91Ó°ÊÓ

For the following exercises, solve the system of inequalities. Use a calculator to graph the system to confirm the answer. $$\begin{aligned} x y &<1 \\ y &>\sqrt{x} \end{aligned}$$

For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. You invest \(\$ 10,000\) into two accounts, which receive 8\(\%\) interest and 5\(\%\) interest. At the end of a year, you had \(\$ 10,710\) in your combined accounts. How much was invested in each account?

Find the decomposition of the partial fraction for the irreducible repeating quadratic factor. \(\frac{2 x-9}{\left(x^{2}-x\right)^{2}}\)

For the following exercises, set up the augmented matrix that describes the situation, and solve for the desired solution. At a competing cupcake store, \(\$ 4,520\) worth of cupcakes are sold daily. The chocolate cupcakes cost \(\$ 2.25\) and the red velvet cupcakes cost \(\$ 1.75 .\) If the total number of cupcakes sold per day is \(2,200,\) how many of each flavor are sold each day?

Solve the system of inequalities. Use a calculator to graph the system to confirm the answer. $$ \begin{aligned} x y &<1 \\ y &>\sqrt{x} \end{aligned} $$

For the following exercises, find the decomposition of the partial fraction for the irreducible repeating quadratic factor. $$\frac{2 x-9}{\left(x^{2}-x\right)^{2}}$$

Use the matrices below to perform the indicated operation if possible. If not possible, explain why the operation cannot be performed. Use a calculator to verify your solution. \(A=\left[\begin{array}{rrr}-2 & 0 & 9 \\ 1 & 8 & -3 \\ 0.5 & 4 & 5\end{array}\right], B=\left[\begin{array}{rrr}0.5 & 3 & 0 \\ -4 & 1 & 6 \\\ 8 & 7 & 2\end{array}\right], C=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 0 \\\ 1 & 0 & 1\end{array}\right]\). \(B C\)

For the following exercises, solve each system in terms of \(A, B, C, D, E,\) and \(F\) where \(A-F\) are nonzero numbers. Note that \(A \neq B\) and \(A E \neq B D .\) $$ \begin{array}{l}{A x+y=0} \\ {B x+y=1}\end{array} $$

Solve each system in terms of \(A, B, C, D, E,\) and \(F\) where \(A-F\) are nonzero numbers. Note that \(A \neq B\) and \(A E \neq B D\). $$ \begin{array}{l} A x+y=0 \\ B x+y=1 \end{array} $$

For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule. You invest \(\$ 80,000\) into two accounts, \(\$ 22,000\) in one account, and \(\$ 58,000\) in the other account. At the end of one year, assuming simple interest, you have earned \(\$ 2,470\) in interest. The second account receives half a percent less than twice the interest on the first account. What are the interest rates for your accounts?