Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
Debbie is in a boat in the ocean 48 mi from point A, the closest point along a straight shoreline. She needs to dock the boat at a marina x miles farther up the coast, and then drive along the coast to point B, 96 mi from point A. Her boat travels 20 mph, and she drives 60 mph. If the total trip took 4 hr, determine the distance x along the shoreline.Solve the inequality. Graph the solution set and write the solution set in set-builder notation and in interval notation. 5t624Solve the inequality. Graph the solution set and write the solution set-builder notation and in interval notation. m423m+4103m5Solve. 14y1or3+y5Solve. 0.36w0.54and12w3Solve. 163y42Solve the inequality and write the solution set in interval notation. 35x+214Solve the inequality and write the solution set in interval notation 1832y4Solve the inequality and write the solution set in interval notation where appropriate. a.x32b.x32c.1x+10d.x+10For a recent year, the monthly snowfall (in inches) for Chicago, Illinois, for November, December, January, and February was 2, 8.4, 11.2, and 7.9, respectively. How much snow would be necessary in March for Chicago to exceed its monthly average snowfall of 7.28 in. for these five months?The multiplication and division properties of inequality indicate that if both sides of an inequality are multiplied or divided by a negative real number, the direction of the sign must be reversed.If a compound inequality consists of two inequalities joined by the word “and,� the solution set is the of the solution sets of the individual inequalities.The compound inequality axandxb can be written as the three-part inequality .4PEIf k is a positive real number, then the inequality xk is equivalent to x.6PEIf k is a positive real number, then the solution set to the inequality xkis.If k is a positive real number, then the solution set to the inequality xkis.For Exercise 9-26, solve the inequality. Graph the solution set, and write the solution set builder notation and interval notation. (See Examples 1-2) 2x517For Exercise 9-26, solve the inequality. Graph the solution set, and write the solution set builder notation and interval notation. (See Examples 1-2) 8t+11711PE12PEFor Exercise 9-26, solve the inequality. Graph the solution set, and write the solution set builder notation and interval notation. (see Examples 1-2) 1.2+0.6a0.4a+0.514PE15PEFor Exercise 9-26, solve the inequality. Graph the solution set, and write the solution set builder notation and interval notation. (see Examples 1-2) 143m7+717PEFor Exercise 9-26, solve the inequality. Graph the solution set, and write the solution set builder notation and interval notation. (See Examples 1-2) y+343y+16112For Exercise 9-26, solve the inequality. Graph the solution set, and write the solution set builder notation and interval notation. (See Examples 1-2) 13x+456x312x+120PEFor Exercise 9-26, solve the inequality. Graph the solution set, and write the solution set builder notation and interval notation. (See Examples 1-2) 57x+2x6x29xFor Exercise 9-26, solve the inequality. Graph the solution set, and write the solution set builder notation and interval notation. (See Examples 1-2) 23x+14x2x+8523PEFor Exercise 9-26, solve the inequality. Graph the solution set, and write the solution set builder notation and interval notation. (See Examples 1-2) 8610x12132x+425PEFor Exercise 9-26, solve the inequality. Graph the solution set, and write the solution set builder notation and interval notation. (See Examples 1-2) 2x96x14xFor Exercise 27-34, solve the compound inequality. Graph the solution set, and write the solution set in interval notation. (See Examples 3-4) a.x4andx2b.x4orx2For Exercise 27-34, solve the compound inequality. Graph the solution set, and write the solution set in interval notation. (See Examples 3-4) a.y2andy5b.y2ory5For Exercise 27-34, solve the compound inequality. Graph the solution set, and write the solution set in interval notation. (see Examples 3-4) a.m+16or13m2b.m+16and13m2For Exercise 27-34, solve the compound inequality. Graph the solution set, and write the solution set in interval notation. (See Examples 3-4) a.n61or34n6b.n6and34n631PEFor Exercise 27-34, solve the compound inequality. Graph the solution set, and write the solution set in interval notation. (See Examples 3-4) a.45m8and0.850.34mb.45m8or0.850.34m33PE34PEWrite 2.8y15 as two separate inequalities joined by “and.�Write 12z2.4 as two separate inequalities joined by “and.�For Exercise 37-42, solve the compound inequality. Graph the solution set, and write the solution set in interval notation. (See Examples 5) 32x+19For Exercise 37-42, solve the compound inequality. Graph the solution set, and write the solution set in interval notation. (See Examples 5) 63x+90For Exercise 37-42, solve the compound inequality. Graph the solution set, and write the solution set in interval notation. (See Examples 5) 15x423For Exercise 37-42, solve the compound inequality. Graph the solution set, and write the solution set in interval notation. (See Examples 5) 24x135For Exercise 37-42, solve the compound inequality. Graph the solution set, and write the solution set in interval notation. (See Examples 5) 22x+13442PE43PEFor Exercise 43-46, solve the equation or inequality. Write the solution set to each inequality interval notation. a.y=8b.y8c.y845PEFor Exercise 43-46, solve the equation or inequality. Write the solution set to each inequality interval notation. a.b+14=1b.b+141c.b+141For Exercises 47-60, solve the inequality, and write the solution set in interval notation if possible. (See Examples 6-7) 34x216For Exercises 47-60, solve the inequality, and write the solution set in interval notation if possible. (See Examples 6-7) 27y+11749PE50PEFor Exercises 47-60, solve the inequality, and write the solution set in interval notation if possible. (See Examples 6-7) 4w5+62For Exercises 47-60, solve the inequality, and write the solution set in interval notation if possible. (See Examples 6-7) 2x+7+5153PEFor Exercises 47-60, solve the inequality, and write the solution set in interval notation if possible. (See Examples 6-7) 1127x+5455PE56PEFor Exercises 47-60, solve the inequality, and write the solution set in interval notation if possible. (See Examples 6-7) 105c4+2For Exercises 47-60, solve the inequality, and write the solution set in interval notation if possible. (See Examples 6-7) 152d3+6For Exercises 47-60, solve the inequality, and write the solution set in interval notation if possible. (See Examples 6-7) y+362For Exercises 47-60, solve the inequality, and write the solution set in interval notation if possible. (See Examples 6-7) m4214For Exercises 61-68, write the solution set. (See Example 8) a.x=9b.x9c.x962PE63PEFor Exercises 61-68, write the solution set. (See Example 8) a.15=2p3b.152p3c.152p365PEFor Exercises 61-68, write the solution set. (See Example 8) a.2w=0b.2w0c.2w0d.2w0e.2w0For Exercises 61-68, write the solution set. (See Example 8) a.k+4=0b.k+40c.k+40d.k+40e.k+40For Exercises 61-68, write the solution set. (See Example 8) a.c3=0b.c30c.c30d.c30e.c30Marilee wants to earn an “A� in a class and needs an overall average of at least 92. Her test grades are 88, 92, 100, and 80. The average of her quizzes is 90 and counts as one test grade. The final exam counts as 2.5 test grades. What scores on the final exam would result in Marilee's overall average of 92 or greater? (See Example 9)A 10-yr-old competes in gymnastics. For several competitions she received the following “All-Around� scores: 36, 36.9, 37.1, and 37.4. Her coach recommends that gymnasts whose “All-Around� scores average at least 37 move up to the next level. What “All-Around� scores in the next competition would result in the child being eligible to move up?Rita earns scores of 78, 82, 90, 80, and 75 on her five chapter tests for a certain class and a grade of 85 on the class project. The overall average for the course is computed as follows: the average of the five chapter tests makes up 60 of the course grade; the project accounts for 10 of the grade; and the final exam accounts for 30 . What scores can Rita earn on the final exam to earn a “B� in the course if the cut-off for a “B� is an overall score greater then or equal to 80, but less than 90? Assume that 100 is the biggest score that can be earned on the final exam and that only whole- number scores are given.Trent earns scores of 66, 84, and 72 on three chapter tests for a certain class. His homework grade is 60 and his grade for a class project is 85. The overall average for the course is computed as follows: the average of the three chapter tests makes up 50 of the course grade; homework accounts for 20 of the grade; the project accounts for 10 and the final exam accounts for 20. What scores can Trent earn on the final exam to pass the course if he needs a “C� or better? A “C� or better requires an overall score of 70 or better, and 100 is the highest score that can be earned on the final exam. Assume that only whole-number scores are given.A car travels 50 mph and passes a truck traveling 40 mph. How long will it take the car to be more than 16 mi ahead?A rectangular garden is to be constructed so that the width is 100 ft. What are the possible values for the length of the garden if at most 800 ft of fencing is to be used?For a certain bowling league, a beginning bowler computes her handicap by taking 90 of the difference between 220 and her average score in league play. Determine the average scores that would produce a handicap of 72 or less. Also assume that a negative handicap is not possible in this league.76PE77PENancy wants to vacation in Austin, Texas. Hotel A charges $179 per night with a 14% nightly room tax and free parking. Hotel B charges $169 per night with an18 nightly room tax plus a one-time $40 parking fee. After how many nights will Hotel B be less expensive?Absolute value inequalities are often used to represent measurement error. For example, suppose that a machine is calibrated to dispense 8 fl oz of orange juice with a measurement error of on more than 0.05 fl oz. If x represents the actual amount of orange juice poured into the bottle, then x is a solution to the inequality x80.05. For Exercises 79-82. a. Write an absolute value inequality to represent each statement. b. Solve the inequality. Write the solution set in interval notation. The variation between the measured value vand16 oz is less than 0.01 oz.Absolute value inequalities are often used to represent measurement error. For example, suppose that a machine is calibrated to dispense 8 fl oz of orange juice with a measurement error of on more than 0.05 fl oz. If x represents the actual amount of orange juice poured into the bottle, then x is a solution to the inequality x80.05. For Exercises 79-82. a. Write an absolute value inequality to represent each statement. b. Solve the inequality. Write the solution set in interval notation. The variation between the measured value tand60 min is less than 0.2 min.81PE82PEA refrigerator manufacturer recommends that temperature tinoF inside a refrigerator be 36.5oF, if the thermostat has a margin of error of no more than 1.5oF, a. Write an absolute value inequality that represents an interval in which to estimate t. b. Solve the inequality and interpret the answer.84PEThe results of a political poll indicate that the leading candidate will receive 51 of the votes with a margin of error of no more than 3 . Let x represent the true percentage of votes received by this candidate. a. Write an absolute value inequality that represents an interval in which to estimate x . b. Solve the inequality and interpret the answer.86PE87PEFor Exercises 87-92, determine the set of value for x for which the radical expression would produce a real number. For example, the expression x1 is a real number if xx2212;10 or equivalently. x1. a.x6b.6x89PEFor Exercises 87-92, determine the set of value for x for which the radical expression would produce a real number. For example, the expression x1 is a real number if xx2212;10 or equivalently. x1. a.x+7b.x+73For Exercises 87-92, determine the set of value for x for which the radical expression would produce a real number. For example, the expression x1 is a real number if xx2212;10 or equivalently. x1. a.2x9b.2x94For Exercises 87-92, determine the set of value for x for which the radical expression would produce a real number. For example, the expression x1 is a real number if xx2212;10 or equivalently. x1. a.3x7b.3x7493PEFor Exercises 93-96, answer true or false given that a0,b0,c0,andd0. abc95PE96PEHow is the process to solve a linear inequality different from the process to solve a linear equation?98PE99PEExplain why x2=4 is equivalent to the equation x=2.101PE102PEFor Exercises 101-106, solve the inequality and write the solution set in interval notation. 1x9For Exercises 101-106, solve the inequality and write the solution set in interval notation. 2y11For Exercises 101-106, solve the inequality and write the solution set in interval notation. 52x+17For Exercises 101-106, solve the inequality and write the solution set in interval notation. 73x513107PESolve the inequality for :xzn. (Do not rationalize the denominator.)For Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree2 • Compound inequality x2525x25+4=02PREFor Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree2 • Compound inequality 2y534=1For Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree2 • Compound inequality 93z7+1=45PREFor Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree2 • Compound inequality 48x3+80x23x5=07PRE8PRE9PREFor Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree2 • Compound inequality 2xx4+7=2x23x+52+x11PREFor Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree2 • Compound inequality 3x2+11=4For Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree2 • Compound inequality 16x5714PREFor Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree2 • Compound inequality 4x5=3x216PRE17PREFor Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree2 • Compound inequality y4y12=019PREFor Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree2 • Compound inequality 2z14+84For Exercise 1-2, write an inequality using an absolute value that represents the given condition. The distance between Y and L is less than (epsilon).For Exercise 1-2, write an inequality using an absolute value that represents the given condition. The distance between x and c is less than (delta).Simplify x+8x+8 a.forx8.b.forx8.4ACFor Exercise 5-10, a. Simplify the expression. b. Substitute 0 for h in the simplified expression. 2x+h2+3x+h2x2+3xh6ACFor Exercise 5-10, a. Simplify the expression. b. Substitute 0 for h in the simplified expression. 1x+h21x2h8ACFor Exercise 5-10, a. Simplify the expression. b. Substitute 0 for h in the simplified expression. x+h3x3hFor Exercise 5-10, a. Simplify the expression. b. Substitute 0 for h in the simplified expression. x+h4x4hFor exercise 11-12 a. Rationalize the numerator of the expression and simplify. b. Substitute 0 for h in the simplified expression. x+h+1x+1hFor exercise 11-12 a. Rationalize the numerator of the expression and simplify. b. Substitute 0 for h in the simplified expression. 2x+h2xh13ACFor exercise 13-22, factor completely and write the answer with no negative exponents. Do not rationalize the dominator. 76x1/616x5/615ACFor exercise 13-22, factor completely and write the answer with no negative exponents. Do not rationalize the dominator. 32x+3224x252+2x+3324x258x17AC18ACFor exercise 13-22, factor completely and write the answer with no negative exponents. Do not rationalize the dominator. x2+41/2+x12x2+41/22x20AC21ACFor exercise 13-22, factor completely and write the answer with no negative exponents. Do not rationalize the dominator. 63x11/3+6x133x12/3323AC24ACFor exercise 23-28, write the answer as a single term and simplify. It is not necessary to rationalize the denominator. x41/3+x3x42/326AC27ACFor exercise 23-28, write the answer as a single term and simplify. It is not necessary to rationalize the denominator. 133xx2+12/3x2+133x2xx2+12In Calculus you will see the symbol y . For Exercise 1-4, treat y as a variable and solve the equation for y . 2x25+2y9y=02EIC3EICIn Calculus you will see the symbol y . For Exercise 1-4, treat y as a variable and solve the equation for y . 3x+y2+3x+y2y3y2y=3x25EICFor Exercise 5-7, simplify the expression. Do not rationalize the denominator. 2x2x71/2x2122x71/222x71/227EICFor Exercise 8-10, a. Simplify the expression. Do not rationalize the denominator. b. Find the value of x for which the expression equals zero. c. Find the values of x for which the denominator is zero. 4x4x52x244x529EICFor Exercise 8-10, a. Simplify the expression. Do not rationalize the denominator. b. Find the value of x for which the expression equals zero. c. Find the values of x for which the denominator is zero. 4x2x1214x22x11EIC12EICA 6-ft man walks away from a lamppost. At the instant the man is 14 ft away from the lamppost, the shadow is 10 ft. Find the height of the lamppost.14EIC15EICFor Exercises 1-2, a. Find the exact distance between the points. b. Find the midpoint of the line segment whose endpoints are the given points. 1,8and4,2For Exercises 1-2, a. Find the exact distance between the points. b. Find the midpoint of the line segment whose endpoints are the given points. 3,6and33,46Determine if the given ordered pair is a solution to the equation 4x1+y=18. a.3,2b.5,24REFor Exercises 4-6, determine the x-andy-intercepts of the graph of the equation. x=y+73For Exercises 4-6, determine the x-andy-intercepts of the graph of the equation. x+429+y24=1Graph the equation by plotting points. y=x22xFind the length of the diagonal shown.9RE10RE11RE12RE13RE14RE15RE16REFor Exercises 17-18, determine the solution set to the equation. x+32+y52=0For Exercises 17-18, determine the solution set to the equation. x2+y2+6x4y+15=0The table list four Olympic athletes and the number of Olympic medals won by the athlete. a. Write a set of ordered pairs x,y that defines the relation. b. Write the domain of the relation. c. Write the range of the relation. d. Determine if the relation defines y as a function of x .For Exercises 20-23, determine if the relation defines y as a function of x .For Exercises 20-23, determine if the relation defines y as a function of x .22RE23REEvaluate fx=2x2+4x for the values of x given. a.f0b.f1c.f3d.fte.fx+425REA department store marks up the price of a power drill by 32 of the price from the manufacture. The price Pxin$ to a customer after a 6.5 sales tax is given by Px=1.065x+0.32x, where x is the cost of the drill from the manufacture, Evaluate P189 and interpret the meaning in the context of this problem.27RE28RE29REFor Exercises 29-30, determine the domain and range of the function.For Exercises 31-34, write the domain in interval notation. fx=x2x532RE33RE34RE35RE36RE37RE38RE39RE40RE41REFor Exercises 41-43, determine the slope of the line passing through the given points. 3,23and1,4343RE44RE45RE46RE47RE48RE49RE50RE51REThe function given by y=fx shows the value of $8000 invested at 6% interest compounded continuously, x years after the money was originally invested. a. Find the average amount earned per year between the 5th year and the 10th year. b. Find the average amount earned per year between the 20th year and the 25th year. c. Based on the answer from parts (a) and (b), does it appear that the rate at which annual income increases is increasing or decreasing time?53RE54RE55RE56RE57RE58RE59REFor Exercises 57-63, write an equation of the line having the given conditions. Write the answer in slope-intercept form if possible. Passes through 5,7 and the slope is undefined.61RE62RE63REA car has a 15-gal tank for gasoline and gets 30 mpg on a highway while driving 60 mph. Suppose that the driver starts a trip with a full tank of gas and travels 450 mi on the highway at an average speed of 60 mph. a. Write a linear model representing the amount of gas Gt left in the tank t hours into a trip. b. Evaluate G4.5 and interpret the meaning in the context of this problem.A dance studio has fixed monthly costs of $1500 that include rent, utilities, insurance, and advertising. The studio charges $60 for each private lesson, but has a variable cost for each lesson of $35 to pay the instructor. a. Write a linear cost function representing the cost to the studio Cx to hold x private lessons for a given month. b. Write a linear revenue function representing the revenue Rx for holding x private lessons for the month. c. Write a linear profit function representing the profit Px for holding x private lessons for the month. d. Determine the number of private lessons that must be held for the studio to make a profit. e. If 82 private lessons are held during a given month, how much money will the studio make or lose?66RE67RE68RE69RE70RE71RE72RE73RE74RE75RE76RE77RE78RE79RE80RE81RE82RE83REFor Exercises 79-84, use the graph of y=fx to graph the given function. y=12fx+2385RE86RE87RE88RE89RE90RE91RE92RE93RE94RE95RE96RE97RE98RE99REFor Exercises 100-101, use interval notation to write the interval(s) over which f is a. Increasing. b. Decreasing. c. Constant.For Exercises 100-101, use interval notation to write the interval(s) over which f is a. Increasing. b. Decreasing. c. Constant.102RE103RE104RE105RE106RE107RE108RE109RE110RE111RE112REFor Exercises 111-116, refer to the functions m,n,p,andq. Find the function and write the domain in interval notation. mx=4xnx=x24xpx=x2qx=1x5 npx114REFor Exercises 111-116, refer to the functions m,n,p,andq. Find the function and write the domain in interval notation. mx=4xnx=x24xpx=x2qx=1x5 qnxFor Exercises 111-116, refer to the functions m,n,p,andq. Find the function and write the domain in interval notation. mx=4xnx=x24xpx=x2qx=1x5 qpx117RE118RE119RE