91Ó°ÊÓ

In Problems 13–46, write the partial fraction decomposition of each rational expression.

$\frac{x^2-11x-18}{x(x^2+3x+3)}$

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\left\{\begin{array}{c}3x-y=7\\ 9x-3y=21\end{array}\right.$

Graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}2x^2-xy+y^2=8\\ xy=4\end{array}\right.$

Animal Nutrition Kevin’s dog Amadeus likes two kinds of canned dog food. Gourmet Dog costs $40$cents a can and has $20$units of a vitamin complex; the calorie content is $75$calories. Chow Hound costs $32$cents a can and has $35$units of vitamins and $50$calories. Kevin likes Amadeus to have at least $1175$units of vitamins a month and at least role="math" localid="1647007561474" $2375$ calories during the same time period. Kevin has space to store only $60$ cans of dog food at a time. How much of each kind of dog food should Kevin buy each month to minimize his cost?

The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x₁, x₂, x₃, x₄ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.

$\left[\begin{array}{cccc}1& 0& 4|& 4\\ 0& 1& 3|& 2\\ 0& 0& 0|& 0\end{array}\right]$

In Problems 23–34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

$\left\{\begin{array}{l}x+4y≤8\\ x+4yâ‰\yen 4\end{array}\right.$

In Problems 25– 30, find the product.

$\left[\begin{array}{ccc}4& -2& 3\\ 0& 1& 2\\ -1& 0& 1\end{array}\right]\left[\begin{array}{cc}2& 6\\ 1& -1\\ 0& 2\end{array}\right]$

In Problems 13–46, write the partial fraction decomposition of each rational expression.

$\frac{x}{(3x-2)(2x+1)}$

In Problems 23–34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

$\left\{\begin{array}{l}2x+yâ‰\yen -2\\ 2x+yâ‰\yen 2\end{array}\right.$

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\left\{\begin{array}{c}2x-3y=-1\\ 10x+y=11\end{array}\right.$