Solve the system in terms of the arbitrary variable x. -\[\begin{array} { r } x + y + z = 9 \\ 4 x - 3 y + 2 z = 7 \end{array}\]

A) $\left\{ \left( x , \frac { 2 x + 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$ B) $\left\{ \left( x , \frac { 2 x - 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$ C) $\left\{ \left\{ x , \frac { 2 x + 11 } { 5 } , \frac { x + 34 } { 5 } \right) \right\}$ D) $\varnothing$ A) $\left\{ \left( x , \frac { 2 x + 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$ B) $\left\{ \left( x , \frac { 2 x - 11 } { 5 } , \frac { - 7 x + 34 } { 5 } \right) \right\}$ C) $\left\{ \left\{ x , \frac { 2 x + 11 } { 5 } , \frac { x + 34 } { 5 } \right) \right\}$ D) $\varnothing$

If the system has infinitely many solutions, write the solution set with x arbitrary. -\[\begin{array} { l } 2 x + 6 y - z = - 2 \\ 4 x - y + 2 z = 1 \\ - 4 x - 12 y + 2 z = 0 \end{array}\]

A) $\left\{ \left[ x , - \frac { 1 } { 3 } - \frac { 1 } { 3 } x , - 2 - 2 x \right) \right\}$ B) $\varnothing$ C) $\{ ( 0,0 ) \}$ D) $\left\{ \left\{ x , \frac { 1 } { 2 } - 2 x , 4 x - 1 \right) \right\}$ A) $\left\{ \left[ x , - \frac { 1 } { 3 } - \frac { 1 } { 3 } x , - 2 - 2 x \right) \right\}$ B) $\varnothing$ C) $\{ ( 0,0 ) \}$ D) $\left\{ \left\{ x , \frac { 1 } { 2 } - 2 x , 4 x - 1 \right) \right\}$

Write the augmented matrix for the system. Do not -\[\begin{aligned} 4 x + 4 z & = 8 \\ 9 y + 9 z & = 72 \\ 6 x + 5 y + 2 z & = 25 \end{aligned}\]

A) $\left[ \begin{array} { l l l } 4 & 0 & 4 \\ 0 & 9 & 9 \\ 6 & 5 & 2 \end{array} \right]$ B) $\left[ \begin{array} { r r r | r } 4 & 0 & 6 & 8 \\ 0 & 9 & 5 & 72 \\ 4 & 9 & 2 & 25 \end{array} \right]$ C) $\left[ \begin{array} { l l l | r } 4 & 0 & 4 & 8 \\ 0 & 9 & 9 & 72 \\ 6 & 5 & 2 & 25 \end{array} \right]$ D) $\left[ \begin{array} { l l l | r } 4 & 4 & 0 & 8 \\ 9 & 9 & 0 & 72 \\ 6 & 5 & 2 & 25 \end{array} \right]$ A) $\left[ \begin{array} { l l l } 4 & 0 & 4 \\ 0 & 9 & 9 \\ 6 & 5 & 2 \end{array} \right]$ B) $\left[ \begin{array} { r r r | r } 4 & 0 & 6 & 8 \\ 0 & 9 & 5 & 72 \\ 4 & 9 & 2 & 25 \end{array} \right]$ C) $\left[ \begin{array} { l l l | r } 4 & 0 & 4 & 8 \\ 0 & 9 & 9 & 72 \\ 6 & 5 & 2 & 25 \end{array} \right]$ D) $\left[ \begin{array} { l l l | r } 4 & 4 & 0 & 8 \\ 9 & 9 & 0 & 72 \\ 6 & 5 & 2 & 25 \end{array} \right]$

Exam 10: Systems and Matrices

Use a graphing calculator and the method of matrix inverses to Give five decimal places, if necessary. -A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 100 black, 110 white and 90 red wires. How many of each type of cable were made?

(Multiple Choice)

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Question 261

Solve the problem. -Two different gasohol mixtures are available. One contains $5 \%$ alcohol and the other $12 \%$ alcohol. How much of each should be mixed to obtain $500 \mathrm { gal }$ of gasohol containing $10 \%$ alcohol?

(Multiple Choice)

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Question 262

Find the partial fraction decomposition for the rational expression. - $\frac { 4 } { x ^ { 2 } \left( x ^ { 2 } + 3 \right) }$

(Multiple Choice)

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Question 263

Graph the solution set of the system of inequalities. - 2x+y\geq4 x-1\geq0 $Graph the solution set of the system of inequalities. - \begin{array} { r } 2 x + y \geq 4 \\ x - 1 \geq 0 \end{array}$

(Multiple Choice)

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Question 264

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } 0 & - 5 \\- 2 & 2\end{array} \right]$

(Multiple Choice)

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Question 265

Find the partial fraction decomposition for the rational expression. - $\frac { 7 x ^ { 2 } - 94 x + 35 } { \left( x ^ { 2 } + 2 x - 7 \right) ( x - 7 ) }$

(Multiple Choice)

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Question 266

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l l } 0 & 0 \\\mathrm { a } & \mathrm { b }\end{array} \right] = \left[ \begin{array} { c c } 0 & \mathrm { q } \\7 & - 3\end{array} \right]$

(Multiple Choice)

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Question 267

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

(Essay)

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Question 268

Solve the system in terms of the arbitrary variable x. - x+y+z=9 4x-3y+2z=7

(Multiple Choice)

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Question 269

Find the partial fraction decomposition for the rational expression. - $\frac { 3 x - 22 } { ( x - 6 ) ^ { 2 } }$

(Multiple Choice)

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Question 270

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $x - y < - 5$

(Multiple Choice)

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Question 271

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - +=36 -=36

(Multiple Choice)

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Question 272

Solve the system by substitution. - $x - 4 y = - 13$ $- 5 x - 4 y = - 7$

(Multiple Choice)

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Question 273

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y=(x+7) y=

(Multiple Choice)

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Question 274

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y\leq3 y\geq $Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - \begin{array} { l } y \leq 3 \\ y \geq 2 ^ { x } \end{array}$

(Multiple Choice)

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Question 275

If the system has infinitely many solutions, write the solution set with x arbitrary. - 2x+6y-z=-2 4x-y+2z=1 -4x-12y+2z=0

(Multiple Choice)

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Question 276

Write the augmented matrix for the system. Do not - 4x+4z =8 9y+9z =72 6x+5y+2z =25

(Multiple Choice)

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Question 277

Graph the solution set of the system of inequalities. - 3x-2y\geq-6 x-1<0 $Graph the solution set of the system of inequalities. - \begin{array} { c } 3 x - 2 y \geq - 6 \\ x - 1 < 0 \end{array}$

(Multiple Choice)

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Question 278

Graph the solution set of the system of inequalities. - y\geqx y\leq|x-5| $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq \log x \\ y \leq|x-5| \end{array}$

(Multiple Choice)

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Question 279

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -The sum of the squares of the digits of a positive two-digit number is 20 , and the tens digit is 2 more than the units digit. Find the number.

(Multiple Choice)

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Question 280

Showing 261 - 280 of 507

Solve the problem. -Two different gasohol mixtures are available. One contains $5 \%$ alcohol and the other $12 \%$ alcohol. How much of each should be mixed to obtain $500 \mathrm { gal }$ of gasohol containing $10 \%$ alcohol?

Find the partial fraction decomposition for the rational expression. - $\frac { 4 } { x ^ { 2 } \left( x ^ { 2 } + 3 \right) }$

Graph the solution set of the system of inequalities. - 2x+y\geq4 x-1\geq0 $Graph the solution set of the system of inequalities. - \begin{array} { r } 2 x + y \geq 4 \\ x - 1 \geq 0 \end{array}$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } 0 & - 5 \\- 2 & 2\end{array} \right]$

Find the partial fraction decomposition for the rational expression. - $\frac { 7 x ^ { 2 } - 94 x + 35 } { \left( x ^ { 2 } + 2 x - 7 \right) ( x - 7 ) }$

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l l } 0 & 0 \\\mathrm { a } & \mathrm { b }\end{array} \right] = \left[ \begin{array} { c c } 0 & \mathrm { q } \\7 & - 3\end{array} \right]$

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

Solve the system in terms of the arbitrary variable x. - x+y+z=9 4x-3y+2z=7

Find the partial fraction decomposition for the rational expression. - $\frac { 3 x - 22 } { ( x - 6 ) ^ { 2 } }$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $x - y < - 5$

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - +=36 -=36

Solve the system by substitution. - $x - 4 y = - 13$ $- 5 x - 4 y = - 7$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y=(x+7) y=

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y\leq3 y\geq $Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - \begin{array} { l } y \leq 3 \\ y \geq 2 ^ { x } \end{array}$

If the system has infinitely many solutions, write the solution set with x arbitrary. - 2x+6y-z=-2 4x-y+2z=1 -4x-12y+2z=0

Write the augmented matrix for the system. Do not - 4x+4z =8 9y+9z =72 6x+5y+2z =25

Graph the solution set of the system of inequalities. - 3x-2y\geq-6 x-1<0 $Graph the solution set of the system of inequalities. - \begin{array} { c } 3 x - 2 y \geq - 6 \\ x - 1 < 0 \end{array}$

Graph the solution set of the system of inequalities. - y\geqx y\leq|x-5| $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq \log x \\ y \leq|x-5| \end{array}$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -The sum of the squares of the digits of a positive two-digit number is 20 , and the tens digit is 2 more than the units digit. Find the number.

Review of Basic Concepts

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

Filters

Exam 10: Systems and Matrices

Solve the problem. -Two different gasohol mixtures are available. One contains 5%5 \%5% alcohol and the other 12%12 \%12% alcohol. How much of each should be mixed to obtain 500gal500 \mathrm { gal }500gal of gasohol containing 10%10 \%10% alcohol?

Find the partial fraction decomposition for the rational expression. - 4x2(x2+3)\frac { 4 } { x ^ { 2 } \left( x ^ { 2 } + 3 \right) }x2(x2+3)4​

Graph the solution set of the system of inequalities. - 2x+y\geq4 x-1\geq0

Find the inverse, if it exists, for the matrix. - [0−5−22]\left[ \begin{array} { r r } 0 & - 5 \\- 2 & 2\end{array} \right][0−2​−52​]

Find the partial fraction decomposition for the rational expression. - 7x2−94x+35(x2+2x−7)(x−7)\frac { 7 x ^ { 2 } - 94 x + 35 } { \left( x ^ { 2 } + 2 x - 7 \right) ( x - 7 ) }(x2+2x−7)(x−7)7x2−94x+35​

Find the values of the variables for which the statement is true, if possible. - [00ab]=[0q7−3]\left[ \begin{array} { l l } 0 & 0 \\\mathrm { a } & \mathrm { b }\end{array} \right] = \left[ \begin{array} { c c } 0 & \mathrm { q } \\7 & - 3\end{array} \right][0a​0b​]=[07​q−3​]

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

Solve the system in terms of the arbitrary variable x. - x+y+z=9 4x-3y+2z=7

Find the partial fraction decomposition for the rational expression. - 3x−22(x−6)2\frac { 3 x - 22 } { ( x - 6 ) ^ { 2 } }(x−6)23x−22​

Which method should be used to solve the system? Explain your answer, including a description of the first step. - x−y<−5x - y < - 5x−y<−5

Give all solutions of the nonlinear system of equations, including those with nonreal complex components. - +=36 -=36

Solve the system by substitution. - x−4y=−13x - 4 y = - 13x−4y=−13 −5x−4y=−7- 5 x - 4 y = - 7−5x−4y=−7

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y=(x+7) y=

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y\leq3 y\geq

If the system has infinitely many solutions, write the solution set with x arbitrary. - 2x+6y-z=-2 4x-y+2z=1 -4x-12y+2z=0

Write the augmented matrix for the system. Do not - 4x+4z =8 9y+9z =72 6x+5y+2z =25

Graph the solution set of the system of inequalities. - 3x-2y\geq-6 x-1<0

Graph the solution set of the system of inequalities. - y\geqx y\leq|x-5|

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. -The sum of the squares of the digits of a positive two-digit number is 20 , and the tens digit is 2 more than the units digit. Find the number.

Review of Basic Concepts

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

Filters

Solve the problem. -Two different gasohol mixtures are available. One contains $5 \%$ alcohol and the other $12 \%$ alcohol. How much of each should be mixed to obtain $500 \mathrm { gal }$ of gasohol containing $10 \%$ alcohol?

Find the partial fraction decomposition for the rational expression. - $\frac { 4 } { x ^ { 2 } \left( x ^ { 2 } + 3 \right) }$

Graph the solution set of the system of inequalities. - 2x+y\geq4 x-1\geq0 $Graph the solution set of the system of inequalities. - \begin{array} { r } 2 x + y \geq 4 \\ x - 1 \geq 0 \end{array}$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } 0 & - 5 \\- 2 & 2\end{array} \right]$

Find the partial fraction decomposition for the rational expression. - $\frac { 7 x ^ { 2 } - 94 x + 35 } { \left( x ^ { 2 } + 2 x - 7 \right) ( x - 7 ) }$

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l l } 0 & 0 \\\mathrm { a } & \mathrm { b }\end{array} \right] = \left[ \begin{array} { c c } 0 & \mathrm { q } \\7 & - 3\end{array} \right]$

Find the partial fraction decomposition for the rational expression. - $\frac { 3 x - 22 } { ( x - 6 ) ^ { 2 } }$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $x - y < - 5$

Solve the system by substitution. - $x - 4 y = - 13$ $- 5 x - 4 y = - 7$

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y\leq3 y\geq $Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - \begin{array} { l } y \leq 3 \\ y \geq 2 ^ { x } \end{array}$

Graph the solution set of the system of inequalities. - 3x-2y\geq-6 x-1<0 $Graph the solution set of the system of inequalities. - \begin{array} { c } 3 x - 2 y \geq - 6 \\ x - 1 < 0 \end{array}$

Graph the solution set of the system of inequalities. - y\geqx y\leq|x-5| $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq \log x \\ y \leq|x-5| \end{array}$