Chapter 8

The power generated by a windmill can be modeled by \(w=0.015 s^{3},\) where \(w\) is the power measured in watts and s is the wind speed in miles per hour. Find the ratio of the power generated when the wind speed is 5 miles per hour to the power generated when the wind speed is 10 miles per hour.

Simplify the expression \(\frac{x^{-9}}{x^{-3}}\) A. \(\frac{1}{x^{-6}}\) B. \(\frac{1}{x^{6}}\) C. \(x^{-3}\) D. \(x^{3}\)

Write in point-slope form the equation of the line that passes through the given point and has the given slope. $$(2,5), m=3$$

Write the number in scientific notation. The mass of a carbon atom is 0.00000000000000000000002 gram.

Write the equation in standard form with integer coefficients. $$y=-\frac{3}{16} x+\frac{9}{16}$$

Someone offers to double the amount of money you have every day for 1 month (30 days). You have 1 penny. At the end of the first day, you will have \(2 \cdot 1=2\) pennies. On the second day, you will have \(2 \cdot 2=4\) pennies. On the third day, you will have \(2 \cdot 4=8\) pennies. Write each of these equations using only powers of 2

Simplify the expression \(\left(\frac{2}{9}\right)^{-3}\) F. \(-\frac{6}{27}\) G. \(\frac{27}{6}\) H. \(-\frac{8}{729}\) J. \(\frac{729}{8}\)

Write in point-slope form the equation of the line that passes through the given point and has the given slope. $$ (0,-3), m=5 $$

Write the number in scientific notation. Science Link , Light travels at a spced of about \(3 \times 10^{5}\) kilometers per esecond. It takes about \(1.5 \times 10^{4}\) seconds for light to travel from the sun to IN cptunc. What is the approximate distance (in kilometers) between Neptune eand the sun?

Write the equation in standard form with integer coefficients. $$y=\frac{1}{10} x-\frac{9}{10}$$

Simplify the expression \(\frac{4 x^{3} y}{18 x^{2}} \cdot \frac{9}{16 x^{2} y}\) A. \(\frac{x}{16}\) B. \(\frac{x}{8}\) C. \(\frac{x^{3}}{8}\) D. \(\frac{1}{8 x}\)

Write in point-slope form the equation of the line that passes through the given point and has the given slope. $$ (-1,-4), m=4 $$

Use the graphing method to tell how many solutions the system has. $$\begin{array}{r} {2 x-2 y=4} \\ {x+3 y=9} \end{array}$$

Someone offers to double the amount of money you have every day for 1 month (30 days). You have 1 penny. How many pennies will you have on the 30th day?

Which expression equals \(\frac{1}{8} ?\) A. \(-8\) B. \(4^{-2}\) C. \(2^{-3}\) D. \(1^{-8}\)

Simplify the expression \(\frac{x^{-2}}{y^{-3}} \cdot\left(\frac{x}{y}\right)^{-1}\) F. \(\frac{y^{2}}{x}\) G. \(\frac{y^{4}}{x^{3}}\) H. \(\frac{x^{2}}{y^{3}}\) J. \(\frac{x^{3}}{y^{4}}\)

Write in point-slope form the equation of the line that passes through the given point and has the given slope. $$ (6,3), m=-1 $$

Use the graphing method to tell how many solutions the system has. $$\begin{array}{l} {-x+y=-1} \\ {2 x+3 y=12} \end{array}$$

Someone offers to double the amount of money you have every day for 1 month (30 days). You have 1 penny. How much money (in dollars) will you have after 30 days?

Evaluate the expression \(\left(4^{-1}\right)^{-2}\) F. \(\frac{1}{64}\) G. \(\frac{1}{16}\) H. 16 J. 64

Evaluate the expression. $$ 10^{5} $$

Write in point-slope form the equation of the line that passes through the given point and has the given slope. $$ (-1,7), m=-6 $$

Jupiter, the largest planet in our solar system, has a radius of about \(7.15 \times 10^{4}\) kilometers. Use the formula for the volume of a sphere, \(V=\frac{4}{3} \pi r^{3},\) to estimate Jupiter's volume.

Use the graphing method to tell how many solutions the system has. $$\begin{aligned} &6 x+2 y=3\\\ &3 x+y=-2 \end{aligned}$$

Fill in the blanks and give a reason for each step to complete a convincing argument that the power of a power property is true for this case. \(\left(b^{3}\right)^{2}=b^{3} \cdot ?\) \(=? \cdot ? \cdot ? \cdot ? \cdot ? \cdot ?\) \(=?\)

Evaluate the expression \(3 \cdot 3^{-5}\) A. \(\frac{1}{81}\) B. \(\frac{1}{5}\) C. 45 D. 81

Evaluate the expression. $$ 10^{1} $$

Write in point-slope form the equation of the line that passes through the given point and has the given slope. $$ (-4,-5), m=-2 $$

Use the graphing method to tell how many solutions the system has. $$\begin{array}{c} {x+y=0} \\ {x+2 y=6} \end{array}$$

Simplify the expression \(5^{2} \cdot 5^{4}\) A) \(5^{6}\) B) \(5^{8}\) C) \(10^{6}\) D) \(25^{8}\)

Rewrite the expression \(\frac{3 x^{-2}}{y^{3} z^{-1}}\) with positive exponents. F. \(\frac{z}{3 x^{2} y^{3}}\) G. \(\frac{3 z}{x^{2} y^{3}}\) H. \(\frac{3 y^{3} z}{x^{2}}\) J. \(3 x^{2} y^{3} z\)

Evaluate the expression. $$ 10^{0} $$

Divide. $$ 0.5 \div 0.2 $$

Evaluate \(\frac{1.1 \times 10^{-1}}{5.5 \times 10^{-5}}\) $$f. 0.2 \times 10^{-6}$$ $$g. 0.2 \times 10^{-4}$$ $$h. 2 \times 10^{3}$$ $$i. 2 \times 10^{4}$$

Use the graphing method to tell how many solutions the system has. $$\begin{aligned} 4 x-y &=-2 \\ -12 x+3 y &=6 \end{aligned}$$

Evaluate the expression \(\left(2^{3}\right)^{2}.\) F) 18 G) 32 H) 36 J) 64

Evaluate the expression. Then simplify the answer. $$ \frac{6 \cdot 5}{1+7 \cdot 2} $$

Evaluate the expression. $$ 10^{-4} $$

Divide. $$ 4.62 \div 0.4 $$

Use the graphing method to tell how many solutions the system has. $$\begin{aligned} -x+3 y &=3 \\ 2 x-y &=-8 \end{aligned}$$

Evaluate the expression \((4 \cdot 6)^{2}.\) A) 48 B) 96 C) 144 D) 576

Evaluate the expression. Then simplify the answer. $$ \frac{8 \cdot 8}{10+3 \cdot 2} $$

Write in slope-intercept form the equation of the line that passes through the given points. $$ (-4,2) \text { and }(4,6) $$

Divide. $$ 0.074 \div 0.37 $$

Use the graphing method to tell how many solutions the system has. $$ \begin{aligned} &3 x-2 y=0\\\ &3 x-2 y=-4 \end{aligned} $$

Write the numbers in increasing order. $$-4,-5,6$$

Simplify the expression \(\left(3 x^{2} y\right)^{3}.\) F) \(3 x^{2} y^{3}\) G) \(9 x^{5} y^{3}\) H) \(9 x^{6} y^{3}\) J) \(27 x^{6} y^{3}\)

Evaluate the expression. Then simplify the answer. $$ \frac{2 \cdot 4^{2}}{1+3^{2}-2} $$

Write in slope-intercept form the equation of the line that passes through the given points. $$ (-4,-5) \text { and }(0,3) $$

Divide. $$ 0.084 \div 0.007 $$