Chapter 9

Solve the inequality and graph the solution. -3<-x<1

SIMPLIFYING EXPRESSIONS Simplify. Write your answer as a power or as an expression containing powers. $$(3 t)^{3}\left(-t^{4}\right)$$

Solve the inequality and graph the solution. |2 x+9| \leq 15

SIMPLIFYING EXPRESSIONS Simplify. Write your answer as a power or as an expression containing powers. $$\left(-3 a^{2} b^{2}\right)^{3}$$

Solve the inequality and graph the solution. |2 x+9| \leq 15

SCIENTIFIC NOTATION Rewrite the number in scientific notation. $$0.0012$$

Use the following information. Scientists simulate a gravity-free environment called microgravity in free- fall situations. A similar microgravity environment can be felt on free-fall rides at amusement parks or when stepping off a high diving platform. The distance \(d\) (in meters) that an object that is dropped falls in \(t\) seconds can be modeled by the equation \(d=\frac{1}{2} g\left(t^{2}\right),\) where \(g\) is the acceleration due to gravity (9.8 meters per second per second). The NASA Lewis Research Center has two microgravity facilities. One provides a 132 -meter drop into a hole and the other provides a 24 -meter drop inside a tower. How long will each free-fall period be?

Sketch the graph of the function. Label the vertex. y=6 x^{2}-4 x-1

SCIENTIFIC NOTATION Rewrite the number in scientific notation. $$987,000$$

Use the following information. Scientists simulate a gravity-free environment called microgravity in free- fall situations. A similar microgravity environment can be felt on free-fall rides at amusement parks or when stepping off a high diving platform. The distance \(d\) (in meters) that an object that is dropped falls in \(t\) seconds can be modeled by the equation \(d=\frac{1}{2} g\left(t^{2}\right),\) where \(g\) is the acceleration due to gravity (9.8 meters per second per second). In Japan a 490 -meter-deep mine shaft has been converted into a microgravity facility. This creates the longest period of free fall currently available on Earth. How long will a period of free-fall be?

Sketch the graph of the function. Label the vertex. y=-3 x^{2}-5 x+3

SCIENTIFIC NOTATION Rewrite the number in scientific notation. $$3,984,328$$

Use the following information. Scientists simulate a gravity-free environment called microgravity in free- fall situations. A similar microgravity environment can be felt on free-fall rides at amusement parks or when stepping off a high diving platform. The distance \(d\) (in meters) that an object that is dropped falls in \(t\) seconds can be modeled by the equation \(d=\frac{1}{2} g\left(t^{2}\right),\) where \(g\) is the acceleration due to gravity (9.8 meters per second per second). If you want to double the free-fall time, how much do you have to increase the height from which the object was dropped?

Sketch the graph of the function. Label the vertex. y=-2 x^{2}-3 x+2

SCIENTIFIC NOTATION Rewrite the number in scientific notation. $$1,229,000,000$$

Use the following information. Scientists simulate a gravity-free environment called microgravity in free- fall situations. A similar microgravity environment can be felt on free-fall rides at amusement parks or when stepping off a high diving platform. The distance \(d\) (in meters) that an object that is dropped falls in \(t\) seconds can be modeled by the equation \(d=\frac{1}{2} g\left(t^{2}\right),\) where \(g\) is the acceleration due to gravity (9.8 meters per second per second). How are these formulas similar? \(d=\frac{1}{2} g\left(t^{2}\right)\) when \(d\) is distance, \(g\) is gravity, and \(t\) is time \(h=-16 t^{2}+s\) when \(h\) is height, \(s\) is initial height, and \(t\) is time

Sketch the graph of the function. Label the vertex. y=\frac{1}{2} x^{2}+2 x-1

SCIENTIFIC NOTATION Rewrite the number in scientific notation. $$0.000432$$

Write the prime factorization. (Skills Review, p. \(T T T\) ) $$11$$

Sketch the graph of the function. Label the vertex. y=4 x^{2}-\frac{1}{4} x+4

SCIENTIFIC NOTATION Rewrite the number in scientific notation. $$0.00999$$

Write the prime factorization. (Skills Review, p. \(T T T\) ) $$24$$

Sketch the graph of the function. Label the vertex. y=-5 x^{2}-0.5 x+0.5

Write the prime factorization. (Skills Review, p. \(T T T\) ) $$72$$

Write the prime factorization. (Skills Review, p. \(T T T\) ) $$108$$

Use a graph to solve the linear system. Check your solution algebraically. (Review 7.1 ) $$\begin{aligned}&-3 x+4 y=-5\\\&4 x+2 y=-8\end{aligned}$$

Use a graph to solve the linear system. Check your solution algebraically. (Review 7.1 ) $$\begin{aligned}&4 x+5 y=20\\\&\frac{5}{4} x+y=4\end{aligned}$$

Use a graph to solve the linear system. Check your solution algebraically. (Review 7.1 ) $$\begin{aligned}&\frac{1}{2} x+3 y=18\\\&2 x+6 y=-12\end{aligned}$$

Use linear combinations to solve the system. (Review 7.3 ) $$\begin{aligned}&12 x-4 y=-32\\\&x+3 y=4\end{aligned}$$

Use linear combinations to solve the system. (Review 7.3 ) $$\begin{aligned}&10 x-3 y=17\\\&-7 x+y=9\end{aligned}$$

Use linear combinations to solve the system. (Review 7.3 ) $$\begin{aligned}&8 x-5 y=100\\\&2 x+\frac{1}{2} y=4\end{aligned}$$

Use linear combinations to solve the system. (Review 7.3 ) You are selling tickets at a high school basketball game. Student tickets cost 2 dollars and general admission tickets cost 3 dollars. You sell 2342 tickets and collect 5801 dollars. How many of each type of ticket did you sell? (Review 7.2)

You are buying a combination of irises and white tulips for a flower arrangement. The irises are 1 dollars each and the white tulips are 50 dollars You spend 20 dollars total to purchase an arrangement of 25 flowers. How many of each kind did you purchase? (Review 7.2)