Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for College Algebra (MindTap Course List)
98ESolve each formula for the indicated variable. x2a2y2b2=1;a100E101E102EUse the discriminant to determine the number and type of roots. Do not solve the equation. x2+6x+9=0.104EUse the discriminant to determine the number and type of roots. Do not solve the equation. 3x22x+5=0.106E107E108E109E110E111E112E113E114E115E116EChange each rational equation to quadratic form and solve it by the most efficient method. 5x=4x26118E119E120EChange each rational equation to quadratic form and solve it by the most efficient method. 1x+3x+2=2.122E123E124E125E126E127E128EChange each rational equation to quadratic form and solve it by the most efficient method. x+36x=0130E131E132E133E134E135E136E137E138E139E140E141E142ESelf Check The length of a rectangle exceeds its width by 10 feet. If its area is 375 square feet, find its dimensions.2SC3SC4SC5SC6SC1E2EPractice Solve each problem. Geometric problem A rectangle is 4 feet longer than it is wide. If its area is 32 square feet, find its dimensions.Practice Solve each problem. Geometric problem A rectangle is 5 times as long as it is wide. If the area is 125 square feet, find its perimeter.Practice Solve each problem. Dallas Cowboys video screen The Dallas Cowboys stadium has the worlds largest video screen. The rectangular screens length is 88 feet more than its width. If the video screen has an area of 11,520 square feet, find the dimensions of the screen.Practice Solve each problem. IMAX screen A large movie screen is in the Panasonic IMAX theater at Darling Harbor, Sydney, Australia. The rectangular screen has an area of 11,349 square feet. Find the dimensions of the screen if it is 20 feet longer than it is wide.Practice Solve each problem. Geometric problem The side of a square is 4 centimeters shorter than the side of a second square. If the sum of their areas is 106 square centimeters, find the length of one side of the larger square.Practice Solve each problem. Geometric problem If two opposite sides of a square are increased by 10 meters and the other sides are decreased by 8 meters, the area of the rectangle that is formed is 63 square meters. Find the area of the original square.Practice Solve each problem. Geometric problem Find the dimensions of a rectangle whose area is 180 cm2 and whose perimeter is 54 cm.Practice Solve each problem. Flags In 1912, an order by President Taft fixed the width and length of the U.S. flag in the ratio of 1 to 1.9. If 100 square feet of cloth are to be used to make a U.S. flag, estimate its dimensions to the nearest 14 foot.Practice Solve each problem. Metal fabrication A piece of tin, 12 inches on a side, is to have four equal squares cut from its corners, as in the illustration. If the edges are then to be folded up to make a box with a floor area of 64 square inches, find the depth of the box.Practice Solve each problem. Making gutters A piece of sheet metal, 18 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 36 square inches, find the depth of the gutter.Practice Solve each problem. Geometric problem The base of a triangle is one-third as long as its height. If the area of the triangle is 24 square meters, how long is its base?Practice Solve each problem. Geometric problem The base of a triangle is one-half as long as its height. If the area of the triangle is 100 square yards, find its height.Practice Solve each problem. Right triangle If one leg of a right triangle is 14 meters shorter than the other leg, and the hypotenuse is 26 meters, find the length of the two legs.Practice Solve each problem. Right triangle If one leg of a right triangle is five times the other leg, and the hypotenuse is 1026 centimeters, find the length of the two legs.Practice Solve each problem. Manufacturing A manufacturer of television sets for a news studio received an order for sets with a 46-inch screen measured along the diagonal. If the televisions are 1712 inches wider than they are high, find the dimensions of the screen to the nearest tenth of an inch.Practice Solve each problem. Finding dimensions An oriental rug is 2 feet longer than it is wide. If the diagonal of the rug is 12 feet, to the nearest tenth of a foot, find its dimensions.Practice Solve each problem. Cycling rates A cyclist rides from DeKalb to Rock-ford, a distance of 40 miles. His return trip takes 2 hours longer, because his speed decreases by 10 mph. How fast does he ride each way?Practice Solve each problem. Travel times Jake drives a tractor from one town to another, a distance of 120 kilometers. He drives 10 kilometers per hour faster on the return trip, cutting 1 hour off the time. How fast does he drive each way?21EPractice Solve each problem. Uniform motion problem By increasing her usual speed by 25 kilometers per hour, a bus driver decreases the time on a 25-kilometer trip by 10 minutes. Find the usual speed.Practice Solve each problem. Ballistics The height of a projectile fired upward with an initial velocity of 400 feet per second is given by the formula h=16t2+400t, where h is the height in feet and t is the time in seconds. Find the time required for the projectile to return to earth.Practice Solve each problem. Ballistics The height of an object tossed upward with an initial velocity of 104 feet per second is given by the formula h=16t2+104t, where h is the height in feet and t is the time in seconds. Find the time required for the object to return to its point of departure.Practice Solve each problem. Falling coins An object will fall s feet in t seconds, where s=16t2. How long will it take for a penny to hit the ground if it is dropped from the top of the Sears Tower in Chicago? Hint: The tower is 1454 feet tall.Practice Solve each problem. Movie stunts According to the Guinness Book of World Records, 1998, stuntman Dan Koko fell a distance of 312 feet into an airbag after jumping from the Vegas World Hotel and Casino. The distance d in feet traveled by a free-falling object in t seconds is given by the formula d=16t2. To the nearest tenth of a second, how long did the fall last?Practice Solve each problem. Accidents The height h in feet of an object that is dropped from a height of s feet is given by the formula h=s16t2, where t is the time the object has been falling. A 5-foot-tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from 4 stories up. How long does she have to get out of the way? Round to the nearest tenth. A story is 12 feet.Practice Solve each problem. Ballistics The height of an object thrown upward with an initial velocity of 32 feet per second is given by the formula h=16t2+32t, where t is the time in seconds. How long will it take the object to reach a height of 16 feet?29E30EPractice Solve each problem. Concert receipts Tickets for the annual symphony orchestra pops concert cost 15, and the average attendance at the concerts has been 1200 persons. Management projects that for each 50 decrease in ticket price, 40 more patrons will attend. How many people attended the concert if the receipts were 17,280?Practice Solve each problem. Projecting demand The Vilas County News earns a profit of 20 per year for each of its 3000 subscribers. Management projects that the profit per subscriber would increase by 1 for each additional subscriber over the current 3000. How many subscribers are needed to bring a total profit of 120,000?33EPractice Solve each problem. Investment problem Scott and Laura have both invested some money. Scott invested 3000 more than Laura and at a 2 higher interest rate. If Scott received 800 annual interest and Laura received 400, how much did Scott invest?Practice Solve each problem. Buying microwave ovens Some mathematics professors would like to purchase a 150 microwave oven for the department workroom. If four of the professors dont contribute, everyones share will increase by 10. How many professors are in the department?36E37E38EPractice Solve each problem. Mowing lawns Kristy can mow a lawn in 1 hour less time than her brother Steven. Together they can finish the job in 5 hours. How long would it take Kristy if she worked alone?Practice Solve each problem. Cleaning the garage Working together, Sarah and Heidi can clean the garage in 2 hours. If they work alone, it takes Heidi 3 hours longer than it takes Sarah. How long would it take Heidi to clean the garage alone?41E42EPractice Solve each problem. Architecture A golden rectangle is one of the most visually appealing of all geometric forms. The front of the Parthenon, built in Athens in the 5th century B.C. and shown in the illustration, is a golden rectangle. In a golden rectangle, the length l and the height h of the rectangle must satisfy the following equation. If a rectangular billboard is to have a height of 15 feet, how long should it be if it is to form a golden rectangle? Round to the nearest tenth of a foot. lh=hlh44E45E46E47EDiscovery and Writing Describe why it is important to check your solutions to an application problem.49EDiscovery and Writing Is it possible for a rectangle to have a width that is 3 units shorter than its diagonal and a length that is 4 units longer than its diagonal?Self Check Solve by factoring: 2x3+3x22x=0.2SC3SC4SC5SC6SC7SC8SC1E2E3E4EPractice Use factoring to solve each equation. x3+9x2+20x=06EPractice Use factoring to solve each equation. 6a35a24a=0Practice Use factoring to solve each equation. 8b310b2+3b=0Practice Use factoring to solve each equation. y426y2+25=0Practice Use factoring to solve each equation. y413y2+36=0Practice Use factoring to solve each equation. 2y446y2=180Practice Use factoring to solve each equation. 2x4102x2=196Practice Use factoring to solve each equation. x4=8x2+9Practice Use factoring to solve each equation. x412x2=64Practice Use factoring to solve each equation. 4y4+7y236=016ESolve each equation by factoring or by making an appropriate substitution. x437x2+36=018ESolve each equation by factoring or by making an appropriate substitution. 2m2/3+3m1/32=0Solve each equation by factoring or by making an appropriate substitution. 6t2/5+11t1/5+3=0Solve each equation by factoring or by making an appropriate substitution. x13x1/2+12=022ESolve each equation by factoring or by making an appropriate substitution. 6p+p1/2=124ESolve each equation by factoring or by making an appropriate substitution. 2t1/3+3t1/62=026ESolve each equation by factoring or by making an appropriate substitution. x210x1+16=028ESolve each equation by factoring or by making an appropriate substitution. z3/2z1/2=030E31EFind all real solutions of each equation. a35=0Find all real solutions of each equation. 3x+1=634E35E36EFind all real solutions of each equation. 2x2+3=16x338E39E40EFind all real solutions of each equation. x+37=x542E43E44EFind all real solutions of each equation. x7x12=046E47E48EFind all real solutions of each equation. x21x2=2250E51E52EFind all real solutions of each equation. x+3=2x+8154E55E56EFind all real solutions of each equation. 2b+3b+1=b258E59E60EFind all real solutions of each equation. 7x+13=462E63EFind all real solutions of each equation. x373+1=xFind all real solutions of each equation. 8x3+613=2x+166E67E68EFind all real solutions of each equation. 2x115=14570E71EApplications Horizon distance The higher a lookout tower, the farther an observer can see. See the illustration. The distance d called the horizon distance, measured in miles is related to the height h of the observer measured in feet by the following formula. d=1.5h How tall must a tower be for the observer to see 30 miles?Applications Carpentry During construction, carpenters often brace walls, as shown in the illustration. The appropriate length of the brace is given by the following formula. l=f2+h2 If a carpenter nails a 10-foot brace to the wall 6 feet above the floor, how far from the base of the wall should he nail the brace to the floor?74E75E76E77EDiscovery and Writing Describe what it means for an equation to be quadratic in form.79E80E81E82E83E84E85E86E87E88E89E90ESelf Check Write an inequality symbol to make the true statement: a. 2512 b. 55 c. 12202SC3SCSelf Check If the empty truck and driver in Example 4 weigh 3800 pounds, how many bushels can the truck legally carry?5SC6SC7SC8SC9SC10SC11SC1E2E3E4E5E6E7E8E9EGetting Ready You should be able to complete these vocabulary and concept statements before you proceed to the practice exercises. Fill in the blanks. ax2+bxc0a0 and 3x26x0 are examples of ____ inequalities.11E12EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 3x+2514EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 3x+2516EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 5x+3218EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 5x+3220EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 2(x3)2(x3)22EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 35x+4>224EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x+34<2x4326EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 6(x4)53(x+2)428EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 59(a+3)a43(a3)130EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 23a34a<35(a+23)+1332EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 4<2x81034EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 9x42>2Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 5<x26<6Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 04x35Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 05x21039EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 21x2<10Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 3x>2x>xPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 3x<2x<x43EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x>2x>3xPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 2x+1<3x2<12Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 2x<3x+5<1847EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x>2x+3>4x7Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 3+x>7x2>5x10Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 2x<3x+1<10x51EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x2x+13x+1Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x2+7x+12<0Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x213x+120Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x25x+60Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 6x2+5x6>0Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x2+5x+6<0Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x2+9x+200Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 59. 6x2+5x+1060EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 6x25x<1Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 9x2+24x>16Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 2x23xPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 9x224x16Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x230Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x270Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x211<0Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x220>0Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x+3x2<0Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x+3x2>0Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x2+xx21>0Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x24x29<0Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. x2+5x+6x2+x6074EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 6x2x1x2+4x+4>076EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 3x>278EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 6x<480EPractice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry about drawing your graphs exactly to scale. 3x2582E83E84EGolfing lessons Macy decides to take golfing lessons. If her new set of golf clubs cost 250 and private lessons are 60 per hour lesson, what is the maximum number of lessons she can take if the total spent for lessons and purchasing clubs is at most 970?Surfing lessons Dylan and Dusty plan to take weekly surfing lessons together. If the 2-hour lessons are 40 per person and they plan to spend 200 each on new surfboards, what is the maximum number of lessons the two can take if the total amount spent for lessons and surfboards is at most 960?Applications Solve each problem. Long distance A long-distance telephone call costs 40c for the first three minutes and 10c for each additional minute. At most how many minutes can a person talk and not exceed 2?88EApplications Solve each problem. Musical items Andy can spend up to 275 on a guitar and some music books. If he can buy a guitar for 150 and music books for 9.75, what is the greatest number of music books that he can buy?Applications Solve each problem. Buying DVDs Audrey wants to spend less than 600 for a DVD recorder and some DVDs. If the recorder of her choice costs 425 and DVDs cost 7.50 each, how many DVDs can she buy?