Chapter 8

Match the rational expression \((1-6)\) with the form of the partial-fraction decomposition \((a-f)\). a. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}\) b. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}+\frac{D x+E}{\left(x^{2}+25\right)^{2}}\) c. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}\) d. \(\frac{A}{x}+\frac{B}{x+5}+\frac{C}{x-5}\) e. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}+\frac{E x+F}{\left(x^{2}+25\right)^{2}}\) f. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{x+5}+\frac{D}{x-5}\) $$\frac{3 x+2}{x\left(x^{2}-25\right)}$$

state the order of each matrix. $$\left[\begin{array}{rrr}-1 & 2 & 4 \\\7 & -3 & 9\end{array}\right]$$

Evaluate each \(2 \times 2\) determinant. $$\left|\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right|$$

solve each system of linear equations. $$\begin{array}{r} x-y+z=6 \\ -x+y+z=3 \\ -x-y-z=0 \end{array}$$

Determine the order of each matrix. $$\left[\begin{array}{rrr} -1 & 3 & 4 \\ 2 & 7 & 9 \end{array}\right]$$

Solve each system of linear equations by substitution. $$\begin{aligned} &x+y=7\\\ &x-y=9 \end{aligned}$$

Evaluate each \(2 \times 2\) determinant. $$\left|\begin{array}{rr}1 & -2 \\\\-3 & -4\end{array}\right|$$

Match the rational expression \((1-6)\) with the form of the partial-fraction decomposition \((a-f)\). a. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}\) b. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}+\frac{D x+E}{\left(x^{2}+25\right)^{2}}\) c. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}\) d. \(\frac{A}{x}+\frac{B}{x+5}+\frac{C}{x-5}\) e. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}+\frac{E x+F}{\left(x^{2}+25\right)^{2}}\) f. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{x+5}+\frac{D}{x-5}\) $$\frac{3 x+2}{x\left(x^{2}+25\right)}$$

state the order of each matrix. $$\left[\begin{array}{rr}3 & 5 \\\2 & 6 \\\\-1 & -4\end{array}\right]$$

Solve each system of linear equations. $$\begin{array}{rr} -x-y+z= & -1 \\ -x+y-z= & 3 \\ x-y-z= & 5 \end{array}$$

Determine the order of each matrix. $$\left[\begin{array}{ll} 0 & 1 \\ 3 & 9 \\ 7 & 8 \end{array}\right]$$

Solve each system of linear equations by substitution. $$\begin{aligned} &x-y=-10\\\ &x+y=4 \end{aligned}$$

Evaluate each \(2 \times 2\) determinant. $$\left|\begin{array}{rr} 7 & 9 \\ -5 & -2 \end{array}\right|$$

Match the rational expression \((1-6)\) with the form of the partial-fraction decomposition \((a-f)\). a. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}\) b. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}+\frac{D x+E}{\left(x^{2}+25\right)^{2}}\) c. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}\) d. \(\frac{A}{x}+\frac{B}{x+5}+\frac{C}{x-5}\) e. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}+\frac{E x+F}{\left(x^{2}+25\right)^{2}}\) f. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{x+5}+\frac{D}{x-5}\) $$ \frac{3 x+2}{x^{2}\left(x^{2}+25\right)} $$

state the order of each matrix. $$\left[\begin{array}{rr}-4 & 5 \\\0 & 1\end{array}\right]$$

Solve each system of linear equations. $$\begin{array}{rr} x+y-z= & 2 \\ -x-y-z= & -3 \\ -x+y-z= & 6 \end{array}$$

Determine the order of each matrix. $$\left[\begin{array}{llll} 1 & 2 & 3 & 4 \end{array}\right]$$

Solve each system of linear equations by substitution. $$\begin{array}{r} 2 x-y=3 \\ x-3 y=4 \end{array}$$

Evaluate each \(2 \times 2\) determinant. $$\left|\begin{array}{rr} -3 & -11 \\ 7 & 15 \end{array}\right|$$

Match the rational expression \((1-6)\) with the form of the partial-fraction decomposition \((a-f)\). a. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}\) b. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}+\frac{D x+E}{\left(x^{2}+25\right)^{2}}\) c. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}\) d. \(\frac{A}{x}+\frac{B}{x+5}+\frac{C}{x-5}\) e. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}+\frac{E x+F}{\left(x^{2}+25\right)^{2}}\) f. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{x+5}+\frac{D}{x-5}\) $$\frac{3 x+2}{x^{2}\left(x^{2}-25\right)}$$

state the order of each matrix. $$\left[\begin{array}{llll}-4 & 5 & 3 & 71\end{array}\right]$$

Solve each system of linear equations. $$\begin{array}{rr} x+y+z= & -1 \\ -x+y-z= & 3 \\ -x-y+z= & 8 \end{array}$$

Determine the order of each matrix. $$\left[\begin{array}{r} 3 \\ 7 \\ -1 \\ 10 \end{array}\right]$$

Solve each system of linear equations by substitution. $$\begin{aligned} &4 x+3 y=3\\\ &2 x+y=1 \end{aligned}$$

In Exercises \(5-20,\) graph each linear inequality. $$y>x-1$$

Match the rational expression \((1-6)\) with the form of the partial-fraction decomposition \((a-f)\). a. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}\) b. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}+\frac{D x+E}{\left(x^{2}+25\right)^{2}}\) c. \(\frac{A}{x}+\frac{B x+C}{x^{2}+25}\) d. \(\frac{A}{x}+\frac{B}{x+5}+\frac{C}{x-5}\) e. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C x+D}{x^{2}+25}+\frac{E x+F}{\left(x^{2}+25\right)^{2}}\) f. \(\frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{x+5}+\frac{D}{x-5}\) $$\frac{3 x+2}{x\left(x^{2}+25\right)^{2}}$$

Evaluate each \(2 \times 2\) determinant. $$\left|\begin{array}{rr} 0 & 7 \\ 4 & -1 \end{array}\right|$$

state the order of each matrix. $$\left[\begin{array}{ccc}-3 & 4 & 1 \\\10 & 8 & 0 \\\\-2 & 5 & 7\end{array}\right]$$

Solve each system of linear equations. $$\begin{array}{rr} -x+y-z= & -1 \\ x-y-z= & 3 \\ x+y-z= & 9 \end{array}$$

Determine the order of each matrix. $$[0]$$

Solve each system of linear equations by substitution. $$\begin{aligned} &3 x+y=5\\\ &2 x-5 y=-8 \end{aligned}$$

In Exercises \(5-20,\) graph each linear inequality. $$y \geq-x+1$$

Evaluate each \(2 \times 2\) determinant. $$\left|\begin{array}{ll} 0 & 0 \\ 1 & 0 \end{array}\right|$$

state the order of each matrix. $$\left[\begin{array}{l}1 \\\2 \\\3 \\\4\end{array}\right]$$

Solve each system of linear equations. $$\begin{array}{r} x-y-z=2 \\ -x-y+z=4 \\ -x+y-z=6 \end{array}$$

Determine the order of each matrix. $$\left[\begin{array}{rrrr} -1 & 3 & 6 & 8 \\ 2 & 9 & 7 & 3 \\ 5 & 4 & -2 & -10 \\ 6 & 3 & 1 & 5 \end{array}\right]$$

Solve each system of linear equations by substitution. $$\begin{aligned} &6 x-y=-15\\\ &2 x-4 y=-16 \end{aligned}$$

In Exercises \(5-20,\) graph each linear inequality. $$y \leq-x$$

Write the form of the partial-fraction decomposition. Do not solve for the constants. $$\frac{9}{x^{2}-x-20}$$

Evaluate each \(2 \times 2\) determinant. $$\left|\begin{array}{cc} -1.2 & 2.4 \\ -0.5 & 1.5 \end{array}\right|$$

state the order of each matrix. $$\left[\begin{array}{rrrr}-3 & 6 & 0 & 5 \\\4 & -9 & 2 & 7 \\\1 & 8 & 3 & 6 \\\5 & 0 & -4 & 11 \end{array}\right]$$

Write the augmented matrix for each system of linear equations. $$\begin{array}{r} 3 x-2 y=7 \\ -4 x+6 y=-3 \end{array}$$

Solve each system of linear equations. $$\begin{array}{l} 2 x-3 y+4 z=-3 \\ -x+y+2 z=1 \\ 5 x-2 y-3 z=7 \end{array}$$

Solve each system of linear equations by substitution. $$\begin{aligned} &2 u+5 v=7\\\ &3 u-v=5 \end{aligned}$$

In Exercises \(5-20,\) graph each linear inequality. $$y > -x$$

Write the form of the partial-fraction decomposition. Do not solve for the constants. $$\frac{8}{x^{2}-3 x-10}$$

Evaluate each \(2 \times 2\) determinant. $$\left|\begin{array}{rr} -1.0 & 1.4 \\ 1.5 & -2.8 \end{array}\right|$$

Write the augmented matrix for each system of linear equations. $$\begin{array}{r} -x+y=2 \\ x-y=-4 \end{array}$$

state the order of each matrix. $$\left[\begin{array}{rrrr}-1 & 3 & 6 & 9 \\\2 & 5 & -7 & 8\end{array}\right]$$

Solve each system of linear equations. $$\begin{array}{rr} x-2 y+z= & 0 \\ -2 x+y-z= & -5 \\ 13 x+7 y+5 z= & 6 \end{array}$$