Write the augmented matrix for the system. Do not solve the system. -$\begin{aligned} 3 x+5 y & &=8 \\ -5 y-8 z &=4 \\ -3 z &=-9 \end{aligned}$

A) $\left[ \begin{array} { r r r | r } 3 & 5 & 8 & 0 \\ - 5 & - 8 & 0 & 4 \\ - 3 & 0 & 0 & - 9 \end{array} \right]$ B) $\left[ \begin{array} { r r r | r } 3 & 5 & 8 & 0 \\ - 5 & - 8 & 4 & 0 \\ - 3 & - 9 & 0 & 0 \end{array} \right]$ C) $\left[ \begin{array} { r r r | r } 3 & 5 & 0 & 8 \\ - 5 & - 8 & 0 & 4 \\ - 9 & 0 & 0 & - 9 \end{array} \right]$ D) $\left[ \begin{array} { r r r | r } 3 & 5 & 0 & 8 \\ 0 & - 5 & - 8 & 4 \\ 0 & 0 & - 3 & - 9 \end{array} \right]$ A) $\left[ \begin{array} { r r r | r } 3 & 5 & 8 & 0 \\ - 5 & - 8 & 0 & 4 \\ - 3 & 0 & 0 & - 9 \end{array} \right]$ B) $\left[ \begin{array} { r r r | r } 3 & 5 & 8 & 0 \\ - 5 & - 8 & 4 & 0 \\ - 3 & - 9 & 0 & 0 \end{array} \right]$ C) $\left[ \begin{array} { r r r | r } 3 & 5 & 0 & 8 \\ - 5 & - 8 & 0 & 4 \\ - 9 & 0 & 0 & - 9 \end{array} \right]$ D) $\left[ \begin{array} { r r r | r } 3 & 5 & 0 & 8 \\ 0 & - 5 & - 8 & 4 \\ 0 & 0 & - 3 & - 9 \end{array} \right]$

Solve the system by elimination. -\[\begin{array} { l } \frac { 9 x } { 4 } + \frac { y } { 4 } = - 2 \\ \frac { x } { 4 } + \frac { y } { 4 } = 0 \end{array}\]

A) $\left\{ \left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right) \right\}$ B) $\left\{ \left( - \frac { 4 } { 5 } , \frac { 4 } { 5 } \right) \right\}$ C) $\{ ( - 16,16 ) \}$ D) $\{ ( - 1,1 ) \}$ A) $\left\{ \left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right) \right\}$ B) $\left\{ \left( - \frac { 4 } { 5 } , \frac { 4 } { 5 } \right) \right\}$ C) $\{ ( - 16,16 ) \}$ D) $\{ ( - 1,1 ) \}$

Solve the system. -$\begin{array}{l} \frac{8}{x}-\frac{1}{y}+\frac{3}{z}=-\frac{8}{21} \\ -\frac{1}{x}+\frac{5}{y}-\frac{8}{z}=-\frac{8}{3} \\ \frac{6}{x}-\frac{1}{y}-\frac{1}{z}=-\frac{2}{3} \end{array}$

A) $\left\{ \left( - \frac { 1 } { 7 } , - \frac { 1 } { 3 } , - \frac { 1 } { 7 } \right) \right\}$ B) $\left\{ \left( - \frac { 1 } { 7 } , - \frac { 1 } { 3 } , \frac { 1 } { 7 } \right) \right\}$ C) $\{ ( - 7 , - 3 , - 7 ) \}$ D) $\{ ( - 7 , - 3,7 ) \}$ A) $\left\{ \left( - \frac { 1 } { 7 } , - \frac { 1 } { 3 } , - \frac { 1 } { 7 } \right) \right\}$ B) $\left\{ \left( - \frac { 1 } { 7 } , - \frac { 1 } { 3 } , \frac { 1 } { 7 } \right) \right\}$ C) $\{ ( - 7 , - 3 , - 7 ) \}$ D) $\{ ( - 7 , - 3,7 ) \}$

Exam 9: Systems and Matrices

Write the word or phrase that best completes each statement or answers the question. - $\text { Let } A \text { be a } 5 \times 1 \text { matrix. Write a matrix } B \text { such that } A B \text { can be found. }$

(Short Answer)

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Question 41

Provide an appropriate response. -Suppose that you attempt to solve a system of equations and find that D = 0. What can you conclude about the solutions of this system?

(Multiple Choice)

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Question 42

Find the partial fraction decomposition for the rational expression. - $\frac { 6 x - 17 } { ( x + 3 ) ( x - 2 ) }$

(Multiple Choice)

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Question 43

Solve the problem. -The following table shows the number of rectifiers, in thousands, produced by Allied Electronics in the three years considered. For a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ that fits this data, what is the value of $b$ ? $Solve the problem. -The following table shows the number of rectifiers, in thousands, produced by Allied Electronics in the three years considered. For a function of the form f ( x ) = a x ^ { 2 } + b x + c that fits this data, what is the value of b ?$

(Multiple Choice)

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Question 54

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } > 49$

(Multiple Choice)

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Question 55

Graph the solution set of the system of inequalities. - y\geq y\leq8 $Graph the solution set of the system of inequalities. - \begin{array} { l } y \geq 3 ^ { x } \\ y \leq 8 \end{array}$

(Multiple Choice)

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Question 56

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - x-8y=2 -3x+24y=-6

(Multiple Choice)

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Question 57

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 4x+y+z =0 x-y+2z =-8 4x+y+z =-3

(Multiple Choice)

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Question 58

Solve the system. - -+=- -+-=- --=-

(Multiple Choice)

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Question 59

Find the cofactor of the indicated element. - $a_{12}$ $\left|\begin{array}{rrr}-2 & -1 & 0 \\5 & 5 & 2 \\3 & 4 & 5\end{array}\right|$

(Multiple Choice)

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Question 60

Showing 41 - 60 of 505

Write the word or phrase that best completes each statement or answers the question. - $\text { Let } A \text { be a } 5 \times 1 \text { matrix. Write a matrix } B \text { such that } A B \text { can be found. }$

Provide an appropriate response. -Suppose that you attempt to solve a system of equations and find that D = 0. What can you conclude about the solutions of this system?

Find the partial fraction decomposition for the rational expression. - $\frac { 6 x - 17 } { ( x + 3 ) ( x - 2 ) }$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l } 0 & 6 \\ 5 & 3 \end{array} \right]$

Write the augmented matrix for the system. Do not solve the system. - 3x+5y =8 -5y-8z =4 -3z =-9

Solve the problem using matrices. -A chemist has prepared two acid solutions, one of which is $4 \%$ acid by volume, another $11 \%$ acid. How many cubic centimeters of each should the chemist mix together to obtain $50 \mathrm {~cm} ^ { 3 }$ of a solution that is $6.8 \%$ acid.

Solve the equation for x. - $\left| \begin{array} { r r } - 2 & 5 \\1 & x\end{array} \right| = - 7$

Solve the system by elimination. - +=-2 +=0

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - x-y+2z+w=5 y+z=1 z-w=4

Find the dimension of the matrix. - $[ 2 - 7 - 4 ]$

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - $A$ is $3 \times 1$ ; B is $1 \times 3$ .

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } > 49$

Graph the solution set of the system of inequalities. - y\geq y\leq8 $Graph the solution set of the system of inequalities. - \begin{array} { l } y \geq 3 ^ { x } \\ y \leq 8 \end{array}$

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - x-8y=2 -3x+24y=-6

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 4x+y+z =0 x-y+2z =-8 4x+y+z =-3

Solve the system. - -+=- -+-=- --=-

Find the cofactor of the indicated element. - $a_{12}$ $\left|\begin{array}{rrr}-2 & -1 & 0 \\5 & 5 & 2 \\3 & 4 & 5\end{array}\right|$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 9: Systems and Matrices

Provide an appropriate response. -Suppose that you attempt to solve a system of equations and find that D = 0. What can you conclude about the solutions of this system?

Find the partial fraction decomposition for the rational expression. - 6x−17(x+3)(x−2)\frac { 6 x - 17 } { ( x + 3 ) ( x - 2 ) }(x+3)(x−2)6x−17​

Solve the problem. -The following table shows the number of rectifiers, in thousands, produced by Allied Electronics in the three years considered. For a function of the form f(x)=ax2+bx+cf ( x ) = a x ^ { 2 } + b x + cf(x)=ax2+bx+c that fits this data, what is the value of bbb ?

Find the inverse, if it exists, for the matrix. - [0653]\left[ \begin{array} { l l } 0 & 6 \\ 5 & 3 \end{array} \right][05​63​]

Write the augmented matrix for the system. Do not solve the system. - 3x+5y =8 -5y-8z =4 -3z =-9

Solve the equation for x. - ∣−251x∣=−7\left| \begin{array} { r r } - 2 & 5 \\1 & x\end{array} \right| = - 7​−21​5x​​=−7

Solve the system by elimination. - +=-2 +=0

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. - x-y+2z+w=5 y+z=1 z-w=4

Find the dimension of the matrix. - [2−7−4][ 2 - 7 - 4 ][2−7−4]

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - AAA is 3×13 \times 13×1 ; B is 1×31 \times 31×3 .

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? (x+2)2+(y+4)2>49( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } > 49(x+2)2+(y+4)2>49

Graph the solution set of the system of inequalities. - y\geq y\leq8

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - x-8y=2 -3x+24y=-6

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 4x+y+z =0 x-y+2z =-8 4x+y+z =-3

Solve the system. - -+=- -+-=- --=-

Find the cofactor of the indicated element. - a12a_{12}a12​ ∣−2−10552345∣\left|\begin{array}{rrr}-2 & -1 & 0 \\5 & 5 & 2 \\3 & 4 & 5\end{array}\right|​−253​−154​025​​

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Find the partial fraction decomposition for the rational expression. - $\frac { 6 x - 17 } { ( x + 3 ) ( x - 2 ) }$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l } 0 & 6 \\ 5 & 3 \end{array} \right]$

Solve the equation for x. - $\left| \begin{array} { r r } - 2 & 5 \\1 & x\end{array} \right| = - 7$

Find the dimension of the matrix. - $[ 2 - 7 - 4 ]$

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - $A$ is $3 \times 1$ ; B is $1 \times 3$ .

Provide an appropriate response. -Which one of the following is a description of the graph of the inequality? $( x + 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } > 49$

Graph the solution set of the system of inequalities. - y\geq y\leq8 $Graph the solution set of the system of inequalities. - \begin{array} { l } y \geq 3 ^ { x } \\ y \leq 8 \end{array}$

Find the cofactor of the indicated element. - $a_{12}$ $\left|\begin{array}{rrr}-2 & -1 & 0 \\5 & 5 & 2 \\3 & 4 & 5\end{array}\right|$