91Ó°ÊÓ

Graph the solution set of each system of inequalities by hand. $$\begin{aligned}2 x+3 y & \leq 12 \\\2 x+3 y &>-6 \\\3 x+y &<4 \\\x & \geq 0 \\\y & \geq 0\end{aligned}$$

Solve each nonlinear system of equations analytically. $$\begin{aligned}&y=-x^{2}+2\\\&x-y=0\end{aligned}$$

Given \(A=\left[\begin{array}{rr}4 & -2 \\ 3 & 1\end{array}\right], B=\left[\begin{array}{rr}5 & 1 \\ 0 & -2 \\ 3 & 7\end{array}\right],\) and \(C=\left[\begin{array}{rrr}-5 & 4 & 1 \\ 0 & 3 & 6\end{array}\right]\), find each product if possible. $$B A$$

Solve each system. Write solutions in terms of \(z\) if necessary. $$\begin{aligned} 3 x+6 y-3 z &=12 \\ -x-2 y+z &=16 \\ x+y-2 z &=20 \end{aligned}$$

Given \(A=\left[\begin{array}{rr}4 & -2 \\ 3 & 1\end{array}\right], B=\left[\begin{array}{rr}5 & 1 \\ 0 & -2 \\ 3 & 7\end{array}\right],\) and \(C=\left[\begin{array}{rrr}-5 & 4 & 1 \\ 0 & 3 & 6\end{array}\right]\), find each product if possible. $$A C$$

Solve each nonlinear system of equations analytically. $$\begin{aligned}&y=(x-1)^{2}\\\&x-3 y=-1\end{aligned}$$

Find the equation of the parabola (with vertical axis that passes through the data points shown or specified. Check your answer. $$(-2,2),(0,2),(2,-6)$$

Graph the solution set of each system of inequalities by hand. $$\begin{aligned}&y \geq 3^{x}\\\&y \geq 2\end{aligned}$$

Given \(A=\left[\begin{array}{rr}4 & -2 \\ 3 & 1\end{array}\right], B=\left[\begin{array}{rr}5 & 1 \\ 0 & -2 \\ 3 & 7\end{array}\right],\) and \(C=\left[\begin{array}{rrr}-5 & 4 & 1 \\ 0 & 3 & 6\end{array}\right]\), find each product if possible. $$B C$$

Graph the solution set of each system of inequalities by hand. $$\begin{aligned}&y \leq\left(\frac{1}{2}\right)^{x}\\\&y \geq 4\end{aligned}$$