Chapter 5

Perform the indicated operations. $$ \left[\begin{array}{ccc}{4} & {1} & {-3}\end{array}\right]+\left[\begin{array}{ccc}{6} & {-5} & {8}\end{array}\right] $$

REASONING Determine if each statement is true or false. If false, find a counterexample. a. Every real number is a complex number. b. Every imaginary number is a complex number.

Perform the indicated operations. $$ \left[\begin{array}{ccc}{2} & {-5} & {7}\end{array}\right]-\left[\begin{array}{ccc}{-3} & {8} & {-1}\end{array}\right] $$

Perform the indicated operations. $$ 4\left[\begin{array}{rrr}{-7} & {5} & {-11} \\ {2} & {-4} & {9}\end{array}\right] $$

Evaluate \(b^{2}-4 a c\) for the given values of \(a, b,\) and \(c\). \(a=1, b=7, c=3\)

Perform the indicated operations. $$ -2\left[\begin{array}{ccc}{-3} & {0} & {12} \\ {-7} & {\frac{1}{3}} & {4}\end{array}\right] $$

If \(i^{2}=-1,\) then what is the value of \(i^{71} ?\) \(\mathbf{F}-1\) \(\mathbf{G} 0\) \(\mathbf{H}-\boldsymbol{i}\) \(\mathbf{J} i\)

Evaluate \(b^{2}-4 a c\) for the given values of \(a, b,\) and \(c\). \(a=1, b=2, c=5\)

CONCERTS. The price of two lawn seats and a pavilion seat at an outdoor amphitheater is \(\$ 75 .\) The price of three lawn seats and two pavilion seats is \(\$ 130 .\) How much do lawn and pavilion seats cost?

Write a quadratic equation with the given root(s). Write the equation in the form \(a x^{2}+b x+c=0,\) where \(a, b,\) and \(c\) are integers. $$ -3,9 $$

Evaluate \(b^{2}-4 a c\) for the given values of \(a, b,\) and \(c\). \(a=2, b=-9, c=-5\)

Solve each system of equations. $$ \begin{array}{l}{4 a-3 b=-4} \\ {3 a-2 b=-4}\end{array} $$

Write a quadratic equation with the given root(s). Write the equation in the form \(a x^{2}+b x+c=0,\) where \(a, b,\) and \(c\) are integers. $$ -\frac{1}{3},-\frac{3}{4} $$

Evaluate \(b^{2}-4 a c\) for the given values of \(a, b,\) and \(c\). \(a=4, b=-12, c=9\)

Solve each system of equations. $$ \begin{array}{l}{2 r+s=1} \\ {r-s=8}\end{array} $$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ 3 x^{2}=4-8 x $$

Solve each system of equations. $$ \begin{array}{l}{3 x-2 y=-3} \\ {3 x+y=3}\end{array} $$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. $$ 2 x^{2}+11 x=-12 $$

Graph the system of equations \(y=-3 x\) and \(y-x=4 .\) State the solution. Is the system of equations consistent and independent, consistent and dependent, or inconsistent?

Find the slope of the line that passes through each pair of points. $$ (6,7),(0,-5) $$

Triangle \(A B C\) is reflected over the \(x\) -axis. Write the reflection matrix.

Find the slope of the line that passes through each pair of points. $$ (-3,-2),(-1,-4) $$

Find the slope of the line that passes through each pair of points. $$ (-3,2),(5,6) $$

Find the slope of the line that passes through each pair of points. $$ (-2,8),(1,-7) $$

FURNITURE A new sofa, love seat, and coffee table cost \(\$ 2050\) . The sofa costs twice as much as the love seat. The sofa and the coffee table together cost \(\$ 1450 .\) How much does each piece of furniture cost?

Find the slope of the line that passes through each pair of points. $$ (3,8),(7,22) $$

DECORATION. Samantha is going to use more than 75 but less than 100 bricks to make a patio off her back porch. If each brick costs \(\$ 2.75,\) write and solve a compound inequality to determine the amount she will spend on bricks.

Find the slope of the line that passes through each pair of points. $$ (4,21),(9,12) $$

Determine whether each polynomial is a perfect square trinomial. $$ x^{2}-10 x+16 $$

Solve each equation. Check your solutions. $$ |x-3|=7 $$

Determine whether each polynomial is a perfect square trinomial. $$ x^{2}+18 x+81 $$

Solve each equation. Check your solutions. $$ -4|d+2|=-12 $$

Determine whether each polynomial is a perfect square trinomial. $$ x^{2}-9 $$

Solve each equation. Check your solutions. $$ 5|k-4|=k+8 $$

Determine whether each polynomial is a perfect square trinomial. $$ x^{2}-12 x-36 $$

Determine whether each polynomial is a perfect square trinomial. $$ x^{2}-x+\frac{1}{4} $$

PREREQUISITE SKILL. Evaluate each function for the given value. $$ f(x)=x^{2}+2 x-3, x=2 $$

Determine whether each polynomial is a perfect square trinomial. $$ 2 x^{2}-15 x+25 $$

PREREQUISITE SKILL. Evaluate each function for the given value. $$ f(x)=-x^{2}-4 x+5, x=-3 $$

PREREQUISITE SKILL. Evaluate each function for the given value. $$ f(x)=3 x^{2}+7 x, x=-2 $$

PREREQUISITE SKILL. Evaluate each function for the given value. $$ f(x)=\frac{2}{3} x^{2}+2 x-1, x=-3 $$