Exam 6: Systems of Equations and Inequalities

Write the augmented matrix for the system. - $\left\{ \begin{array} { l } 9 x - 2 y + 6 z = 54 \\6 x + 2 y + 9 z = 51 \\5 x + 3 y + 2 z = 41\end{array} \right.$

(Multiple Choice)

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Question 121

Find the inverse of the matrix. - $\left[ \begin{array} { r r r } 1 & 0 & 0 \\1 & 1 & 0 \\0 & - 9 & 1\end{array} \right]$

(Multiple Choice)

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Question 122

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? - x² + y² = 25 2y + x = 5

(Multiple Choice)

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Question 123

Write the partial fraction decomposition of the rational expression. - $\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$

(Multiple Choice)

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Question 124

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x ^ { 3 } - 2 } { x ^ { 2 } ( x + 1 ) ^ { 3 } }$

(Essay)

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Question 125

Perform the row operation(s) on the given augmented matrix. - =41+ -7 -5 -1 -10 6 -2 9 5 28 -6 6 18

(Essay)

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Question 126

Write the partial fraction decomposition of the rational expression. - $\frac { x + 2 } { x ^ { 3 } - 2 x ^ { 2 } + x }$

(Multiple Choice)

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Question 127

Find the value of the determinant. - $\left| \begin{array} { r r r } - 4 & - 3 & - 3 \\3 & - 5 & - 2 \\2 & - 3 & - 1\end{array} \right|$

(Multiple Choice)

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Question 128

Solve the problem. -The Family Fine Arts Center charges $24 per adult and $10 per senior citizen for its performances. On a recent weekend evening when 538 people paid admission, the total receipts were $7592. How many who paid were Senior citizens?

(Multiple Choice)

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Question 129

Write the augmented matrix for the system. - $\left. \begin{array} { r r r | r } 4 & 8 & 8 & - 2 \\ 9 & 0 & 5 & 4 \\ 5 & 9 & 0 & 2 \end{array} \right]$

(Multiple Choice)

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Question 130

Graph the inequality. -

(Multiple Choice)

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Question 131

Solve the problem. -In a 1-mile race, the winner crosses the finish line 11 feet ahead of the second-place runner and 26 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how Many feet does the second-place runner beat the third-place runner? (5280 feet in 1 mile.)

(Multiple Choice)

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Question 132

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x ^ { 2 } - x - 13 } { x ( x + 1 ) ( x - 1 ) }$

(Multiple Choice)

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Question 133

Find the value of the determinant. - $\left| \begin{array} { r r r } x & - 4 & - 1 \\- 2 & 2 & 0 \\- 1 & - 2 & 8\end{array} \right| = 10$

(Short Answer)

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Question 134

Write the augmented matrix for the system. - $\left\{ \begin{array} { l } 9 x - 2 y + 6 z = 54 \\6 x + 2 y + 9 z = 51 \\5 x + 3 y + 2 z = 41\end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { r r r } 1 & 0 & 0 \\1 & 1 & 0 \\0 & - 9 & 1\end{array} \right]$

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? - x² + y² = 25 2y + x = 5

Write the partial fraction decomposition of the rational expression. - $\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x ^ { 3 } - 2 } { x ^ { 2 } ( x + 1 ) ^ { 3 } }$

Perform the row operation(s) on the given augmented matrix. - =41+ -7 -5 -1 -10 6 -2 9 5 28 -6 6 18

Write the partial fraction decomposition of the rational expression. - $\frac { x + 2 } { x ^ { 3 } - 2 x ^ { 2 } + x }$

Find the value of the determinant. - $\left| \begin{array} { r r r } - 4 & - 3 & - 3 \\3 & - 5 & - 2 \\2 & - 3 & - 1\end{array} \right|$

Solve the problem. -The Family Fine Arts Center charges $24 per adult and $10 per senior citizen for its performances. On a recent weekend evening when 538 people paid admission, the total receipts were $7592. How many who paid were Senior citizens?

Write the augmented matrix for the system. - $\left. \begin{array} { r r r | r } 4 & 8 & 8 & - 2 \\ 9 & 0 & 5 & 4 \\ 5 & 9 & 0 & 2 \end{array} \right]$

Graph the inequality. -

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x ^ { 2 } - x - 13 } { x ( x + 1 ) ( x - 1 ) }$

Find the value of the determinant. - $\left| \begin{array} { r r r } x & - 4 & - 1 \\- 2 & 2 & 0 \\- 1 & - 2 & 8\end{array} \right| = 10$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Exam 6: Systems of Equations and Inequalities

Write the augmented matrix for the system. - {9x−2y+6z=546x+2y+9z=515x+3y+2z=41\left\{ \begin{array} { l } 9 x - 2 y + 6 z = 54 \\6 x + 2 y + 9 z = 51 \\5 x + 3 y + 2 z = 41\end{array} \right.⎩⎨⎧​9x−2y+6z=546x+2y+9z=515x+3y+2z=41​

Find the inverse of the matrix. - [1001100−91]\left[ \begin{array} { r r r } 1 & 0 & 0 \\1 & 1 & 0 \\0 & - 9 & 1\end{array} \right]​110​01−9​001​​

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? - x2 + y2 = 25 2y + x = 5

Write the partial fraction decomposition of the rational expression. - x2−111x4−x2−72\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }x4−x2−72x2−111​

Write the partial fraction decomposition of the rational expression. - 7x3−2x2(x+1)3\frac { 7 x ^ { 3 } - 2 } { x ^ { 2 } ( x + 1 ) ^ { 3 } }x2(x+1)37x3−2​

Perform the row operation(s) on the given augmented matrix. - =41+ -7 -5 -1 -10 6 -2 9 5 28 -6 6 18

Write the partial fraction decomposition of the rational expression. - x+2x3−2x2+x\frac { x + 2 } { x ^ { 3 } - 2 x ^ { 2 } + x }x3−2x2+xx+2​

Find the value of the determinant. - ∣−4−3−33−5−22−3−1∣\left| \begin{array} { r r r } - 4 & - 3 & - 3 \\3 & - 5 & - 2 \\2 & - 3 & - 1\end{array} \right|​−432​−3−5−3​−3−2−1​​

Solve the problem. -The Family Fine Arts Center charges $24 per adult and $10 per senior citizen for its performances. On a recent weekend evening when 538 people paid admission, the total receipts were $7592. How many who paid were Senior citizens?

Write the augmented matrix for the system. - 488−290545902]\left. \begin{array} { r r r | r } 4 & 8 & 8 & - 2 \\ 9 & 0 & 5 & 4 \\ 5 & 9 & 0 & 2 \end{array} \right]495​809​850​−242​​

Graph the inequality. -

Write the partial fraction decomposition of the rational expression. - 2x2−x−13x(x+1)(x−1)\frac { 2 x ^ { 2 } - x - 13 } { x ( x + 1 ) ( x - 1 ) }x(x+1)(x−1)2x2−x−13​

Find the value of the determinant. - ∣x−4−1−220−1−28∣=10\left| \begin{array} { r r r } x & - 4 & - 1 \\- 2 & 2 & 0 \\- 1 & - 2 & 8\end{array} \right| = 10​x−2−1​−42−2​−108​​=10

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Write the augmented matrix for the system. - $\left\{ \begin{array} { l } 9 x - 2 y + 6 z = 54 \\6 x + 2 y + 9 z = 51 \\5 x + 3 y + 2 z = 41\end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { r r r } 1 & 0 & 0 \\1 & 1 & 0 \\0 & - 9 & 1\end{array} \right]$

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? - x² + y² = 25 2y + x = 5

Write the partial fraction decomposition of the rational expression. - $\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x ^ { 3 } - 2 } { x ^ { 2 } ( x + 1 ) ^ { 3 } }$

Write the partial fraction decomposition of the rational expression. - $\frac { x + 2 } { x ^ { 3 } - 2 x ^ { 2 } + x }$

Find the value of the determinant. - $\left| \begin{array} { r r r } - 4 & - 3 & - 3 \\3 & - 5 & - 2 \\2 & - 3 & - 1\end{array} \right|$

Write the augmented matrix for the system. - $\left. \begin{array} { r r r | r } 4 & 8 & 8 & - 2 \\ 9 & 0 & 5 & 4 \\ 5 & 9 & 0 & 2 \end{array} \right]$

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x ^ { 2 } - x - 13 } { x ( x + 1 ) ( x - 1 ) }$

Find the value of the determinant. - $\left| \begin{array} { r r r } x & - 4 & - 1 \\- 2 & 2 & 0 \\- 1 & - 2 & 8\end{array} \right| = 10$