91Ó°ÊÓ

Finding Minimum and Maximum Values, find the minimum and maximum values of the objective function and where they occur, subject to the constraints \(x \geq 0, y \geq 0, x+4 y \leq 20\) \(x+y \leq 18,\) and \(2 x+2 y \leq 21 .\) $$ z=2 x+4 y $$

\(\begin{array}{l}{\text { Solving a System by Substitution In Exercises }} \\\ {25-28 \text { , you are given the total annual interest earned }} \\ {\text { from a total of } \$ 12,000 \text { invested in two funds paying the }} \\\ {\text { given rates of simple interest. Write and solve a system of }} \\\ {\text { equations to find the amount invested at each rate. }}\end{array}\) \(\begin{array}{l}{\text { Annual Interest }} \\ {\$ 630}\end{array}\) \( \begin{array}{ll}{\text { Rate } 1} & {\text { Rate } 2} \\ {4 \%} & {6 \%}\end{array} \)

Writing the Partial Fraction Decomposition. Write the partial fraction decomposition of the rational expression. Check your result algebraically. $$\frac{x+2}{x\left(x^{2}-9\right)}$$

In Exercises 19-28, use a graphing utility to graph the inequality. $$2 x^{2}-y-3>0$$

Solving a System by Elimination In Exercises \(13-30,\) solve the system by the method of elimination and check any solutions algebraically. $$ \left\\{\begin{array}{l}{0.05 x-0.03 y=0.21} \\ {0.07 x+0.02 y=0.16}\end{array}\right. $$

Solving a System by Elimination In Exercises \(13-30\) , solve the system by the method of elimination and check any solutions algebraically. $$ \left\\{\begin{array}{l}{4 b+3 m=3} \\ {3 b+11 m=13}\end{array}\right. $$

In Exercises 19-28, use a graphing utility to graph the inequality. $$\frac{5}{2} y-3 x^{2}-6 \geq 0$$

Finding Minimum and Maximum Values, find the minimum and maximum values of the objective function and where they occur, subject to the constraints \(x \geq 0, y \geq 0, x+4 y \leq 20\) \(x+y \leq 18,\) and \(2 x+2 y \leq 21 .\) $$ z=4 x+5 y $$

\(\begin{array}{l}{\text { Solving a System by Substitution In Exercises }} \\\ {25-28 \text { , you are given the total annual interest earned }} \\ {\text { from a total of } \$ 12,000 \text { invested in two funds paying the }} \\\ {\text { given rates of simple interest. Write and solve a system of }} \\\ {\text { equations to find the amount invested at each rate. }}\end{array}\) \(\begin{array}{l}{\text { Annual Interest }} \\ {\$ 396}\end{array}\) \( \begin{array}{ll}{\text { Rate } 1} & {\text { Rate } 2} \\ {2.8 \%} & {3.8 \%}\end{array} \)

Solving a System of Linear Equations In Exercises \(25 - 46\) , solve the system of linear equations and check any solutions algebraically. $$\left\\{ \begin{aligned} 2 x & \+ 2 z = 2 \\ 5 x + 3 y & = 4 \\ 3 y - 4 z & = 4 \end{aligned} \right.$$