91Ó°ÊÓ

Determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. $$ \frac{5 x^{3}+2 x-1}{x^{2}-4} $$

Use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, write "not defined" $$ A=\left[\begin{array}{rrr} 0 & 3 & -5 \\ 1 & 2 & 6 \end{array}\right] \quad B=\left[\begin{array}{rrr} 4 & 1 & 0 \\ -2 & 3 & -2 \end{array}\right] \quad C=\left[\begin{array}{rr} 4 & 1 \\ 6 & 2 \\ -2 & 3 \end{array}\right] $$ 3A-2B

Graph each equation of the system. Then solve the system to find the points of intersection. $$ \left\\{\begin{array}{r} x^{2}+y^{2}=4 \\ x^{2}+2 x+y^{2}=0 \end{array}\right. $$

Verify that the values of the variables listed are solutions of the system of equations. $$ \begin{array}{l} \left\\{\begin{array}{l} x-y=3 \\ \frac{1}{2} x+y=3 \end{array}\right. \\ x=4, y=1 ;(4,1) \end{array} $$

Find the value of each determinant. \(\left|\begin{array}{rrr}4 & -1 & 2 \\ 6 & -1 & 0 \\ 1 & -3 & 4\end{array}\right|\)

Graph each inequality. $$x \geq 4$$

Determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. $$ \frac{3 x^{4}+x^{2}-2}{x^{3}+8} $$

Graph each equation of the system. Then solve the system to find the points of intersection. $$ \left\\{\begin{array}{r} x^{2}+y^{2}=8 \\ x^{2}+y^{2}+4 y=0 \end{array}\right. $$

Use the following matrices. Determine whether the given expression is defined. If it is defined, express the result as a single matrix; if it is not, write "not defined" $$ A=\left[\begin{array}{rrr} 0 & 3 & -5 \\ 1 & 2 & 6 \end{array}\right] \quad B=\left[\begin{array}{rrr} 4 & 1 & 0 \\ -2 & 3 & -2 \end{array}\right] \quad C=\left[\begin{array}{rr} 4 & 1 \\ 6 & 2 \\ -2 & 3 \end{array}\right] $$ 2 A+4 B

Write the augmented matrix of the given system of equations. $$ \left\\{\begin{array}{r} 5 x-y-z=0 \\ x+y=5 \\ 2 x-3 z=2 \end{array}\right. $$