Chapter 11

The variables \(x\) and \(y\) vary directly. Use the given values of the variables to write an equation that relates \(x\) and \(y .\) $$x=33, y=9$$

Solve the equation. $$3 x^{2}+11 x+10=0$$

In an inverse variation, the product \(x y\) is constant. If \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\) are solutions of \(x y=k,\) then \(x_{1} y_{1}=x_{2} y_{2} .\) Use this equation to find the missing value. Find \(x_{2}\) when \(x_{1}=9, y_{1}=-3,\) and \(y_{2}=12\).

You will write and simplify a general expression for the average speed traveled when making a round trip. Let \(d\) represent the one-way distance. Let \(x\) represent the speed while traveling there and let \(y\) represent the speed while traveling back. What do you notice about the variables in the final answer? If your distance is doubled what happens to the average speed?

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

You investigate how long it would take you and a friend to fold 1000 origami cranes. You take 2 minutes to fold 1 crane. Let \(x\) represent the number of minutes it might take a friend to fold 1 crane. Working alone, you would take 2000 minutes to fold 1000 cranes, so your work rate is \(\frac{1}{2000}\) of the job per minute. Find your work rate per hour.

Find all square roots of the number or write no square roots. Check the results by squaring each root. $$-20$$

The variables \(x\) and \(y\) vary directly. Use the given values of the variables to write an equation that relates \(x\) and \(y .\) $$x=-2, y=-1$$

Add or subtract. $$\left(4 t^{2}+5 t+2\right)-\left(t^{2}-3 t-8\right)$$

Suppose you are 14 years old and your brother is 4 years old. a. In \(t\) years, your age will be \(14+t\). What will your brother's age be? b. Write the ratio of your age in \(t\) years to your brother's age in \(t\) years. Then use long division to rewrite this ratio. c. Use the rewritten ratio to find the ratio of your ages now, in 5 years, in 10 years, in 25 years, in 50 years, and in 80 years. d. Use your answers to part (c). Is the ratio of your ages getting smaller or larger as time goes by? What value do the ratios approach? e. Writing Look at the original form of the ratio and the rewritten form of the ratio. Which form of the ratio makes it easier for you to recognize the trend that you described in part (d)? Explain your choice.

Simplify the fraction. $$\frac{36}{48}$$

Simplify the expression. (Review \(8.3 \text { for } 11.7)\) $$\frac{5}{10 x}$$

Sketch the graph of the function. $$y=-3 x^{2}-x+7$$

You investigate how long it would take you and a friend to fold 1000 origami cranes. You take 2 minutes to fold 1 crane. Let \(x\) represent the number of minutes it might take a friend to fold 1 crane. The expression \(\frac{60}{1000 x}\) is your friend's work rate per hour. Explain why.

Find all square roots of the number or write no square roots. Check the results by squaring each root. $$50$$

The variables \(x\) and \(y\) vary directly. Use the given values of the variables to write an equation that relates \(x\) and \(y .\) $$x=6.3, y=1.5$$

Add or subtract. $$\left(16 p^{3}-p^{2}+24\right)+\left(12 p^{2}-8 p-16\right)$$

Simplify the fraction. $$\frac{27}{108}$$

Simplify the expression. (Review \(8.3 \text { for } 11.7)\) $$\frac{4 m^{2}}{6 m}$$

You investigate how long it would take you and a friend to fold 1000 origami cranes. You take 2 minutes to fold 1 crane. Let \(x\) represent the number of minutes it might take a friend to fold 1 crane. . Write an expression for the combined work rate per hour of you and your friend (the part of the job completed in 1 hour if you both work together).

Find all square roots of the number or write no square roots. Check the results by squaring each root. $$\frac{9}{25}$$

Add or subtract. $$\left(a^{4}-12 a\right)+\left(4 a^{3}+11 a-1\right)$$

Simplify the fraction. $$\frac{96}{180}$$

Simplify the expression. (Review \(8.3 \text { for } 11.7)\) $$\frac{16 x^{4}}{32 x^{8}}$$

Find all square roots of the number or write no square roots. Check the results by squaring each root. $$0.04$$

The variables \(x\) and \(y\) vary directly. Use the given values of the variables to write an equation that relates \(x\) and \(y .\) $$x=9.8, y=3.6$$

Add or subtract. $$\left(-5 x^{2}+2 x-12\right)-\left(6-9 x-7 x^{2}\right)$$

Simplify the fraction. $$\frac{-15}{125}$$

Simplify the expression. (Review \(8.3 \text { for } 11.7)\) $$\frac{42 x^{4} y^{3}}{6 x^{3} y^{9}}$$

You will compare the types of graphs in 11.3 with those in this lesson. Graph \(f(x)=\frac{6}{x}\) and \(f(x)=\frac{6}{x-2}+1\) in the same coordinate plane.

Simplify the radical expression. $$\sqrt{18}$$

Decide whether the ordered pair is a solution of the inequality. $$y

After two years, an investment of \(\$ 1000\) compounded annually at an interest rate \(r\) will grow to the amount \(1000(1+r)^{2}\) in dollars. Write this product as a trinomial.

Find the probability. You roll a die. What is the probability that you will roll a four?

Write the equation in standard form. (Lesson 9.5 for 11.7 ) $$6 x^{2}=5 x-7$$

Simplify the radical expression. $$\sqrt{20}$$

Decide whether the ordered pair is a solution of the inequality. $$y \leq x^{2}-7 x+9 ;(-1,2)$$

Find the probability. You roll a die. What is the probability that you will roll an odd number?

Write the equation in standard form. (Lesson 9.5 for 11.7 ) $$9-6 x=2 x^{2}$$

Simplify the radical expression. $$\sqrt{80}$$

Decide whether the ordered pair is a solution of the inequality. $$y>2 x^{2}-7 x-15 ;(2,5)$$

Solve the equation. $$\frac{x}{5}=3$$

Simplify the fraction. $$\frac{y^{4} \cdot y^{7}}{y^{5}}$$

Write the equation in standard form. (Lesson 9.5 for 11.7 ) $$-4+3 y^{2}=y$$

What is the solution of the equation \(\frac{9}{x+5}=\frac{7}{x-5} ?\) (A) 5 (B) 8 (C) 20 (D) 40 (E) 80

Simplify the radical expression. $$\sqrt{162}$$

Decide whether the ordered pair is a solution of the inequality. $$y \geq x^{2}+6 x+12 ;(1,-4)$$

Solve the equation. $$\frac{a}{-3}=7$$

Simplify the fraction. $$\frac{5 x y}{5 x^{2}}$$

Make a scatter plot of the data. Then tell whether a linear, exponential, or quadratic model fits the data. (Review 9.81) $$(-1,16),(0,4),(1,-2),(2,-2),(3,4),(5,34)$$