Chapter 9

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ -\sqrt{400} $$

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. Gold: \(H=50\)

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 175 \% $$

Write the expression as a single power of the base. $$ m \cdot m^{4} \cdot m^{3} $$

Evaluate the radical expression when $a=-1 \text { and } b=5. $$\sqrt{b^{2}+9 a}$$

Find the x-intercepts of the graph of the function. $$y=2 x^{2}-6 x-8$$

Find the product. \(0.09 \times 0.02\)

Write the radical expression in simplest form. $$ -6 \sqrt{4} $$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ -\sqrt{20} $$

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. Galena: \(H=80\)

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 8 \% $$

Write the expression as a single power of the base. $$ 5 \cdot 5^{2} \cdot 5^{3} $$

Evaluate the radical expression when $a=-1 \text { and } b=5. $$ \sqrt{a^{2}+8} $$

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

Find the product. \(0.06 \times 0.0004\)

Write the radical expression in simplest form. $$ 3 \sqrt{44} $$

Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. $$ \pm \sqrt{144} $$

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. Platinum: \(H=125\)

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 91 \% $$

Write the expression as a single power of the base. $$ 2(2)^{4} $$

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

Find the x-intercepts of the graph of the function. $$y=2 x^{2}+4 x-6$$

Write the radical expression in simplest form. $$ -\frac{1}{7} \sqrt{49} $$

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

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. Copper: \(H=140\)

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 2 \% $$

Write the numbers in order from least to greatest. $$ \frac{1}{2}, \frac{2}{3}, \frac{5}{12} $$

Evaluate the radical expression when $a=-1 \text { and } b=5. $$\frac{\sqrt{b^{2}+24 a}}{a}$$

Find the x-intercepts of the graph of the function. $$y=-3 x^{2}+17 x-20$$

Write the radical expression in simplest form. $$ \frac{1}{2} \sqrt{32} $$

Evaluate \(\sqrt{b^{2}-4 a c}\) for the given values. $$ a=2, b=4, c=-6 $$

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. Hematite: \(H=755\)

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 25 \% $$

Write the numbers in order from least to greatest. $$ \frac{1}{3}, \frac{4}{15}, \frac{2}{5} $$

Evaluate the radical expression when $a=-1 \text { and } b=5. $$\frac{\sqrt{b^{2}-75 a}}{b}$$

Six balloonists compete in a field target event at a hot-air balloon festival. Calculate the amount of time it takes for the marker to reach the target when thrown down from the given initial height (in feet) with the given initial downward velocity (in feet per second). Round to the nearest hundredth of a second. $$s=200 ; v=-50$$

Write the radical expression in simplest form. $$ \frac{3}{2} \sqrt{24} $$

Evaluate \(\sqrt{b^{2}-4 a c}\) for the given values. $$ a=-2, b=8, c=-8 $$

Use the following information. Population estimates for the 1800 s lead a student to model the population of the United States by \(P=5,500,400+683,300 t^{2},\) where \(t=0,1,2,3, \ldots\) represents the years \(1800,1810,1820,1830, \ldots\). Use this population model to estimate the United States population in 1800 , \(1850,\) and 1900

Write the percent as a fraction or as a mixed number in simplest form. (Skills Review p. 768 ) $$ 16 \% $$

Write the numbers in order from least to greatest. $$ \frac{3}{5}, \frac{4}{10}, \frac{5}{15} $$

Evaluate the radical expression when $a=-1 \text { and } b=5. $$\frac{\sqrt{65-a^{2}}}{-a}$$

Six balloonists compete in a field target event at a hot-air balloon festival. Calculate the amount of time it takes for the marker to reach the target when thrown down from the given initial height (in feet) with the given initial downward velocity (in feet per second). Round to the nearest hundredth of a second. $$s=150 ; v=-25$$

Write the radical expression in simplest form. $$ \frac{1}{8} \sqrt{56} $$

Evaluate \(\sqrt{b^{2}-4 a c}\) for the given values. $$ a=-5, b=5, c=10 $$

Use the following information. Population estimates for the 1800 s lead a student to model the population of the United States by \(P=5,500,400+683,300 t^{2},\) where \(t=0,1,2,3, \ldots\) represents the years \(1800,1810,1820,1830, \ldots\). Use this model to estimate the year in which the United States population reached 50 million.

Write the numbers in order from least to greatest. $$ \frac{9}{10}, \frac{7}{8}, \frac{3}{4} $$

Evaluate the radical expression when $a=-1 \text { and } b=5. $$\frac{\sqrt{86+a b}}{a}$$

Write the radical expression in simplest form. $$ -\frac{1}{2} \sqrt{360} $$

Evaluate the radical expression when a = 2 and b = 4. $$ \sqrt{b^{2}+10 a} $$