Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1 and 2, find the missing numerator or denominator. \(\frac{2 x}{x-3}=\frac{?}{x^{2}+x-12}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 1 and 2, find the missing numerator or denominator. \(\frac{x-1}{x+1}=\frac{x^{2}-1}{?}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 36, find the LCD and rewrite the expression as a single fraction reduced to lowest terms. \(\frac{5}{12}+\frac{7}{18}-\frac{5}{6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 36, find the LCD and rewrite the expression as a single fraction reduced to lowest terms. \(\frac{3}{x-1}-\frac{1}{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 36, find the LCD and rewrite the expression as a single fraction reduced to lowest terms. \(\frac{x}{2 x+1}-\frac{2}{x-3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 36, find the LCD and rewrite the expression as a single fraction reduced to lowest terms. \(\frac{x+1}{x^{2}-5 x+6}-\frac{3 x+11}{x^{2}-x-6}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 710, use the quadratic formula to find the zeros of the quadratic polynomials. \(2 x^{2}-3 x-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 710, use the quadratic formula to find the zeros of the quadratic polynomials. \(2 x^{2}-5 x-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 710, use the quadratic formula to find the zeros of the quadratic polynomials. \(3 x^{2}+2 x-2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 710, use the quadratic formula to find the zeros of the quadratic polynomials. \(x^{2}-3 x-9\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, solve the equation algebraically. Support your answer numerically and identify any extraneous solutions. \(\frac{x-2}{3}+\frac{x+5}{3}=\frac{1}{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, solve the equation algebraically. Support your answer numerically and identify any extraneous solutions. \(x+2=\frac{15}{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, solve the equation algebraically. Support your answer numerically and identify any extraneous solutions. \(x+5=\frac{14}{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, solve the equation algebraically. Support your answer numerically and identify any extraneous solutions. \(\frac{1}{x}-\frac{2}{x-3}=4\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, solve the equation algebraically. Support your answer numerically and identify any extraneous solutions. \(x+\frac{4 x}{x-3}=\frac{12}{x-3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 16, solve the equation algebraically. Support your answer numerically and identify any extraneous solutions. \(\frac{3}{x-1}+\frac{2}{x}=8\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, solve the equation algebraically and graphically. Check for extraneous solutions. \(x+\frac{10}{x}=7\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, solve the equation algebraically and graphically. Check for extraneous solutions. \(x+2=\frac{15}{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, solve the equation algebraically and graphically. Check for extraneous solutions. \(x+\frac{12}{x}=7\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, solve the equation algebraically and graphically. Check for extraneous solutions. \(x+\frac{6}{x}=-7\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, solve the equation algebraically and graphically. Check for extraneous solutions. \(2-\frac{1}{x+1}=\frac{1}{x^{2}+x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 712, solve the equation algebraically and graphically. Check for extraneous solutions. \(2-\frac{3}{x+4}=\frac{12}{x^{2}+4 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, solve the equation algebraically. Check for extraneous solutions. Support your answer graphically. \(\frac{3 x}{x+5}+\frac{1}{x-2}=\frac{7}{x^{2}+3 x-10}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, solve the equation algebraically. Check for extraneous solutions. Support your answer graphically. \(\frac{4 x}{x+4}+\frac{3}{x-1}=\frac{15}{x^{2}+3 x-4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, solve the equation algebraically. Check for extraneous solutions. Support your answer graphically. \(\frac{x-3}{x}-\frac{3}{x+1}+\frac{3}{x^{2}+x}=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, solve the equation algebraically. Check for extraneous solutions. Support your answer graphically. \(\frac{x+2}{x}-\frac{4}{x-1}+\frac{2}{x^{2}-x}=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, solve the equation algebraically. Check for extraneous solutions. Support your answer graphically. \(\frac{3}{x+2}+\frac{6}{x^{2}+2 x}=\frac{3-x}{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1318, solve the equation algebraically. Check for extraneous solutions. Support your answer graphically. \(\frac{x+3}{x}-\frac{2}{x+3}=\frac{6}{x^{2}+3 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1922, two possible solutions to the equation \(f(x)=0\) are listed. Use the given graph of \(y=f(x)\) to decide which, if any, are extraneous. x = -5 or x = -2

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1922, two possible solutions to the equation \(f(x)=0\) are listed. Use the given graph of \(y=f(x)\) to decide which, if any, are extraneous. x = -2 or x = 3

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1922, two possible solutions to the equation \(f(x)=0\) are listed. Use the given graph of \(y=f(x)\) to decide which, if any, are extraneous. x = -2 or x = 2

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1922, two possible solutions to the equation \(f(x)=0\) are listed. Use the given graph of \(y=f(x)\) to decide which, if any, are extraneous. x = 0 or x = 3

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2330, solve the equation. \(\frac{2}{x-1}+x=5\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2330, solve the equation. \(\frac{x^{2}-6 x+5}{x^{2}-2}=3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2330, solve the equation. \(\frac{x^{2}-2 x+1}{x+5}=0\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2330, solve the equation. \(\frac{3 x}{x+2}+\frac{2}{x-1}=\frac{5}{x^{2}+x-2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2330, solve the equation. \(\frac{4 x}{x+4}+\frac{5}{x-1}=\frac{15}{x^{2}+3 x-4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2330, solve the equation. \(\frac{3 x}{x+1}+\frac{5}{x-2}=\frac{15}{x^{2}-x-2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2330, solve the equation. \(x^{2}+\frac{5}{x}=8\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2330, solve the equation. \(x^{2}-\frac{3}{x}=7\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Acid Mixture Suppose that x mL of pure acid are added to 125 mL of a 60% acid solution. How many mL of pure acid must be added to obtain a solution of 83% acid? a) Explain why the concentration \(C(x)\) of the new mixture is \(C(x)=\frac{x+0.6(125)}{x+125}\). (b) Suppose the viewing window in

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Acid Mixture Suppose that x mL of pure acid are added to 100 mL of a 35% acid solution. (a) Express the concentration \(C(x)\)\ of the new mixture as a function of x. (b) Use a graph to determine how much pure acid should be added to the 35% solution to produce a new solution that is 75% aci

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Breaking Even Mid Town Sports Apparel, Inc., has found that it needs to sell golf hats for $2.75 each in order to be competitive. It costs $2.12 to produce each hat, and it has weekly overhead costs of $3000. (a) Let x be the number of hats produced each week. Express the average cost (including

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Bear Population The number of bears at any time t (in years) in a federal game reserve is given by \(P(t)=\frac{500+250 t}{10+0.5 t}\). (a) Find the population of bears when the value of t is 10, 40, and 100. (b) Does the graph of the bear population have a horizontal asymptote? If so, what i

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Minimizing Perimeter Consider all rectangles with an area of \(182 \mathrm{ft}^{2}\). Let x be the length of one side of such a rectangle. (a) Express the perimeter P as a function of x. (b) Find the dimensions of the rectangle that has the least perimeter. What is the least perimeter?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Page Design Hendrix Publishing Co. wants to design a page that has a 0.75-in. left border, a 1.5-in. top border, and borders on the right and bottom of 1-in. They are to surround \(40 \text { in. }^{2}\) of print material. Let x be the width of the print material. (a) Express the a

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Industrial Design Drake Cannery will pack peaches in 0.5-L cylindrical cans. Let x be the radius of the can in cm. (a) Express the surface area S of the can as a function of x. (b) Find the radius and height of the can if the surface area is \(900 \mathrm{~cm}^{2}\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Designing a Swimming Pool Thompson Recreation, Inc., wants to build a rectangular swimming pool with the top of the pool having surface area \(1000 \mathrm{ft}^{2}\) . The pool is required to have a walk of uniform width 2 ft surrounding it. Let x be the length of one side of the pool.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Resistors The total electrical resistance R of two resistors connected in parallel with resistances \(R_{1}\) and \(R_{1}\) is given by \(\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}\). One resistor has a resistance of 2.3 ohms. Let x be the resistance of the second resistor. (a) Express the t

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Designing Rectangles Consider all rectangles with an area of \(200 \mathrm{~m}^{2}\). Let x be the length of one side of such a rectangle. (a) Express the perimeter P as a function of x. (b) Find the dimensions of a rectangle whose perimeter is 70 m.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Swimming Pool Drainage Drains A and B are used to empty a swimming pool. Drain A alone can empty the pool in 4.75 h. Let t be the time it takes for drain B alone to empty the pool. (a) Express as a function of t the part D of the drainage that can be done in 1 h with both drains open at the same

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Time-Rate Problem Josh rode his bike 17 mi from his home to Columbus, and then traveled 53 mi by car from Columbus to Dayton. Assume that the average rate of the car was 43 mph faster than the average rate of the bike. (a) Express the total time required to complete the 70-mi trip (bike and car)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Late Expectations Table 2.20 shows the average number of remaining years to be lived by U.S. residents surviving to particular ages. (a) Draw a scatter plot of these data together with the model \(E(a)=\frac{170}{a-58}\), where a is a persons age and E is the expected years remaining in t

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Number of Wineries The number of wineries for several years is given in Table 2.21. Let \(x=0\) represent 1970, \(x=1\) represent 1971, and so forth. A model for these data is given by \(y=3000-\frac{39,500}{x+9}\) (a) Graph the model together with a scatter plot of the data. (b) Use the

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False An extraneous solution of a rational equation is also a solution of the equation. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The equation \(1 /\left(x^{2}-4\right)=0\) has no solution. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, solve the problem without using a calculator. Multiple Choice Which of the following are the solutions of the equation \(x-\frac{3 x}{x+2}=\frac{6}{x+2}\)? (A) x = -2 or x = 3 (B) x = -1 or x = 3 (C) Only x = -2 (D) Only x = 3 (E) There are no solutions.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, solve the problem without using a calculator. Multiple Choice Which of the following are the solutions of the equation \(1-\frac{3}{x}=\frac{6}{x^{2}+2 x}\)?. (A) x = -2 or x = 4 (B) x = -3 or x = 0 (C) x = -3 or x = 4 (D) Only x = -3 (E) There are no soluti

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, solve the problem without using a calculator. Multiple Choice Which of the following are the solutions of the equation \(\frac{x}{x+2}+\frac{2}{x-5}=\frac{14}{x^{2}-3 x-10}\)? (A) x = -5 or x = 3 (B) x = -2 or x = 5 (C) Only x = 3 (D) Only x = -5 (E) There a

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, solve the problem without using a calculator. Multiple Choice Ten liters of a 20% acid solution are mixed with 30 liters of a 30% acid solution. Which of the following is the percent of acid in the final mixture? (A) 21% (B) 22.5% (C) 25% (D) 27.5% (E) 28%

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Revisit Example 4 Consider the following equation, which we solved in Example 4. \(\frac{x-3}{x}+\frac{3}{x+2}+\frac{6}{x^{2}+2 x}=0\) Let \(f(x)=\frac{x-3}{x}+\frac{3}{x+2}+\frac{6}{x^{2}+2 x}\). (a) Combine the fractions in \(f(x)\) but do not reduce to lowest terms. (b) What is the

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5255, solve for x. \(y=1+\frac{1}{1+x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5255, solve for x. \(y=1-\frac{1}{1-x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5255, solve for x. \(y=1+\frac{1}{1+\frac{1}{x}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5255, solve for x. \(y=1+\frac{1}{1+\frac{1}{1-x}}\)