91Ó°ÊÓ

Make a rough sketch in a rectangular coordinate system of the graphs representing the equations in each system. The system, whose graphs are a line with negative slope and a parabola whose equation has a negative leading coefficient, has one solution.

Explain how to find the partial fraction decomposition of a rational expression with distinct linear factors in the denominator.

Graph the solution set of system of inequalities or indicate that the system has no solution. $$\left\\{\begin{aligned}x^{2}+y^{2} &<4 \\\y-x^{2} & \geq 0\end{aligned}\right.$$

Graph the solution set of system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{l}x^{2}+y^{2}<16 \\\y \geq 2^{x}\end{array}\right.$$

A planet's orbit follows a path described by \(16 x^{2}+4 y^{2}=64\) A comet follows the parabolic path \(y=x^{2}-4 .\) Where might the comet intersect the orbiting planet?

$$\text { Solve: } \frac{x+3}{4}-\frac{x+1}{10}=\frac{x-2}{5}-1$$

A wine company needs to blend a California wine with a \(5 \%\) alcohol content and a French wine with a \(9 \%\) alcohol content to obtain 200 gallons of wine with a \(7 \%\) alcohol content. How many gallons of each kind of wine must be used?

Explain how to find the partial fraction decomposition of a rational expression with a repeated linear factor in the denominator.

Graph the solution set of system of inequalities or indicate that the system has no solution. $$\left\\{\begin{array}{l}x^{2}+y^{2} \leq 16 \\\y<2^{x}\end{array}\right.$$

A system for tracking ships indicates that a ship lies on a path described by \(2 y^{2}-x^{2}=1 .\) The process is repeated and the ship is found to lie on a path described by \(2 x^{2}-y^{2}=1 .\) If it is known that the ship is located in the first quadrant of the coordinate system, determine its exact location.