91Ó°ÊÓ

Find the fourth-degree polynomial \(P(x)\) that satisfies the following conditions: \(P(-2)=13\) \(P(-1)=2, P(0)=-1, P(1)=4,\) and \(P(2)=41\)

If possible, find \(A B\) and \(B A\). $$A=\left[\begin{array}{rr}3 & -1 \\ 1 & 0 \\ -2 & -4\end{array}\right], \quad B=\left[\begin{array}{rrr}-2 & 5 & -3 \\ 9 & -7 & 0\end{array}\right]$$

Draw a sketch of the two graphs described with the indicated number of points of intersection. A line and a circle; no points

Use the determinant theorems to find each determinant. $$\operatorname{det}\left[\begin{array}{rrr}6 & 8 & -12 \\\\-1 & 0 & 2 \\\4 & 0 & -8\end{array}\right]$$

Graph the solution set of each system of inequalities by hand. $$\begin{aligned}4 x-3 y & \leq 12 \\\y & \leq x^{2}\end{aligned}$$

Three students buy different combinations of tickets for a baseball game. The first student buys 2 senior, 1 adult, and 2 student tickets for \(\$ 51 .\) The second student buys 1 adult and 5 student tickets for \(\$ 55 .\) The third student buys 2 senior, 2 adult, and 7 student tickets for \(\$ 75\). If possible, find the price of each type of ticket. Interpret your answer.

Graph the solution set of each system of inequalities by hand. $$\begin{aligned}&y \leq-x^{2}\\\&y \geq x^{2}-6\end{aligned}

Find the fifth-degree polynomial \(P(x)\) that satisfies the following conditions: \(P(-2)=-8\) \(P(-1)=-1, P(0)=-4, P(1)=-5, P(2)=8,\) and \(P(3)=167\)

A total of \(\$ 5000\) is invested at \(2 \%, 3 \%,\) and \(4 \%\). The amount invested at \(4 \%\) equals the total amount invested at \(2 \%\) and \(3 \%\). The total interest for one year is \$145. If possible, find the amount invested at each interest rate. Interpret your answer.

If possible, find \(A B\) and \(B A\). $$A=\left[\begin{array}{rrr}-1 & 0 & -2 \\ 4 & -2 & 1\end{array}\right], \quad B=\left[\begin{array}{rr}2 & -2 \\ 5 & -1 \\ 0 & 1\end{array}\right]$$