Find the partial fraction decomposition of the given rational expression.

$$\frac{x^3+3 x^2-4 x-8}{x^2-4}$$

Solve system of equations by using the substitution method.

$$\left\{\begin{array}{l}3 x-4 y=8 \\ 6 x-8 y=9\end{array}\right.$$

Sketch the graph of the inequality: $25 x^2-16 y^2-100 x-64 y<64$

Solve:

$$\left\{\begin{aligned} 6 x-3 y & =-9 \\ -2 x+y & =3\end{aligned}\right.$$

Write $\log _6(x-5)+3 \log _6(2 x)$ as a single logarithm with a coefficient of 1 .

Solve the system of equations.

$$\left\{\begin{aligned} 2 x^2+3 y^2 & =5 \\ x^2-3 y^2 & =4\end{aligned}\right.$$

Find the partial fraction decomposition of the given rational expression.

$$\frac{1}{(x+7)(2 x-5)}$$

Minimize C = 4x + 2y with the constraints

$$\left\{\begin{aligned} x+y & \geq 9 \\ 3 x+4 y & \geq 32 \\ x+2 y & \geq 12\end{aligned}\right.$$

Sketch the graph of the inequality: $4 x^2+9 y^2-8 x+18 y \geq 23$

Solve system of equations.

$$\left\{\begin{array}{l}2 x+3 y-6 z=4 \\ 3 x-2 y-9 z=-7 \\ 2 x+5 y-6 z=8\end{array}\right.$$

Solve: $\cos ^{-1} x+\tan ^{-1} x=\frac{\pi}{2}$

A parking garage charges its customers a certain amount for the first hour and another an1ount for each additional half-hour or part of the half-hour. One day Nicole parked her car for 3 hours and 50 minutes. The parking fee was 14.50 dollars. The next day she parked her car for 4 hours and 45 minutes. The parking fee was 18.00 dollars. Determine the fee the parking garage charges for the first hour and the fee the garage charges for each additional half-hour or a portion of the half-hour.

Solve each system of equations.

$$\left\{\begin{array}{l}y=x^2-2 x-3 \\ y=2 x-7\end{array}\right.$$

Solve system of equations by using the substitution method.

$$\left\{\begin{array}{l}3 x-3 y=5 \\ 4 x-4 y=9\end{array}\right.$$