Use the properties of determinants to find the value of the second determinant, given the value of the first. -\[\text { Given } \left| \begin{array} { l l l } \mathrm { s } & \mathrm { t } & \mathrm { u } \\ \mathrm { v } & \mathrm { w } & \mathrm { x } \\ 4 & 2 & 8 \end{array} \right| = 3 \text {, find the value of } \mid \begin{array} { c c c } 32 - \mathrm { s } & 16 - \mathrm { t } & 64 - \mathrm { u } \\ \mathrm { v } & \mathrm { w } & \mathrm { x } \\ 4 & 2 & 8 \end{array} .\]

A) -24 B) 3 C) -3 D) 24 A) -24 B) 3 C) -3 D) 24

Perform the row operation(s) on the given augmented matrix. -\[\begin{array} { l } \mathrm { R } _ { 1 } = \frac { 1 } { 5 } \mathrm { r } _ { 1 } \\ { \left[ \begin{array} { r r | r } 5 & - 10 & 25 \\ 4 & 2 & - 5 \end{array} \right] } \end{array}\]

A) $\left[ \begin{array} { r r | r } 1 & - 2 & 25 \\ 4 & 2 & - 5 \end{array} \right]$ B) $\left[ \begin{array} { r r | r } 1 & - 2 & 5 \\ \frac { 4 } { 5 } & \frac { 2 } { 5 } & - 1 \end{array} \right]$ C) $\left[ \begin{array} { r r | r } 1 & - 2 & 5 \\ 4 & 2 & - 5 \end{array} \right]$ D) $\left[ \begin{array} { r r | r } 1 & - 2 & 5 \\ 5 & 0 & 0 \end{array} \right]$ A) $\left[ \begin{array} { r r | r } 1 & - 2 & 25 \\ 4 & 2 & - 5 \end{array} \right]$ B) $\left[ \begin{array} { r r | r } 1 & - 2 & 5 \\ \frac { 4 } { 5 } & \frac { 2 } { 5 } & - 1 \end{array} \right]$ C) $\left[ \begin{array} { r r | r } 1 & - 2 & 5 \\ 4 & 2 & - 5 \end{array} \right]$ D) $\left[ \begin{array} { r r | r } 1 & - 2 & 5 \\ 5 & 0 & 0 \end{array} \right]$

Perform the row operation(s) on the given augmented matrix. -\[\begin{array} { l } R _ { 2 } = 5 r _ { 1 } + r _ { 2 } \\ { \left[ \begin{array} { c c | c } 1 & 6 & 11 \\ - 5 & 9 & - 6 \end{array} \right] } \end{array}\]

A) $\left[ \begin{array} { r r | r } 5 & 30 & 55 \\ - 5 & 9 & - 6 \end{array} \right]$ B) $\left[ \begin{array} { r r | r } 1 & 6 & 11 \\ 0 & 39 & 49 \end{array} \right]$ C) $\left[ \begin{array} { r r | r } 1 & 6 & 11 \\ 0 & - 21 & - 61 \end{array} \right]$ D) $\left[ \begin{array} { l l | l } 5 & 30 & 55 \\ 0 & 39 & 49 \end{array} \right]$ A) $\left[ \begin{array} { r r | r } 5 & 30 & 55 \\ - 5 & 9 & - 6 \end{array} \right]$ B) $\left[ \begin{array} { r r | r } 1 & 6 & 11 \\ 0 & 39 & 49 \end{array} \right]$ C) $\left[ \begin{array} { r r | r } 1 & 6 & 11 \\ 0 & - 21 & - 61 \end{array} \right]$ D) $\left[ \begin{array} { l l | l } 5 & 30 & 55 \\ 0 & 39 & 49 \end{array} \right]$

Exam 6: Systems of Equations and Inequalities

Solve the problem. -A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given by the equation h = -16t² + 600 where h is measured in feet and t is the number of seconds since the yellow ball was Dropped. A second person, in the same building but on a lower floor that is 408 feet from the ground, drops a White ball 2 seconds after the yellow ball was dropped. The height of the white ball is given by the equation H = -16(t - 2)² + 408 where h is measured in feet and t is the number of seconds since the yellow ball was Dropped. Find the time that the balls are the same distance above the ground and find this distance.

(Multiple Choice)

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Question 41

Graph the system of inequalities. - $\left\{ \begin{aligned}4 x + 3 y & \geq 12 \\x & \geq y\end{aligned} \right.$ $Graph the system of inequalities. - \left\{ \begin{aligned} 4 x + 3 y & \geq 12 \\ x & \geq y \end{aligned} \right.$

(Multiple Choice)

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Question 42

Use the properties of determinants to find the value of the second determinant, given the value of the first. - start text Given end text open vertical bar 4 2 8 close vertical bar equals3 start textcomma find the value of end text \mid 32- 16- 64- 4 2 8 point

(Multiple Choice)

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Question 43

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

(Multiple Choice)

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Question 44

Perform the row operation(s) on the given augmented matrix. - = 5 -10 25 4 2 -5

(Multiple Choice)

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Question 45

Perform the row operation(s) on the given augmented matrix. - =5+ 1 6 11 -5 9 -6

(Multiple Choice)

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Question 46

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x - 26 } { ( x + 2 ) ( x - 3 ) }$

(Multiple Choice)

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Question 47

Graph the inequality. - $x ^ { 2 } + y ^ { 2 } \leq 25$ $Graph the inequality. - x ^ { 2 } + y ^ { 2 } \leq 25$

(Multiple Choice)

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(32)

Question 48

Graph the system of inequalities. - $\left\{\begin{array}{r}2 x+3 y \geq 6 \\x-y \geq 3 \\y \leq 2\end{array}\right.$ $Graph the system of inequalities. - \left\{\begin{array}{r} 2 x+3 y \geq 6 \\ x-y \geq 3 \\ y \leq 2 \end{array}\right.$

(Multiple Choice)

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Question 49

Use the properties of determinants to find the value of the second determinant, given the value of the first. - $\left| \begin{array} { c c c } x & y & z \\u & v & w \\1 & 2 & - 3\end{array} \right| = 118 \left| \begin{array} { c c c } x - 3 & y - 6 & z + 9 \\- 3 u - 1 & - 3 v - 2 & - 3 w + 3 \\1 & 2 & - 3\end{array} \right| = ?$

(Multiple Choice)

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Question 50

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } 2 x ^ { 2 } + x y - y ^ { 2 } = 3 \\x ^ { 2 } + 2 x y + y ^ { 2 } = 3\end{array} \right.$

(Multiple Choice)

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Question 51

Solve the problem. -The difference of two numbers is 5 and the difference of their squares is 55. Find the numbers.

(Short Answer)

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Question 52

Solve the problem. -An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

(Multiple Choice)

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Question 53

Find the inverse of the matrix. - $\left[ \begin{array} { l l } 6 & - 3 \\3 & - 6\end{array} \right]$

(Multiple Choice)

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Question 54

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 64 inches. The length is 14 inches longer than the width. Find the width.

(Multiple Choice)

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Question 55

Solve the problem. - $\text { Given that } \left| \begin{array} { l l l } x & y & z \\a & b & c \\2 & 4 & 5\end{array} \right| = 3 \text {, find the value of the determinant } \left| \begin{array} { l l l } 2 & 4 & 5 \\3 a & 3 b & 3 c \\x - 2 & y - 4 & z - 5\end{array} \right| \text {. }$

(Multiple Choice)

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Question 56

Graph the system of inequalities. -

(Multiple Choice)

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Question 57

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x ^ { 3 } - 1 x ^ { 2 } + 13 x - 5 } { \left( x ^ { 2 } + 4 \right) ^ { 3 } }$

(Multiple Choice)

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Question 58

Graph the system of inequalities. -

(Multiple Choice)

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Question 59

Use the properties of determinants to find the value of the second determinant, given the value of the first. -

(Multiple Choice)

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(43)

Question 60

Graph the system of inequalities. - $\left\{ \begin{aligned}4 x + 3 y & \geq 12 \\x & \geq y\end{aligned} \right.$ $Graph the system of inequalities. - \left\{ \begin{aligned} 4 x + 3 y & \geq 12 \\ x & \geq y \end{aligned} \right.$

Use the properties of determinants to find the value of the second determinant, given the value of the first. - start text Given end text open vertical bar 4 2 8 close vertical bar equals3 start textcomma find the value of end text \mid 32- 16- 64- 4 2 8 point

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

Perform the row operation(s) on the given augmented matrix. - = 5 -10 25 4 2 -5

Perform the row operation(s) on the given augmented matrix. - =5+ 1 6 11 -5 9 -6

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x - 26 } { ( x + 2 ) ( x - 3 ) }$

Graph the inequality. - $x ^ { 2 } + y ^ { 2 } \leq 25$ $Graph the inequality. - x ^ { 2 } + y ^ { 2 } \leq 25$

Graph the system of inequalities. - $\left\{\begin{array}{r}2 x+3 y \geq 6 \\x-y \geq 3 \\y \leq 2\end{array}\right.$ $Graph the system of inequalities. - \left\{\begin{array}{r} 2 x+3 y \geq 6 \\ x-y \geq 3 \\ y \leq 2 \end{array}\right.$

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } 2 x ^ { 2 } + x y - y ^ { 2 } = 3 \\x ^ { 2 } + 2 x y + y ^ { 2 } = 3\end{array} \right.$

Solve the problem. -The difference of two numbers is 5 and the difference of their squares is 55. Find the numbers.

Solve the problem. -An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

Find the inverse of the matrix. - $\left[ \begin{array} { l l } 6 & - 3 \\3 & - 6\end{array} \right]$

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 64 inches. The length is 14 inches longer than the width. Find the width.

Solve the problem. - $\text { Given that } \left| \begin{array} { l l l } x & y & z \\a & b & c \\2 & 4 & 5\end{array} \right| = 3 \text {, find the value of the determinant } \left| \begin{array} { l l l } 2 & 4 & 5 \\3 a & 3 b & 3 c \\x - 2 & y - 4 & z - 5\end{array} \right| \text {. }$

Graph the system of inequalities. -

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x ^ { 3 } - 1 x ^ { 2 } + 13 x - 5 } { \left( x ^ { 2 } + 4 \right) ^ { 3 } }$

Graph the system of inequalities. -

Use the properties of determinants to find the value of the second determinant, given the value of the first. -

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

Graph the system of inequalities. - {4x+3y≥12x≥y\left\{ \begin{aligned}4 x + 3 y & \geq 12 \\x & \geq y\end{aligned} \right.{4x+3yx​≥12≥y​

Use the properties of determinants to find the value of the second determinant, given the value of the first. - start text Given end text open vertical bar 4 2 8 close vertical bar equals3 start textcomma find the value of end text \mid 32- 16- 64- 4 2 8 point

Write the partial fraction decomposition of the rational expression. - x−1(x−3)(x−2)\frac { x - 1 } { ( x - 3 ) ( x - 2 ) }(x−3)(x−2)x−1​

Perform the row operation(s) on the given augmented matrix. - = 5 -10 25 4 2 -5

Perform the row operation(s) on the given augmented matrix. - =5+ 1 6 11 -5 9 -6

Write the partial fraction decomposition of the rational expression. - 7x−26(x+2)(x−3)\frac { 7 x - 26 } { ( x + 2 ) ( x - 3 ) }(x+2)(x−3)7x−26​

Graph the inequality. - x2+y2≤25x ^ { 2 } + y ^ { 2 } \leq 25x2+y2≤25

Graph the system of inequalities. - {2x+3y≥6x−y≥3y≤2\left\{\begin{array}{r}2 x+3 y \geq 6 \\x-y \geq 3 \\y \leq 2\end{array}\right.⎩⎨⎧​2x+3y≥6x−y≥3y≤2​

Solve the system of equations using elimination. - {2x2+xy−y2=3x2+2xy+y2=3\left\{ \begin{array} { l } 2 x ^ { 2 } + x y - y ^ { 2 } = 3 \\x ^ { 2 } + 2 x y + y ^ { 2 } = 3\end{array} \right.{2x2+xy−y2=3x2+2xy+y2=3​

Solve the problem. -The difference of two numbers is 5 and the difference of their squares is 55. Find the numbers.

Solve the problem. -An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

Find the inverse of the matrix. - [6−33−6]\left[ \begin{array} { l l } 6 & - 3 \\3 & - 6\end{array} \right][63​−3−6​]

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 64 inches. The length is 14 inches longer than the width. Find the width.

Graph the system of inequalities. -

Write the partial fraction decomposition of the rational expression. - 2x3−1x2+13x−5(x2+4)3\frac { 2 x ^ { 3 } - 1 x ^ { 2 } + 13 x - 5 } { \left( x ^ { 2 } + 4 \right) ^ { 3 } }(x2+4)32x3−1x2+13x−5​

Graph the system of inequalities. -

Use the properties of determinants to find the value of the second determinant, given the value of the first. -

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Graph the system of inequalities. - $\left\{ \begin{aligned}4 x + 3 y & \geq 12 \\x & \geq y\end{aligned} \right.$ $Graph the system of inequalities. - \left\{ \begin{aligned} 4 x + 3 y & \geq 12 \\ x & \geq y \end{aligned} \right.$

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

Write the partial fraction decomposition of the rational expression. - $\frac { 7 x - 26 } { ( x + 2 ) ( x - 3 ) }$

Graph the inequality. - $x ^ { 2 } + y ^ { 2 } \leq 25$ $Graph the inequality. - x ^ { 2 } + y ^ { 2 } \leq 25$

Graph the system of inequalities. - $\left\{\begin{array}{r}2 x+3 y \geq 6 \\x-y \geq 3 \\y \leq 2\end{array}\right.$ $Graph the system of inequalities. - \left\{\begin{array}{r} 2 x+3 y \geq 6 \\ x-y \geq 3 \\ y \leq 2 \end{array}\right.$

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } 2 x ^ { 2 } + x y - y ^ { 2 } = 3 \\x ^ { 2 } + 2 x y + y ^ { 2 } = 3\end{array} \right.$

Find the inverse of the matrix. - $\left[ \begin{array} { l l } 6 & - 3 \\3 & - 6\end{array} \right]$

Write the partial fraction decomposition of the rational expression. - $\frac { 2 x ^ { 3 } - 1 x ^ { 2 } + 13 x - 5 } { \left( x ^ { 2 } + 4 \right) ^ { 3 } }$