Exam 6: Systems and Matrices

Graph the solution set of the system of inequalities. - y\geq--6x-4 y\geq+6x+4

Graph the solution set of the system of inequalities. - 3x-2y\leq6 x-1\geq0

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. y= -4=11

Solve the linear programming problem. -An airline with two types of airplanes, $\mathrm { P } _ { 1 }$ and $\mathrm { P } _ { 2 }$ , has contracted with a tour group to provide transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers. For a certain trip, airplane $\mathrm { P } _ { 1 }$ costs $\$ 10,000$ to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane $P _ { 2 }$ costs $\$ 8500$ to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

Graph the inequality. - $-2 x-5 y \leq-10$

Find the dimension of the matrix. - $\left[ \begin{array} { l l } 5 & 0 \\0 & 5\end{array} \right]$

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

Michael's bank contains only nickels, dimes, and quarters. There are 67 coins in all, valued at $5.25. The number of nickels is 1 short of being three times the sum of the number of dimes and quarters. How many dimes are in The bank?

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } - 3 & 4 \\6 & - 4\end{array} \right]$

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - $A$ is $1 \times 3 ; B$ is $3 \times 1$ .

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. x-y +5z=4 3x +z=0 x+4y +z=-16

Solve the linear programming problem. -An airline with two types of airplanes, $\mathrm { P } _ { 1 }$ and $\mathrm { P } _ { 2 }$ , has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers. For a certain trip, airplane $\mathrm { P } _ { 1 }$ costs $\$ 10,000$ to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane $\mathrm { P } _ { 2 }$ costs $\$ 8500$ to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { r r r } - 0.3 & 5.3 & - 4 \\- 0.6 & 7.9 & - 3.1 \\- 9.8 & 6.1 & 4.6\end{array} \right|$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 1 & 0 & 8 \\ 1 & 2 & 3 \\ 2 & 5 & 3 \end{array} \right]$

The sum of a student's three scores is 223. If the first is 11 points more than the second, and the sum of the first two is 43 more than twice the third, what was the first score?

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 95 black, 100 white and 80 red wires. How many of each type of cable were made?

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l l } 0 & 0 \\\mathrm { a } & \mathrm { b }\end{array} \right] = \left[ \begin{array} { r r } 0 & \mathrm { q } \\5 & - 7\end{array} \right]$

Find the equation of the circle, written in the form $x ^ { 2 } + y ^ { 2 } + a x + b y + c = 0$ passing through the points (10,3),(5,-2) , and (8,7) .

Graph the solution set of the system of inequalities. - 2x+3y\geq6 x-y\geq3 y\leq2

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. y= +=5.7