91Ó°ÊÓ

Fill in the blanks. You obtain the ________ ________ after multiplying each side of the partial fraction decomposition form by the least common denominator.

Interchanging two equations of a system of linear equations is a __________ ___________ that produces an equivalent system.

Sketch the graph of the inequality. $$y<5-x^{2}$$

A system of equations is called ___________ when the number of equations differs from the number of variables in the system.

Match the rational expression with the form of its decomposition. [The decompositions are labeled (a), (b), (c), and (d).] $$\text { (a) } \frac{A}{x}+\frac{B}{x+2}+\frac{C}{x-2}$$ $$\text { (b) } \frac{A}{x}+\frac{B}{x-4}$$ $$\text { (c) } \frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{x-4}$$ $$\text { (d) } \frac{A}{x}+\frac{B x+C}{x^{2}+4}$$ $$\frac{3 x-1}{x(x-4)}$$

Determine whether each ordered pair is a solution of the system. $$\left\\{\begin{array}{l} 2 x-y=4 \\ 8 x+y=-9 \end{array}\right.$$ (a) (0,-4) (b) (-2,7) (c) \(\left(\frac{3}{2},-1\right)\) (d) \(\left(-\frac{1}{2},-5\right)\)

Sketch the graph of the inequality. $$y^{2}-x<0$$

Determine whether each ordered pair is a solution of the system. $$\left\\{\begin{array}{l} 4 x^{2}+y=3 \\ -x-y=11 \end{array}\right.$$ (a) (2,-13) (b) (2,-9) (c) \(\left(-\frac{3}{2},-\frac{31}{3}\right)\) (d) \(\left(-\frac{7}{4},-\frac{37}{4}\right)\)

The equation \(s=\frac{1}{2} a t^{2}+v_{0} t+s_{0}\) is called the ___________ equation, and it models the height \(s\) of an object at time \(t\) that is moving in a vertical line with a constant acceleration \(a .\)

Fill in the blanks. If a linear programming problem has a solution, then it must occur at a_______of the set of feasible solutions.