Perform the row operation(s) on the given augmented matrix. -\[\begin{array} { l } \mathrm { R } _ { 2 } = - 2 \mathrm { r } _ { 2 } + \mathrm { r } 1 \\ { \left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \\ 1 & 2 & 3 & 6 \\ 4 & 6 & 7 & 1 \end{array} \right] } \end{array}\]

A) $\left[ \begin{array} { l l l | r } 2 & 4 & 6 & - 8 \\ 0 & 0 & 0 & 0 \\ 4 & 6 & 7 & 1 \end{array} \right]$ B) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \\ - 4 & - 8 & - 12 & - 20 \\ 4 & 6 & 7 & 1 \end{array} \right]$ C) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \\ 0 & 0 & 0 & - 20 \\ 4 & 6 & 7 & 1 \end{array} \right]$ D) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \\ - 4 & - 8 & - 12 & 6 \\ 4 & 6 & 7 & 1 \end{array} \right]$ A) $\left[ \begin{array} { l l l | r } 2 & 4 & 6 & - 8 \\ 0 & 0 & 0 & 0 \\ 4 & 6 & 7 & 1 \end{array} \right]$ B) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \\ - 4 & - 8 & - 12 & - 20 \\ 4 & 6 & 7 & 1 \end{array} \right]$ C) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \\ 0 & 0 & 0 & - 20 \\ 4 & 6 & 7 & 1 \end{array} \right]$ D) $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \\ - 4 & - 8 & - 12 & 6 \\ 4 & 6 & 7 & 1 \end{array} \right]$

Exam 6: Systems of Equations and Inequalities

Solve the problem. -A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 7 soft drinks for $36.53. The second group bought 6 slices of pizza and 5 soft drinks for $ 26)93. How much does one slice of pizza cost?

(Multiple Choice)

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Question 61

Write the augmented matrix for the system. - $\left\{ \begin{array} { r } 5 x + 5 z = 65 \\3 y + 9 z = 96 \\9 x - 2 y + 6 z = 77\end{array} \right.$

(Multiple Choice)

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Question 62

Graph the system of inequalities. - +y\leq1 -y\leq3 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y \leq 1 \\ x^{2}-y \leq 3 \end{array}$

(Multiple Choice)

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Question 63

Solve the problem. -The perimeter of a rectangle is 46 inches and its area is 126 square inches. What are its dimensions?

(Multiple Choice)

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Question 64

Solve the problem. -Find real numbers a, b, and c such that the graph of the function y = ax² + bx + c contains the points (1, 1), (2, 4), and (-3, 29).

(Short Answer)

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Question 65

Perform the row operation(s) on the given augmented matrix. - =-2+1 2 4 6 -8 1 2 3 6 4 6 7 1

(Multiple Choice)

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Question 66

Use the properties of determinants to find the value of the second determinant, given the value of the first. - $\left| \begin{array} { c c c } x & y & z \\u & v & w \\1 & - 2 & - 1\end{array} \right| = 2 \quad \left| \begin{array} { c c c } u & v & w \\2 & - 4 & - 2 \\x & y & z\end{array} \right| = ?$

(Multiple Choice)

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Question 67

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -8-=16 -5+7=64

(Essay)

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Question 68

Write the partial fraction decomposition of the rational expression. - $\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }$

(Multiple Choice)

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Question 69

Graph the inequality. -2x + 5y ≤10

(Multiple Choice)

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Question 70

Perform the indicated operations and simplify. -Let $\mathrm { A } = \left[ \begin{array} { r r } 3 & - 4 \\ - 2 & 5 \end{array} \right] , \mathrm { B } = \left[ \begin{array} { r r r } 5 & - 2 & 8 \\ 1 & 0 & - 3 \end{array} \right]$ , and $\mathrm { C } = \left[ \begin{array} { r r r } 7 & - 9 & 0 \\ 3 & - 5 & 1 \\ - 1 & 6 & 2 \end{array} \right]$ . Find $\mathrm { AB } + \mathrm { BC }$ .

(Multiple Choice)

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Question 71

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? - x² + y² = 52 2y+3x = 0

(Multiple Choice)

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Question 72

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?

(Multiple Choice)

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Question 73

Which method should be used to solve the system? Explain your answer, including a description of the first step. - 8-10=64 3-9=49

(Essay)

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Question 74

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 4 \\x + y = 2\end{array} \right.$

(Multiple Choice)

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Question 75

Write the partial fraction decomposition of the rational expression. - $\frac { 3 x - 2 } { x ^ { 3 } - 1 }$

(Multiple Choice)

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Question 76

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 169 \\x + y = 17\end{array} \right.$

(Multiple Choice)

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Question 77

Tell whether the given rational expression is proper or improper. - $\frac { x ^ { 3 } - 13 x + 42 } { x ^ { 2 } - 8 x + 15 }$

(Multiple Choice)

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Question 78

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x² + y² = 1 -10x - y = -1

(Essay)

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Question 79

Graph the inequality. --3x - 4y ≤12

(Multiple Choice)

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Question 80

Solve the problem. -A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 7 soft drinks for $36.53. The second group bought 6 slices of pizza and 5 soft drinks for $ 26)93. How much does one slice of pizza cost?

Write the augmented matrix for the system. - $\left\{ \begin{array} { r } 5 x + 5 z = 65 \\3 y + 9 z = 96 \\9 x - 2 y + 6 z = 77\end{array} \right.$

Graph the system of inequalities. - +y\leq1 -y\leq3 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y \leq 1 \\ x^{2}-y \leq 3 \end{array}$

Solve the problem. -The perimeter of a rectangle is 46 inches and its area is 126 square inches. What are its dimensions?

Solve the problem. -Find real numbers a, b, and c such that the graph of the function y = ax² + bx + c contains the points (1, 1), (2, 4), and (-3, 29).

Perform the row operation(s) on the given augmented matrix. - =-2+1 2 4 6 -8 1 2 3 6 4 6 7 1

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -8-=16 -5+7=64

Write the partial fraction decomposition of the rational expression. - $\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }$

Graph the inequality. -2x + 5y ≤10

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? - x² + y² = 52 2y+3x = 0

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. - 8-10=64 3-9=49

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 4 \\x + y = 2\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { 3 x - 2 } { x ^ { 3 } - 1 }$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 169 \\x + y = 17\end{array} \right.$

Tell whether the given rational expression is proper or improper. - $\frac { x ^ { 3 } - 13 x + 42 } { x ^ { 2 } - 8 x + 15 }$

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x² + y² = 1 -10x - y = -1

Graph the inequality. --3x - 4y ≤12

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Exam 6: Systems of Equations and Inequalities

Solve the problem. -A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 7 soft drinks for $36.53. The second group bought 6 slices of pizza and 5 soft drinks for $ 26)93. How much does one slice of pizza cost?

Write the augmented matrix for the system. - {5x+5z=653y+9z=969x−2y+6z=77\left\{ \begin{array} { r } 5 x + 5 z = 65 \\3 y + 9 z = 96 \\9 x - 2 y + 6 z = 77\end{array} \right.⎩⎨⎧​5x+5z=653y+9z=969x−2y+6z=77​

Graph the system of inequalities. - +y\leq1 -y\leq3

Solve the problem. -The perimeter of a rectangle is 46 inches and its area is 126 square inches. What are its dimensions?

Solve the problem. -Find real numbers a, b, and c such that the graph of the function y = ax2 + bx + c contains the points (1, 1), (2, 4), and (-3, 29).

Perform the row operation(s) on the given augmented matrix. - =-2+1 2 4 6 -8 1 2 3 6 4 6 7 1

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -8-=16 -5+7=64

Write the partial fraction decomposition of the rational expression. - 12x2+162x+384(x+8)(x+2)(x+11)\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }(x+8)(x+2)(x+11)12x2+162x+384​

Graph the inequality. -2x + 5y ≤10

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? - x2 + y2 = 52 2y+3x = 0

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. - 8-10=64 3-9=49

Solve the system of equations using substitution. - {x2+y2=4x+y=2\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 4 \\x + y = 2\end{array} \right.{x2+y2=4x+y=2​

Write the partial fraction decomposition of the rational expression. - 3x−2x3−1\frac { 3 x - 2 } { x ^ { 3 } - 1 }x3−13x−2​

Solve the system of equations using substitution. - {x2+y2=169x+y=17\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 169 \\x + y = 17\end{array} \right.{x2+y2=169x+y=17​

Tell whether the given rational expression is proper or improper. - x3−13x+42x2−8x+15\frac { x ^ { 3 } - 13 x + 42 } { x ^ { 2 } - 8 x + 15 }x2−8x+15x3−13x+42​

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x2 + y2 = 1 -10x - y = -1

Graph the inequality. --3x - 4y ≤12

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Write the augmented matrix for the system. - $\left\{ \begin{array} { r } 5 x + 5 z = 65 \\3 y + 9 z = 96 \\9 x - 2 y + 6 z = 77\end{array} \right.$

Graph the system of inequalities. - +y\leq1 -y\leq3 $Graph the system of inequalities. - \begin{array}{l} x^{2}+y \leq 1 \\ x^{2}-y \leq 3 \end{array}$

Solve the problem. -Find real numbers a, b, and c such that the graph of the function y = ax² + bx + c contains the points (1, 1), (2, 4), and (-3, 29).

Write the partial fraction decomposition of the rational expression. - $\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }$

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? - x² + y² = 52 2y+3x = 0

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 4 \\x + y = 2\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { 3 x - 2 } { x ^ { 3 } - 1 }$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 169 \\x + y = 17\end{array} \right.$

Tell whether the given rational expression is proper or improper. - $\frac { x ^ { 3 } - 13 x + 42 } { x ^ { 2 } - 8 x + 15 }$

Which method should be used to solve the system? Explain your answer, including a description of the first step. -x² + y² = 1 -10x - y = -1