Question 1

Solve the system by substitution, if possible.  $\left\{ \begin{array} { l } 
- 6 x + 7 y = 50 \
12 x + 14 y = 124
\end{array} \right.$

Accepted Answer

A) (9, -6) 
B) (1, 8) 
C) (-6, 9) 
D) (-7, 10) 
E) No solutions 
A) (9, -6) 
B) (1, 8) 
C) (-6, 9) 
D) (-7, 10) 
E) No solutions

Question 2

An accounting firm has 780 hours of staff time and 272 hours of reviewing time available each week.The firm charges $1700 for an audit and $410 for a tax return.Each audit requires 60 hours of staff time and 16 hours of review time.Each tax return requires 10 hours of staff time and 4 hours of review time.What numbers of audits and tax returns will yield an optimal revenue? What is the optimal revenue?

Accepted Answer

A) 0 audit
65 tax returns
Optimal revenue: $6,560 
B) 5 audits
48 tax return
Optimal revenue: $28,180 
C) 16 audits
0 tax return
Optimal revenue: $27,200 
D) 10 audits
10 tax returns
Optimal revenue: $21,100 
E) 13 audit
0 tax returns
Optimal revenue: $28,180 
A) 0 audit
65 tax returns
Optimal revenue: $6,560 
B) 5 audits
48 tax return
Optimal revenue: $28,180 
C) 16 audits
0 tax return
Optimal revenue: $27,200 
D) 10 audits
10 tax returns
Optimal revenue: $21,100 
E) 13 audit
0 tax returns
Optimal revenue: $28,180

Question 3

Solve the system of linear equations.  $$\left\{ \begin{array} { c c c } 
x + y + z & = 2 \
x - y + 2 z & = - 13 \
- 4 y - z & = - 33
\end{array} \right.$$

Accepted Answer

A)   $( - 7,8,1 )$ 
B)   $( 8 , - 7,1 )$ 
C)   $( 7 , - 8,3 )$ 
D)   $( - 8,7,3 )$ 
E)   $( - 4,6,0 )$ 
A)   $( - 7,8,1 )$ 
B)   $( 8 , - 7,1 )$ 
C)   $( 7 , - 8,3 )$ 
D)   $( - 8,7,3 )$ 
E)   $( - 4,6,0 )$

Question 4

Write the partial fraction decomposition of the rational expression.  $\frac { 5 - x } { 2 x ^ { 2 } + x - 1 }$

Accepted Answer

A)  $\frac { 3 } { 2 x - 1 } - \frac { 2 } { x + 1 }$ 
B)   $\frac { 3 } { 2 x + 1 } + \frac { 2 } { x + 1 }$ 
C)  $\frac { 3 } { 2 x - 1 } - \frac { 2 } { x - 1 }$ 
D)  $\frac { 3 } { 2 x - 1 } + \frac { 2 } { x + 1 }$ 
E)  $\frac { 3 } { 2 x + 1 } - \frac { 2 } { x + 1 }$ 
A)  $\frac { 3 } { 2 x - 1 } - \frac { 2 } { x + 1 }$ 
B)   $\frac { 3 } { 2 x + 1 } + \frac { 2 } { x + 1 }$ 
C)  $\frac { 3 } { 2 x - 1 } - \frac { 2 } { x - 1 }$ 
D)  $\frac { 3 } { 2 x - 1 } + \frac { 2 } { x + 1 }$ 
E)  $\frac { 3 } { 2 x + 1 } - \frac { 2 } { x + 1 }$

Question 5

A health insurance company advertises on television, on radio, and in the local newspaper.The marketing department has an advertising budget of $45,000 per month.A television ad costs $1,000, a radio ad costs $200 , and a newspaper ad costs $500 .The department wants to run 70 ads per month, and have as many television ads as radio and newspaper ads combined.How many of each type of ad can the department run each month? ​

Accepted Answer

A) Television = 35 adsRadio = 25 adsNewspaper = 10 ads 
B) Television = 20 adsRadio = 25 adsNewspaper = 10 ads 
C) Television = 25 adsRadio = 10 adsNewspaper = 35 ads 
D) Television = 35 adsRadio = 30 adsNewspaper = 10 ads 
E) Television = 35 adsRadio = 10 adsNewspaper = 25 ads 
A) Television = 35 adsRadio = 25 adsNewspaper = 10 ads 
B) Television = 20 adsRadio = 25 adsNewspaper = 10 ads 
C) Television = 25 adsRadio = 10 adsNewspaper = 35 ads 
D) Television = 35 adsRadio = 30 adsNewspaper = 10 ads 
E) Television = 35 adsRadio = 10 adsNewspaper = 25 ads

Question 6

Select the correct graph of the inequality.  $4 x + 4 y \geq - 16$

Accepted Answer

A)    
B)    
C)     
D)     
E)     
A)    
B)    
C)     
D)     
E)

Question 7

Solve the system by the method of substitution.Check your solution(s) graphically.  $$\left\{ \begin{array} { r } 
x ^ { 2 } + 2 y = 0 \
x ^ { 2 } - 6 x - y = 0
\end{array} \right.$$

Accepted Answer

A) (0, 4), (0, -8) 
B) (0, 0), (4, 8) 
C) (0, 0), (-4, -8) 
D) (4, 0), (0, -8) 
E) (0, 0), (4, -8) 
A) (0, 4), (0, -8) 
B) (0, 0), (4, 8) 
C) (0, 0), (-4, -8) 
D) (4, 0), (0, -8) 
E) (0, 0), (4, -8)

Question 8

Write the form of the partial fraction decomposition of the rational expression.  $\frac { 5 x - 1 } { x \left( x ^ { 2 } + 5 \right) }$

Accepted Answer

A)  $\frac { A x + B } { x } + \frac { C x + D } { x ^ { 2 } + 5 }$ 
B)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x - 5 }$ 
C)  $\frac { A } { x ^ { 2 } } + \frac { B } { x + 5 }$ 
D)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x + 5 }$ 
E)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 5 }$ 
A)  $\frac { A x + B } { x } + \frac { C x + D } { x ^ { 2 } + 5 }$ 
B)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C x + D } { x - 5 }$ 
C)  $\frac { A } { x ^ { 2 } } + \frac { B } { x + 5 }$ 
D)  $\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { x + 5 }$ 
E)  $\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 5 }$

Question 9

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically.  $$\left\{ \begin{array} { l } 
9 x - 6 y = 6 \
6 x + 6 y = 24
\end{array} \right.$$

Accepted Answer

A)  (2, -2) 
B)  (2, 2) 
C)  (2, 9) 
D)  (-2, -2) 
E)  (-2, 2) 
A)  (2, -2) 
B)  (2, 2) 
C)  (2, 9) 
D)  (-2, -2) 
E)  (-2, 2)

Question 10

Select the correct graph of the inequality.  $x < - 4$

Accepted Answer

A)     
B)     
C)    
D)    
E)     
A)     
B)     
C)    
D)    
E)

Question 11

Select the correct graph of the inequality.  $x ^ { 2 } + 4 y - 8 \leq 0$

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 12

Solve the system by substitution, if possible.  $\left\{ \begin{array} { l } 
4 x + 3 y = 23 \
8 x + 6 y = 24
\end{array} \right.$

Accepted Answer

A) (6, 5) 
B) (4, 7) 
C) (-5, -1) 
D) (2, 5) 
E) No solution; inconsistent system 
A) (6, 5) 
B) (4, 7) 
C) (-5, -1) 
D) (2, 5) 
E) No solution; inconsistent system

Question 13

Select the correct graph of the inequality.  $y > \frac { - 21 } { x ^ { 2 } + x + 3 }$

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 14

Solve the system of linear equations and check any solution algebraically . $\left\{ \begin{aligned}
5 x - 3 y + 2 z & = 3 \
2 x + 4 y - z & = 7 \
x - 11 y + 4 z & = 3
\end{aligned} \right.$

Accepted Answer

A)   $( - 3,7,3 )$ 
B) No solution 
C)   $( 3,7 , - 3 )$ 
D)   $( - 3,7 , - 3 )$ 
E)   $( 3,7,3 )$ 
A)   $( - 3,7,3 )$ 
B) No solution 
C)   $( 3,7 , - 3 )$ 
D)   $( - 3,7 , - 3 )$ 
E)   $( 3,7,3 )$

Question 15

Solve the system of linear equations.  $$\left\{ \begin{array} { l l } 
- 2 x + 3 y - 4 z & = - 19 \
4 x - y - z & = 22 \
4 x + y - z & = 12
\end{array} \right.$$

Accepted Answer

A)   $( 1 , - 4 , - 4 )$ 
B)   $( 4 , - 5 , - 1 )$ 
C)   $( - 5 , - 1,4 )$ 
D) inconsistent 
E)   $( - 4,1 , - 4 )$ 
A)   $( 1 , - 4 , - 4 )$ 
B)   $( 4 , - 5 , - 1 )$ 
C)   $( - 5 , - 1,4 )$ 
D) inconsistent 
E)   $( - 4,1 , - 4 )$

Question 16

Write the partial fraction decomposition of the rational expression.Check your result algebraically.  $\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }$

Accepted Answer

A)  $\frac { 7 } { x - 1 } + \frac { 1 } { ( x + 1 ) ^ { 3 } }$ 
B)  $\frac { 7 } { x - 1 } - \frac { 1 } { ( x + 1 ) ^ { 2 } }$ 
C)  $\frac { 7 } { ( x - 1 ) ^ { 2 } } - \frac { 1 } { ( x - 1 ) ^ { 3 } }$ 
D)  $\frac { 7 } { x - 1 } - \frac { 1 } { ( x - 1 ) ^ { 2 } }$ 
E)  $\frac { 7 } { x - 1 } + \frac { 1 } { ( x - 1 ) ^ { 2 } }$ 
A)  $\frac { 7 } { x - 1 } + \frac { 1 } { ( x + 1 ) ^ { 3 } }$ 
B)  $\frac { 7 } { x - 1 } - \frac { 1 } { ( x + 1 ) ^ { 2 } }$ 
C)  $\frac { 7 } { ( x - 1 ) ^ { 2 } } - \frac { 1 } { ( x - 1 ) ^ { 3 } }$ 
D)  $\frac { 7 } { x - 1 } - \frac { 1 } { ( x - 1 ) ^ { 2 } }$ 
E)  $\frac { 7 } { x - 1 } + \frac { 1 } { ( x - 1 ) ^ { 2 } }$

Question 17

A total of $32,000 is invested in two municipal bonds that pay 5.75% and 6.25% simple interest.The investor wants an annual interest income of $1,900 from the investments.What amount should be invested in the 5.75% bond? ​

Accepted Answer

A) $31,800 
B) $20,000 
C) $32,000 
D) $20,300 
E) $20,100 
A) $31,800 
B) $20,000 
C) $32,000 
D) $20,300 
E) $20,100

Question 18

Select the correct graph of the inequality. $3 y - x \geq 6$

Accepted Answer

A)    
B)     
C)     
D)     
E)     
A)    
B)     
C)     
D)     
E)

Question 19

Select the ordered pair that is a solution of the system of equations.  $\left\{ \begin{aligned}
y & = - 6 e ^ { x } \
- 7 x - y & = 6
\end{aligned} \right.$

Accepted Answer

A) (0, -6) 
B) (0, 6) 
C)  $\left( \frac { 1 } { 6 } , 0 \right)$ 
D)  $\left( - \frac { 1 } { 6 } , 0 \right)$ 
E) (-6, 0) 
A) (0, -6) 
B) (0, 6) 
C)  $\left( \frac { 1 } { 6 } , 0 \right)$ 
D)  $\left( - \frac { 1 } { 6 } , 0 \right)$ 
E) (-6, 0)

Question 20

Write the partial fraction decomposition of the rational expression.  $\frac { 1 } { x ( x + q ) }$

Accepted Answer

A)  $\frac { q } { x } - \frac { q } { x + q }$ 
B)  $\frac { 1 } { q } \left( \frac { 1 } { x } + \frac { 1 } { x + q } \right)$ 
C)  $\frac { 1 } { q } \left( \frac { 1 } { x } - \frac { 1 } { x + q } \right)$ 
D)  $\frac { 1 } { x } - \frac { 1 } { x + q }$ 
E)  $\frac { 1 } { x } - \frac { 1 } { x - q }$ 
A)  $\frac { q } { x } - \frac { q } { x + q }$ 
B)  $\frac { 1 } { q } \left( \frac { 1 } { x } + \frac { 1 } { x + q } \right)$ 
C)  $\frac { 1 } { q } \left( \frac { 1 } { x } - \frac { 1 } { x + q } \right)$ 
D)  $\frac { 1 } { x } - \frac { 1 } { x + q }$ 
E)  $\frac { 1 } { x } - \frac { 1 } { x - q }$

Solve the system by substitution, if possible. $\left\{ \begin{array} { l } - 6 x + 7 y = 50 \\12 x + 14 y = 124\end{array} \right.$

Solve the system of linear equations. $\left\{ \begin{array} { c c c } x + y + z & = 2 \\x - y + 2 z & = - 13 \\- 4 y - z & = - 33\end{array} \right.$

Write the partial fraction decomposition of the rational expression. $\frac { 5 - x } { 2 x ^ { 2 } + x - 1 }$

Select the correct graph of the inequality. $4 x + 4 y \geq - 16$

Write the form of the partial fraction decomposition of the rational expression. $\frac { 5 x - 1 } { x \left( x ^ { 2 } + 5 \right) }$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } 9 x - 6 y = 6 \\6 x + 6 y = 24\end{array} \right.$

Select the correct graph of the inequality. $x < - 4$

Select the correct graph of the inequality. $x ^ { 2 } + 4 y - 8 \leq 0$

Solve the system by substitution, if possible. $\left\{ \begin{array} { l } 4 x + 3 y = 23 \\8 x + 6 y = 24\end{array} \right.$

Select the correct graph of the inequality. $y > \frac { - 21 } { x ^ { 2 } + x + 3 }$

Solve the system of linear equations and check any solution algebraically . $\left\{ \begin{aligned}5 x - 3 y + 2 z & = 3 \\2 x + 4 y - z & = 7 \\x - 11 y + 4 z & = 3\end{aligned} \right.$

Solve the system of linear equations. $\left\{ \begin{array} { l l } - 2 x + 3 y - 4 z & = - 19 \\4 x - y - z & = 22 \\4 x + y - z & = 12\end{array} \right.$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }$

A total of $32,000 is invested in two municipal bonds that pay 5.75% and 6.25% simple interest.The investor wants an annual interest income of $1,900 from the investments.What amount should be invested in the 5.75% bond?

Select the correct graph of the inequality. $3 y - x \geq 6$

Select the ordered pair that is a solution of the system of equations. $\left\{ \begin{aligned}y & = - 6 e ^ { x } \\- 7 x - y & = 6\end{aligned} \right.$

Write the partial fraction decomposition of the rational expression. $\frac { 1 } { x ( x + q ) }$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 7: Systems Of Equations and Inequalities

Solve the system by substitution, if possible. {−6x+7y=5012x+14y=124\left\{ \begin{array} { l } - 6 x + 7 y = 50 \\12 x + 14 y = 124\end{array} \right.{−6x+7y=5012x+14y=124​

Solve the system of linear equations. {x+y+z=2x−y+2z=−13−4y−z=−33\left\{ \begin{array} { c c c } x + y + z & = 2 \\x - y + 2 z & = - 13 \\- 4 y - z & = - 33\end{array} \right.⎩⎨⎧​x+y+zx−y+2z−4y−z​=2=−13=−33​

Write the partial fraction decomposition of the rational expression. 5−x2x2+x−1\frac { 5 - x } { 2 x ^ { 2 } + x - 1 }2x2+x−15−x​

Select the correct graph of the inequality. 4x+4y≥−164 x + 4 y \geq - 164x+4y≥−16

Solve the system by the method of substitution.Check your solution(s) graphically. {x2+2y=0x2−6x−y=0\left\{ \begin{array} { r } x ^ { 2 } + 2 y = 0 \\x ^ { 2 } - 6 x - y = 0\end{array} \right.{x2+2y=0x2−6x−y=0​

Write the form of the partial fraction decomposition of the rational expression. 5x−1x(x2+5)\frac { 5 x - 1 } { x \left( x ^ { 2 } + 5 \right) }x(x2+5)5x−1​

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. {9x−6y=66x+6y=24\left\{ \begin{array} { l } 9 x - 6 y = 6 \\6 x + 6 y = 24\end{array} \right.{9x−6y=66x+6y=24​

Select the correct graph of the inequality. x<−4x < - 4x<−4

Select the correct graph of the inequality. x2+4y−8≤0x ^ { 2 } + 4 y - 8 \leq 0x2+4y−8≤0

Solve the system by substitution, if possible. {4x+3y=238x+6y=24\left\{ \begin{array} { l } 4 x + 3 y = 23 \\8 x + 6 y = 24\end{array} \right.{4x+3y=238x+6y=24​

Select the correct graph of the inequality. y>−21x2+x+3y > \frac { - 21 } { x ^ { 2 } + x + 3 }y>x2+x+3−21​

Solve the system of linear equations and check any solution algebraically . {5x−3y+2z=32x+4y−z=7x−11y+4z=3\left\{ \begin{aligned}5 x - 3 y + 2 z & = 3 \\2 x + 4 y - z & = 7 \\x - 11 y + 4 z & = 3\end{aligned} \right.⎩⎨⎧​5x−3y+2z2x+4y−zx−11y+4z​=3=7=3​

Solve the system of linear equations. {−2x+3y−4z=−194x−y−z=224x+y−z=12\left\{ \begin{array} { l l } - 2 x + 3 y - 4 z & = - 19 \\4 x - y - z & = 22 \\4 x + y - z & = 12\end{array} \right.⎩⎨⎧​−2x+3y−4z4x−y−z4x+y−z​=−19=22=12​

Write the partial fraction decomposition of the rational expression.Check your result algebraically. 7x−8(x−1)2\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }(x−1)27x−8​

A total of $32,000 is invested in two municipal bonds that pay 5.75% and 6.25% simple interest.The investor wants an annual interest income of $1,900 from the investments.What amount should be invested in the 5.75% bond? ​

Select the correct graph of the inequality. 3y−x≥63 y - x \geq 63y−x≥6

Select the ordered pair that is a solution of the system of equations. {y=−6ex−7x−y=6\left\{ \begin{aligned}y & = - 6 e ^ { x } \\- 7 x - y & = 6\end{aligned} \right.{y−7x−y​=−6ex=6​

Write the partial fraction decomposition of the rational expression. 1x(x+q)\frac { 1 } { x ( x + q ) }x(x+q)1​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Solve the system by substitution, if possible. $\left\{ \begin{array} { l } - 6 x + 7 y = 50 \\12 x + 14 y = 124\end{array} \right.$

Solve the system of linear equations. $\left\{ \begin{array} { c c c } x + y + z & = 2 \\x - y + 2 z & = - 13 \\- 4 y - z & = - 33\end{array} \right.$

Write the partial fraction decomposition of the rational expression. $\frac { 5 - x } { 2 x ^ { 2 } + x - 1 }$

Select the correct graph of the inequality. $4 x + 4 y \geq - 16$

Write the form of the partial fraction decomposition of the rational expression. $\frac { 5 x - 1 } { x \left( x ^ { 2 } + 5 \right) }$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } 9 x - 6 y = 6 \\6 x + 6 y = 24\end{array} \right.$

Select the correct graph of the inequality. $x < - 4$

Select the correct graph of the inequality. $x ^ { 2 } + 4 y - 8 \leq 0$

Solve the system by substitution, if possible. $\left\{ \begin{array} { l } 4 x + 3 y = 23 \\8 x + 6 y = 24\end{array} \right.$

Select the correct graph of the inequality. $y > \frac { - 21 } { x ^ { 2 } + x + 3 }$

Solve the system of linear equations and check any solution algebraically . $\left\{ \begin{aligned}5 x - 3 y + 2 z & = 3 \\2 x + 4 y - z & = 7 \\x - 11 y + 4 z & = 3\end{aligned} \right.$

Solve the system of linear equations. $\left\{ \begin{array} { l l } - 2 x + 3 y - 4 z & = - 19 \\4 x - y - z & = 22 \\4 x + y - z & = 12\end{array} \right.$

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }$

A total of $32,000 is invested in two municipal bonds that pay 5.75% and 6.25% simple interest.The investor wants an annual interest income of $1,900 from the investments.What amount should be invested in the 5.75% bond?

Select the correct graph of the inequality. $3 y - x \geq 6$

Select the ordered pair that is a solution of the system of equations. $\left\{ \begin{aligned}y & = - 6 e ^ { x } \\- 7 x - y & = 6\end{aligned} \right.$

Write the partial fraction decomposition of the rational expression. $\frac { 1 } { x ( x + q ) }$