Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for College Algebra (MindTap Course List)
Practice Solve each problem. Delivering ads A university of Florida student earns 20 per day delivering advertising brochures door-to-door, plus 1.50 for each person he interviews. How many people did he interview on a day when he earned 56?Practice Solve each problem. Electronic LED billboard An electronic LED billboard in Times Square is 26 feet taller than it is wide. If its perimeter is 92 feet, find the dimensions of the billboard.16EPractice Solve each problem. Width of a picture frame The picture frame with the dimensions shown in the illustration was built with 14 feet of framing material. Find x its width.Practise Solve each problem. Fencing a garden If a gardener fences in the total rectangular area shown in the illustration instead of just a square area, he will need twice as much fencing to enclose the garden. How much fencing will he need?Practise Solve each problem. Swimming pool A rectangular swimming pool measures 12 meters by 6 meters and is surrounded by a 116 meter rectangular wooden fence. If the fence dorms a boarder around the pool of uniform width, determine the width of the border.Practise Solve each problem. Aquarium A rectangular glass aquarium has a length 15 yards, a width of 10 yards, and is placed inside a rectangular room for viewing at a museum. If the room has a perimeter of 146 yards and forms a walkway of uniform width that surrounds the aquarium, determine the width of the walkway.Practise Solve each problem. Wading pool dimensions The area of the triangular swimming pool shown in the illustration is doubled by adding a rectangular wading pool. Find the dimensions of the wading pool. Hint: The area of a triangle =12bh, and the area of a rectangle =lwPractise Solve each problem. House construction A builder wants to install a triangular window with the angles in the illustration. What angles will he have to cut to make the window fit? Hint: The sum of the angles in a triangle equals 1800.Practise Solve each problem. Length of a living room If a carpenter adds a porch with dimensions shown in the illustration to the living room, the living area will be increased by 50. Find the length of the living room.Practise Solve each problem. Depth of water in a trough The trough in the illustration has a cross-sectional area of 54 square inches. Find the depth, d, of the trough. Hint: Area of a trapezoid =12h(b1+b2).Practise Solve each problem. Investment Jeffrey invested 16,000 in two accounts paying 4 and 6 annual interest. If the total interest earned in one year was 815, how much did he invest at each rate?Practise Solve each problem. Investment An executive invests 22,000, some at 7 and the rest at 6 annual interest. If he receives an annual return of 1420, how much is invested at each rate?Practise Solve each problem. Financial planning After inheriting some money, a woman wants to invest enough to have an annual income of 5000. If she can invest 20000 at 9 annual interest, how much more will she have to invest at 7 to achieve her goal? See the table. Type Rate Amount Income 9 investment 0.09 20,000 .0920,000 7 investment 0.07 x .07 xPractise Solve each problem. Investment A woman invests 37,000, part at 8 and the rest at 912 annual interest. If the 912 investment provides 452.50 more income than the 8 investment, how much is invested at each rate?29E30EPractise Solve each problem. Ticket sales A full-price ticket for a college basketball game costs 2.50, and a student ticket costs 1.75. If 585 tickets were sold, and the total receipts were 1,217.25, how many tickets were student tickets?Practise Solve each problem. Ticket sales Of the 800 tickets sold to a movie, 480 were full-price tickets costing 7 each. If the gate receipts were 4960, what did a student ticket cost?Practise Solve each problem. Discount An iPad Air is on sale for 413.08. What was the original price of the iPad if it was discounted 8?34EPractise Solve each problem. Mark up A business owner increases the wholesale cost of a kayak by 70 and sells it for 365.50. Find the wholesale cost.Practise Solve each problem. Mark up A merchant increases the wholesale cost of a surfboard by 30% to determine the selling price. If the surfboard sells for 588.90, find the wholesale cost.Practise Solve each problem. Break-point analysis A machine to mill a brass plate has a setup cost of 600 and a unit cost of 3 for each plate manufactured. A bigger machine has a setup cost of 800 but a unit cost of 800 but a unit cost of only 2 for each plate manufactured. Find the break point.38EPractise Solve each problem. Computer sales A computer store has fixed costs of 8925 per month and a unit cost of 850 for every computer it sells. If the store can sell all the computers it can get for 1275 each, how many must be sold for the store to break even? Hint: The break-even point occurs when costs equal income.Practise Solve each problem. Restaurant management A restaurant has fixed costs of 137.50 per day and an average unit cost of 4.75 for each meal served. If a typical meal costs 6, how many customers must eat at the restaurant each day for the owner to break even?Solve each problem. Roofing houses Kyle estimates that it will take him 7 days to roof his house, A professional roofer estimates that it will take him 4 days to roof the same house. How long will it take if they work together?Solve each problem. Sealing asphalt One crew can seal a parking lot in 8 hours and another in 10 hours. How long will it take to seal the parking lot if the two crews work together?Solve each problem. Mowing lawns Julie can mow a lawn with a lawn tractor in 2 hours, and her husband can mow the same lawn with a push mower in 4 hours. How long will it take to mow the lawn if they work together?Solve each problem. Filling swimming pool A garden hose can fill a swimming pool in 3 days, and a larger hose can fill the pool in 2 days. How long will it take to fill the pool if both hoses are used?45E46ESolve each problem. Diluting solutions How much water should be added to 20 ounces of a 15 solution of alcohol to dilute it to a 10 solution?48E49ESolve each problem. Mixing milk If a bottle holding 3 liters of milk contains 312 butterfat, how much skimmed milk must be added to dilute the milk to 2 butterfat?Solve each problem. Preparing solutions A nurse has 1 liter of a solution that is 20 alcohol. How much pure alcohol must she add to bring the solution up to a 25 concentration?52EPractice Solve each problem. Cleaning swimming pools A swimming pool contains 15,000 gallons of water. How many gallons of chlorine must be added to "shock the pool" and bring the water to a 3100 solution?54ESolve each problem. Evaporation How many liters of water must evaporate to turn 12 liters of a 24 salt solution into a 36 solution?Solve each problem. Increasing concentrations A beaker contains 320 ml of a 5 saltwater solution. How much water should be boiled away to increase the concentration to 6?57E58ESolve each problem. Mixing solutions How many gallons of a 5 alcohol solution must be mixed with 90 gallons of 1 solution to obtain a 2 solution?Solve each problem. Preparing medicines A doctor prescribes an ointment that is 2 hydrocortisone. A pharmacist has 1 and 5 concentrations in stock. How much of each should the pharmacist use to make a 1-ounce tube?61E62ESolve each problem. Driving rates John drove to Daytona Beach, Florida, in 5 hours. When he returned, there was less traffic, and the trip took only 3 hours. If John averaged 26 mph faster on the return trip, how fast did he drive each way?Solve each problem. Distance problem Allison drove home at 60 mph, but her brother Austin, who left at the same time, could drive at only 48 mph. When Allison arrived, Austin still had 60 miles to go. How far did Allison drive?Solve each problem. Distance problem Two cars leave Hinds Community College traveling in opposite directions. One car travels at 60 mph and the other at 64 mph. In how many hours will they be 310 miles apart?Practice Solve each problem. Bank robbery Some bank robbers leave town, speeding at 70 mph. Ten minutes later, the police give chase, traveling at 78 mph. How long, after the robbery, will it take the police to overtake the robbers?Solve each problem. Jogging problem Two Michigan State University cross-country runners are 440 yards apart and are running toward each other, one at 8 mph and the other at 10 mph. In how many seconds will they meet?Solve each problem. Driving rates One morning, Justin drove 5 hours before stopping to eat lunch at Chick-fil-A. After lunch, he increased his speed by 10 mph. If he completed a 430-mile trip in 8 hours of driving time, how fast did he drive in the morning?69ESolve each problem. Wind velocity A plane can fly 340 mph in still air. If it can fly 200 miles downwind in the same amount of time it can fly 140 miles upwind, find the velocity of the wind.Use a calculator to help solve each problem. Machine tool design 712.51 cubic millimeters of material was removed by drilling the blind hole as shown in the illustration. Find the depth of the hole. Hint: The volume of a cylinder is given by V=r2h72E73E74E75ESelf Check Find x :a+x+3i=a-2x-1i.2SC3SC4SC5SC6SC7SC8SC9SC10SC1E2E3E4E5E6E7E8E9E10ESimplify the imaginary numbers. --12812ESimplify the imaginary numbers. -2-2414ESimplify the imaginary numbers. -50916ESimplify the imaginary numbers. -7-3818EFind the values of x and y. x+x+yi=3+8i20EFind the values of x and y. 3x-2yi=2+x+yi22EPerform all operations. Give all answers in a+bi form. 2-7i+3+i24EPerform all operations. Give all answers in a+bi form. 5-6i-7+4i26EPerform all operations. Give all answers in a+bi form. 14i+2+2--1628EPerform all operations. Give all answers in a+bi form. 3+-4-2+-930EPerform all operations. Give all answers in a+bi form. 4+7i+8-2i-5+4i32EPerform all operations. Give all answers in a+bi form. 3+-16-4--36+5--14434E35E36EPerform all operations. Give all answers in a+bi form. 7i4-8i38EPerform all operations. Give all answers in a+bi form. 2+3i3+5i40EPerform all operations. Give all answers in a+bi form. 2+3i242E43E44E45E46EPerform all operations. Give all answers in a+bi form. 1-i48E49E50EPerform all operations. Give all answers in a+bi form. 12+i52EPerform all operations. Give all answers in a+bi form. 2i7+i54EPerform all operations. Give all answers in a+bi form. 2+i3-i56EPerform all operations. Give all answers in a+bi form. 4-5i2+3i58EPerform all operations. Give all answers in a+bi form. 5--16-8+-460EPerform all operations. Give all answers in a+bi form. 2+i33+iPerform all operations. Give all answers in a+bi form. 3+i4-i263E64E65E66E67E68E69E70E71ESimplify each expression. i073E74ESimplify each expression. 1i3Simplify each expression. 3i577ESimplify each expression. -10i24Write without absolute value symbols. 3+4iWrite without absolute value symbols. 5+12iWrite without absolute value symbols. 2+3iWrite without absolute value symbols. 5-iWrite without absolute value symbols. -7+-49Write without absolute value symbols. -2--16Write without absolute value symbols. 12+12iWrite without absolute value symbols. 12-14iWrite without absolute value symbols. -6iWrite without absolute value symbols. 5iWrite without absolute value symbols. 21+iWrite without absolute value symbols. 33+iWrite without absolute value symbols. -3i2+iWrite without absolute value symbols. 5ii-2Write without absolute value symbols. i+2i-2Write without absolute value symbols. 2+i2-iFactor each expression over the set of complex numbers. x2+496E97E98EFactor each expression over the set of complex numbers. 2y2+8z2100E101E102E103E104E105EFractals Complex numbers are fundamental in the creation of the intricate geometric shape shown below, called a fractal. The process of creating this image is based on the following sequence of steps, which begins by picking any complex number, which we will call z. 1. Square z, and then add that result to z. 2. Square the result from step1, and then add it to z. 3. Square the result from step2, and then add it to z. If we begin with the complex number i, what is the result after performing steps 1, 2 and 3?107E108E109E110E111E112E113E114E115E116E117E118E119E120ESolve: 6x23=7x.2SC3SC4SC5SC6SC7SC8SC9SC10SC11SCFill in the blanks. A quadratic equation is an equation that can be written in the form__________, where a0.2E3E4E5E6ESolve each equation by factoring. x2x6=0Solve each equation by factoring. x2+8x+15=0Solve each equation by factoring. x2144=0Solve each equation by factoring. x2+4x=0Solve each equation by factoring. 2x2+x10=0Solve each equation by factoring. 3x2+4x4=0Solve each equation by factoring. 5x213x+6=0Solve each equation by factoring. 2x2+5x12=0Solve each equation by factoring. 15x2+16x=15Solve each equation by factoring. 6x225x=25Solve each equation by factoring. 12x2+9=24xSolve each equation by factoring. 24x2+6=24xUse the Square Root Property to solve each equation. x2=9Use the Square Root Property to solve each equation. x2=64Use the Square Root Property to solve each equation. x2=169Use the Square Root Property to solve each equation. x2=81Use the Square Root Property to solve each equation. y250=0Use the Square Root Property to solve each equation. x275=0Use the Square Root Property to solve each equation. y2+54=0Use the Square Root Property to solve each equation. x2+125=027E28EUse the Square Root Property to solve each equation. 2x2=9030E31E32E33E34E35EUse the Square Root Property to solve each equation. 3x2=1137EUse the Square Root Property to solve each equation. 5x2=1139EUse the Square Root Property to solve each equation. (y+2)298=041E42E43E44E45E46EComplete the square to make each a perfect-square trinomial. x2+6x48E49E50EComplete the square to make each a perfect-square trinomial. a2+5a52E53E54EComplete the square to make each a perfect-square trinomial. y2+34y56E57E58ESolve each equation by completing the square. x2+12x=860E61E62E63E64E65E66E67E68E69E70ESolve each equation by completing the square. 2x2=3x+172EUse the Quadratic Formula to solve each equation. 9x2=18x1474EUse the Quadratic Formula to solve each equation. 2x2=14x30i76EUse the Quadratic Formula to solve each equation. 3x2=5x1Use the Quadratic Formula to solve each equation. 2x2=5x+11Use the Quadratic Formula to solve each equation. x2+1=7x80EUse the Quadratic Formula to solve each equation. 3x2+6x=182EUse the Quadratic Formula to solve each equation. 7x2=2x+284EUse the Quadratic Formula to solve each equation. x2+2x+2=086EUse the Quadratic Formula to solve each equation. y2+4y+5=088EUse the Quadratic Formula to solve each equation. x22x=5Use the Quadratic Formula to solve each equation. z23z=8Use the Quadratic Formula to solve each equation. x223x=2992E93E94ESolve each formula for the indicated variable. h=64t16t2; t96ESolve each formula for the indicated variable. x2a2+y2b2=1; y