Chapter 11

Solve the equation. Check your solutions. \(\frac{1}{x}-\frac{2}{x^{2}}=\frac{1}{9}\)

Write in standard form the equation of the line that passes through the given point and has the given slope. (Lesson 5.4 ) $$ (10,6), m=-2 $$

Use the following information.Scientists are monitoring two distinct prairie dog populations,\(P_{1}\) and \(P_{2},\)modeled as follows. \(P_{1}=\frac{100 x^{2}}{x+1}\) and \(P_{2}=\frac{100 x^{2}}{x+3}\) where x is time in years. Find the ratio in simplest form of Population 1 to Population 2, that is \(\frac{P_{1}}{P_{2}}.\)

The air pressure at sea level is about 14.7 pounds per square inch. As the altitude increases, the air pressure decreases. For altitudes between 0 and \(60,000\) feet, a model that relates air pressure to altitude is $$P=\frac{2952 x-44 x^{2}}{200 x+5 x^{2}}, \text { where } P \text { is }$$ measured in pounds per square inch and xis measured in thousands of feet. Simplify this rational expression. Suppose you are in Breitling Orbiter 3 at 36,000feet. What is the pressure at that altitude? (GRAPH CANNOT COPY)

Evaluate. $$ 150 \% \text { of } 300 $$

Simplify \(\frac{24 y^{2}+24}{8 y-3}-\frac{73 y}{8 y-3}\). A. \(\frac{(8 y+3)(3 y+8)}{8 y-3}\) B. \(\frac{3 y-8}{(8 y-3)^{2}}\) C. \(\frac{3 y-8}{8 y-3}\) D. \(3 y-8\)

With your new lawn mower, you can mow a lawn in 4 hours. With an older mower, your friend can mow the same lawn in 5 hours. How long will it take you to mow the lawn, working together?

Use the following information.Scientists are monitoring two distinct prairie dog populations,\(P_{1}\) and \(P_{2},\)modeled as follows. \(P_{1}=\frac{100 x^{2}}{x+1}\) and \(P_{2}=\frac{100 x^{2}}{x+3}\) where x is time in years. Add another row to your table labeled \(\frac{P_{1}}{P_{2}}\) and evaluate for each value of x.

Write in standard form the equation of the line that passes through the given point and has the given slope. (Lesson 5.4 ) $$ (-7,-7), m=\frac{1}{2} $$

Evaluate. $$ 11 \% \text { of } 50 $$

Rewrite the expression with positive exponents. (Lesson 8.2) $$ x^{5} y^{-6} $$

The county’s new asphalt paving machine can surface one mile of highway in 10 hours. A much older machine can surface one mile in 18 hours. How long will it take them to surface 1 mile of highway, working together? How long will it take them to surface 20 miles?

Write in standard form the equation of the line that passes through the given point and has the given slope. (Lesson 5.4 ) $$ (1,8), m=\frac{3}{4} $$

Simplify the expression \(\frac{6+2 x}{x^{2}+5 x+6}\) $$(A)\frac{2}{x+2}$$ $$(B)\frac{2}{x+3}$$ $$(C)\frac{2}{x+5}$$ $$(D)\frac{2 x}{x^{2}+5 x}$$

Evaluate. $$ 99 \% \text { of } 10,000 $$

Rewrite the expression with positive exponents. (Lesson 8.2) $$ 8 x^{-1} y^{-3} $$

Arthur can wash a car in 30 minutes, Bonnie can wash a car in 40 minutes, and Claire can wash a car in 60 minutes. How will it take them to wash a car, working together?

Write in standard form the equation of the line that passes through the given point and has the given slope. (Lesson 5.4 ) $$ (0,5), m=3 $$

Simplify the expression \(\frac{3-x}{x^{2}-5 x+6}\) $$(A) \frac{1}{x+2}$$ $$(B) \frac{1}{x-2}$$ $$(C) \frac{-1}{x+2}$$ $$(D) \frac{-1}{x-2}$$

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

Rewrite the expression with positive exponents. (Lesson 8.2) $$ \frac{1}{2 x^{8} y^{-5}} $$

Write the expression in simplest form. $$ \frac{x^{2}+11 x+18}{x^{2}-25} \div \frac{14 x^{3}}{x^{2}-x-20} \cdot \frac{x}{x+4} \div \frac{2 x-1}{6 x} \cdot \frac{2 x^{2}+9 x-5}{x^{2}+3 x+2} $$

A grocer mixes 5 pounds of egg noodles costing \(\$ .80\) per pound with 2 pounds of spinach noodles costing \(\$ 1.50\) per pound. What is the cost per pound of the mixture?

Simplify. $$\left(-\frac{1}{2}\right)\left(\frac{2}{3}\right)$$

Write in standard form the equation of the line that passes through the given point and has the given slope. (Lesson 5.4 ) $$ (6,12), m=-12 $$

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

Rewrite the expression with positive exponents. (Lesson 8.2) $$ \frac{3}{10 t^{-3} r^{-1}} $$

Which of the following represents the expression \(\frac{x^{2}-3 x}{x^{2}-5 x+6} \cdot \frac{(x-2)^{2}}{2 x}\) in simplest form? $$A.)\frac{x(x-3)}{2}$$ $$B.)\frac{x^{2}-4 x+4}{x-2}$$ $$C.)\frac{x-2}{2}$$ $$D.)\frac{x}{2}$$

Find the LCD of \(\frac{15}{3 t^{6}}\) and \(\frac{9}{2 t^{4}}\) $$ (A) \frac{1}{6 t^{6}} $$ $$ (B) 6 t^{2} $$ $$ (C) 6 t^{6} $$ $$ (D) 6 t^{10} $$

A farm stand owner mixes apple juice and cranberry juice. How much should he charge if he mixes 8 liters of apple juice selling for \(\$ 0.45\) per liter with 10 liters of cranberry juice selling for \(\$ 1.08\) per liter?

Simplify. $$ (-15)\left(-\frac{5}{6}\right) $$

Write in standard form the equation of the line that passes through the given point and has the given slope. (Lesson 5.4 ) $$ (6,-1), m=0 $$

Decide whether the ordered pair is a solution of the inequality. $$ y \geq x^{2}-25 ;(5,5) $$

Rewrite the expression with positive exponents. (Lesson 8.2) $$ (-6 c)^{-4} $$

Which product represents \((2 x+2) \div \frac{x^{2}+x}{4} ?\) $$F.)\frac{2 x+2}{2 x+2} \cdot \frac{4}{x^{2}+x}$$ $$G.)\frac{2 x+2}{1} \cdot \frac{x^{2}+x}{4}$$ $$H.)\frac{1}{2 x+2} \cdot \frac{4}{x^{2}+x}$$ $$J.)\frac{2 x+2}{1} \cdot \frac{4}{x^{2}+x}$$

Find the missing numerator \(\frac{5 x+6}{8 x^{2}}=\frac{?}{48 x^{3}}\) $$(F) 6 x$$ $$(G 41 x$$ $$(H) 30 x^{2}+36 x \quad $$ $$(J) 11 x+6$$

You have 12 coins worth \(\$ 1.95 .\) If you only have dimes and quarters, how many of each do you have?

Simplify. $$ \frac{2}{7} \div \frac{14}{24} $$

Evaluate the expression. Check the results by squaring the answer. (Lesson 9.1) $$ \sqrt{64} $$

What is the difference of \(\frac{x}{x-1}\) and \(\frac{1}{2 x+1}\) in simplest form? $$ (A)\frac{x-1}{(x-1)(2 x+1)} $$ $$ (B)-\frac{x}{x-1} $$ $$ (C) \frac{2 x^{2}+1}{(x-1)(2 x+1)} $$ $$ (D)\frac{2 x^{2}-1}{(x-1)(2 x+1)} $$

Decide whether the ordered pair is a solution of the inequality. $$ y>x^{2}-2 x+5 ;(1,-7) $$

Rewrite the expression with positive exponents. (Lesson 8.2) $$ (-y)^{0} n $$

You have 35 hits in 140 times at bat. Your batting average is \(\frac{35}{140}=0.250 .\) How many consecutive hits must you get to increase your batting average to \(0.300 ?\) Use the following verbal model to answer the question. Desired Batting average \(=\frac{\text { Past hits }+\text { Future hits }}{\text { Past times at bat }+\text { Future times at bat }}\)

Simplify. $$ \frac{4}{9} \div(-36) $$

Evaluate the expression. Check the results by squaring the answer. (Lesson 9.1) $$ -\sqrt{9} $$

Completely factor the expression. $$ x^{2}+5 x-14 $$

Rewrite the expression with positive exponents. (Lesson 8.2) $$ \frac{d}{c^{-2}} $$

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

How many liters of water must be added to 50 liters of a 30% acid solution in order to produce a 20% acid solution? Copy and complete the chart to help you solve the problem. \(\begin{array}{|c|c|c|c|}\hline & {\text { Number of liters } \times \% \text { acid }=\text { Liters of acid }} & {} & {} \\ \hline \text { Original Solution } & {?} & {?} & {?} \\ \hline \text { Water Added } & {x} & {?} & {?} \\ \hline \text { New Solution } & {?} & {?} & {?} \\ \hline\end{array}\)

Simplify. $$ \left(-\frac{3}{4}\right)\left(\frac{3 y}{-5}\right) $$