91Ó°ÊÓ

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. \(y<\frac{1}{2} x-4\) \(y>-2 x+1\)

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. \(y \geq \frac{1}{3} x-2\) \(y \leq x-4\)

Solve the system using any method. $$ \begin{array}{l} \frac{x+1}{2}-\frac{y-2}{10}=-1 \\ \frac{x+1}{6}+\frac{y-2}{2}=21 \end{array} $$

An electronic sign for a grocery store is in the shape of a rectangle. The perimeter of the sign is \(72 \mathrm{ft}\) and the area is \(320 \mathrm{ft}^{2}\). Find the length and width of the sign.

Find an equation of the form \(y=a x^{2}+b x+c\) that defines the parabola through the three noncollinear points given. $$ (0,6),(2,-6),(-1,9) $$

a. Factor. \(x^{3}-x^{2}-21 x+45\) (Hint: Use the rational zero theorem.) b. Find the partial fraction decomposition for \(\frac{-3 x^{2}+35 x-70}{x^{3}-x^{2}-21 x+45}\)

A rental truck has a cargo capacity of \(288 \mathrm{ft}^{3}\). A 10 -ft pipe just fits resting diagonally on the floor of the truck. If the cargo space is \(6 \mathrm{ft}\) high, find the dimensions of the truck.

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. \(2 x+5 y \leq 5\) \(-3 x+4 y \geq 4\)

A rectangular window has a 15 -yd diagonal and an area of \(108 \mathrm{yd}^{2}\). Find the dimensions of the window.

A pharmacist wants to mix a \(30 \%\) saline solution with a \(10 \%\) saline solution to get \(200 \mathrm{~mL}\) of a \(12 \%\) saline solution. How much of each solution should she use?