2 } - 56 x + 49$

Factor the expression. $6 x ^ { 2 } + 13 x + 6$

Solve the equation $A = 2 l w + 2 l h + 2 w$ for $h$ .

Find the slope of the line through $P ( 5,1 )$ and $Q ( 7,6 )$ .

Find the slope and $y$ - intercept of the line $- 2 x + 2 y + 15 = 0$ and draw its graph.

Evaluate the expression. $- | | ( - 2 ) | - | ( - 2 ) | |$

Simplify the expression. $\frac { 6 x ^ { 2 } - x y - y ^ { 2 } } { 3 x ^ { 2 } - 5 y x - 2 y ^ { 2 } } \cdot \frac { x ^ { 2 } - 3 x y + 2 y ^ { 2 } } { x ^ { 2 } + x y - 2 y ^ { 2 } }$

Simplify $\frac { x ^ { 1 / 3 } y ^ { 1 / 3 } } { ( x y ) ^ { - 2 / 3 } }$ and eliminate any negative exponents.

State the property of real numbers being used. $3 x y = y x 3$

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Exam 1: Fundamentals

Find all real solutions of the equation. ∣7x+1∣=7| 7 x + 1 | = 7∣7x+1∣=7

Use a graphing calculator or computer to determine which of the viewing rectangles produces the most appropriate graph of the equation y=−∣x+2∣−3y = - | x + 2 | - 3y=−∣x+2∣−3 .

Determine an appropriate viewing rectangle for the equation y=5x+1y = \sqrt { 5 x + 1 }y=5x+1​ and use it to draw the graph.

Factor the expression. x2+7x−8x ^ { 2 } + 7 x - 8x2+7x−8

Factor the expression. 64s2−y264 s ^ { 2 } - y ^ { 2 }64s2−y2

Evaluate the expression. ∣25−5252−25∣\left| \frac { 25 - 52 } { 52 - 25 } \right|​52−2525−52​​

A prescription label for a certain type of medicine indicates that the medicine needs to be stored in the refrigerator at a temperature between 5∘5 ^ { \circ }5∘ C and 10∘10 ^ { \circ }10∘ C. What range of temperatures does this correspond to on the Fahrenheit scale?

Factor the expression completely. x2(x2−4)−16(x2−4)x ^ { 2 } \left( x ^ { 2 } - 4 \right) - 16 \left( x ^ { 2 } - 4 \right)x2(x2−4)−16(x2−4)

Let S={−1,0,12,2,2}S = \left\{ - 1,0 , \frac { 1 } { 2 } , \sqrt { 2 } , 2 \right\}S={−1,0,21​,2​,2} . Use substitution to determine which of the elements of SSS satisfy the inequality x−1≤0x - 1 \leq 0x−1≤0 .

Use a Factoring Formula to factor the expression. 16x2−56x+4916 x ^ { 2 } - 56 x + 4916x2−56x+49

Factor the expression. 6x2+13x+66 x ^ { 2 } + 13 x + 66x2+13x+6

Solve the equation A=2lw+2lh+2wA = 2 l w + 2 l h + 2 wA=2lw+2lh+2w for hhh .

Find the slope of the line through P(5,1)P ( 5,1 )P(5,1) and Q(7,6)Q ( 7,6 )Q(7,6) .

Find the slope and yyy - intercept of the line −2x+2y+15=0- 2 x + 2 y + 15 = 0−2x+2y+15=0 and draw its graph.

Evaluate the expression. −∣∣(−2)∣−∣(−2)∣∣- | | ( - 2 ) | - | ( - 2 ) | |−∣∣(−2)∣−∣(−2)∣∣

Simplify the expression. 6x2−xy−y23x2−5yx−2y2⋅x2−3xy+2y2x2+xy−2y2\frac { 6 x ^ { 2 } - x y - y ^ { 2 } } { 3 x ^ { 2 } - 5 y x - 2 y ^ { 2 } } \cdot \frac { x ^ { 2 } - 3 x y + 2 y ^ { 2 } } { x ^ { 2 } + x y - 2 y ^ { 2 } }3x2−5yx−2y26x2−xy−y2​⋅x2+xy−2y2x2−3xy+2y2​

Simplify x1/3y1/3(xy)−2/3\frac { x ^ { 1 / 3 } y ^ { 1 / 3 } } { ( x y ) ^ { - 2 / 3 } }(xy)−2/3x1/3y1/3​ and eliminate any negative exponents.

State the property of real numbers being used. 3xy=yx33 x y = y x 33xy=yx3

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Find all real solutions of the equation. $| 7 x + 1 | = 7$

Use a graphing calculator or computer to determine which of the viewing rectangles produces the most appropriate graph of the equation $y = - | x + 2 | - 3$ .

Determine an appropriate viewing rectangle for the equation $y = \sqrt { 5 x + 1 }$ and use it to draw the graph.

Factor the expression. $x ^ { 2 } + 7 x - 8$

Factor the expression. $64 s ^ { 2 } - y ^ { 2 }$

Evaluate the expression. $\left| \frac { 25 - 52 } { 52 - 25 } \right|$

A prescription label for a certain type of medicine indicates that the medicine needs to be stored in the refrigerator at a temperature between $5 ^ { \circ }$ C and $10 ^ { \circ }$ C. What range of temperatures does this correspond to on the Fahrenheit scale?

Factor the expression completely. $x ^ { 2 } \left( x ^ { 2 } - 4 \right) - 16 \left( x ^ { 2 } - 4 \right)$

Let $S = \left\{ - 1,0 , \frac { 1 } { 2 } , \sqrt { 2 } , 2 \right\}$ . Use substitution to determine which of the elements of $S$ satisfy the inequality $x - 1 \leq 0$ .

Use a Factoring Formula to factor the expression. $16 x ^ { 2 } - 56 x + 49$

Factor the expression. $6 x ^ { 2 } + 13 x + 6$

Solve the equation $A = 2 l w + 2 l h + 2 w$ for $h$ .

Find the slope of the line through $P ( 5,1 )$ and $Q ( 7,6 )$ .

Find the slope and $y$ - intercept of the line $- 2 x + 2 y + 15 = 0$ and draw its graph.

Evaluate the expression. $- | | ( - 2 ) | - | ( - 2 ) | |$

Simplify the expression. $\frac { 6 x ^ { 2 } - x y - y ^ { 2 } } { 3 x ^ { 2 } - 5 y x - 2 y ^ { 2 } } \cdot \frac { x ^ { 2 } - 3 x y + 2 y ^ { 2 } } { x ^ { 2 } + x y - 2 y ^ { 2 } }$

Simplify $\frac { x ^ { 1 / 3 } y ^ { 1 / 3 } } { ( x y ) ^ { - 2 / 3 } }$ and eliminate any negative exponents.

State the property of real numbers being used. $3 x y = y x 3$