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Solve the absolute value equation or indicate that the equation has no solution. - ∣x∣=5| x | = 5


A) {−5,5}\{ - 5,5 \}
B) {5}\{ 5 \}
C) {−5}\{ - 5 \}
D) {25}\{ 25 \}

E) None of the above
F) B) and D)

Correct Answer

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Use the five-step strategy for solving word problems to find the number or numbers described in the following exercise. -Inclusive of a 6.8%6.8 \% sales tax, a diamond ring sold for $2029.20\$ 2029.20 . Find the price of the ring before the tax was added. (Round to the nearest cent, if necessary.)


A) $1900\$ 1900
B) $2167.19\$ 2167.19
C) $1891.21\$ 1891.21
D) $137.99\$ 137.99

E) B) and C)
F) A) and D)

Correct Answer

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Solve the formula for the specified variable. - P=s1+s2+s3\mathrm { P } = \mathrm { s } _ { 1 } + \mathrm { s } _ { 2 } + \mathrm { s } _ { 3 } for s2\mathrm { s } _ { 2 }


A) s2=P−s1−s3s _ { 2 } = P - s _ { 1 } - s _ { 3 }
B) s2=P+s1+s3s _ { 2 } = P + s _ { 1 } + s _ { 3 }
C) s2=s1+s3−Ps _ { 2 } = s _ { 1 } + s _ { 3 } - P
D) s2=P+s1−s3s _ { 2 } = P + s _ { 1 } - s _ { 3 }

E) B) and C)
F) All of the above

Correct Answer

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Solve the absolute value equation or indicate that the equation has no solution. - ∣x2−4x−4∣=8\left| x ^ { 2 } - 4 x - 4 \right| = 8


A) {−2,2,6}\{ - 2,2,6 \}
B) {2,6}\{ 2,6 \}
C) {−2,2}\{ - 2,2 \}
D) {−2,2,−6}\{ - 2,2 , - 6 \}

E) C) and D)
F) B) and D)

Correct Answer

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6 Determine the Most Efficient Method to Use When Solving a Quadratic Equation - 7x2−14=07 x ^ { 2 } - 14 = 0


A) {−2,2}\{ - \sqrt { 2 } , \sqrt { 2 } \}
B) {−14,14}\{ - \sqrt { 14 } , \sqrt { 14 } \}
C) {−147,147}\left\{ - \frac { \sqrt { 14 } } { 7 } , \frac { \sqrt { 14 } } { 7 } \right\}
D) {2}\{ \sqrt { 2 } \}

E) None of the above
F) A) and B)

Correct Answer

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Solve the equation by the square root property. - (2x+3) 2=10( 2 x + 3 ) ^ { 2 } = 10


A) {−3−102,−3+102}\left\{ \frac { - 3 - \sqrt { 10 } } { 2 } , \frac { - 3 + \sqrt { 10 } } { 2 } \right\}
B) {3−102,3+102}\left\{ \frac { 3 - \sqrt { 10 } } { 2 } , \frac { 3 + \sqrt { 10 } } { 2 } \right\}
C) {10−32,10+32}\left\{ \frac { \sqrt { 10 } - 3 } { 2 } , \frac { \sqrt { 10 } + 3 } { 2 } \right\}
D) {−132,72}\left\{ - \frac { 13 } { 2 } , \frac { 7 } { 2 } \right\}

E) B) and D)
F) None of the above

Correct Answer

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Add or subtract as indicated and write the result in standard form. - 6i+(−9−i) 6 \mathrm { i } + ( - 9 - \mathrm { i } )


A) −9+5i- 9 + 5 i
B) −9+7i- 9 + 7 i
C) 9−5i9 - 5 \mathrm { i }
D) 9−7i9 - 7 \mathrm { i }

E) C) and D)
F) None of the above

Correct Answer

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Solve Radical Equations - x+3=7\sqrt { x + 3 } = 7


A) {46}\{ 46 \}
B) {49}\{ 49 \}
C) {52}\{ 52 \}
D) {100}\{ 100 \}

E) B) and C)
F) A) and B)

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Match the graph with its function using the x-intercepts. - Match the graph with its function using the x-intercepts. - A) y = x ^ { - 2 } + 2 x ^ { - 1 } - 3 B) y = x ^ { - 2 } - 2 x ^ { - 1 } - 3 C) y = x ^ { - 2 } + 2 x ^ { - 1 } + 3 D) y = x ^ { - 2 } - 2 x ^ { - 1 } + 3


A) y=x−2+2x−1−3y = x ^ { - 2 } + 2 x ^ { - 1 } - 3
B) y=x−2−2x−1−3y = x ^ { - 2 } - 2 x ^ { - 1 } - 3
C) y=x−2+2x−1+3y = x ^ { - 2 } + 2 x ^ { - 1 } + 3
D) y=x−2−2x−1+3y = x ^ { - 2 } - 2 x ^ { - 1 } + 3

E) B) and D)
F) None of the above

Correct Answer

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Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. -Claire has received scores of 85, 88, 87, and 90 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 87?


A) 85 or greater
B) 86 or greater
C) 84 or greater
D) 83 or greater

E) All of the above
F) C) and D)

Correct Answer

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Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. - −4≤−4x−12<4- 4 \leq - 4 x - 12 < 4 Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. - - 4 \leq - 4 x - 12 < 4 A) ( - 4 , - 2 ] B) ( - \infty , - 4 ] C) ( - \infty , - 4 ) or [ - 2 , \infty ) D) [ - 4 , - 2 )


A) (−4,−2]( - 4 , - 2 ]
Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. - - 4 \leq - 4 x - 12 < 4 A) ( - 4 , - 2 ] B) ( - \infty , - 4 ] C) ( - \infty , - 4 ) or [ - 2 , \infty ) D) [ - 4 , - 2 )
B) (−∞,−4]( - \infty , - 4 ]
Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. - - 4 \leq - 4 x - 12 < 4 A) ( - 4 , - 2 ] B) ( - \infty , - 4 ] C) ( - \infty , - 4 ) or [ - 2 , \infty ) D) [ - 4 , - 2 )
C) (−∞,−4) ( - \infty , - 4 ) or [−2,∞) [ - 2 , \infty )
Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. - - 4 \leq - 4 x - 12 < 4 A) ( - 4 , - 2 ] B) ( - \infty , - 4 ] C) ( - \infty , - 4 ) or [ - 2 , \infty ) D) [ - 4 , - 2 )
D) [−4,−2) [ - 4 , - 2 )
Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. - - 4 \leq - 4 x - 12 < 4 A) ( - 4 , - 2 ] B) ( - \infty , - 4 ] C) ( - \infty , - 4 ) or [ - 2 , \infty ) D) [ - 4 , - 2 )

E) None of the above
F) All of the above

Correct Answer

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Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. - 2x+5x=6x2 \mathrm { x } + 5 \mathrm { x } = 6 \mathrm { x }


A) Identity
B) Conditional equation
C) Inconsistent equation

D) A) and B)
E) All of the above

Correct Answer

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Solve the equation by making an appropriate substitution. - x−2−12x−1+31=0x ^ { - 2 } - 12 x ^ { - 1 } + 31 = 0


A) {6±531}\left\{ \frac { 6 \pm \sqrt { 5 } } { 31 } \right\}
B) {6±2531}\left\{ \frac { 6 \pm 2 \sqrt { 5 } } { 31 } \right\}
C) {−6±531}\left\{ \frac { - 6 \pm \sqrt { 5 } } { 31 } \right\}
D) {6±541}\left\{ \frac { 6 \pm \sqrt { 5 } } { 41 } \right\}

E) A) and D)
F) C) and D)

Correct Answer

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Solve the equation by making an appropriate substitution. - x4−14x2+45=0x ^ { 4 } - 14 x ^ { 2 } + 45 = 0


A) {−3,3,−5,5}\{ - 3,3 , - \sqrt { 5 } , \sqrt { 5 } \}
B) {−3,3,−i5,i5}\{ - 3,3 , - \mathrm { i } \sqrt { 5 } , \mathrm { i } \sqrt { 5 } \}
C) {9,5}\{ 9,5 \}
D) {3,5}\{ 3 , \sqrt { 5 } \}

E) B) and C)
F) All of the above

Correct Answer

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Match the story with the correct figure. -The height of an animal as a function of time.


A)
Match the story with the correct figure. -The height of an animal as a function of time. A) B) C) D)
B)
Match the story with the correct figure. -The height of an animal as a function of time. A) B) C) D)
C)
Match the story with the correct figure. -The height of an animal as a function of time. A) B) C) D)
D)
Match the story with the correct figure. -The height of an animal as a function of time. A) B) C) D)

E) B) and C)
F) C) and D)

Correct Answer

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6 Determine the Most Efficient Method to Use When Solving a Quadratic Equation - 1x+13+1x=12\frac { 1 } { x + 13 } + \frac { 1 } { x } = \frac { 1 } { 2 }


A) {−9±1852}\left\{ \frac { - 9 \pm \sqrt { 185 } } { 2 } \right\}
B) {−17±1852}\left\{ \frac { - 17 \pm \sqrt { 185 } } { 2 } \right\}
C) {17±1852}\left\{ \frac { 17 \pm \sqrt { 185 } } { 2 } \right\}
D) {9±1852}\left\{ \frac { 9 \pm \sqrt { 185 } } { 2 } \right\}

E) A) and D)
F) A) and C)

Correct Answer

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Graph the equation. - y=1xy=\frac{1}{x} Graph the equation. - y=\frac{1}{x} A) B) C) D) Write the English sentence as an equation in two variables. Then graph the equation.


A)
Graph the equation. - y=\frac{1}{x} A) B) C) D) Write the English sentence as an equation in two variables. Then graph the equation.
B)
Graph the equation. - y=\frac{1}{x} A) B) C) D) Write the English sentence as an equation in two variables. Then graph the equation.
C)
Graph the equation. - y=\frac{1}{x} A) B) C) D) Write the English sentence as an equation in two variables. Then graph the equation.
D)
Graph the equation. - y=\frac{1}{x} A) B) C) D) Write the English sentence as an equation in two variables. Then graph the equation.
Write the English sentence as an equation in two variables. Then graph the equation.

E) B) and D)
F) C) and D)

Correct Answer

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Express the interval in set-builder notation and graph the interval on a number line. - [−4,∞) [ - 4 , \infty ) Express the interval in set-builder notation and graph the interval on a number line. - [ - 4 , \infty ) A) \{ x \mid x \geq - 4 \} B) \{ x \mid x > - 4 \} C) \{ x \mid x > - 4 \} D) \{ x \mid x \geq - 4 \}


A) {x∣x≥−4}\{ x \mid x \geq - 4 \}
Express the interval in set-builder notation and graph the interval on a number line. - [ - 4 , \infty ) A) \{ x \mid x \geq - 4 \} B) \{ x \mid x > - 4 \} C) \{ x \mid x > - 4 \} D) \{ x \mid x \geq - 4 \}
B) {x∣x>−4}\{ x \mid x > - 4 \}
Express the interval in set-builder notation and graph the interval on a number line. - [ - 4 , \infty ) A) \{ x \mid x \geq - 4 \} B) \{ x \mid x > - 4 \} C) \{ x \mid x > - 4 \} D) \{ x \mid x \geq - 4 \}
C) {x∣x>−4}\{ x \mid x > - 4 \}
Express the interval in set-builder notation and graph the interval on a number line. - [ - 4 , \infty ) A) \{ x \mid x \geq - 4 \} B) \{ x \mid x > - 4 \} C) \{ x \mid x > - 4 \} D) \{ x \mid x \geq - 4 \}
D) {x∣x≥−4}\{ x \mid x \geq - 4 \}
Express the interval in set-builder notation and graph the interval on a number line. - [ - 4 , \infty ) A) \{ x \mid x \geq - 4 \} B) \{ x \mid x > - 4 \} C) \{ x \mid x > - 4 \} D) \{ x \mid x \geq - 4 \}

E) A) and B)
F) All of the above

Correct Answer

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Solve the absolute value inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. -A spinner has ten regions numbered 1 through 10 . If the spinner is spun 100 times, we would expect about 10 of the outcomes to be Region 1. It can be determined that the spinner is unbalanced if xx , the number of outcomes that result in Region 1, satisfies ∣x−103∣≥1.645\left| \frac { x - 10 } { 3 } \right| \geq 1.645 . Describe the number of outcomes that determine an unbalanced spinner that is spun 100 times.


A) Fewer than 6 or more than 14 outcomes
B) Between 6 and 14 outcomes
C) Fewer than 9 or more than 17 outcomes
D) Between 9 and 17 outcomes

E) B) and C)
F) A) and B)

Correct Answer

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Use a Graph to Determine Intercepts Use the graph to determine the x- and y-intercepts. - Use a Graph to Determine Intercepts Use the graph to determine the x- and y-intercepts. - A) x -intercept: - 1 ; -intercept: 8 B) x -intercept: 1 ; y -intercept: 8 C) x-intercept: - 1 ; y -intercept: - 8 D) x -intercept: - 8 ; y -intercept: 8


A) xx -intercept: −1- 1 ; -intercept: 8
B) xx -intercept: 1 ; yy -intercept: 8
C) x-intercept: −1;y- 1 ; y -intercept: −8- 8
D) xx -intercept: −8;y- 8 ; y -intercept: 8

E) All of the above
F) None of the above

Correct Answer

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