Question 1

Solve Compound Inequalities
Solve the compound inequality. Other than  ∅\varnothing∅  use interval notation to express the solution set and graph the
solution set on a number line.
- −1<x−1≤4- 1 < x - 1 \leq 4−1<x−1≤4

Accepted Answer

A)    (0,5]( 0,5 ](0,5] 
B)    (−2,3]( - 2,3 ](−2,3] 
C)    [0,5) [ 0,5 ) [0,5)  
D)    [−2,3) [ - 2,3 ) [−2,3)   E) A) and B)
F) A) and C)

Question 2

Divide Complex Numbers
Divide and express the result in standard form.
- 62−i\frac { 6 } { 2 - i }2−i6​

Accepted Answer

A)    125+65i\frac { 12 } { 5 } + \frac { 6 } { 5 } \mathrm { i }512​+56​i 
B)    125−65i\frac { 12 } { 5 } - \frac { 6 } { 5 } \mathrm { i }512​−56​i 
C)    4+2i4 + 2 i4+2i 
D)    4−2i4 - 2 \mathrm { i }4−2iE) C) and D)
F) A) and C)

Question 3

Solve Compound Inequalities
Solve the compound inequality. Other than  ∅\varnothing∅  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 < 4−4≤−4x−12<4

Accepted Answer

A)    (−4,−2]( - 4 , - 2 ](−4,−2] 
B)    (−∞,−4]( - \infty , - 4 ](−∞,−4] 
C)    (−∞,−4) ( - \infty , - 4 ) (−∞,−4)   or  [−2,∞) [ - 2 , \infty ) [−2,∞)  
D)    [−4,−2) [ - 4 , - 2 ) [−4,−2)   E) A) and D)
F) All of the above

Question 4

Graph the equation.
- y=1xy = \frac { 1 } { x }y=x1​

Accepted Answer

A)  
B)  
C)  
D)   Write the English sentence as an equation in two variables. Then graph the equation. E) None of the above
F) A) and D)

Question 5

Solve Quadratic Equations by the Square Root Property
Solve the equation by the square root property.
- 2x2+4=3962 x ^ { 2 } + 4 = 3962x2+4=396

Accepted Answer

A)    {−14,14}\{ - 14,14 \}{−14,14} 
B)    {14}\{ 14 \}{14} 
C)    {−15,15}\{ - 15,15 \}{−15,15} 
D)    {198}\{ 198 \}{198}E) All of the above
F) B) and C)

Question 6

Solve the equation by completing the square.
- x2+8x=7x ^ { 2 } + 8 x = 7x2+8x=7

Accepted Answer

A)    {−4−11.5,−4+11.5}\{ - 4 - \sqrt { 11.5 } , - 4 + \sqrt { 11.5 } \}{−4−11.5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​,−4+11.5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​} 
B)    {4+11.5}\{ 4 + \sqrt { 11.5 } \}{4+11.5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​} 
C)    {−1−11.5,−1+11.5}\{ - 1 - \sqrt { 11.5 } , - 1 + \sqrt { 11.5 } \}{−1−11.5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​,−1+11.5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​} 
D)    {−4−111.5,−4+111.5}\{ - 4 - 1 \sqrt { 11.5 } , - 4 + 1 \sqrt { 11.5 } \}{−4−111.5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​,−4+111.5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​}E) All of the above
F) B) and C)

Question 7

Solve the problem.
-There are 22 more sophomores than juniors in an 8 AM algebra class. If there are 46 students in this class, find the number of sophomores and the number of juniors in the class.

Accepted Answer

A)  34 sophomores; 12 juniors
B)  12 sophomores; 34 juniors
C)  68 sophomores; 24 juniors
D)  46 sophomores; 24 juniorsE) B) and D)
F) All of the above

Question 8

Solve Radical Equations
Solve the radical equation, and check all proposed solutions.
- x−3x−2=4x - \sqrt { 3 x - 2 } = 4x−3x−2​=4

Accepted Answer

A)    {9}\{ 9 \}{9} 
B)    {2,9}\{ 2,9 \}{2,9} 
C)    {−1}\{ - 1 \}{−1} 
D)    {1,2}\{ 1,2 \}{1,2}E) All of the above
F) A) and B)

Question 9

Solve Linear Inequalities
Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set
on a number line.
- −12x+12≤−3(3x−2) - 12 x + 12 \leq - 3 ( 3 x - 2 ) −12x+12≤−3(3x−2)

Accepted Answer

A)    [2,∞) [ 2 , \infty ) [2,∞)  
B)    (−∞,2]( - \infty , 2 ](−∞,2] 
C)    (2,∞) ( 2 , \infty ) (2,∞)  
D)    (−∞,2) ( - \infty , 2 ) (−∞,2)   E) B) and C)
F) A) and B)

Question 10

Solve the problem.
-For a culture of 70,000 bacteria of a certain strain, the number of bacteria  N\mathrm { N }N  that will survive  xxx  hours is modeled by the formula  N=7000100−x\mathrm { N } = 7000 \sqrt { 100 - \mathrm { x } }N=7000100−x​ . After how many hours will 21,000 bacteria survive?

Accepted Answer

A)    91hr91 \mathrm { hr }91hr 
B)    97hr97 \mathrm { hr }97hr 
C)    79hr79 \mathrm { hr }79hr 
D)    9hr9 \mathrm { hr }9hrE) A) and B)
F) A) and C)

Question 11

Perform Operations with Square Roots of Negative Numbers
Perform the indicated operations and write the result in standard form.
- −4−−282\frac { - 4 - \sqrt { - 28 } } { 2 }2−4−−28​​

Accepted Answer

A)    −2−i7- 2 - i \sqrt { 7 }−2−i7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    −2+i7- 2 + i \sqrt { 7 }−2+i7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    2+i72 + i \sqrt { 7 }2+i7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    −2−i2- 2 - \mathrm { i } \sqrt { 2 }−2−i2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​E) B) and C)
F) A) and C)

Question 12

Solve Quadratic Equations Using the Quadratic Formula
Solve the equation using the quadratic formula.
- 3x2+x−6=03 x ^ { 2 } + x - 6 = 03x2+x−6=0

Accepted Answer

A)    {−1−736,−1+736}\left\{ \frac { - 1 - \sqrt { 73 } } { 6 } , \frac { - 1 + \sqrt { 73 } } { 6 } \right\}{6−1−73c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,6−1+73c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​} 
B)    {−1−732,−1+732}\left\{ \frac { - 1 - \sqrt { 73 } } { 2 } , \frac { - 1 + \sqrt { 73 } } { 2 } \right\}{2−1−73c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,2−1+73c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​} 
C)    {1−736,1+736}\left\{ \frac { 1 - \sqrt { 73 } } { 6 } , \frac { 1 + \sqrt { 73 } } { 6 } \right\}{61−73c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,61+73c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​} 
D)    ∅\varnothing∅E) All of the above
F) C) and D)

Question 13

Solve Equations with Rational Exponents
Solve and check the equation.
- (5x+2) 1/2=2( 5 x + 2 )  ^ { 1 / 2 } = 2(5x+2) 1/2=2

Accepted Answer

A)    {25}\left\{ \frac { 2 } { 5 } \right\}{52​} 
B)    {45}\left\{ \frac { 4 } { 5 } \right\}{54​} 
C)    {−25}\left\{ - \frac { 2 } { 5 } \right\}{−52​} 
D)   10 E) None of the above
F) B) and C)

Question 14

Determine the Most Efficient Method to Use When Solving a Quadratic Equation
Solve the equation by the method of your choice.
- 1x+5+1x=115\frac { 1 } { x + 5 } + \frac { 1 } { x } = \frac { 1 } { 15 }x+51​+x1​=151​

Accepted Answer

A)    {25±5372}\left\{ \frac { 25 \pm 5 \sqrt { 37 } } { 2 } \right\}{225±537c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​} 
B)    {−35±5372}\left\{ \frac { - 35 \pm 5 \sqrt { 37 } } { 2 } \right\}{2−35±537c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​} 
C)    {35±5372}\left\{ \frac { 35 \pm 5 \sqrt { 37 } } { 2 } \right\}{235±537c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​} 
D)    {−25±5372}\left\{ \frac { - 25 \pm 5 \sqrt { 37 } } { 2 } \right\}{2−25±537c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​}E) A) and B)
F) A) and C)

Question 15

Solve Quadratic Equations by Completing the Square
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
- x2−12xx ^ { 2 } - 12 xx2−12x

Accepted Answer

A)    36;x2−12x+36=(x−6) 236 ; x ^ { 2 } - 12 x + 36 = ( x - 6 )  ^ { 2 }36;x2−12x+36=(x−6) 2 
B)    −36;x2−12x−36=(x−6) 2- 36 ; x ^ { 2 } - 12 x - 36 = ( x - 6 )  ^ { 2 }−36;x2−12x−36=(x−6) 2 
C)    −144;x2−12x−144=(x−12) 2- 144 ; x ^ { 2 } - 12 x - 144 = ( x - 12 )  ^ { 2 }−144;x2−12x−144=(x−12) 2 
D)    144;x2−12x+144=(x−12) 2144 ; x ^ { 2 } - 12 x + 144 = ( x - 12 )  ^ { 2 }144;x2−12x+144=(x−12) 2E) C) and D)
F) B) and D)

Question 16

Find all values of x satisfying the given conditions.
- y=(x+12) 3/2y = ( x + 12 )  ^ { 3 / 2 }y=(x+12) 3/2  and  y=343y = 343y=343

Accepted Answer

A)    {37}\{ 37 \}{37} 
B)    {−5}\{ - 5 \}{−5} 
C)    {73−12}\{ \sqrt [ 3 ] { 7 } - 12 \}{37c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​−12} 
D)    {61}\{ 61 \}{61}E) None of the above
F) A) and D)

Question 17

Solve the problem.
-ABC phone company charges $25 per month plus 7¢ per minute of phone calls. XYZ phone company charges $16 per month plus 10¢ per minute of phone calls. How many minutes of phone calls in a month
Make XYZ phone company the better deal?

Accepted Answer

A)  Less than 300 minutes
B)  More than 300 minutes
C)  More than 30 minutes
D)  Less than 30 minutesE) C) and D)
F) B) and D)

Question 18

Solve Equations That Are Quadratic in Form
Solve the equation by making an appropriate substitution.
- x4−4x2+3=0x ^ { 4 } - 4 x ^ { 2 } + 3 = 0x4−4x2+3=0

Accepted Answer

A)    {−1,1,−3,3}\{ - 1,1 , - \sqrt { 3 } , \sqrt { 3 } \}{−1,1,−3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​,3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​} 
B)    {−1,1,−i3,i3}\{ - 1,1 , - \mathrm { i } \sqrt { 3 } , \mathrm { i } \sqrt { 3 } \}{−1,1,−i3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​,i3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​} 
C)    {1,3}\{ 1,3 \}{1,3} 
D)    {1,3}\{ 1 , \sqrt { 3 } \}{1,3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​}E) B) and C)
F) A) and C)

Question 19

Use the graph to determine the x- and y-intercepts.
-

Accepted Answer

A)  x-intercept: -1
B)  y-intercept: -1
C)  x-intercept: 1
D)  y-intercept: 1E) B) and D)
F) B) and C)

Question 20

Add or subtract as indicated and write the result in standard form.
- (−4−6i) +(−1−5i) +(−1−3i) ( - 4 - 6 i )  + ( - 1 - 5 i )  + ( - 1 - 3 i ) (−4−6i) +(−1−5i) +(−1−3i)

Accepted Answer

A)    −6−14i- 6 - 14 i−6−14i 
B)    −4−4i- 4 - 4 i−4−4i 
C)    −4−8i- 4 - 8 i−4−8i 
D)    −5−11i- 5 - 11 \mathrm { i }−5−11iE) B) and D)
F) B) and C)

Exam 1: Equations and Inequalities

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

Correct Answer
verified

Solve the equation by completing the square. - $x ^ { 2 } + 8 x = 7$

Correct Answer
verified

Add or subtract as indicated and write the result in standard form. - $( - 4 - 6 i ) + ( - 1 - 5 i ) + ( - 1 - 3 i )$

Correct Answer
verified

Use the graph to determine the x- and y-intercepts. -

Correct Answer
verified

Solve Quadratic Equations by the Square Root Property Solve the equation by the square root property. - $2 x ^ { 2 } + 4 = 396$

Correct Answer
verified

Solve Radical Equations Solve the radical equation, and check all proposed solutions. - $x - \sqrt { 3 x - 2 } = 4$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Solve Equations That Are Quadratic in Form Solve the equation by making an appropriate substitution. - $x ^ { 4 } - 4 x ^ { 2 } + 3 = 0$

Correct Answer
verified

Solve Quadratic Equations by Completing the Square Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. - $x ^ { 2 } - 12 x$

Correct Answer
verified

Solve Quadratic Equations Using the Quadratic Formula Solve the equation using the quadratic formula. - $3 x ^ { 2 } + x - 6 = 0$

Correct Answer
verified

Determine the Most Efficient Method to Use When Solving a Quadratic Equation Solve the equation by the method of your choice. - $\frac { 1 } { x + 5 } + \frac { 1 } { x } = \frac { 1 } { 15 }$

Correct Answer
verified

Solve the problem. -For a culture of 70,000 bacteria of a certain strain, the number of bacteria $\mathrm { N }$ that will survive $x$ hours is modeled by the formula $\mathrm { N } = 7000 \sqrt { 100 - \mathrm { x } }$ . After how many hours will 21,000 bacteria survive?

Correct Answer
verified

Solve Equations with Rational Exponents Solve and check the equation. - $( 5 x + 2 ) ^ { 1 / 2 } = 2$

Correct Answer
verified

Solve the problem. -There are 22 more sophomores than juniors in an 8 AM algebra class. If there are 46 students in this class, find the number of sophomores and the number of juniors in the class.

Correct Answer
verified

Solve the problem. -ABC phone company charges $25 per month plus 7¢ per minute of phone calls. XYZ phone company charges $16 per month plus 10¢ per minute of phone calls. How many minutes of phone calls in a month Make XYZ phone company the better deal?

Correct Answer
verified

Perform Operations with Square Roots of Negative Numbers Perform the indicated operations and write the result in standard form. - $\frac { - 4 - \sqrt { - 28 } } { 2 }$

Correct Answer
verified

Find all values of x satisfying the given conditions. - $y = ( x + 12 ) ^ { 3 / 2 }$ and $y = 343$

Correct Answer
verified

Divide Complex Numbers Divide and express the result in standard form. - $\frac { 6 } { 2 - i }$

Correct Answer
verified

Exam 1: Equations and Inequalities

Graph the equation. - y=1xy = \frac { 1 } { x }y=x1​

Correct AnswerverifiedShow Answer

Solve the equation by completing the square. - x2+8x=7x ^ { 2 } + 8 x = 7x2+8x=7

Correct AnswerverifiedShow Answer

Add or subtract as indicated and write the result in standard form. - (−4−6i) +(−1−5i) +(−1−3i) ( - 4 - 6 i ) + ( - 1 - 5 i ) + ( - 1 - 3 i ) (−4−6i) +(−1−5i) +(−1−3i)

Correct AnswerverifiedShow Answer

Use the graph to determine the x- and y-intercepts. -

Correct AnswerverifiedShow Answer

Solve Quadratic Equations by the Square Root Property Solve the equation by the square root property. - 2x2+4=3962 x ^ { 2 } + 4 = 3962x2+4=396

Correct AnswerverifiedShow Answer

Solve Radical Equations Solve the radical equation, and check all proposed solutions. - x−3x−2=4x - \sqrt { 3 x - 2 } = 4x−3x−2​=4

Correct AnswerverifiedShow Answer

Solve Compound Inequalities Solve the compound inequality. Other than ∅\varnothing∅ use interval notation to express the solution set and graph the solution set on a number line. - −1<x−1≤4- 1 < x - 1 \leq 4−1<x−1≤4

Correct AnswerverifiedShow Answer

Solve Compound Inequalities Solve the compound inequality. Other than ∅\varnothing∅ 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 < 4−4≤−4x−12<4

Correct AnswerverifiedShow Answer

Solve Linear Inequalities Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. - −12x+12≤−3(3x−2) - 12 x + 12 \leq - 3 ( 3 x - 2 ) −12x+12≤−3(3x−2)

Correct AnswerverifiedShow Answer

Solve Equations That Are Quadratic in Form Solve the equation by making an appropriate substitution. - x4−4x2+3=0x ^ { 4 } - 4 x ^ { 2 } + 3 = 0x4−4x2+3=0

Correct AnswerverifiedShow Answer

Solve Quadratic Equations by Completing the Square Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. - x2−12xx ^ { 2 } - 12 xx2−12x

Correct AnswerverifiedShow Answer

Solve Quadratic Equations Using the Quadratic Formula Solve the equation using the quadratic formula. - 3x2+x−6=03 x ^ { 2 } + x - 6 = 03x2+x−6=0

Correct AnswerverifiedShow Answer

Determine the Most Efficient Method to Use When Solving a Quadratic Equation Solve the equation by the method of your choice. - 1x+5+1x=115\frac { 1 } { x + 5 } + \frac { 1 } { x } = \frac { 1 } { 15 }x+51​+x1​=151​

Correct AnswerverifiedShow Answer

Solve the problem. -For a culture of 70,000 bacteria of a certain strain, the number of bacteria N\mathrm { N }N that will survive xxx hours is modeled by the formula N=7000100−x\mathrm { N } = 7000 \sqrt { 100 - \mathrm { x } }N=7000100−x​ . After how many hours will 21,000 bacteria survive?

Correct AnswerverifiedShow Answer

Solve Equations with Rational Exponents Solve and check the equation. - (5x+2) 1/2=2( 5 x + 2 ) ^ { 1 / 2 } = 2(5x+2) 1/2=2

Correct AnswerverifiedShow Answer

Solve the problem. -There are 22 more sophomores than juniors in an 8 AM algebra class. If there are 46 students in this class, find the number of sophomores and the number of juniors in the class.

Correct AnswerverifiedShow Answer

Solve the problem. -ABC phone company charges $25 per month plus 7¢ per minute of phone calls. XYZ phone company charges $16 per month plus 10¢ per minute of phone calls. How many minutes of phone calls in a month Make XYZ phone company the better deal?

Correct AnswerverifiedShow Answer

Perform Operations with Square Roots of Negative Numbers Perform the indicated operations and write the result in standard form. - −4−−282\frac { - 4 - \sqrt { - 28 } } { 2 }2−4−−28​​

Correct AnswerverifiedShow Answer

Find all values of x satisfying the given conditions. - y=(x+12) 3/2y = ( x + 12 ) ^ { 3 / 2 }y=(x+12) 3/2 and y=343y = 343y=343

Correct AnswerverifiedShow Answer

Divide Complex Numbers Divide and express the result in standard form. - 62−i\frac { 6 } { 2 - i }2−i6​

Correct AnswerverifiedShow Answer

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

Correct Answer
verified

Solve the equation by completing the square. - $x ^ { 2 } + 8 x = 7$

Correct Answer
verified

Add or subtract as indicated and write the result in standard form. - $( - 4 - 6 i ) + ( - 1 - 5 i ) + ( - 1 - 3 i )$

Correct Answer
verified

Correct Answer
verified

Solve Quadratic Equations by the Square Root Property Solve the equation by the square root property. - $2 x ^ { 2 } + 4 = 396$

Correct Answer
verified

Solve Radical Equations Solve the radical equation, and check all proposed solutions. - $x - \sqrt { 3 x - 2 } = 4$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Solve Equations That Are Quadratic in Form Solve the equation by making an appropriate substitution. - $x ^ { 4 } - 4 x ^ { 2 } + 3 = 0$

Correct Answer
verified

Solve Quadratic Equations by Completing the Square Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. - $x ^ { 2 } - 12 x$

Correct Answer
verified

Solve Quadratic Equations Using the Quadratic Formula Solve the equation using the quadratic formula. - $3 x ^ { 2 } + x - 6 = 0$

Correct Answer
verified

Determine the Most Efficient Method to Use When Solving a Quadratic Equation Solve the equation by the method of your choice. - $\frac { 1 } { x + 5 } + \frac { 1 } { x } = \frac { 1 } { 15 }$

Correct Answer
verified

Solve the problem. -For a culture of 70,000 bacteria of a certain strain, the number of bacteria $\mathrm { N }$ that will survive $x$ hours is modeled by the formula $\mathrm { N } = 7000 \sqrt { 100 - \mathrm { x } }$ . After how many hours will 21,000 bacteria survive?

Correct Answer
verified

Solve Equations with Rational Exponents Solve and check the equation. - $( 5 x + 2 ) ^ { 1 / 2 } = 2$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Perform Operations with Square Roots of Negative Numbers Perform the indicated operations and write the result in standard form. - $\frac { - 4 - \sqrt { - 28 } } { 2 }$

Correct Answer
verified

Find all values of x satisfying the given conditions. - $y = ( x + 12 ) ^ { 3 / 2 }$ and $y = 343$

Correct Answer
verified

Divide Complex Numbers Divide and express the result in standard form. - $\frac { 6 } { 2 - i }$

Correct Answer
verified