91Ó°ÊÓ

In Exercises 1–26, graph each inequality. $$y>2^{x}$$

Solve each system by the addition method. \(\left\\{\begin{array}{l}x+2 y-2 \\ -4 x+3 y-25\end{array}\right.\)

In Exercises \(23-24\), let \(x\) represent the first number, \(y\) the second number, and \(z\) the third number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The following is known about three numbers: Three times the first number plus the second number plus twice the third number is \(5 .\) If 3 times the second number is subtracted from the sum of the first number and 3 times the third number, the result is \(2 .\) If the third number is subtracted from 2 times the first number and 3 times the second number, the result is \(1 .\) Find the numbers.

Solve each system by the addition method. \(\left\\{\begin{array}{l}2 x-7 y-2 \\ 3 x+y--20\end{array}\right.\)

Write the partial fraction decomposition of each rational expression. $$\frac{2 x^{2}+8 x+3}{(x+1)^{3}}$$

In Exercises 1–26, graph each inequality. $$y \leq 3^{x}$$

What kinds of problems are solved using the linear programming method?

What is an objective function in a linear programming problem?

Solve each system in Exercises \(25-26\) $$ \left\\{\begin{array}{l} \frac{x+2}{6}-\frac{y+4}{3}+\frac{z}{2}=0 \\ \frac{x+1}{2}+\frac{y-1}{2}-\frac{z}{4}=\frac{9}{2} \\ \frac{x-5}{4}+\frac{y+1}{3}+\frac{z-2}{2}=\frac{19}{4} \end{array}\right. $$

In Exercises 1–26, graph each inequality. $$y \geq \log _{2}(x+1)$$