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mathematics
college algebra
College Algebra 11th Edition Michael Sullivan, Michael Sullivan III - Solutions
In Problems 9–36, find the real solutions, if any, of each equation. |x² - 2x| = 3
In Problems 9–36, find the real solutions, if any, of each equation. |x² + x1 = 1
A nut store normally sells cashews for $9.00 per pound and almonds for $4.50 per pound. But at the end of the month the almonds had not sold well, so, in order to sell 60 pounds of almonds, the manager decided to mix the 60 pounds of almonds with some cashews and sell the mixture for $7.75 per
In Problems 9–36, find the real solutions, if any, of each equation. |x² + 3x - 2| = 2
A candy store sells boxes of candy containing caramels and cremes. Each box sells for $12.50 and holds 30 pieces of candy (all pieces are the same size). If the caramels cost $0.25 to produce and the cremes cost $0.45 to produce, how many of each should be in a box to yield a profit of $3?
In Problems 9–42, find the real solutions, if any, of each equation. √3x + 1 Vx - 1 = 2 -
A motorboat heads upstream on a river that has a current of 3 miles per hour. The trip upstream takes 5 hours, and the return trip takes 2.5 hours. What is the speed of the motorboat? (Assume that the boat maintains a constant speed relative to the water.)
In Problems 25–32, write each inequality using interval notation, and graph each inequality on the real number line. x < -4
In Problems 9–36, find the real solutions, if any, of each equation. 5x 3 3x - 5 = = 2
A motorboat maintained a constant speed of 15 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was 1.5 hours. Use this information to find the speed of the current.
In Problems 9–42, find the real solutions, if any, of each equation. V2x + 3√x + 1 = 1
In Problems 25–32, write each inequality using interval notation, and graph each inequality on the real number line. x > 1
Two cars enter the Florida Turnpike at Commercial Boulevard at 8:00 am, each heading for Wildwood. One car’s average speed is 10 miles per hour more than the other’s. The faster car arrives at Wildwood at 11:00 am, 1/2 hour before the other car. What was the average speed of each car? How far
In Problems 9–36, find the real solutions, if any, of each equation. 2x + 1 3x + 4 = 1
In Problems 9–42, find the real solutions, if any, of each equation. √3-2√x Vx
The speed of a moving walkway is typically about 2.5 feet per second. Walking on such a moving walkway, it takes Karen a total of 48 seconds to travel 50 feet with the movement of the walkway and then back again against the movement of the walkway. What is Karen’s normal walking speed?
In Problems 9–36, find the real solutions, if any, of each equation. |x² + 3x| = |x² - 2x|
In Problems 9–42, find the real solutions, if any, of each equation. V10+ 3√x = √x Vx
Toronto’s Pearson International Airport has a high-speed version of a moving walkway. If Liam walks while riding this moving walkway, he can travel 280 meters in 60 seconds less time than if he stands still on the moving walkway. If Liam walks at a normal rate of 1.5 meters per second, what is
In Problems 9–42, find the real solutions, if any, of each equation. (3x + 1)¹/2 = 4
In Problems 9–42, find the real solutions, if any, of each equation. (3x - 5)¹/2 = 2
A regulation doubles tennis court has an area of 2808 square feet. If it is 6 feet longer than twice its width, determine the dimensions of the court.
In Problems 9–36, find the real solutions, if any, of each equation. |x² − 2x| = |x² + 6x|
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2x| V 8
In Problems 33–40, write each interval as an inequality involving x, and graph each inequality on the real number line. [2, 5]
It takes a Xerox VersaLink C500 laser printer 9 minutes longer to complete a 1440-page print job by itself than it takes a Brother HL-L8350CDW to complete the same job by itself. Together the two printers can complete the job in 20 minutes. How long does it take each printer to complete the print
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. |3x| < 15
In Problems 9–42, find the real solutions, if any, of each equation. (5x – 2)1/3 = 2
In Problems 33–40, write each interval as an inequality involving x, and graph each inequality on the real number line.(1, 2)
Trent can deliver his newspapers in 30 minutes. It takes Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they worked together?
In Problems 33–40, write each interval as an inequality involving x, and graph each inequality on the real number line.(-4, 3]
Patrice, by himself, can paint four rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint four rooms?
In Problems 9–42, find the real solutions, if any, of each equation. (2x + 1)¹/3 = -1
In Problems 33–40, write each interval as an inequality involving x, and graph each inequality on the real number line. (-∞, 2]
In Problems 33–40, write each interval as an inequality involving x, and graph each inequality on the real number line.[0, 1)
In Problems 33–40, write each interval as an inequality involving x, and graph each inequality on the real number line.[4, ∞)
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. |7x|> 42
In Problems 9–42, find the real solutions, if any, of each equation. (x² + 9)¹/2 = 5
In Problems 33–40, write each interval as an inequality involving x, and graph each inequality on the real number line. (-∞, -3)
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. |2x|> 6
In Problems 9–42, find the real solutions, if any, of each equation. (x²-16)¹/2 16)¹/2 = 9
In Problems 33–40, write each interval as an inequality involving x, and graph each inequality on the real number line. (-8, ∞)
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 21 x2 + 2
In Problems 9–42, find the real solutions, if any, of each equation. x3/23x¹/2 3x¹/2 = 0
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. x + 4 + 3 < 5
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2u + 5 ≤ 7
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. |3t - 2 ≤ 4
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. |3x + 4 ≥ 2
Therese, an outside salesperson, uses her car for both business and pleasure. Last year, she traveled 30,000 miles, using 900 gallons of gasoline. Her car gets 40 miles per gallon on the highway and 25 in the city. She can deduct all highway travel, but no city travel, on her taxes. How many miles
In Problems 41–58, fill in the blank to form a correct inequality statement. If x 3, then 2x 6.
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. |2x - 3| ≥ 2
Mike can run the mile in 6 minutes, and Dan can run the mile in 9 minutes. If Mike gives Dan a head start of 1 minute, how far from the start will Mike pass Dan? How long does it take? See the figure. 112 114 mi mi Dan Mike 314 mi Start
How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 60% antifreeze?
The cooling system of a certain foreign-made car has a capacity of 15 liters. If the system is filled with a mixture that is 40% antifreeze, how much of this mixture should be drained and replaced by pure antifreeze so that the system is filled with a solution that is 60% antifreeze?
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 14x7 < -2
How much water must be evaporated from 32 ounces of a 4% salt solution to make a 6% salt solution?
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 12x - 4 < -1
How much water must be evaporated from 240 gallons of a 3% salt solution to produce a 5% salt solution?
In Problems 43–74, find the real solutions of each equation.2x4 - 5x2 - 12 = 0
A sugar molecule has twice as many atoms of hydrogen as it does oxygen and one more atom of carbon than of oxygen. If a sugar molecule has a total of 45 atoms, how many are oxygen? How many are hydrogen?
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi.i8 + i6 - i4 - i2
In Problems 43–74, find the real solutions of each equation.x6 + 7x3 - 8 = 0
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi.i7 + i5 + i3 + i
In Problems 41–58, fill in the blank to form a correct inequality statement. If x>-2, then - 4x 8.
In Problems 11–58, perform the indicated operation, and write each expression in the standard form a + bi. V-4
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. |5-2x|> 7
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. |-4x +-5| ≤ 1
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2 - 3x| > 1
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. |-x|-|4| ≤ 2
In Problems 43–74, find the real solutions of each equation.x6 - 7x3 - 8 = 0
An air rescue plane averages 300 miles per hour in still air. It carries enough fuel for 5 hours of flying time. If, upon takeoff, it encounters a head wind of 30 mi/h, how far can it fly and return safely? (Assume that the wind remains constant.)
An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the tanker in 9 hours. If the main pump is started at 9 am, when should the auxiliary pump be started so that the tanker is emptied by noon?
A 20-pound bag of Economy brand cement mix contains 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement?
A bathroom tub will fill in 15 minutes with both faucets open and the stopper in place. With both faucets closed and the stopper removed, the tub will empty in 20 minutes. How long will it take for the tub to fill if both faucets are open and the stopper is removed?
A 5-horsepower (hp) pump can empty a pool in 5 hours. A smaller, 2-hp pump empties the same pool in 8 hours. The pumps are used together to begin emptying the pool. After two hours, the 2-hp pump breaks down. How long will it take the larger pump to finish emptying the pool?
A man is walking at an average speed of 4 miles per hour alongside a railroad track. A freight train, going in the same direction at an average speed of 30 miles per hour, requires 5 seconds to pass the man. How long is the freight train? Give your answer in feet. Length of train 1317 30
Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race. During your run, your average speed is 6 miles per hour, and during your bicycle race, your average speed is 25 miles per hour. You finish the race in 5 hours. What is the distance of the run? What is the
Two cyclists leave a city at the same time, one going east and the other going west. The westbound cyclist bikes 5 mph faster than the eastbound cyclist. After 6 hours they are 246 miles apart. How fast is each cyclist riding?
In the 2016 Olympics, Usain Bolt of Jamaica won the gold medal in the 100-meter race with a time of 9.81 seconds. In the 1896 Olympics, Thomas Burke of the United States won the gold medal in the 100-meter race in 12.0 seconds. If they ran in the same race, repeating their respective times, by how
A 30.5-ounce can of Hills Bros.® coffee requires 58.9π square inches of aluminum. If its height is 6.4 inches, what is its radius? The surface area S of a closed right circular cylinder is S = 2πr2 + 2πrh, where r is the radius and h is the height. Automatic. Drip HILLS BROS Coffee 30.5 oz. 6.4
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 12x+3 3 2
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 72 3 - x + 1 < 1/1/2
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 18- 4x = -13
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. |7x + 4
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 4x 6 15 ≥ 0 AI
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 5 - 2x 9 ≥ 8
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 5 + x - 1 > 1 2
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 7 - 2x 3 ≤0
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 3x - 7 5 > 4
You are the manager of a clothing store and have just purchased 100 dress shirts for $20.00 each. After 1 month of selling the shirts at the regular price, you plan to have a sale giving 40% off the original selling price. However, you still want to make a profit of $4 on each shirt at the sale
In Problems 37–70, solve each inequality. Express your answer using set notation or interval notation. Graph the solution set. 2x - 3 2 + 3 > 1
In going from Chicago to Atlanta, a car averages 45 miles per hour, and in going from Atlanta to Miami, it averages 55 miles per hour. If Atlanta is halfway between Chicago and Miami, what is the average speed from Chicago to Miami? Discuss an intuitive solution. Write a paragraph defending your
On a recent flight from Phoenix to Kansas City, a distance of 919 nautical miles, the plane arrived 20 minutes early. On leaving the aircraft, I asked the captain, “What was our tail wind?” He replied, “I don’t know, but our ground speed was 550 knots.” Has enough information been
Make up a word problem that requires solving a linear equation as part of its solution. Exchange problems with a friend. Write a critique of your friend’s problem.
In Problems 79–84, find a and b. If x + 42, then a ≤ 2x - 3≤ b.
In Problems 79–84, find a and b. If x 31, then a ≤ 3x + 1 ≤ b.
In Problems 79–84, find a and b. If|x2| ≤ 7, then a ≤ X 1 - 10 ≤ b.
In Problems 79–84, find a and b. If |x-1|< 3, then a < x + 4 < b.
In Problems 79–84, find a and b. If x + 1 ≤ 3, then a ≤ 1 x + 5 ≤ b.
In Problems 79–84, find a and b. If x + 2 < 5, then a < x2 < b.
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