Question 1

Find the inverse of the matrix.
-$$\left[ \begin{array} { l l l } 
1 & - 1 & 8 \
1 & 0 & 2 \
2 & - 1 & 10
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { l l l } 1 & 0 & 2 \ 0 & 1 & - 6 \ 0 & 0 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 1 & 1 & 2 \ - 1 & 0 & - 1 \ 8 & 2 & 10 \end{array} \right]$ 
C)  No inverse 
D)  $\left[ \begin{array} { l l l } 1 & 0 & 2 \ 0 & 1 & - 6 \ 0 & 7 & 0 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l l } 1 & 0 & 2 \ 0 & 1 & - 6 \ 0 & 0 & 0 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c c } 1 & 1 & 2 \ - 1 & 0 & - 1 \ 8 & 2 & 10 \end{array} \right]$ 
C)  No inverse 
D)  $\left[ \begin{array} { l l l } 1 & 0 & 2 \ 0 & 1 & - 6 \ 0 & 7 & 0 \end{array} \right]$

Question 2

Write the augmented matrix for the system.
-$$\left\{ \begin{array} { c } 
- 2 x + 6 y = 8 \
5 y = 20
\end{array} \right.$$

Accepted Answer

A)  $\left[ \begin{array} { r r | r } 8 & 6 & - 2 \ 20 & 0 & 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 5 & 0 & 20 \ - 2 & 6 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } - 2 & 6 & 8 \ 0 & 5 & 20 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } - 2 & 6 & 8 \ 5 & 20 & 0 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r | r } 8 & 6 & - 2 \ 20 & 0 & 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 5 & 0 & 20 \ - 2 & 6 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } - 2 & 6 & 8 \ 0 & 5 & 20 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } - 2 & 6 & 8 \ 5 & 20 & 0 \end{array} \right]$

Question 3

Use the elimination method to solve the system.
-$$\left\{ \begin{array} { c } 
2 x + 24 y = - 154 \
9 x + 4 y = 35
\end{array} \right.$$

Accepted Answer

A)  x = 9, y = -9 
B)  x = 7, y = -7 
C)  x = -4, y = 7 
D)  x = -7, y = 7 
A)  x = 9, y = -9 
B)  x = 7, y = -7 
C)  x = -4, y = 7 
D)  x = -7, y = 7

Question 4

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c r } 
x & y & z \
u & v & w \
1 & - 2 & 3
\end{array} \right| = 22 \left| \begin{array} { c c c } 
x & y & z - x \
u & v & w - u \
1 & - 2 & 2
\end{array} \right| = ?$$

Accepted Answer

A)  0 
B)  -22 
C)  22 
D)  Cannot determine 
A)  0 
B)  -22 
C)  22 
D)  Cannot determine

Question 5

Solve the system.
-$$\left\{ \begin{array} { l } 
x + y = 1 \
x + y = - 3
\end{array} \right.$$

Accepted Answer

A)  inconsistent (no solution) 
B)  (0, -2) 
C)  dependent (many solutions) 
D)  (1, -3) 
A)  inconsistent (no solution) 
B)  (0, -2) 
C)  dependent (many solutions) 
D)  (1, -3)

Question 6

Write the word or phrase that best completes each statement or answers the question.
-A company has sales (measured in millions of dollars) of 50, 60, and 75 during the first three consecutive years. Find a quadratic function that fits these data, and use the result to predict the sales during the fourth year.
Assume that the quadratic function is of the form y = ax2 + bx + c

Accepted Answer

A)  $$y = \frac { 5 } { 2 } x ^ { 2 } + \frac { 5 } { 2 } x + 45$$ 45; sales during the fourth year = $95 million 
B)  $$y = - 5 x ^ { 2 } + 40 x + 15$$ 15; sales during the fourth year = $95 million 
C)  $$y = 5 x ^ { 2 } + 5 x + 40$$ 40; sales during the fourth year = $180 million 
D)  $$y = \frac { 15 } { 2 } x ^ { 2 } - \frac { 25 } { 2 } x + \frac { 325 } { 4 }$$ ; sales during the fourth year = $151.25 million 
A)  $$y = \frac { 5 } { 2 } x ^ { 2 } + \frac { 5 } { 2 } x + 45$$ 45; sales during the fourth year = $95 million 
B)  $$y = - 5 x ^ { 2 } + 40 x + 15$$ 15; sales during the fourth year = $95 million 
C)  $$y = 5 x ^ { 2 } + 5 x + 40$$ 40; sales during the fourth year = $180 million 
D)  $$y = \frac { 15 } { 2 } x ^ { 2 } - \frac { 25 } { 2 } x + \frac { 325 } { 4 }$$ ; sales during the fourth year = $151.25 million

Question 7

Solve the problem.
-A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given by the equation $$h = - 16 t ^ { 2 } + 600$$ where h is measured in feet and t is the number of seconds since the yellow ball was
Dropped. A second person, in the same building but on a lower floor that is 408 feet from the ground, drops a
White ball 3 seconds after the yellow ball was dropped. The height of the white ball is given by the equation $$h = - 16 ( t - 3 ) ^ { 2 } + 408$$ where h is measured in feet and t is the number of seconds since the yellow ball was
Dropped. Find the time that the balls are the same distance above the ground and find this distance.

Accepted Answer

A)  2.5 sec; 500 ft 
B)  3.5 sec; 404 ft 
C)  3 sec; 456 ft 
D)  4 sec; 344 ft 
A)  2.5 sec; 500 ft 
B)  3.5 sec; 404 ft 
C)  3 sec; 456 ft 
D)  4 sec; 344 ft

Question 8

Find the inverse of the matrix.
-$$\left[ \begin{array} { r r r } 
1 & 0 & 0 \
- 1 & 1 & 0 \
1 & 1 & 1
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { r r r } 1 & - 1 & 1 \ 0 & 1 & - 1 \ 0 & 0 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } 1 & 1 & 1 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 1 & 0 & 0 \ 1 & 1 & 0 \ - 2 & - 1 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 1 & 0 & 0 \ - 1 & - 1 & 0 \ - 1 & - 1 & - 1 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 1 & - 1 & 1 \ 0 & 1 & - 1 \ 0 & 0 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l } 1 & 1 & 1 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } 1 & 0 & 0 \ 1 & 1 & 0 \ - 2 & - 1 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 1 & 0 & 0 \ - 1 & - 1 & 0 \ - 1 & - 1 & - 1 \end{array} \right]$

Question 9

Solve the system of equations using elimination.
-$$\left\{ \begin{array} { c } 
2 x ^ { 2 } + y ^ { 2 } = 17 \
3 x ^ { 2 } - 2 y ^ { 2 } = - 6
\end{array} \right.$$

Accepted Answer

A)  x= 1, y = 3; x = 1, y = -3; x = -1, y = 3; x = -1, y = -3 
B)  x = 2, y = 3; x = 2, y = -3; x = -2, y = 3; x = -2, y = -3 
C)  x = 2, y = -3; x = -2, y = 3 
D)  x = 1, y = 3; x = -1, y= -3 
A)  x= 1, y = 3; x = 1, y = -3; x = -1, y = 3; x = -1, y = -3 
B)  x = 2, y = 3; x = 2, y = -3; x = -2, y = 3; x = -2, y = -3 
C)  x = 2, y = -3; x = -2, y = 3 
D)  x = 1, y = 3; x = -1, y= -3

Question 10

Verify that the values of the variables listed are solutions of the system of equations.
-$$\begin{array} { l } 
\left\{ \begin{array} { l } 
x + y = 8 \
x - y = 4
\end{array} \right. \
x = 6 , y = 2
\end{array}$$

Accepted Answer

A)  not a solution 
B)  solution 
A)  not a solution 
B)  solution

Question 11

Solve the system using the inverse method.
-$$\left\{ \begin{array} { l } 
2 x + 6 y = 2 \
2 x - y = - 5
\end{array} \right.$$

Accepted Answer

A)  x = -1, y = 2 
B)  x = -2, y = 1 
C)  x = 1, y = -2 
D)  x = 2, y = -1 
A)  x = -1, y = 2 
B)  x = -2, y = 1 
C)  x = 1, y = -2 
D)  x = 2, y = -1

Question 12

Solve the problem.
-A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many of them were adults?

Accepted Answer

A)  10 adults 
B)  29 adults 
C)  16 adults 
D)  24 adults 
A)  10 adults 
B)  29 adults 
C)  16 adults 
D)  24 adults

Question 13

Solve the problem using matrices.
-Melody has $45,000 to invest and wishes to receive an annual income of $4290 from this money. She has chosen
investments that pay 5%, 8%, and 12% simple interest. Melody wants to have the amount invested at 12% to be
double the amount invested at 8%. How much should she invest at each rate?

Accepted Answer

$9000 at 5

Question 14

Write a system of linear inequalities that has the given graph.
-  A) $y \geq 0 , x \geq 0 , y \leq 7$, and $y + x \geq 2$

Accepted Answer

B)  $y \geq 0 , x \geq 0 , x \leq 6$, and $y + x \geq 2$ 
C)  $x \leq 6 , y \leq 7$, and $y + x \geq 2$ 
D)  $y \geq 0 , x \geq 0 , x \leq 6 , y \leq 7$, and $y + x \geq 2$ 
B)  $y \geq 0 , x \geq 0 , x \leq 6$, and $y + x \geq 2$ 
C)  $x \leq 6 , y \leq 7$, and $y + x \geq 2$ 
D)  $y \geq 0 , x \geq 0 , x \leq 6 , y \leq 7$, and $y + x \geq 2$

Question 15

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$\begin{array} { r } 
- 3 x ^ { 2 } + 8 y ^ { 2 } = 1 \
9 x + 9 y = 1
\end{array}$$

Accepted Answer

Substitution should be used, b

Question 16

Find the value of the determinant.
-$$\left| \begin{array} { r r } 
- 6 & - 4 \
- 8 & 8
\end{array} \right|$$

Accepted Answer

A)  80 
B)  88 
C)  -16 
D)  -80 
A)  80 
B)  88 
C)  -16 
D)  -80

Question 17

Tell whether the given rational expression is proper or improper.
-$$\frac { x ^ { 3 } - 9 x + 20 } { x ^ { 2 } - 16 x + 64 }$$

Accepted Answer

A)  Improper 
B)  Proper 
A)  Improper 
B)  Proper

Question 18

Solve the problem.
-A flat rectangular piece of aluminum has a perimeter of 68 inches. The length is 14 inches longer than the width. Find the width.

Accepted Answer

A)  28 inches 
B)  26 inches 
C)  8 inches 
D)  18 inches 
A)  28 inches 
B)  26 inches 
C)  8 inches 
D)  18 inches

Question 19

Find the maximum or minimum value of the objective function, subject to the constraints graphed in this feasible region.  
-z = x + 8y. Find maximum.

Accepted Answer

A)  Maximum 27 
B)  Maximum 34 
C)  Maximum 20 
D)  Maximum 42 
A)  Maximum 27 
B)  Maximum 34 
C)  Maximum 20 
D)  Maximum 42

Question 20

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
-$$\left\{ \begin{array} { l } 
5 x + 6 y = 20 \
2 x + 8 y = 36
\end{array} \right.$$

Accepted Answer

A)  $x = - 2 , y = - 5$ 
B)  $x = 5 , y = - 2$ 
C)  $x = - 2 , y = 5$ 
D)  Inconsistent 
A)  $x = - 2 , y = - 5$ 
B)  $x = 5 , y = - 2$ 
C)  $x = - 2 , y = 5$ 
D)  Inconsistent

Find the inverse of the matrix. - $\left[ \begin{array} { l l l } 1 & - 1 & 8 \\1 & 0 & 2 \\2 & - 1 & 10\end{array} \right]$

Write the augmented matrix for the system. - $\left\{ \begin{array} { c } - 2 x + 6 y = 8 \\5 y = 20\end{array} \right.$

Use the elimination method to solve the system. - $\left\{ \begin{array} { c } 2 x + 24 y = - 154 \\9 x + 4 y = 35\end{array} \right.$

Solve the system. - $\left\{ \begin{array} { l } x + y = 1 \\x + y = - 3\end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { r r r } 1 & 0 & 0 \\- 1 & 1 & 0 \\1 & 1 & 1\end{array} \right]$

Solve the system of equations using elimination. - $\left\{ \begin{array} { c } 2 x ^ { 2 } + y ^ { 2 } = 17 \\3 x ^ { 2 } - 2 y ^ { 2 } = - 6\end{array} \right.$

Verify that the values of the variables listed are solutions of the system of equations. - x+y=8 x-y=4 x=6,y=2

Solve the system using the inverse method. - $\left\{ \begin{array} { l } 2 x + 6 y = 2 \\2 x - y = - 5\end{array} \right.$

Solve the problem. -A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and the theater collected $272.00 at the end of the day, how many of them were adults?

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -3+8=1 9x+9y=1

Find the value of the determinant. - $\left| \begin{array} { r r } - 6 & - 4 \\- 8 & 8\end{array} \right|$

Tell whether the given rational expression is proper or improper. - $\frac { x ^ { 3 } - 9 x + 20 } { x ^ { 2 } - 16 x + 64 }$

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 68 inches. The length is 14 inches longer than the width. Find the width.

Find the maximum or minimum value of the objective function, subject to the constraints graphed in this feasible region. -z = x + 8y. Find maximum.

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. - $\left\{ \begin{array} { l } 5 x + 6 y = 20 \\2 x + 8 y = 36\end{array} \right.$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

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Exam 10: Systems of Equations and Inequalities

Find the inverse of the matrix. - [1−181022−110]\left[ \begin{array} { l l l } 1 & - 1 & 8 \\1 & 0 & 2 \\2 & - 1 & 10\end{array} \right]​112​−10−1​8210​​

Write the augmented matrix for the system. - {−2x+6y=85y=20\left\{ \begin{array} { c } - 2 x + 6 y = 8 \\5 y = 20\end{array} \right.{−2x+6y=85y=20​

Use the elimination method to solve the system. - {2x+24y=−1549x+4y=35\left\{ \begin{array} { c } 2 x + 24 y = - 154 \\9 x + 4 y = 35\end{array} \right.{2x+24y=−1549x+4y=35​

Solve the system. - {x+y=1x+y=−3\left\{ \begin{array} { l } x + y = 1 \\x + y = - 3\end{array} \right.{x+y=1x+y=−3​

Find the inverse of the matrix. - [100−110111]\left[ \begin{array} { r r r } 1 & 0 & 0 \\- 1 & 1 & 0 \\1 & 1 & 1\end{array} \right]​1−11​011​001​​

Solve the system of equations using elimination. - {2x2+y2=173x2−2y2=−6\left\{ \begin{array} { c } 2 x ^ { 2 } + y ^ { 2 } = 17 \\3 x ^ { 2 } - 2 y ^ { 2 } = - 6\end{array} \right.{2x2+y2=173x2−2y2=−6​