Question 1

Solve the problem.
-How many liters of a 30% alcohol solution must be mixed with 50 liters of a 90% solution to get a 50% solution?

Accepted Answer

A)  150 L 
B)  100 L 
C)  15 L 
D)  10 L 
A)  150 L 
B)  100 L 
C)  15 L 
D)  10 L

Question 2

Solve the equation by the zero-factor property.
-Which one of the following equations is set up for direct use of the square root property?

Accepted Answer

A)  $3 x ^ { 2 } + 5 x + 7 = 0$ 
B)  $( 3 x + 5 ) ^ { 2 } = 7$ 
C)  $x ^ { 2 } + x = 7$ 
D)  $( 3 x + 5 ) ( x + 7 ) = 0$ 
A)  $3 x ^ { 2 } + 5 x + 7 = 0$ 
B)  $( 3 x + 5 ) ^ { 2 } = 7$ 
C)  $x ^ { 2 } + x = 7$ 
D)  $( 3 x + 5 ) ( x + 7 ) = 0$

Question 3

Decide whether the statement is true or false.
-$- 15 \text { is a solution of } - 8 x = 125 \text {. }$

Accepted Answer

A) True 
 B)False

Question 4

Solve the equation for the indicated variable. Assume no denominator is 0.
-$\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv }^ 2$, for $\mathrm { v }$

Accepted Answer

A)  $v = \pm \sqrt { 2 \mathrm { Ve } }$ 
B)  $v = \frac { \pm \sqrt { 2 \mathrm { mVe } } } { \mathrm { m } }$ 
C)  $v = \pm \sqrt { \frac { \mathrm { Ve } } { 2 \mathrm {~m} } }$ 
D)  $v = \pm 2 \frac { \sqrt { \mathrm { Ve } } } { \mathrm { m } }$ 
A)  $v = \pm \sqrt { 2 \mathrm { Ve } }$ 
B)  $v = \frac { \pm \sqrt { 2 \mathrm { mVe } } } { \mathrm { m } }$ 
C)  $v = \pm \sqrt { \frac { \mathrm { Ve } } { 2 \mathrm {~m} } }$ 
D)  $v = \pm 2 \frac { \sqrt { \mathrm { Ve } } } { \mathrm { m } }$

Question 5

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt [ 3 ] { 3 x + 7 } = - 1$$

Accepted Answer

A)  $\left\{ \frac { 8 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 8 } { 3 } \right\}$ 
C)  $\{ - 2 \}$ 
D)  $\{ - 8 \}$ 
A)  $\left\{ \frac { 8 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 8 } { 3 } \right\}$ 
C)  $\{ - 2 \}$ 
D)  $\{ - 8 \}$

Question 6

Decide what values of the variable cannot possibly be solutions for the equation.
-$\sqrt [ 3 ] { 2 x - 5 } + 5 = 3$

Accepted Answer

A)  $\left\{ \frac { 5 } { 2 } \right\}$ 
B)  $\{ - 4 \rangle$ 
C)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
D)  $\{ - 13 \}$ 
A)  $\left\{ \frac { 5 } { 2 } \right\}$ 
B)  $\{ - 4 \rangle$ 
C)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
D)  $\{ - 13 \}$

Question 7

Solve for y.
-$$2 x = 9 y - 8$$

Accepted Answer

A)  $y = 17 + 2 x$ 
B)  $y = \frac { 2 x + 8 } { 9 }$ 
C)  $\mathrm { y } = \frac { 2 \mathrm { x } - 8 } { 9 }$ 
D)  $y = 17 - 2 x$ 
A)  $y = 17 + 2 x$ 
B)  $y = \frac { 2 x + 8 } { 9 }$ 
C)  $\mathrm { y } = \frac { 2 \mathrm { x } - 8 } { 9 }$ 
D)  $y = 17 - 2 x$

Question 8

The stadium vending company finds that sales of hot dogs average 45,000 hot dogs per game when the hot dogs sell for $2.50 each. For each 50 cent increase in the price, the sales per game drop by 5000 hot dogs. What price
Per hot dog should the vending company charge to realize the maximum revenue?

Accepted Answer

A)  $2.00 
B)  $4.50 
C)  $3.75 
D)  $3.50 
A)  $2.00 
B)  $4.50 
C)  $3.75 
D)  $3.50

Question 9

Determine whether or not the equation is linear.
-$0.03 x + 0.07 x = 0.40$

Accepted Answer

A)  Linear 
B)  Not linear 
A)  Linear 
B)  Not linear

Question 10

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 4 x - 12 < 0$$

Accepted Answer

A)  $( - 2,6 )$ 
B)  $( 6 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( 6 , \infty )$ 
D)  $( - \infty , - 2 )$ 
A)  $( - 2,6 )$ 
B)  $( 6 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( 6 , \infty )$ 
D)  $( - \infty , - 2 )$

Question 11

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { 3 x - 2 } + \sqrt { 11 + x } = - 1$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
B)  $\{ 0 \}$ 
C)  $\varnothing$ 
D)  $\{ 5 \}$ 
A)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
B)  $\{ 0 \}$ 
C)  $\varnothing$ 
D)  $\{ 5 \}$

Question 12

Simplify the power of i.
-$i ^ { 61 }$

Accepted Answer

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

Question 13

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( - 7 x + 3 ) ^ { 2 } = 4 ( - 7 x + 3 ) + 5$$

Accepted Answer

A)  $\left\{ \frac { 2 } { 7 } , - \frac { 4 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 8 } { 7 } , - \frac { 2 } { 7 } \right\}$ 
C)  $\{ 5 , - 1 \}$ 
D)  $\left\{ - \frac { 2 } { 7 } , \frac { 4 } { 7 } \right\}$ 
A)  $\left\{ \frac { 2 } { 7 } , - \frac { 4 } { 7 } \right\}$ 
B)  $\left\{ - \frac { 8 } { 7 } , - \frac { 2 } { 7 } \right\}$ 
C)  $\{ 5 , - 1 \}$ 
D)  $\left\{ - \frac { 2 } { 7 } , \frac { 4 } { 7 } \right\}$

Question 14

Decide what values of the variable cannot possibly be solutions for the equation.
-Frank can type a report in 3 hours. James takes 7 hours to type it. How long will it take the two of them typing together?

Accepted Answer

A)  $\frac { 1 } { 10 } \mathrm { hr }$ 
B)  $\frac { 1 } { 21 } \mathrm { hr }$ 
C)  $\frac { 21 } { 10 } \mathrm { hr }$ 
D)  $\frac { 21 } { 4 } \mathrm { hr }$ 
A)  $\frac { 1 } { 10 } \mathrm { hr }$ 
B)  $\frac { 1 } { 21 } \mathrm { hr }$ 
C)  $\frac { 21 } { 10 } \mathrm { hr }$ 
D)  $\frac { 21 } { 4 } \mathrm { hr }$

Question 15

The mat around the picture shown measures x inches across. Which one of the following equations says that the area of the picture itself is 900 square inches?

Accepted Answer

A)  $( 43 ) ( 34 ) - x ^ { 2 } = 900$ 
B)  $2 ( 43 - 2 x ) + 2 ( 34 - 2 x ) = 900$ 
C)  $( 43 - 2 x ) ( 34 - 2 x ) = 900$ 
D)  $( 43 - x ) ( 34 - x ) = 900$ 
A)  $( 43 ) ( 34 ) - x ^ { 2 } = 900$ 
B)  $2 ( 43 - 2 x ) + 2 ( 34 - 2 x ) = 900$ 
C)  $( 43 - 2 x ) ( 34 - 2 x ) = 900$ 
D)  $( 43 - x ) ( 34 - x ) = 900$

Question 16

Solve the inequality. Write the solution set in interval notation.
-$$| 2 - 3 x | \leq 11$$

Accepted Answer

A)  $\left[ - \frac { 13 } { 3 } , 3 \right]$ 
B)  $( - \infty , - 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right]$ 
C)  $\left[ - 3 , \frac { 13 } { 3 } \right]$ 
D)  $( - \infty , 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
A)  $\left[ - \frac { 13 } { 3 } , 3 \right]$ 
B)  $( - \infty , - 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right]$ 
C)  $\left[ - 3 , \frac { 13 } { 3 } \right]$ 
D)  $( - \infty , 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$

Question 17

Write the inequality in interval notation.
-

Accepted Answer

A)  $( - \infty , 6 ]$ 
B)  $[ - 5 , \infty )$ 
C)  $[ 6 , \infty )$ 
D)  $( - \infty , - 5 ]$ 
A)  $( - \infty , 6 ]$ 
B)  $[ - 5 , \infty )$ 
C)  $[ 6 , \infty )$ 
D)  $( - \infty , - 5 ]$

Question 18

Multiply or divide, as indicated. Simplify the answer.
-$$\frac { \sqrt { - 10 } } { \sqrt { - 250 } }$$

Accepted Answer

A)  $- \frac { 1 } { 5 } \mathrm { i }$ 
B)  $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 5 \mathrm { i } }$ 
A)  $- \frac { 1 } { 5 } \mathrm { i }$ 
B)  $- \frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 1 } { 5 \mathrm { i } }$

Question 19

Solve the equation by the square root property.
-$$( 7 x + 5 ) ^ { 2 } = 14$$

Accepted Answer

A)  $\left\{ \pm \frac { \sqrt { 3 } } { 7 } \mathrm { i } \right\}$ 
B)  $\left\{ \frac { - 5 \pm \sqrt { 14 } } { 7 } \right\}$ 
C)  $\left\{ \frac { - 5 + \sqrt { 14 } } { 7 } \right\}$ 
D)  $\{ - 5 \pm \sqrt { 14 } \}$ 
A)  $\left\{ \pm \frac { \sqrt { 3 } } { 7 } \mathrm { i } \right\}$ 
B)  $\left\{ \frac { - 5 \pm \sqrt { 14 } } { 7 } \right\}$ 
C)  $\left\{ \frac { - 5 + \sqrt { 14 } } { 7 } \right\}$ 
D)  $\{ - 5 \pm \sqrt { 14 } \}$

Question 20

Solve the problem.
-Kevin invested part of his $5000 bonus in a certificate of deposit that paid 2% annual simple interest, and the remainder in a mutual fund that paid 4% annual simple interest. If his total interest for that year was $120, how
Much did Kevin invest in the mutual fund?

Accepted Answer

A)  $4988.00 
B)  $1120.00 
C)  $4868.00 
D)  $1000.00 
A)  $4988.00 
B)  $1120.00 
C)  $4868.00 
D)  $1000.00

Solve the problem. -How many liters of a 30% alcohol solution must be mixed with 50 liters of a 90% solution to get a 50% solution?

Solve the equation by the zero-factor property. -Which one of the following equations is set up for direct use of the square root property?

Decide whether the statement is true or false. - $- 15 \text { is a solution of } - 8 x = 125 \text {. }$

Solve the equation for the indicated variable. Assume no denominator is 0. - $\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv }^ 2$ , for $\mathrm { v }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 3 x + 7 } = - 1$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 2 x - 5 } + 5 = 3$

Solve for y. - $2 x = 9 y - 8$

The stadium vending company finds that sales of hot dogs average 45,000 hot dogs per game when the hot dogs sell for $2.50 each. For each 50 cent increase in the price, the sales per game drop by 5000 hot dogs. What price Per hot dog should the vending company charge to realize the maximum revenue?

Determine whether or not the equation is linear. - $0.03 x + 0.07 x = 0.40$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 4 x - 12 < 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 3 x - 2 } + \sqrt { 11 + x } = - 1$

Simplify the power of i. - $i ^ { 61 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $( - 7 x + 3 ) ^ { 2 } = 4 ( - 7 x + 3 ) + 5$

Decide what values of the variable cannot possibly be solutions for the equation. -Frank can type a report in 3 hours. James takes 7 hours to type it. How long will it take the two of them typing together?

The mat around the picture shown measures x inches across. Which one of the following equations says that the area of the picture itself is 900 square inches?

Solve the inequality. Write the solution set in interval notation. - $| 2 - 3 x | \leq 11$

Write the inequality in interval notation. -

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 10 } } { \sqrt { - 250 } }$

Solve the equation by the square root property. - $( 7 x + 5 ) ^ { 2 } = 14$

Solve the problem. -Kevin invested part of his $5000 bonus in a certificate of deposit that paid 2% annual simple interest, and the remainder in a mutual fund that paid 4% annual simple interest. If his total interest for that year was $120, how Much did Kevin invest in the mutual fund?

Review of Basic Concepts

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 2: Equations and Inequalities

Solve the problem. -How many liters of a 30% alcohol solution must be mixed with 50 liters of a 90% solution to get a 50% solution?

Solve the equation by the zero-factor property. -Which one of the following equations is set up for direct use of the square root property?

Decide whether the statement is true or false. - −15 is a solution of −8x=125. - 15 \text { is a solution of } - 8 x = 125 \text {. }−15 is a solution of −8x=125.

Solve the equation for the indicated variable. Assume no denominator is 0. - Ve=12mv2\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv }^ 2Ve=21​mv2 , for v\mathrm { v }v

Decide what values of the variable cannot possibly be solutions for the equation. - 3x+73=−1\sqrt [ 3 ] { 3 x + 7 } = - 133x+7​=−1

Decide what values of the variable cannot possibly be solutions for the equation. - 2x−53+5=3\sqrt [ 3 ] { 2 x - 5 } + 5 = 332x−5​+5=3

Solve for y. - 2x=9y−82 x = 9 y - 82x=9y−8

The stadium vending company finds that sales of hot dogs average 45,000 hot dogs per game when the hot dogs sell for $2.50 each. For each 50 cent increase in the price, the sales per game drop by 5000 hot dogs. What price Per hot dog should the vending company charge to realize the maximum revenue?

Determine whether or not the equation is linear. - 0.03x+0.07x=0.400.03 x + 0.07 x = 0.400.03x+0.07x=0.40

Solve the quadratic inequality. Write the solution set in interval notation. - x2−4x−12<0x ^ { 2 } - 4 x - 12 < 0x2−4x−12<0

Decide what values of the variable cannot possibly be solutions for the equation. - 3x−2+11+x=−1\sqrt { 3 x - 2 } + \sqrt { 11 + x } = - 13x−2​+11+x​=−1

Simplify the power of i. - i61i ^ { 61 }i61

Decide what values of the variable cannot possibly be solutions for the equation. - (−7x+3)2=4(−7x+3)+5( - 7 x + 3 ) ^ { 2 } = 4 ( - 7 x + 3 ) + 5(−7x+3)2=4(−7x+3)+5

Decide what values of the variable cannot possibly be solutions for the equation. -Frank can type a report in 3 hours. James takes 7 hours to type it. How long will it take the two of them typing together?

The mat around the picture shown measures x inches across. Which one of the following equations says that the area of the picture itself is 900 square inches?

Solve the inequality. Write the solution set in interval notation. - ∣2−3x∣≤11| 2 - 3 x | \leq 11∣2−3x∣≤11

Write the inequality in interval notation. -

Multiply or divide, as indicated. Simplify the answer. - −10−250\frac { \sqrt { - 10 } } { \sqrt { - 250 } }−250​−10​​

Solve the equation by the square root property. - (7x+5)2=14( 7 x + 5 ) ^ { 2 } = 14(7x+5)2=14

Solve the problem. -Kevin invested part of his $5000 bonus in a certificate of deposit that paid 2% annual simple interest, and the remainder in a mutual fund that paid 4% annual simple interest. If his total interest for that year was $120, how Much did Kevin invest in the mutual fund?

Review of Basic Concepts

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Decide whether the statement is true or false. - $- 15 \text { is a solution of } - 8 x = 125 \text {. }$

Solve the equation for the indicated variable. Assume no denominator is 0. - $\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv }^ 2$ , for $\mathrm { v }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 3 x + 7 } = - 1$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 2 x - 5 } + 5 = 3$

Solve for y. - $2 x = 9 y - 8$

Determine whether or not the equation is linear. - $0.03 x + 0.07 x = 0.40$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 4 x - 12 < 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 3 x - 2 } + \sqrt { 11 + x } = - 1$

Simplify the power of i. - $i ^ { 61 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $( - 7 x + 3 ) ^ { 2 } = 4 ( - 7 x + 3 ) + 5$

Solve the inequality. Write the solution set in interval notation. - $| 2 - 3 x | \leq 11$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 10 } } { \sqrt { - 250 } }$

Solve the equation by the square root property. - $( 7 x + 5 ) ^ { 2 } = 14$