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

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

Solve the system for x and y using Cramer's rule. Assume a and b are nonzero constants $\begin{array} { l } \frac { 1 } { a } x + \frac { 1 } { b } y = a b \\ x + y = a \end{array}$

A) $\left\{ \left( a b ( 1 - a b ) , a ^ { 2 } \left( b ^ { 2 } - 1 \right) \right) \right\}$ B) $\left\{ \left[ \frac { a ( b - a ) \left( b ^ { 2 } - 1 \right) } { a b ^ { 2 } } , \frac { ( b - a ) ( 1 - a b ) } { a b } \right) \right\}$ C) $\left. \left\{ \frac { a ^ { 2 } \left( b ^ { 2 } - 1 \right) } { b - a } , \frac { a b ( 1 - a b ) } { b - a } \right) \right\}$ D) $\left\{ \left( \frac { a ^ { 2 } b \left( b ^ { 2 } - 1 \right) } { b - a } , \frac { a b ( 1 - a b ) } { b - a } \right) \right\}$ A) $\left\{ \left( a b ( 1 - a b ) , a ^ { 2 } \left( b ^ { 2 } - 1 \right) \right) \right\}$ B) $\left\{ \left[ \frac { a ( b - a ) \left( b ^ { 2 } - 1 \right) } { a b ^ { 2 } } , \frac { ( b - a ) ( 1 - a b ) } { a b } \right) \right\}$ C) $\left. \left\{ \frac { a ^ { 2 } \left( b ^ { 2 } - 1 \right) } { b - a } , \frac { a b ( 1 - a b ) } { b - a } \right) \right\}$ D) $\left\{ \left( \frac { a ^ { 2 } b \left( b ^ { 2 } - 1 \right) } { b - a } , \frac { a b ( 1 - a b ) } { b - a } \right) \right\}$

Solve the system by using the inverse of the coefficient matrix. -\[\begin{array} { l } x - 2 y + 3 z = 11 \\ 4 x + y - z = 4 \\ 2 x - y + 3 z = 10 \end{array}\]

A) $\{ ( 2,3,5 ) \}$ B) $\varnothing$ C) $\{ ( 2 , - 3,1 ) \}$ D) $\{ ( - 2 , - 3,3 ) \}$ A) $\{ ( 2,3,5 ) \}$ B) $\varnothing$ C) $\{ ( 2 , - 3,1 ) \}$ D) $\{ ( - 2 , - 3,3 ) \}$

Solve the system. $\begin{array} { l } \frac { 6 } { x } - \frac { 1 } { y } + \frac { 5 } { z } = \frac { 61 } { 14 } \\ - \frac { 1 } { x } + \frac { 4 } { y } - \frac { 3 } { z } = - \frac { 53 } { 42 } \\ \frac { 7 } { x } - \frac { 1 } { y } - \frac { 1 } { z } = \frac { 71 } { 42 } \end{array}$

A) $\{ ( 3,7,2 ) \}$ B) $\{ ( 3,7 , - 2 ) \}$ C) $\left\{ \left( \frac { 1 } { 3 } , \frac { 1 } { 7 } , - \frac { 1 } { 2 } \right) \right\}$ D) $\left\{ \left( \frac { 1 } { 3 } , \frac { 1 } { 7 } , \frac { 1 } { 2 } \right) \right\}$ A) $\{ ( 3,7,2 ) \}$ B) $\{ ( 3,7 , - 2 ) \}$ C) $\left\{ \left( \frac { 1 } { 3 } , \frac { 1 } { 7 } , - \frac { 1 } { 2 } \right) \right\}$ D) $\left\{ \left( \frac { 1 } { 3 } , \frac { 1 } { 7 } , \frac { 1 } { 2 } \right) \right\}$

Solve the system by substitution. -\[\begin{array} { r } x + 7 y = 27 \\ 6 x + 7 y = 57 \end{array}\]

A) $\{ ( 7,2 ) \}$ B) $\{ ( 6,3 ) \}$ C) $\varnothing$ D) $\{ ( - 3,6 ) \}$ A) $\{ ( 7,2 ) \}$ B) $\{ ( 6,3 ) \}$ C) $\varnothing$ D) $\{ ( - 3,6 ) \}$

Solve the system. $\begin{array} { l } \frac { 6 } { x } - \frac { 4 } { y } = \frac { 19 } { 14 } \\ \frac { 6 } { x } + \frac { 5 } { y } = \frac { 13 } { 56 } \end{array}$

A) $\{ ( 7,8 ) \}$ B) $\{ ( - 8 , - 7 ) \}$ C) $\{ ( 7 , - 8 ) \}$ D) $\left\{ \left( - \frac { 546 } { 89 } , - 8 \right) \right\}$ A) $\{ ( 7,8 ) \}$ B) $\{ ( - 8 , - 7 ) \}$ C) $\{ ( 7 , - 8 ) \}$ D) $\left\{ \left( - \frac { 546 } { 89 } , - 8 \right) \right\}$

Exam 6: Systems and Matrices

Mike's Bait Shop sells three types of lures: discount, normal, and professional. Location I sells 29 discount lures, 100 regular lures, and 30 professional lures each day. Location II sells 24 discount lures and Location III sells 60 discount lures each day. Daily sales of regular lures are 90 at Location II and 120 at Location III. At Location II, 12 expert lures are sold each day, and 40 expert lures are sold each day at Location III. Write a $3 \times 3$ matrix that shows the sales figures for the three locations, with the rows representing the three locations.

(Multiple Choice)

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Question 121

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 122

Provide an appropriate response. -Fill in the blank to complete the statement. Each number in a matrix is called _______ of the matrix.

(Multiple Choice)

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Question 123

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

(Multiple Choice)

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Question 124

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 3x-y-2=0 -6x+2y+4=0

(Multiple Choice)

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Question 125

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

(Multiple Choice)

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Question 126

Solve the system by using the inverse of the coefficient matrix. - x-2y+3z=11 4x+y-z=4 2x-y+3z=10

(Multiple Choice)

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Question 127

Find the value of the determinant. - $\left| \begin{array} { l l } - 1 & 1 \\ 3 & 3 \end{array} \right|$

(Multiple Choice)

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Question 128

Le Boulangerie, a bakery, sells four main items: sweet rolls, bread, cakes, and pies. The amount of each ingredient (in cups, except for eggs) required for these items is given by matrix A. The cost (in cents) for each ingredient when purchased in large lots or small lots is given in matrix B. Suppose a day's orders consist of 20 dozen sweet rolls, 200 loaves of bread, 50 cakes, and 60 pies. Use matrix Multiplication to find a matrix giving the costs under the two purchase options to fill the day's orders.

(Multiple Choice)

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Question 129

Find the matrix product when possible. - $\left[ \begin{array} { r r } 3 & - 2 \\4 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 2 \\2 & 6\end{array} \right]$

(Multiple Choice)

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Question 130

The following table shows the number of dog collars, in thousands, produced by Allied Pet Products in the three years considered. Find a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ that fits this data. Using this function, what would you predict the dog collar production of Allied Pet Products to be in year 27 ? $The following table shows the number of dog collars, in thousands, produced by Allied Pet Products in the three years considered. Find a function of the form f ( x ) = a x ^ { 2 } + b x + c that fits this data. Using this function, what would you predict the dog collar production of Allied Pet Products to be in year 27 ?$

(Multiple Choice)

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Question 131

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { c c } x + 3 & y + 4 \\7 & - 6\end{array} \right] = \left[ \begin{array} { l l } 9 & 5 \\7 & k\end{array} \right]$

(Multiple Choice)

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Question 132

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

(Multiple Choice)

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Question 133

Find the matrix product when possible. -Given $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & - 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 1 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 1 & 0 \end{array} \right]$ , find $A B$ and $B A$ .

(Multiple Choice)

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Question 134

A triangle with vertices at (x1, y1), (x2, y2), and (x3, y3) has area equal to the absolute value of D, where $D = \frac { 1 } { 2 } \left| \begin{array} { l l l } x _ { 1 } & y _ { 1 } & 1 \\x _ { 2 } & y _ { 2 } & 1 \\x _ { 3 } & y _ { 3 } & 1\end{array} \right|$ Find the area of the triangle having vertices at P, Q, and R. - $\mathrm { P } ( 0 , - 4 ) , \mathrm { Q } ( 0,2 ) , \mathrm { R } ( 6 , - 2 )$

(Multiple Choice)

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Question 135

Bob fenced in a rectangular garden in his yard. The length of the rectangle is 5 ft longer than the width and the perimeter is 66 ft. What is the width of the rectangle?

(Multiple Choice)

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Question 136

Solve the system by substitution. - x+7y=27 6x+7y=57

(Multiple Choice)

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Question 137

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 138

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 6% cement should he mix with 3 bags of 12% cement to produce a mix containing 7% cement?

(Multiple Choice)

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Question 139

Solve the system. -= +=

(Multiple Choice)

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Question 140

Showing 121 - 140 of 505

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

Provide an appropriate response. -Fill in the blank to complete the statement. Each number in a matrix is called _______ of the matrix.

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

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 3x-y-2=0 -6x+2y+4=0

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

Solve the system by using the inverse of the coefficient matrix. - x-2y+3z=11 4x+y-z=4 2x-y+3z=10

Find the value of the determinant. - $\left| \begin{array} { l l } - 1 & 1 \\ 3 & 3 \end{array} \right|$

Find the matrix product when possible. - $\left[ \begin{array} { r r } 3 & - 2 \\4 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 2 \\2 & 6\end{array} \right]$

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { c c } x + 3 & y + 4 \\7 & - 6\end{array} \right] = \left[ \begin{array} { l l } 9 & 5 \\7 & k\end{array} \right]$

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

Find the matrix product when possible. -Given $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & - 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 1 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 1 & 0 \end{array} \right]$ , find $A B$ and $B A$ .

Bob fenced in a rectangular garden in his yard. The length of the rectangle is 5 ft longer than the width and the perimeter is 66 ft. What is the width of the rectangle?

Solve the system by substitution. - x+7y=27 6x+7y=57

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

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 6% cement should he mix with 3 bags of 12% cement to produce a mix containing 7% cement?

Solve the system. -= +=

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 6: Systems and Matrices

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

Provide an appropriate response. -Fill in the blank to complete the statement. Each number in a matrix is called _______ of the matrix.

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

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary. - 3x-y-2=0 -6x+2y+4=0

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

Solve the system by using the inverse of the coefficient matrix. - x-2y+3z=11 4x+y-z=4 2x-y+3z=10

Find the value of the determinant. - ∣−1133∣\left| \begin{array} { l l } - 1 & 1 \\ 3 & 3 \end{array} \right|​−13​13​​

Find the matrix product when possible. - [3−240][0−226]\left[ \begin{array} { r r } 3 & - 2 \\4 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 2 \\2 & 6\end{array} \right][34​−20​][02​−26​]

Find the values of the variables for which the statement is true, if possible. - [x+3y+47−6]=[957k]\left[ \begin{array} { c c } x + 3 & y + 4 \\7 & - 6\end{array} \right] = \left[ \begin{array} { l l } 9 & 5 \\7 & k\end{array} \right][x+37​y+4−6​]=[97​5k​]

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

Bob fenced in a rectangular garden in his yard. The length of the rectangle is 5 ft longer than the width and the perimeter is 66 ft. What is the width of the rectangle?

Solve the system by substitution. - x+7y=27 6x+7y=57

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 6% cement should he mix with 3 bags of 12% cement to produce a mix containing 7% cement?

Solve the system. -= +=

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Arithmetic Sequence: Common Difference and First n Terms

Filters

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

Find the value of the determinant. - $\left| \begin{array} { l l } - 1 & 1 \\ 3 & 3 \end{array} \right|$

Find the matrix product when possible. - $\left[ \begin{array} { r r } 3 & - 2 \\4 & 0\end{array} \right] \left[ \begin{array} { r r } 0 & - 2 \\2 & 6\end{array} \right]$

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { c c } x + 3 & y + 4 \\7 & - 6\end{array} \right] = \left[ \begin{array} { l l } 9 & 5 \\7 & k\end{array} \right]$