Question 1

Solve the system of equations.
-x - y + z + 2w = -4 x + 2z - w = -1
X + y - z = 6
X + 2y + 3z - w = 1

Accepted Answer

A)  (3, 3, -2, -1) 
B)  (2, 3, -1, -1) 
C)  No solution 
D)  (2, 2, -2, -1) 
A)  (3, 3, -2, -1) 
B)  (2, 3, -1, -1) 
C)  No solution 
D)  (2, 2, -2, -1)

Question 2

Suppose that you are solving a system of three linear equations by the row echelon method and obtain the follon augmented matrix.
$$\left[ \begin{array} { r r r r } 
1 & - 8 & 4 & 17 \
0 & 1 & 2 & 10 \
0 & 0 & 0 & 12
\end{array} \right]$$
What conclusion can you draw about the solutions of the system?

Accepted Answer

A)  There is not enough information to draw any conclusion about the solutions of the system. 
B)  The system has infinitely many solutions. 
C)  The system has exactly one solution. 
D)  The system has no solutions. 
A)  There is not enough information to draw any conclusion about the solutions of the system. 
B)  The system has infinitely many solutions. 
C)  The system has exactly one solution. 
D)  The system has no solutions.

Question 3

Determine whether the matrices are inverses.
-$$\left[ \begin{array} { l l } 
- 5 & 1 \
- 7 & 1
\end{array} \right] , \left[ \begin{array} { c c } 
\frac { 1 } { 2 } & - \frac { 1 } { 2 } \
\frac { 7 } { 2 } & - \frac { 5 } { 2 }
\end{array} \right]$$

B) $Y e s$

Accepted Answer

A) True 
 B)False

Question 4

If the graphs of a system of two equations are both parabolas, what are the possible numbers of solutions (with
real coordinates) of this system?

Accepted Answer

The answer of If the graphs of a system of...

Question 5

Determine which inequality matches the graph.
-

Accepted Answer

A)  $y \geq 9 - x ^ { 2 }$ 
B)  $x ^ { 2 } + y ^ { 2 } \geq 9$ 
C)  $x ^ { 2 } + y ^ { 2 } \leq 9$ 
D)  $x ^ { 2 } + y ^ { 2 } \geq 3$ 
A)  $y \geq 9 - x ^ { 2 }$ 
B)  $x ^ { 2 } + y ^ { 2 } \geq 9$ 
C)  $x ^ { 2 } + y ^ { 2 } \leq 9$ 
D)  $x ^ { 2 } + y ^ { 2 } \geq 3$

Question 6

Write a system of inequalities whose solution set is the region shown.
-

Accepted Answer

A)  $y \leq - 2 x + 4$
$y \geq - \frac { 3 } { 4 } x + 2$ 
B)  $y \geq - 2 x + 4$
$y \leq - \frac { 3 } { 4 } x + 2$ 
C)  $y \geq 2 x + 4$
$y \leq \frac { 3 } { 4 } x + 2$ 
D)  $y \leq 2 x + 4$
$y \geq \frac { 3 } { 4 } x + 2$ 
A)  $y \leq - 2 x + 4$
$y \geq - \frac { 3 } { 4 } x + 2$ 
B)  $y \geq - 2 x + 4$
$y \leq - \frac { 3 } { 4 } x + 2$ 
C)  $y \geq 2 x + 4$
$y \leq \frac { 3 } { 4 } x + 2$ 
D)  $y \leq 2 x + 4$
$y \geq \frac { 3 } { 4 } x + 2$

Question 7

Write the system of equations associated with the augmented matrix. Do not solve.
-$$\left[ \begin{array} { r r r r } 
2 & 6 & 9 & - 2 \
7 & 0 & 4 & 4 \
9 & 5 & 0 & 2
\end{array} \right]$$

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 8

Solve the problem.
-An automotive glass plant must be able to fill orders for 230 truck windshields, 350 auto windshields, and 310 RV windshields. Because the first shift crews are more experienced, they are each able to make 7 truck windshields, 12 auto windshields, and 9 RV windshields. The second shift crews are able to produce 4 truck windshields, 12 auto windshields, and 7 RV windshields. The more experienced first shift crews cost the company $\$ 360.00$ per crew per shift and the second shift crews each cost $\$ 310.00$ per shift. The company's facilities will handle at most 50 crews on each shift, and they must have at least 10 crews come in to keep the plant running. How many first shift and how many second shift crews should they schedule to minimize costs?

Accepted Answer

A)  37 first shift crews and 36 second shift crews 
B)  51 first shift crews and 17 second shift crews 
C)  43 first shift crews and 24 second shift crews 
D)  28 first shift crews and 10 second shift crews 
A)  37 first shift crews and 36 second shift crews 
B)  51 first shift crews and 17 second shift crews 
C)  43 first shift crews and 24 second shift crews 
D)  28 first shift crews and 10 second shift crews

Question 9

Solve the system by elimination.
--7x - 7y = -49 -3x + 4y = -21

Accepted Answer

A)  No solution 
B)  (7, 1) 
C)  (6, 1) 
D)  (7, 0) 
A)  No solution 
B)  (7, 1) 
C)  (6, 1) 
D)  (7, 0)

Question 10

Solve the system of inequalities.
-$\begin{array}{r}
3 x-2 y \leq 6 \
x-1 \geq 0
\end{array}$

Accepted Answer

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

Question 11

Answer the question.
-Determine the function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ so that its graph contains the points $( - 1 , - 9 ) , ( 0 , - 3 ) , ( 1,7 )$, and $( 2,33 )$.

Accepted Answer

A)  $f ( x ) = 2 x ^ { 3 } + 2 x ^ { 2 } + 6 x - 3$ 
B)  $f ( x ) = 3 x ^ { 3 } + 2 x ^ { 2 } + 6 x - 3$ 
C)  $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } + 6 x + 3$ 
D)  $f ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 6 x + 3$ 
A)  $f ( x ) = 2 x ^ { 3 } + 2 x ^ { 2 } + 6 x - 3$ 
B)  $f ( x ) = 3 x ^ { 3 } + 2 x ^ { 2 } + 6 x - 3$ 
C)  $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } + 6 x + 3$ 
D)  $f ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 6 x + 3$

Question 12

Solve the problem.
-Barges from ports X and Y went to cities A and B. X sent 30 barges and Y sent 8. City A received 21 barges and B received 17. Shipping costs $220 from X to A, $300 from X to B, $400 from Y to A, and $180 from Y to B. $8760
Was spent. How many barges went where?

Accepted Answer

A)  15 from X to A 
B)  17 from X to A 
C)  19 from X to A 
D)  21 from X to A 15 from X to B 17 from X to B 11 from X to B 9 from X to B
6 from Y to A 4 from Y to A 2 from Y to A 0 from Y to A
2 from Y to B 4 from Y to B 6 from Y to B 8 from Y to B 
A)  15 from X to A 
B)  17 from X to A 
C)  19 from X to A 
D)  21 from X to A 15 from X to B 17 from X to B 11 from X to B 9 from X to B
6 from Y to A 4 from Y to A 2 from Y to A 0 from Y to A
2 from Y to B 4 from Y to B 6 from Y to B 8 from Y to B

Question 13

Find the partial fraction decomposition.
-$\frac { - 31 x - 46 } { 2 x ^ { 2 } + 10 x + 8 }$

Accepted Answer

A)  $- \frac { 5 } { 2 x - 2 } - \frac { 13 } { x - 4 }$ 
B)  $- \frac { 5 } { x + 2 } - \frac { 13 } { 2 x + 4 }$ 
C)  $\frac { 5 } { 2 x + 2 } + \frac { 13 } { x + 4 }$ 
D)  $- \frac { 5 } { 2 x + 2 } - \frac { 13 } { x + 4 }$ 
A)  $- \frac { 5 } { 2 x - 2 } - \frac { 13 } { x - 4 }$ 
B)  $- \frac { 5 } { x + 2 } - \frac { 13 } { 2 x + 4 }$ 
C)  $\frac { 5 } { 2 x + 2 } + \frac { 13 } { x + 4 }$ 
D)  $- \frac { 5 } { 2 x + 2 } - \frac { 13 } { x + 4 }$

Question 14

Determine whether the matrices are inverses.
-$$\left[ \begin{array} { r r } 
- 2 & 4 \
4 & - 4
\end{array} \right] , \left[ \begin{array} { l l } 
\frac { 1 } { 2 } & \frac { 1 } { 4 } \
\frac { 1 } { 2 } & \frac { 1 } { 4 }
\end{array} \right]$$

Accepted Answer

A) True 
 B)False

Question 15

Solve the system of equations.
-3x + 5y - 2w = -13 2x + 7z - w = -1
4y + 3z + 3w = 1
-x + 2y + 4z = -5

Accepted Answer

A)  -1, - 2013 , 0, 25 
B)  34 , -2, 0, 34 
C)  (1, -2, 0, 3) 
D)  43 , - 1320 , 0, 52 
A)  -1, - 2013 , 0, 25 
B)  34 , -2, 0, 34 
C)  (1, -2, 0, 3) 
D)  43 , - 1320 , 0, 52

Question 16

Solve the problem.
-The total number of cars sold at a used car lot for the years 1996 and 1997 was 1308. From 1996 to 1997 the number of cars sold declined by 158. How many cars were sold in 1997?

Accepted Answer

A)  575 
B)  585 
C)  581 
D)  569 
A)  575 
B)  585 
C)  581 
D)  569

Question 17

Use the graph to estimate any solutions of the system.
-$\begin{array}{l}
x=-y^{2} \
y=x+2
\end{array}$

$[ - 6,6 ]$ by $[ - 6,6 ]$

Accepted Answer

A)  $( - 1,1 )$ and $( - 4 , - 1 )$ 
B)  $( - 1.5,1 )$ and $( - 4.5 , - 2 )$ 
C)  $( - 1,1.5 )$ and $( - 4 , - 3 )$ 
D)  $( - 1,1 )$ and $( - 4 , - 2 )$ 
A)  $( - 1,1 )$ and $( - 4 , - 1 )$ 
B)  $( - 1.5,1 )$ and $( - 4.5 , - 2 )$ 
C)  $( - 1,1.5 )$ and $( - 4 , - 3 )$ 
D)  $( - 1,1 )$ and $( - 4 , - 2 )$

Question 18

Solve the problem.
-A grain dealer sold to one customer 3 bushels of wheat, 3 of corn, and 3 of rye, for $11.40; to another, 3 of wheat, 3 of corn, and 3 of rye, for $11.40; and to a third, 3 of wheat, 3 of corn, and 3 of rye, for $11.40. What was the
Price per bushel for corn?

Accepted Answer

A)  $1.10 
B)  $1.30 
C)  $1.60 
D)  $1.40 
A)  $1.10 
B)  $1.30 
C)  $1.60 
D)  $1.40

Question 19

Solve the system by substitution.
-x + 6y = 9 -2x + 5y = -1

Accepted Answer

A)  (-3, 2) 
B)  (3, 1) 
C)  No solution 
D)  (2, 2) 
A)  (-3, 2) 
B)  (3, 1) 
C)  No solution 
D)  (2, 2)

Question 20

Suppose that you are solving a system of three linear equations and three variables by the row echelon method a obtain the following augmented matrix.
$$\left[ \begin{array} { r r r r } 
1 & 1 & 2 & 28 \
0 & - 9 & 12 & - 13 \
0 & 13 & - 6 & 11
\end{array} \right]$$
What row transformation would you perform next?

Accepted Answer

A)  Add -13 times row 1 to 1 times row 3 to obtain a zero in the third row, second column position. 
B)  Add row 1 to row 2 . 
C)  Multiply row 1 by 1 . 
D)  Multiply row 2 by $- \frac { 1 } { - }$. nd you 9 
A)  Add -13 times row 1 to 1 times row 3 to obtain a zero in the third row, second column position. 
B)  Add row 1 to row 2 . 
C)  Multiply row 1 by 1 . 
D)  Multiply row 2 by $- \frac { 1 } { - }$. nd you 9

Solve the system of equations. -x - y + z + 2w = -4 x + 2z - w = -1 X + y - z = 6 X + 2y + 3z - w = 1

Suppose that you are solving a system of three linear equations by the row echelon method and obtain the follon augmented matrix. $\left[ \begin{array} { r r r r } 1 & - 8 & 4 & 17 \\0 & 1 & 2 & 10 \\0 & 0 & 0 & 12\end{array} \right]$ What conclusion can you draw about the solutions of the system?

Determine whether the matrices are inverses. - $\left[ \begin{array} { l l } - 5 & 1 \\- 7 & 1\end{array} \right] , \left[ \begin{array} { c c } \frac { 1 } { 2 } & - \frac { 1 } { 2 } \\\frac { 7 } { 2 } & - \frac { 5 } { 2 }\end{array} \right]$ B) $Y e s$

If the graphs of a system of two equations are both parabolas, what are the possible numbers of solutions (with real coordinates) of this system?

Determine which inequality matches the graph. -

Write a system of inequalities whose solution set is the region shown. -

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r r r } 2 & 6 & 9 & - 2 \\7 & 0 & 4 & 4 \\9 & 5 & 0 & 2\end{array} \right]$

Solve the system by elimination. --7x - 7y = -49 -3x + 4y = -21

Solve the system of inequalities. - 3x-2y\leq6 x-1\geq0 $Solve the system of inequalities. - \begin{array}{r} 3 x-2 y \leq 6 \\ x-1 \geq 0 \end{array}$

Answer the question. -Determine the function $f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d$ so that its graph contains the points $( - 1 , - 9 ) , ( 0 , - 3 ) , ( 1,7 )$ , and $( 2,33 )$ .

Solve the problem. -Barges from ports X and Y went to cities A and B. X sent 30 barges and Y sent 8. City A received 21 barges and B received 17. Shipping costs $220 from X to A, $300 from X to B, $400 from Y to A, and $180 from Y to B. $8760 Was spent. How many barges went where?

Find the partial fraction decomposition. - $\frac { - 31 x - 46 } { 2 x ^ { 2 } + 10 x + 8 }$

Determine whether the matrices are inverses. - $\left[ \begin{array} { r r } - 2 & 4 \\4 & - 4\end{array} \right] , \left[ \begin{array} { l l } \frac { 1 } { 2 } & \frac { 1 } { 4 } \\\frac { 1 } { 2 } & \frac { 1 } { 4 }\end{array} \right]$

Solve the system of equations. -3x + 5y - 2w = -13 2x + 7z - w = -1 4y + 3z + 3w = 1 -x + 2y + 4z = -5

Solve the problem. -The total number of cars sold at a used car lot for the years 1996 and 1997 was 1308. From 1996 to 1997 the number of cars sold declined by 158. How many cars were sold in 1997?

Use the graph to estimate any solutions of the system. - x=- y=x+2 $Use the graph to estimate any solutions of the system. - \begin{array}{l} x=-y^{2} \\ y=x+2 \end{array} [ - 6,6 ] by [ - 6,6 ]$ $[ - 6,6 ]$ by $[ - 6,6 ]$

Solve the problem. -A grain dealer sold to one customer 3 bushels of wheat, 3 of corn, and 3 of rye, for $11.40; to another, 3 of wheat, 3 of corn, and 3 of rye, for $11.40; and to a third, 3 of wheat, 3 of corn, and 3 of rye, for $11.40. What was the Price per bushel for corn?

Solve the system by substitution. -x + 6y = 9 -2x + 5y = -1

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 7: Systems and Matrices