Chapter 9

Write the quadratic equation in standard form. Then solve using the quadratic formula. $$2 x^{2}+4=6 x$$

Graph the inequality. \(3 x+y \leq 9\)

Simplify the expression. $$ \sqrt{\frac{3}{2}} $$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ -\sqrt{125} $$

Decide whether the statement is true or false. If it is true, give a reason. If it is false, give a counterexample. \(x^{2}=c\) has no real solution when \(c<0\)

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 3 \% $$

Graph the system of linear inequalities. $$ \begin{array}{c} {x+y<10} \\ {2 x+y>10} \\ {x-y<2} \end{array} $$

Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. $$\begin{array}{r} {-2 x+8 y=10} \\ {x+6 y=15} \end{array}$$

Write the quadratic equation in standard form. Then solve using the quadratic formula. $$12=2 x^{2}-2 x$$

Graph the inequality. \(y-4 x<0\)

Simplify the expression. $$ \sqrt{\frac{25}{3}} $$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ -\sqrt{49} $$

Decide whether the statement is true or false. If it is true, give a reason. If it is false, give a counterexample. \(x^{2}=c\) has two solutions when \(c>0\)

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 6 \% $$

Write the expression as a single power of the base. $$ 4^{2} \cdot 4^{5} $$

Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. $$\begin{aligned} -2 x+2 y &=4 \\ x-y &=-2 \end{aligned}$$

Find the x-intercepts of the graph of the function. $$y=-x^{2}+x+6$$

Graph the inequality. \(-2 x-y \geq 4\)

Simplify the expression. $$ \sqrt{\frac{16}{10}} $$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ \pm \sqrt{70} $$

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 24 \% $$

Write the expression as a single power of the base. $$ (-5) \cdot(-5)^{8} $$

Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. $$\begin{array}{r} {8 x+4 y=-4} \\ {4 x-y=-20} \end{array}$$

Find the x-intercepts of the graph of the function. $$y=x^{2}+5 x+6$$

Find the product. \(3 \times 0.02\)

Write the radical expression in simplest form. $$ 4 \sqrt{25} $$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ \pm \sqrt{1} $$

A boulder falls off the top of an overhanging cliff during a storm. The cliff is 96 feet high. Find how long it will take for the boulder to hit the road below. Write a falling object model when \(s=96\)

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 10 \% $$

Write the expression as a single power of the base. $$ x^{2} \cdot x^{4} \cdot x^{6} $$

Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. $$\begin{array}{r} {6 x+4 y=-4} \\ {2 x-y=-6} \end{array}$$

Find the x-intercepts of the graph of the function. $$y=x^{2}-11 x+24$$

Find the product. \(0.7 \times 0.8\)

Write the radical expression in simplest form. $$ 9 \sqrt{100} $$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ \sqrt{10} $$

A boulder falls off the top of an overhanging cliff during a storm. The cliff is 96 feet high. Find how long it will take for the boulder to hit the road below. Solve the falling object model for \(h=0 .\) Round to the nearest tenth.

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 390 \% $$

Write the expression as a single power of the base. $$ x^{3} \cdot x^{5} $$

Use the substitution method or linear combinations to solve the linear system and tell how many solutions the system has. $$\begin{aligned} &5 x+4 y=-3\\\ &15 x+12 y=9 \end{aligned}$$

Find the x-intercepts of the graph of the function. $$y=x^{2}+10 x+16$$

Find the product. \(0.1 \times 0.1\)

Write the radical expression in simplest form. $$ -2 \sqrt{27} $$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ \pm \sqrt{15} $$

Use the following information. Mineralogists use the Vickers scale to measure the hardness of minerals. The hardness \(H\) of a mineral can be determined by hitting the mineral with a pyramid-shaped diamond and measuring the depth \(d\) of the indentation. The harder the mineral, the smaller the depth of the indentation. A model that relates mineral hardness with the indentation depth (in millimeters) is \(H d^{2}=1.89\). Use a calculator to find the depth of the indentation for the mineral with the given value of \(H .\) Round to the nearest hundredth of a millimeter. Graphite: \(H=12\)

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 225 \% $$

Write the expression as a single power of the base. $$ t \cdot\left(t^{3}\right) $$

Evaluate the radical expression when $a=-1 \text { and } b=5. $$\sqrt{b^{2}-11 a}$$

Find the x-intercepts of the graph of the function. $$y=-x^{2}-4 x+2$$

Find the product. \(0.05 \times 0.003\)

Write the radical expression in simplest form. $$ \frac{1}{3} \sqrt{63} $$