If the system has infinitely many solutions, write the solution set with x arbitrary. -\[\begin{array} { l } \frac { 1 } { x } + \frac { 1 } { y } + \frac { 1 } { z } = - 1 \\ \frac { 1 } { x } - \frac { 1 } { y } + \frac { 6 } { z } = - \frac { 10 } { 3 } \\ \frac { 1 } { x } + \frac { 1 } { y } + \frac { 1 } { z } = - 1 \end{array}\]

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

Solve the system for x and y using Cramer's rule. Assume a and b are nonzero constants. -\[\begin{array} { l } a ^ { 2 } x + b ^ { 2 } y = a ^ { 2 } \\ a x + b y = b \end{array}\]

A) $\left\{ \left\{ \frac { a + b } { a } , \frac { a } { b } \right) \right\}$ B) $\left\{ \left( \frac { a - b } { a } , - \frac { a } { b } \right) \right\}$ C) $\left\{ \left( \frac { a + b } { a } , - \frac { a } { b } \right) \right\}$ D) $\left\{ \left\{ \frac { a + b } { a } , \frac { b - a } { b } \right) \right\}$ A) $\left\{ \left\{ \frac { a + b } { a } , \frac { a } { b } \right) \right\}$ B) $\left\{ \left( \frac { a - b } { a } , - \frac { a } { b } \right) \right\}$ C) $\left\{ \left( \frac { a + b } { a } , - \frac { a } { b } \right) \right\}$ D) $\left\{ \left\{ \frac { a + b } { a } , \frac { b - a } { b } \right) \right\}$

Solve the system by using the inverse of the coefficient matrix. -\[\begin{array} { l } - 3 x - y - 6 z = - 54 \\ 9 x + 4 y - 7 z = 65 \\ 2 x - 9 y + z = - 5 \end{array}\]

A) $\{ ( - 9,3,18 ) \}$ B) $\varnothing$ C) $\{ ( 9,3,4 ) \}$ D) $\{ ( 9,4,3 ) \}$ A) $\{ ( - 9,3,18 ) \}$ B) $\varnothing$ C) $\{ ( 9,3,4 ) \}$ D) $\{ ( 9,4,3 ) \}$

Solve the system by substitution. -\[\begin{array} { l } 10 x - 4 y = 3 \\ 10 x + 4 y = 3 \end{array}\]

A) $\varnothing$ B) $\left\{ \left( \frac { 3 } { 10 } , 0 \right) \right\}$ C) $\left\{ \left\{ 0 , \frac { 10 } { 3 } \right) \right\}$ D) $\left\{ \left( \frac { 3 } { 10 } , 1 \right) \right\}$ A) $\varnothing$ B) $\left\{ \left( \frac { 3 } { 10 } , 0 \right) \right\}$ C) $\left\{ \left\{ 0 , \frac { 10 } { 3 } \right) \right\}$ D) $\left\{ \left( \frac { 3 } { 10 } , 1 \right) \right\}$

Exam 10: Systems and Matrices

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 5 $50 \mathrm {~cm} ^ { 3 }$ of a solution That is 6.66% acid.

(Multiple Choice)

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Question 101

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - x-y+4z=7 3x+z=3 x+5y+z=28

(Multiple Choice)

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(39)

Question 102

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { r r } - 5 & - 1 \\6 & 0\end{array} \right] \text { and } \left[ \begin{array} { c } 0 \frac { 1 } { 6 } \\- 1 \frac { 5 } { 6 }\end{array} \right]$

(Multiple Choice)

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Question 103

If the system has infinitely many solutions, write the solution set with x arbitrary. - ++=-1 -+=- ++=-1

(Multiple Choice)

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Question 104

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] \text { and } \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right]$

(Multiple Choice)

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Question 105

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - $y \leq x^{2}+3$ $Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y \leq x^{2}+3$

(Multiple Choice)

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Question 106

Solve the system for x and y using Cramer's rule. Assume a and b are nonzero constants. - x+y= ax+by=b

(Multiple Choice)

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Question 107

Solve the system by using the inverse of the coefficient matrix. - -3x-y-6z=-54 9x+4y-7z=65 2x-9y+z=-5

(Multiple Choice)

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Question 108

Use a graphing calculator and the method of matrix inverses to Give five decimal places, if necessary. -Matt bought 3 pounds of oranges and 2 pounds of apples and paid $\$ 4.06$ , before tax. Andy bought 4 pounds of oranges and 3 pounds of apples and paid \$5.71, before tax. Use this information to set up a matrix equation of the form $\mathrm { AX } = \mathrm { B }$ , which can be solved to determine the price per pound for oras and apples. Solve this matrix equation to find the price per pound of apples. Use the fact that for $A = \left[ \begin{array} { l l } 3 & 2 \\ 4 & 3 \end{array} \right] , A ^ { - 1 } = \left[ \begin{array} { r r } 3 & - 2 \\ - 4 & 3 \end{array} \right]$ .

(Multiple Choice)

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Question 109

Graph the solution set of the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\geq-4 $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq-x^{2} \\ y \leq x+1 \\ y \geq-5 \\ x \geq-4 \end{array}$

(Multiple Choice)

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Question 110

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

(Multiple Choice)

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Question 111

Provide an appropriate response. -Let $P$ be a $5 \times 5$ matrix that has a multiplicative inverse. Which of the following statements are false? (Let 0 represent the $5 \times 5$ zero matrix.) (i) $0 \cdot \mathrm { P } = 0$ (ii) $\mathrm { PP } ^ { - 1 } = 0$ (iii) $\mathrm { P } ^ { - 1 } \mathrm { P } = \mathrm { I } _ { 5 }$ (iv) $\mathrm { PP } ^ { - 1 } = \mathrm { P }$

(Multiple Choice)

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Question 112

Find the partial fraction decomposition for the rational expression. - $\frac { 4 x ^ { 2 } - 3 x + 2 } { \left( x ^ { 2 } - 4 \right) ( x - 1 ) }$

(Multiple Choice)

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Question 113

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-8y+z=5 3x-y+2z=5

(Multiple Choice)

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Question 114

Provide an appropriate response. -Suppose that A and B are both matrices of dimension $\mathrm { r } \times \mathrm { s }$ . Under what conditions can both the product $\mathrm { AB }$ and the product $\mathrm { BA }$ be found?

(Multiple Choice)

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Question 115

Which method should be used to solve the system? Explain your answer, including a description of the first step. - +=16 2x+6y=-2

(Essay)

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Question 116

Solve the system by substitution. - 10x-4y=3 10x+4y=3

(Multiple Choice)

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Question 117

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

(Multiple Choice)

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Question 118

Solve the problem. -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. $\mathrm { C }$ requires 2 black, 1 white, and 2 red. The company used 95 black, 100 white and 85 red wires. How many of each type of cable were made?

(Multiple Choice)

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Question 119

Find the partial fraction decomposition for the rational expression. - $\frac { - 31 x - 77 } { 2 x ^ { 2 } + 14 x + 20 }$

(Multiple Choice)

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Question 120

Showing 101 - 120 of 507

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 5 $50 \mathrm {~cm} ^ { 3 }$ of a solution That is 6.66% acid.

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - x-y+4z=7 3x+z=3 x+5y+z=28

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { r r } - 5 & - 1 \\6 & 0\end{array} \right] \text { and } \left[ \begin{array} { c } 0 \frac { 1 } { 6 } \\- 1 \frac { 5 } { 6 }\end{array} \right]$

If the system has infinitely many solutions, write the solution set with x arbitrary. - ++=-1 -+=- ++=-1

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] \text { and } \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right]$

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - $y \leq x^{2}+3$ $Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y \leq x^{2}+3$

Solve the system for x and y using Cramer's rule. Assume a and b are nonzero constants. - x+y= ax+by=b

Solve the system by using the inverse of the coefficient matrix. - -3x-y-6z=-54 9x+4y-7z=65 2x-9y+z=-5

Graph the solution set of the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\geq-4 $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq-x^{2} \\ y \leq x+1 \\ y \geq-5 \\ x \geq-4 \end{array}$

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

Find the partial fraction decomposition for the rational expression. - $\frac { 4 x ^ { 2 } - 3 x + 2 } { \left( x ^ { 2 } - 4 \right) ( x - 1 ) }$

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-8y+z=5 3x-y+2z=5

Provide an appropriate response. -Suppose that A and B are both matrices of dimension $\mathrm { r } \times \mathrm { s }$ . Under what conditions can both the product $\mathrm { AB }$ and the product $\mathrm { BA }$ be found?

Which method should be used to solve the system? Explain your answer, including a description of the first step. - +=16 2x+6y=-2

Solve the system by substitution. - 10x-4y=3 10x+4y=3

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Solve the problem. -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. $\mathrm { C }$ requires 2 black, 1 white, and 2 red. The company used 95 black, 100 white and 85 red wires. How many of each type of cable were made?

Find the partial fraction decomposition for the rational expression. - $\frac { - 31 x - 77 } { 2 x ^ { 2 } + 14 x + 20 }$

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 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 5 50 cm350 \mathrm {~cm} ^ { 3 }50 cm3 of a solution That is 6.66% acid.

Use a graphing calculator to Express solutions with approximations to the nearest thousandth. - x-y+4z=7 3x+z=3 x+5y+z=28

If the system has infinitely many solutions, write the solution set with x arbitrary. - ++=-1 -+=- ++=-1

Decide whether or not the matrices are inverses of each other. - [5332] and [2−3−35]\left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] \text { and } \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right][53​32​] and [2−3​−35​]

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y≤x2+3y \leq x^{2}+3y≤x2+3

Solve the system for x and y using Cramer's rule. Assume a and b are nonzero constants. - x+y= ax+by=b

Solve the system by using the inverse of the coefficient matrix. - -3x-y-6z=-54 9x+4y-7z=65 2x-9y+z=-5

Graph the solution set of the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\geq-4

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

Find the partial fraction decomposition for the rational expression. - 4x2−3x+2(x2−4)(x−1)\frac { 4 x ^ { 2 } - 3 x + 2 } { \left( x ^ { 2 } - 4 \right) ( x - 1 ) }(x2−4)(x−1)4x2−3x+2​

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-8y+z=5 3x-y+2z=5

Provide an appropriate response. -Suppose that A and B are both matrices of dimension r×s\mathrm { r } \times \mathrm { s }r×s . Under what conditions can both the product AB\mathrm { AB }AB and the product BA\mathrm { BA }BA be found?

Which method should be used to solve the system? Explain your answer, including a description of the first step. - +=16 2x+6y=-2

Solve the system by substitution. - 10x-4y=3 10x+4y=3

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Solve the problem. -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\mathrm { C }C requires 2 black, 1 white, and 2 red. The company used 95 black, 100 white and 85 red wires. How many of each type of cable were made?

Find the partial fraction decomposition for the rational expression. - −31x−772x2+14x+20\frac { - 31 x - 77 } { 2 x ^ { 2 } + 14 x + 20 }2x2+14x+20−31x−77​

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 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 5 $50 \mathrm {~cm} ^ { 3 }$ of a solution That is 6.66% acid.

Decide whether or not the matrices are inverses of each other. - $\left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] \text { and } \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right]$

Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - $y \leq x^{2}+3$ $Use the shading capabilities of your graphing calculator to graph the inequality or system of inequalities. - y \leq x^{2}+3$

Graph the solution set of the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\geq-4 $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq-x^{2} \\ y \leq x+1 \\ y \geq-5 \\ x \geq-4 \end{array}$

Find the partial fraction decomposition for the rational expression. - $\frac { 4 x ^ { 2 } - 3 x + 2 } { \left( x ^ { 2 } - 4 \right) ( x - 1 ) }$

Provide an appropriate response. -Suppose that A and B are both matrices of dimension $\mathrm { r } \times \mathrm { s }$ . Under what conditions can both the product $\mathrm { AB }$ and the product $\mathrm { BA }$ be found?

Solve the problem. -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. $\mathrm { C }$ requires 2 black, 1 white, and 2 red. The company used 95 black, 100 white and 85 red wires. How many of each type of cable were made?

Find the partial fraction decomposition for the rational expression. - $\frac { - 31 x - 77 } { 2 x ^ { 2 } + 14 x + 20 }$