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mathematics
college algebra
College Algebra 12th edition Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels - Solutions
Find each product or quotient. Simplify the answers.√–17 · √–17
Solve each inequality. Give the answer using interval notation.|3x + 7| ≤ 0
Solve each equation.0.04(x - 12) + 0.06 x = 1.52
Solve each problem.Acid Mixture A student needs 10% hydrochloric acid for a chemistry experiment. How much 5% acid should she mix with 60 mL of 20% acid to get a 10% solution? mL of mL of Strength Solution Pure Acid 5% 60 20% x + 60 10%
Solve each inequality. Give the solution set in interval notation.|2x + 5| ≥ 3
Find each product or quotient. Simplify the answers.√–13 · √–13
Solve each equation.0.08 x + 0.06(x + 12) = 7.72
Solve each inequality. Give the answer using interval notation.|2x + 1| - 11 ≥ 0
Solve each problem.Acid Mixture How many gallons of a 5% acid solution must be mixed with 5 gal of a 10% solution to obtain a 7% solution? Gallons of Gallons of Strength Solution Pure Acid 5% 10% 5 x + 5 7%
Solve each inequality. Give the solution set in interval notation.|3x - 4| < 2
Write each number as the product of a real number and i.–√–80
Solve each equation. 2 3 Ex+ 0.25x = x + 2
Solve each inequality. Give the answer using interval notation.|2x - 5| < 9
Solve each problem.Wind Speed Joe traveled against the wind in a small plane for 3 hr. The return trip with the wind took 2.8 hr. Find the speed of the wind to the nearest tenth if the speed of the plane in still air is 180 mph.
Solve each inequality. Give the solution set in interval notation.|2x + 5| < 3
Write each number as the product of a real number and i.–√–18
Solve each equation. 0.5х + —х 3D х + 10 3
Solve each inequality. Give the answer using interval notation. х+1 х — 3
Solve each problem.Boat Speed Callie took 20 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 15 min. If the current in that part of the river is 5 km per hr, what was her boat speed?
Determine the solution set of each equation by inspection.(a) -|x| = |x| (b) |-x| = |x| (c) |x2| = |x| (d) -|x| = 9
Write each number as the product of a real number and i.√-500
Solve each equation.-8(3x + 4) + 6x = 4(x - 8) + 4x
Solve each inequality. Give the answer using interval notation.2x2 - x ≥ 3
Solve each problem.Track Event Speeds On August 16, 2009, at the World Track and Field Championship in Berlin, Usain Bolt set a new world record in the 100-m dash with a time of 9.58 sec. Refer to Exercise 25 and answer the questions using Bolt’s 2009 time.Exercise 25 Track Event Speeds At
Solve each problem.Track Event Speeds At the 2008 Summer Olympics in Beijing, China, Usain Bolt (Jamaica) set a new Olympic and world record in the 100-m dash with a time of 9.69 sec. If this pace could be maintained for an entire 26-mi marathon, what would his time be? How would this time compare
Solve each equation.The equation |7x + 3| = -5x cannot have a positive solution. Why?
Write each number as the product of a real number and i.√–288
Solve each equation.-4(2 x - 6) + 8 x = 5 x + 24 + x
Solve each inequality. Give the answer using interval notation.-2(x - 1) - 12 < 2(x + 1)
Solve each inequality. Give the answer using interval notation. -3
Solve each problem.Running Times If the run in Exercise 23 has a staggered start, and Janet starts first, with Mary starting 10 min later, how long will it be before Mary catches up with Janet?
Write each number as the product of a real number and i.√–15
Solve each inequality. Give the solution set in interval notation.- 2/3 x + 1/6 x + 2/3 (x + 1) ≤ 4/3
Solve each equation.0.01x + 3.1 = 2.03x - 2.96
A projectile is launched straight up from ground level with an initial velocity of 96 ft per sec. Its height in feet, s, after t seconds is given by the equations = -16t2 + 96t.(a) At what time(s) will it reach a height of 80 ft?(b) After how many seconds will it return to the ground?
Solve each problem.Running Times Mary and Janet are running in the Apple Hill Fun Run. Mary runs at 7 mph, Janet at 5 mph. If they start at the same time, how long will it be before they are 1.5 mi apart? Mary Start Janet -1.5 mi-
Solve each inequality. Give the solution set in interval notation.1/3 x + 2/5 x + 1/2 (x + 3) ≤ 1/10
Solve each problem.World Largest Ice Cream Cake The world’s largest ice cream cake, a rectangular cake made by a Dairy Queen in Toronto, Ontario, Canada, on May 10, 2011, had length 0.39 m greater than its width. Its perimeter was 17.02 m. What were the length and width of this 10-ton cake?
Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.)-6 - 2i
The formula for the surface area of a rectangular solid isS = 2HW + 2LW + 2LH,where S, H, W, and L represent surface area, height, width, and length, respectively. Solve this formula for W.
Find all intervals where each product will at least break even.The cost to produce x units of baseball caps is C = 100x + 6000, while the revenue is R = 500x.
Solve each equation.The equation |5x - 6| = 3x cannot have a negative solution. Why?
Write each number as the product of a real number and i.√–10
Solve each equation.0.2 x - 0.5 = 0.1x + 7
The percentage of college freshmen who smoke declined substantially from the year 2004 to the year 2014 and can be modeled by the linear equationy = -0.461x + 6.32,where x represents the number of years since 2004. Thus, x = 0 represents 2004, x = 1 represents 2005, and so on, (Source: Higher
Solve each problem.Speed of a Plane Two planes leave Los Angeles at the same time. One heads south to San Diego, while the other heads north to San Francisco. The San Diego plane flies 50 mph slower than the San Francisco plane. In 1/2 hr, the planes are 275 mi apart. What are their speeds?
Solve each inequality. Give the solution set in interval notation.4x + 7/-3 ≤ 2x + 5
Solve each problem.Distance between Cities Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities to the nearest ten miles if his total traveling time was 32
Solve each equation.|5x - 2| = |2 - 5x|
Write each number as the product of a real number and i.√–36
Solve each equation. (2x + 5) = x + 2 15
Solve each equation.|3 - 2x| = |5 - 2x|
Solve each inequality. Give the solution set in interval notation.2x - 5/8 ≤ 1 - x
An excursion boat travels upriver to a landing and then returns to its starting point. The trip upriver takes 1.2 hr, and the trip back takes 0.9 hr. If the average speed on the return trip is 5 mph faster than on the trip upriver, what is the boat’s speed upriver?
Solve each problem.Distance to Work David gets to work in 20 min when he drives his car. Riding his bike (by the same route) takes him 45 min. His average driving speed is 4.5 mph greater than his average speed on his bike. How far does he travel to work?
Solve each equation.|4x - 3x| = |2 - 3x|
Write each number as the product of a real number and i.√–25
Solve each equation. х+ 10 10 -(Зх — 2) %3D З 14
To make a special mix, the owner of a fruit and nut stand wants to combine cashews that sell for $7.00 per lb with walnuts that sell for $5.50 per lb to obtain 35 lb of a mixture that sells for $6.50 per lb. How many pounds of each type of nut should be used in the mixture?
Solve each equation.|x + 1| = |1 - 3x|
Solve each equation.4[2 x - (3 - x) + 5] = -6 x - 28
Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.)√–36
The perimeter of a rectangle is 620 m. The length is 20 m less than twice the width. What are the length and width?
Solve each problem.Distance to an Appointment Margaret drove to a business appointment at 50 mph. Her average speed on the return trip was 40 mph. The return trip took 1/4 hr longer because of heavy traffic. How far did she travel to the appointment? Morning 50 40 * x +! Afternoon 4
Solve each equation.2[x - (4 + 2 x) + 3] = 2 x + 2
Solve each equation.|2x - 3| = |5x + 4|
Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.)√-25
Ski resorts require large amounts of water in order to make snow. Snow mass Ski Area in Colorado plans to pump between 1120 and 1900 gal of water per minute at least 12 hr per day from Snow mass Creek between mid-October and late December.(a) Determine an equation that will calculate the minimum
Cylinder Dimensions A right circular cylinder has radius 6 in. and volume 144 π in.3. What is its height? (In the figure, h = height.) 6 in. h is in inches.
Solve each equation.|2x + 3/3x - 4| = 1
Solve each equation.5(x + 3) + 4 x - 3 = -(2 x - 4) + 2
Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.)√24
Simplify each power of i.(a) i42 (b) i -31 (c) 1/i19
Solve each problem.Storage Bin Dimensions A storage bin is in the shape of a rectangular box. Find the height of the box if its length is 18 ft, its width is 8 ft, and its surface area is 496 ft2. (In the figure, h = height. Assume that the given surface area includes that of the top lid of the
Solve each equation.|6x + 1/x - 1| = 3
Solve each equation. 4 3 + -x 2 5° 4 4.
Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.)π
Solve each equation.3x + 5 - 5(x + 1) = 6 x + 7
Solve each equation.|3/2x - 1| = 4
Perform each operation. Write answers in standard form.(a) (9 - 3i) - (4 + 5i) (b) (4 + 3i)(-5 + 3i)(c) (8 + 3i)2 (d) 3 + 19i/1 + 3i
Solve each problem.Perimeter of a Plot of Land The perimeter of a triangular plot of land is 2400 ft. The longest side is 200 ft less than twice the shortest. The middle side is 200 ft less than the longest side. Find the lengths of the three sides of the triangular plot.
Solve each equation. 5 5 4 2x + 3 3 6' – 3.
Solve each equation.|5/x - 3| = 10
Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.)5 + i
Solve each equation.4(-2 x + 1) = 6 - (2 x - 4)
Solve each equation.|2x + 1| = |5 - x|
Solve each problem.Dimensions of a Label The length of a rectangular label is 2.5 cm less than twice the width. The perimeter is 40.6 cm. Find the width. (Side lengths in the figure are in centimeters.) 2w – 2.5 HOME FINDERS 55 North Maple St. Philadelphia, PA 19106
Solve each equation.|x + 2/2| = 7
Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.)-7i
Solve each equation.6(3x - 1) = 8 - (10 x - 14)
Solve each problem.Dimensions of a Puzzle Piece A puzzle piece in the shape of a triangle has perimeter 30 cm. Two sides of the triangle are each twice as long as the shortest side. Find the length of the shortest side. (Side lengths in the figure are in centimeters.) 2x 2x
Solve each equation.|x - 4/2| = 5
Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.)13i
Solve each equation.9x + 11 = 7x + 1
Solve each equation.|4x + 3| = 7
Solve each problem.Perimeter of a Storage Shed Michael must build a rectangular storage shed. He wants the length to be 6 ft greater than the width, and the perimeter will be 44 ft. Find the length and the width of the shed.
Solve each equation.|7 - 3x| = 3
Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.)0
Solve each equation.5 x + 4 = 3x - 4
Solve each equation.x4 - 17x2 + 16 = 0
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