91Ó°ÊÓ

Describe the location of each point in coordinate space. $$ (-1,5,0) $$

Find the whole number solutions of each system using tables. $$ \left\\{\begin{array}{l}{y+3 x \leq 8} \\ {y-3>2 x}\end{array}\right. $$

Describe the location of each point in coordinate space. $$ (3,-3,4) $$

Teams chosen from 30 forest rangers and 16 trainees are planting trees. An experienced team consisting of two rangers can plant 500 trees per week. A training team consisting of one ranger and two trainees can plant 200 trees per week. $$\begin{array}{|c|c|c|c|}\hline \text { Number of Teams } & {x} & {y} & {x+y} \\\ \hline \text { Number of Rangers } & {2 x} & {y} & {30} \\ \hline \text { Number of Trainees } & {0} & {2 y} & {16} \\ \hline \text { Number of Trees Planted } & {500 x} & {200 y} & {500 x+200 y} \\ \hline\end{array}$$ a. Write an objective function and constraints for a linear program that models the problem. b. How many of each type of team should be formed to maximize the number of trees planted? How many trainees are used in this solution? How many trees are planted? c. Find a solution that uses all the trainees. How many trees will be planted in this case?

Graph each point in coordinate space. $$ (25,40,-30) $$

Solve each system by substitution. Check your answers. $$ \left\\{\begin{array}{l}{13=3 x-y} \\ {4 y-3 x+2 z=-3} \\ {z=2 x-4 y}\end{array}\right. $$

Graph each system of constraints. Name all vertices. Then find the values of \(x\) and \(y\) that maximize or minimize the objective function. Find the maximum or minimum value. \(\left\\{\begin{aligned} 3 x+y & \leq 7 \\ x+2 y & \leq 9 \\ x \geq 0, y & \geq 0 \end{aligned}\right.\) Maximum for \(P=2 x+y\)

Graph each system of constraints. Name all vertices. Then find the values of \(x\) and \(y\) that maximize or minimize the objective function. Find the maximum or minimum value. \(\left\\{\begin{array}{l}{x+y \leq 11} \\ {2 y \geq x} \\ {x \geq 0, y \geq 0}\end{array}\right.\) Maximum for \(P=3 x+2 y\)

Fund-Raising You want to bake at least 6 and at most 11 loaves of bread for a bake sale. You want at least twice as many loaves of banana bread as nut bread. Write and graph a system of inequalities to model the situation.

The measure of one acute angle of a right triangle is \(30^{\circ}\) more than twice the measure of the other acute angle. Find the measures of the angles.