Chapter 10

Find the greatest common factor. $$ 20,32,40 $$

Use the quadratic formula or factoring to find the roots of the polynomial. Write your solutions in simplest form. \(3 x^{2}-4 x+1=0\)

The area of a square is given by \(4 x^{2}-20 x+25\) Express its perimeter as a function of \(x .\)

$$ \left(m^{2}+2 m-9\right)(m-4) $$

Write the number in decimal form. \(2.1 \times 10^{5}\)

In Exercises 55-57, use the vertical motion model \(h=-16 t^{2}+v t+s\) where \(h\) is the height (in feet), \(t\) is the time in motion (in seconds), \(v\) is the initial velocity (in feet per second), and \(s\) is the initial height (in feet). Solve by factoring. A gymnast dismounts the uneven parallel bars at a height of 8 feet with an initial upward velocity of 8 feet per second. a. Write a quadratic equation that models her height above the ground. b. Use the model to find the time \(t\) (in seconds) it takes for the gymnast to reach the ground. Is your answer reasonable?

Which of the following polynomials is not written in standard form? $$ \begin{array}\text{(A)} \quad 8 n^{2}-16 n+144 & \text {(B)} \quad 3 y^{3}-y^{2}-15+4 y \\ \text {(C)} \quad 3 w^{4}+4 w^{2}-w-9 & \text {(D)} \quad 3 p^{4}-6 p^{3}+2 p+16 \end{array} $$

Solve the equation by factoring. Use a graphing calculator to check your solution if you wish. $$ 6 b^{2}-72 b+216=0 $$

Find the greatest common factor. $$ 36,54,90 $$

Use the quadratic formula or factoring to find the roots of the polynomial. Write your solutions in simplest form. \(6 x^{2}-2 x-7=0\)

The side of a square is \((3 x-4)\) inches. What is its area?

$$ \left(4 y^{2}-3 y-2\right)(y+12) $$

Write the number in decimal form. \(4.443 \times 10^{-2}\)

An acrobat is shot out of a cannon and lands in a safety net that is 10 feet above the ground. Before being shot out of the cannon, she was 4 feet above the ground. She left the cannon with an initial upward velocity of 50 feet per second. A. Write a quadratic model to represent this situation. B.Use the model to find the time \(t\) (in seconds) it takes for her to reach the net. Explain why only one of the two solutions is reasonable.

What is the degree of \(-6 x^{4} ?\) $$ \begin{array}{lllll} {\text{F) } 4} & {\text{G)}-6} & {\text{ H) }-4} & {\text{J) } 6} \end{array} $$

Solve the equation by factoring. Use a graphing calculator to check your solution if you wish. $$ 90 x^{2}-120 x+40=0 $$

Find the product. $$ 3 q\left(q^{3}-5 q^{2}+6\right) $$

Use the quadratic formula or factoring to find the roots of the polynomial. Write your solutions in simplest form. \(3 x^{2}+8 x-2=0\)

Write the number in decimal form. \(8.57 \times 10^{8}\)

and shot from a “T-shirt cannon” into the crowd. The T-shirts are released from a height of 6 feet with an initial upward velocity of 44 feet per second. If you catch a T-shirt at your seat 30 feet above the court, how long was it in the air before you caught it? Is your answer reasonable?

Which of the following is classified as a monomial? $$ \begin{array}{lllll} {\text{A) } x+1} & {\text{B)}5-y^{2}} & {\text{ C) }a^{3}-a-1} & {\text{D) } 2 y} \end{array} $$

Solve the equation by factoring. Use a graphing calculator to check your solution if you wish. $$ 16 x^{2}-56 x+49=0 $$

Find the product. $$ (y+9)(y-4) $$

Use the vertical motion models, where h is the height (in feet), v is the initial upward velocity (in feet per second), s is the initial height (in feet), and t is the time (in seconds) the object spends aloft. Vertical motion model for Earth: \(h=-16 t^{2}+v t+s\) Vertical motion model for the moon: \(h=-\frac{16}{6} t^{2}+v t+s\) Note: the two equations are different because the acceleration due to gravity on the moon’s surface is about one-sixth that of Earth. On Earth, you toss a tennis ball from a height of 96 feet with an initial upward velocity of 16 feet per second. How long will it take the tennis ball to reach the ground?

Write the number in decimal form. \(1.25 \times 10^{6}\)

Factor \(9 x^{2}-6 x-35.\) A. \((9 x-5)(x+7)\) B. \((3 x+5)(3 x-7)\) C. \((9 x+5)(x-7)\) D. \((3 x-5)(3 x+7)\)

Simplify the expression. $$ -3(x+1)-2 $$

Solve the equation by factoring. Use a graphing calculator to check your solution if you wish. $$ 50 x^{2}+60 x+18=0 $$

Find the product. $$ (7 x-11)^{2} $$

Use the vertical motion models, where h is the height (in feet), v is the initial upward velocity (in feet per second), s is the initial height (in feet), and t is the time (in seconds) the object spends aloft. Vertical motion model for Earth: \(h=-16 t^{2}+v t+s\) Vertical motion model for the moon: \(h=-\frac{16}{6} t^{2}+v t+s\) Note: the two equations are different because the acceleration due to gravity on the moon’s surface is about one-sixth that of Earth. On the moon, you toss a tennis ball from a height of 96 feet with an initial upward velocity of 16 feet per second. How long will it take the tennis ball to reach the surface of the moon??

Find the product \((2 x+3)(2 x-3)\) $$A. 2 x^{2}-6 x-9$$ $$B.4 x^{2}-9$$ $$C.2 x^{2}-9$$ $$D.4 x^{2}+12 x+9$$

Write the number in decimal form. \(3.71 \times 10^{-3}\)

Solve \(2 x^{2}+5 x+3=0.\) F. \(-1\) and \(-\frac{3}{2}\) G. \(-\frac{2}{3}\) and \(\frac{5}{3}\) H. \(\frac{3}{2}\) and \(-\frac{3}{2}\) J. 1 and \(\frac{3}{2}\)

Simplify the expression. $$ (2 x-1)(2)+x $$

Find the product. $$ (5-w)(12+3 w) $$

Find the product of \((3 x+5)^{2}\) $$F. 3 x^{2}+15 x+5$$ $$G. 9 x^{2}+25$$ $$H.3 x^{2}+25$$ $$J. 9 x^{2}+30 x+25$$

Write the number in decimal form. \(9.96 \times 10^{6}\)

Use linear combinations to solve the linear system. Then check your solution. $$ \begin{aligned} &4 x+5 y=7\\\ &6 x-2 y=-18 \end{aligned} $$

Simplify the expression. $$ 11 x+3(8-x) $$

The safe working load \(S\) (in tons) for a wire rope is a function of \(D,\) the diameter of the rope (in inches). Safe working load model for wire rope: \(4 \cdot D^{2}=S\) What diameter of wire rope do you need to lift a 9 -ton load and have a safe working load?

Find the product. $$ (3 a-2)(4 a+6) $$

The length \(\ell\) of a box is 3 inches less than the height \(h .\) The width \(w\) is 9 inches less than the height. The box has a volume of 324 cubic inches. Write a model that you can solve to find the length, height, and width of the box.

Simplify the expression. Use only positive exponents. $$\left(\frac{6}{x}\right)^{2}$$

Use the following information about videocassette sales from 1987 to 1996, where t is the number of years since 1987. The number of blank videocassettes B sold annually in the United States can be modeled by B 15t 281, where B is measured in millions. The wholesale price P for a videocassette can be modeled by P 0.21t 3.52, where P is measured in dollars. What conclusions can you make from your model about the revenue over time?

Write the number in decimal form. \(7.22 \times 10^{-4}\)

Use linear combinations to solve the linear system. Then check your solution. $$ \begin{aligned} &6 x-5 y=3\\\ &-12 x+8 y=5 \end{aligned} $$

Simplify the expression. $$ (5 x-1)(-3)+6 $$

The safe working load \(S\) (in tons) for a wire rope is a function of \(D,\) the diameter of the rope (in inches). Safe working load model for wire rope: \(4 \cdot D^{2}=S\) When determining the safe working load \(S\) of a rope that is old or worn, decrease \(S\) by \(50 \% .\) Write a model for \(S\) when using an old wire rope. What diameter of old wire rope do you need to safely lift a 9 -ton load?

Find the product. $$ (5 t-3)(4 t-10) $$

Simplify the expression. Use only positive exponents. $$\frac{x^{3}}{x^{2}}$$