Perform the indicated elementary row operations. -$\begin{array}{l} \mathrm{R}_{13} \\ {\left[\begin{array}{rrr} 14 & 3 & 15 \\ -15 & -6 & 6 \\ -14 & -8 & 12 \end{array}\right]} \end{array}$

A) $\left[\begin{array}{rrr} -15 & -6 & 6 \\ -14 & -8 & 12 \\ 14 & 3 & 15 \end{array}\right]$ B) $\left[\begin{array}{rrr} -14 & -8 & 12 \\ -15 & -6 & 6 \\ 14 & 3 & 15 \end{array}\right]$ C) $\left[\begin{array}{rrr} 15 & 3 & 14 \\ 6 & -6 & -15 \\ 12 & -8 & -14 \end{array}\right]$ D) $\left[\begin{array}{rrr} -15 & -6 & 6 \\ 14 & 3 & 15 \\ -14 & -8 & 12 \end{array}\right]$ A) $\left[\begin{array}{rrr} -15 & -6 & 6 \\ -14 & -8 & 12 \\ 14 & 3 & 15 \end{array}\right]$ B) $\left[\begin{array}{rrr} -14 & -8 & 12 \\ -15 & -6 & 6 \\ 14 & 3 & 15 \end{array}\right]$ C) $\left[\begin{array}{rrr} 15 & 3 & 14 \\ 6 & -6 & -15 \\ 12 & -8 & -14 \end{array}\right]$ D) $\left[\begin{array}{rrr} -15 & -6 & 6 \\ 14 & 3 & 15 \\ -14 & -8 & 12 \end{array}\right]$

Solve the system algebraically. -\[\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 12 \\ 3 x - y = - 2 \end{array}\]

A) $\left( \frac { - 3 + \sqrt { 29 } } { 5 } , \frac { 1 + 3 \sqrt { 29 } } { 5 } \right)$ and $\left( \frac { - 3 - \sqrt { 29 } } { 5 } , \frac { 1 - 3 \sqrt { 29 } } { 5 } \right)$ B) $\left\{ \frac { - 3 + 2 \sqrt { 29 } } { 5 } , \frac { 1 + 3 \sqrt { 29 } } { 5 } \right)$ and $\left( \frac { - 3 - 6 \sqrt { 29 } } { 5 } , \frac { 1 - 6 \sqrt { 29 } } { 5 } \right)$ C) $\left\{ \frac { - 3 + \sqrt { 29 } } { 5 } , \frac { - 7 + 3 \sqrt { 29 } } { 5 } \right)$ and $\left( \frac { - 3 - \sqrt { 29 } } { 5 } , \frac { - 7 - 3 \sqrt { 29 } } { 5 } \right)$ D) $\left( \frac { - 3 + \sqrt { 29 } } { 5 } , \frac { 1 - 3 \sqrt { 29 } } { 5 } \right)$ and $\left( \frac { - 3 - \sqrt { 29 } } { 5 } , \frac { 1 + 3 \sqrt { 29 } } { 5 } \right)$ A) $\left( \frac { - 3 + \sqrt { 29 } } { 5 } , \frac { 1 + 3 \sqrt { 29 } } { 5 } \right)$ and $\left( \frac { - 3 - \sqrt { 29 } } { 5 } , \frac { 1 - 3 \sqrt { 29 } } { 5 } \right)$ B) $\left\{ \frac { - 3 + 2 \sqrt { 29 } } { 5 } , \frac { 1 + 3 \sqrt { 29 } } { 5 } \right)$ and $\left( \frac { - 3 - 6 \sqrt { 29 } } { 5 } , \frac { 1 - 6 \sqrt { 29 } } { 5 } \right)$ C) $\left\{ \frac { - 3 + \sqrt { 29 } } { 5 } , \frac { - 7 + 3 \sqrt { 29 } } { 5 } \right)$ and $\left( \frac { - 3 - \sqrt { 29 } } { 5 } , \frac { - 7 - 3 \sqrt { 29 } } { 5 } \right)$ D) $\left( \frac { - 3 + \sqrt { 29 } } { 5 } , \frac { 1 - 3 \sqrt { 29 } } { 5 } \right)$ and $\left( \frac { - 3 - \sqrt { 29 } } { 5 } , \frac { 1 + 3 \sqrt { 29 } } { 5 } \right)$

Exam 7: Systems and Matrices

Solve the problem. -A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $\$ 2400$ and the average monthly salary of an aide is $\$ 1100$ . The camp can accommodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides, and may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost?

(Multiple Choice)

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Question 141

Graph the linear inequality. - $2 x+3 y \leq 6$ $Graph the linear inequality. - 2 x+3 y \leq 6$

(Multiple Choice)

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Question 142

Use Gaussian elimination to solve the system of equations. -x - y + 2z = 3 3x + z = 0 X + 2y + z = -6

(Multiple Choice)

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Question 143

Determine the order of the matrix. - $\left[ \begin{array} { c c c c } 3 & 0 & 2 & 6 \\- 4 & 8 & - 2 & 7\end{array} \right]$

(Multiple Choice)

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Question 144

Decide whether the ordered pair is a solution of the given system. -(6, 2) 3x + y = 20 4x + 3y = 30

(True/False)

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Question 145

Perform the indicated elementary row operations. -(2) $\mathrm { R } _ { 2 }$ $\left[ \begin{array} { r r } 5 & - 4 \\ - 3 & - 9 \end{array} \right]$

(Multiple Choice)

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Question 146

Graph the linear inequality. - $x \leq-1$ $Graph the linear inequality. - x \leq-1$

(Multiple Choice)

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(35)

Question 147

Use the graph to estimate any solutions of the system. - +=4 x=-2 $[ - 6,6 ]$ by $[ - 6,6 ]$ $Use the graph to estimate any solutions of the system. - \begin{array}{l} x^{2}+y^{2}=4 \\ x=y^{2}-2 \end{array}[ - 6,6 ] by [ - 6,6 ] [-6,6] \text { by }[-6,6]$ $[-6,6] \text { by }[-6,6]$

(Multiple Choice)

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Question 148

Graph the linear inequality. - $-2 x-4 y \leq 8$ $Graph the linear inequality. - -2 x-4 y \leq 8$

(Multiple Choice)

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Question 149

Determine which inequality matches the graph. -

(Multiple Choice)

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Question 150

Determine the value of each variable. - $\left[ \begin{array} { l l l } 7 & \mathrm { p } + 3 & \mathrm { q } - 7 \end{array} \right] = \left[ \begin{array} { l l l } \mathrm { k } + 2 & 3 & - 5 \end{array} \right]$

(Multiple Choice)

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Question 151

Perform the indicated elementary row operations. - 14 3 15 -15 -6 6 -14 -8 12

(Multiple Choice)

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Question 152

Graph the inequality. - $y \geq 7 x^{2}-5$ $Graph the inequality. - y \geq 7 x^{2}-5$

(Multiple Choice)

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(40)

Question 153

Solve the system by elimination. -8x - 3y = 22 3x + 8y = 63

(Multiple Choice)

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(31)

Question 154

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

(Multiple Choice)

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Question 155

Find the matrix product, if possible. - $\left[ \begin{array} { r r } 3 & - 1 \\3 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 1 \\4 & 6\end{array} \right]$

(Multiple Choice)

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Question 156

Solve the system algebraically. - +=12 3x-y=-2

(Multiple Choice)

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(41)

Question 157

Use Gaussian elimination to solve the system of equations. -3x + 3y + z = -14 4x - 2y - z = -13 3x + y + 3z = -26

(Multiple Choice)

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(35)

Question 158

Use Gaussian elimination to solve the system of equations. -x - y + w - 3z = 3 x + 2y = -3 Y + w = -2 -x + w + z = 3

(Multiple Choice)

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Question 159

Find the determinant of the given matrix. - $\left[ \begin{array} { l l l } 9 & 4 & 2 \\ 7 & 2 & 3 \\ 9 & 4 & 3 \end{array} \right]$

(Multiple Choice)

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Question 160

Showing 141 - 160 of 354

Graph the linear inequality. - $2 x+3 y \leq 6$ $Graph the linear inequality. - 2 x+3 y \leq 6$

Use Gaussian elimination to solve the system of equations. -x - y + 2z = 3 3x + z = 0 X + 2y + z = -6

Determine the order of the matrix. - $\left[ \begin{array} { c c c c } 3 & 0 & 2 & 6 \\- 4 & 8 & - 2 & 7\end{array} \right]$

Decide whether the ordered pair is a solution of the given system. -(6, 2) 3x + y = 20 4x + 3y = 30

Perform the indicated elementary row operations. -(2) $\mathrm { R } _ { 2 }$ $\left[ \begin{array} { r r } 5 & - 4 \\ - 3 & - 9 \end{array} \right]$

Graph the linear inequality. - $x \leq-1$ $Graph the linear inequality. - x \leq-1$

Use the graph to estimate any solutions of the system. - +=4 x=-2 $[ - 6,6 ]$ by $[ - 6,6 ]$ $Use the graph to estimate any solutions of the system. - \begin{array}{l} x^{2}+y^{2}=4 \\ x=y^{2}-2 \end{array}[ - 6,6 ] by [ - 6,6 ] [-6,6] \text { by }[-6,6]$ $[-6,6] \text { by }[-6,6]$

Graph the linear inequality. - $-2 x-4 y \leq 8$ $Graph the linear inequality. - -2 x-4 y \leq 8$

Determine which inequality matches the graph. -

Determine the value of each variable. - $\left[ \begin{array} { l l l } 7 & \mathrm { p } + 3 & \mathrm { q } - 7 \end{array} \right] = \left[ \begin{array} { l l l } \mathrm { k } + 2 & 3 & - 5 \end{array} \right]$

Perform the indicated elementary row operations. - 14 3 15 -15 -6 6 -14 -8 12

Graph the inequality. - $y \geq 7 x^{2}-5$ $Graph the inequality. - y \geq 7 x^{2}-5$

Solve the system by elimination. -8x - 3y = 22 3x + 8y = 63

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

Find the matrix product, if possible. - $\left[ \begin{array} { r r } 3 & - 1 \\3 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 1 \\4 & 6\end{array} \right]$

Solve the system algebraically. - +=12 3x-y=-2

Use Gaussian elimination to solve the system of equations. -3x + 3y + z = -14 4x - 2y - z = -13 3x + y + 3z = -26

Use Gaussian elimination to solve the system of equations. -x - y + w - 3z = 3 x + 2y = -3 Y + w = -2 -x + w + z = 3

Find the determinant of the given matrix. - $\left[ \begin{array} { l l l } 9 & 4 & 2 \\ 7 & 2 & 3 \\ 9 & 4 & 3 \end{array} \right]$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

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Discrete Mathematics

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An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 7: Systems and Matrices

Graph the linear inequality. - 2x+3y≤62 x+3 y \leq 62x+3y≤6

Use Gaussian elimination to solve the system of equations. -x - y + 2z = 3 3x + z = 0 X + 2y + z = -6

Determine the order of the matrix. - [3026−48−27]\left[ \begin{array} { c c c c } 3 & 0 & 2 & 6 \\- 4 & 8 & - 2 & 7\end{array} \right][3−4​08​2−2​67​]

Decide whether the ordered pair is a solution of the given system. -(6, 2) 3x + y = 20 4x + 3y = 30

Perform the indicated elementary row operations. -(2) R2\mathrm { R } _ { 2 }R2​ [5−4−3−9]\left[ \begin{array} { r r } 5 & - 4 \\ - 3 & - 9 \end{array} \right][5−3​−4−9​]

Graph the linear inequality. - x≤−1x \leq-1x≤−1

Use the graph to estimate any solutions of the system. - +=4 x=-2 [−6,6][ - 6,6 ][−6,6] by [−6,6][ - 6,6 ][−6,6] [−6,6] by [−6,6][-6,6] \text { by }[-6,6][−6,6] by [−6,6]

Graph the linear inequality. - −2x−4y≤8-2 x-4 y \leq 8−2x−4y≤8

Determine which inequality matches the graph. -

Determine the value of each variable. - [7p+3q−7]=[k+23−5]\left[ \begin{array} { l l l } 7 & \mathrm { p } + 3 & \mathrm { q } - 7 \end{array} \right] = \left[ \begin{array} { l l l } \mathrm { k } + 2 & 3 & - 5 \end{array} \right][7​p+3​q−7​]=[k+2​3​−5​]

Perform the indicated elementary row operations. - 14 3 15 -15 -6 6 -14 -8 12

Graph the inequality. - y≥7x2−5y \geq 7 x^{2}-5y≥7x2−5

Solve the system by elimination. -8x - 3y = 22 3x + 8y = 63

Find a matrix A and a column matrix B that describe the following tables involving credits and tuition costs. Find the matrix product AB, and interpret the significance of the entries of this product. -

Find the matrix product, if possible. - [3−130][0−146]\left[ \begin{array} { r r } 3 & - 1 \\3 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 1 \\4 & 6\end{array} \right][33​−10​][04​−16​]

Solve the system algebraically. - +=12 3x-y=-2

Use Gaussian elimination to solve the system of equations. -3x + 3y + z = -14 4x - 2y - z = -13 3x + y + 3z = -26

Use Gaussian elimination to solve the system of equations. -x - y + w - 3z = 3 x + 2y = -3 Y + w = -2 -x + w + z = 3

Find the determinant of the given matrix. - [942723943]\left[ \begin{array} { l l l } 9 & 4 & 2 \\ 7 & 2 & 3 \\ 9 & 4 & 3 \end{array} \right]​979​424​233​​

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

Prerequisites

Filters

Graph the linear inequality. - $2 x+3 y \leq 6$ $Graph the linear inequality. - 2 x+3 y \leq 6$

Determine the order of the matrix. - $\left[ \begin{array} { c c c c } 3 & 0 & 2 & 6 \\- 4 & 8 & - 2 & 7\end{array} \right]$

Perform the indicated elementary row operations. -(2) $\mathrm { R } _ { 2 }$ $\left[ \begin{array} { r r } 5 & - 4 \\ - 3 & - 9 \end{array} \right]$

Graph the linear inequality. - $x \leq-1$ $Graph the linear inequality. - x \leq-1$

Use the graph to estimate any solutions of the system. - +=4 x=-2 $[ - 6,6 ]$ by $[ - 6,6 ]$ $Use the graph to estimate any solutions of the system. - \begin{array}{l} x^{2}+y^{2}=4 \\ x=y^{2}-2 \end{array}[ - 6,6 ] by [ - 6,6 ] [-6,6] \text { by }[-6,6]$ $[-6,6] \text { by }[-6,6]$

Graph the linear inequality. - $-2 x-4 y \leq 8$ $Graph the linear inequality. - -2 x-4 y \leq 8$

Determine the value of each variable. - $\left[ \begin{array} { l l l } 7 & \mathrm { p } + 3 & \mathrm { q } - 7 \end{array} \right] = \left[ \begin{array} { l l l } \mathrm { k } + 2 & 3 & - 5 \end{array} \right]$

Graph the inequality. - $y \geq 7 x^{2}-5$ $Graph the inequality. - y \geq 7 x^{2}-5$

Find the matrix product, if possible. - $\left[ \begin{array} { r r } 3 & - 1 \\3 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 1 \\4 & 6\end{array} \right]$

Find the determinant of the given matrix. - $\left[ \begin{array} { l l l } 9 & 4 & 2 \\ 7 & 2 & 3 \\ 9 & 4 & 3 \end{array} \right]$