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Questions and Answers of College Algebra

Decide what values of the variable cannot possibly be solutions for each equation. Do not solve.5/2x + 3 - 1/x - 6 = 0
Match each equation in Column I with the correct first step for solving it in Column II.3√x(x + 5) = 3√-6A. Cube each side of the equation.B. Multiply each side of the equation by x(x + 5).C.
A local group of scouts has been collecting old aluminum cans for recycling. The group has already collected 12,000 lb of cans, for which they could currently receive $4 per hundred pounds. The group
The manager of a cherry orchard wants to schedule the annual harvest. If the cherries are picked now, the average yield per tree will be 100 lb, and the cherries can be sold for 40 cents per pound.
A charter bus company charges a fare of $40 per person, plus $2 per person for each unsold seat on the bus. If the bus holds 100 passengers and x represents the number of unsold seats, how many
The cost of a charter flight to Miami is $225 each for 75 passengers, with a refund of $5 per passenger for each passenger in excess of 75. How many passengers must take the flight to produce a
According to the problem, the revenue currently generated is $35,000. Substitute this value for revenue into the equation from Exercise 59. Solve for x to answer the question in the problem.The
Suppose that x represents the number of $20 increases over $300. Represent the number of apartment units that will be rented in terms of x.The manager of an 80-unit apartment complex knows from
Represent the rent per unit in terms of x.The manager of an 80-unit apartment complex knows from experience that at a rent of $300, all the units will be full. On the average, one additional unit
The manager of an 80-unit apartment complex knows from experience that at a rent of $300, all the units will be full. On the average, one additional unit will remain vacant for each $20 increase in
The top cable Internet speeds during the years 2007 through 2013 can be modeled by the equationy = 23.09x2 - 62.12x + 32.78,where x = 0 corresponds to 2007, x = 1 corresponds to 2008, and so on, and
Estimated revenue from Internet publishing and web search portals in the United States during the years 2007 through 2012 can be modeled by the equationy = 710.55x2 + 1333.7x + 32,399where x = 0
The average cost, in dollars, for tuition and fees for in-state students at four-year public colleges over the period 2000–2014 can be modeled by the equation y = 4.065x2 + 370.1x +
The table gives methane gas emissions from all sources in the United States, in millions of metric tons. The quadratic model y = 0.0429x2 - 9.73x + 606 approximates the emissions for these
Refer to Exercise 51. High concentrations of carbon monoxide (CO) can cause coma and death. The time required for a person to reach a COHb level capable of causing a coma can be approximated by the
Carbon monoxide (CO) combines with the hemoglobin of the blood to form carboxyhemoglobin (COHb), which reduces transport of oxygen to tissues. Smokers routinely have a 4% to 6% COHb level in their
Salaries, in millions of dollars, for rookies selected in the first round of the NFL 2014 draft can be approximated by the quadratic model y = 0.0258x2 - 1.30x + 23.3, where x represents
In 1994, the National Football League introduced a salary cap that limits the amount of money spent on players’ salaries. The quadratic modely = 0.2313x2 + 2.600x + 35.17approximates this cap in
The ball in Exercise 47 will never reach a height of 100 ft. How can this be determined algebraically?Exercise 47An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall,
An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall, and the initial velocity of the ball is 30 ft per sec. The height s of the ball in feet is given by the equation
A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given bys = -16t2 + v0t.Find the
A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given bys = -16t2 + v0 t.Find the
A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given bys = -16t2 + v0t.find the
A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given bys = -16t2 + v0t.Find the
Problems involving the Pythagorean theorem have appeared in mathematics for thousands of years. This one is taken from the ancient Chinese work Arithmetic in Nine Sections:There is a bamboo 10 ft
A nature conservancy group decides to construct a raised wooden walkway through a wetland area. To enclose the most interesting part of the wetlands, the walkway will have the shape of a right
Tanner and Sheldon have received communications receivers for Christmas. If they leave from the same point at the same time, Tanner walking north at 2.5 mph and Sheldon walking east at 3 mph, how
A building is 2 ft from a 9-ft fence that surrounds the property. A worker wants to wash a window in the building 13 ft from the ground. He plans to place a ladder over the fence so it rests against
Molly has a solar panel with a width of 26 in. To get the proper inclination for her climate, she needs a right triangular support frame that has one leg twice as long as the other. To the nearest
A square lawn has area 800 ft2. A sprinkler placed at the center of the lawn sprays water in a circular pattern as shown in the figure. What is the radius of the circle? Sprinkler
Grady is flying a kite on 50 ft of string. Its vertical distance from his hand is 10 ft more than its horizontal distance from his hand. Assuming that the string is being held 5 ft above ground
A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 12 ft from the dock, the length of the rope from the boat to the dock is 3 ft longer than twice
The volume of a 15-oz cereal box is 180.4 in.3. The length of the box is 3.2 in. less than the height, and its width is 2.3 in. Find the height and length of the box to the nearest tenth. Frosped kes
A can of Blue Runner Red Kidney Beans has surface area 371 cm2. Its height is 12 cm. What is the radius of the circular top? Round to the nearest hundredth.
A rectangle has an area that is numerically twice its perimeter. If the length is twice the width, what are its dimensions?
What is the length of the side of a square if its area and perimeter are numerically equal?
In Exercise 29, what radius would produce a container with a volume of π times the radius?Exercise 29A manufacturing firm wants to package its product in a cylindrical container 3 ft high with
A manufacturing firm wants to package its product in a cylindrical container 3 ft high with surface area 8π ft2. What should the radius of the circular top and bottom of the container be?
In Exercise 27, suppose that the piece of metal has length twice the width, and 4-in. squares are cut from the corners. If the volume of the box is 1536 in.3, what were the original dimensions of the
A rectangular piece of metal is 10 in. longer than it is wide. Squares with sides 2 in. long are cut from the four corners, and the flaps are folded upward to form an open box. If the volume of the
A landscape architect has included a rectangular flower bed measuring 9 ft by 5 ft in her plans for a new building. She wants to use two colors of flowers in the bed: one in the center and the other
Zachary wants to buy a rug for a room that is 12 ft wide and 15 ft long. He wants to leave a uniform strip of floor around the rug. He can afford to buy 108 ft2 of carpeting. What dimensions should
An ecology center wants to set up an experimental garden using 300 m of fencing to enclose a rectangular area of 5000 m2. Find the dimensions of the garden. 150 – x x is in meters.
Solve each problem.A parking lot has a rectangular area of 40,000 yd2. The length is 200 yd more than twice the width. Find the dimensions of the lot.
The length of each side of a square is 5 in. more than the length of each side of a smaller square. The difference of the areas of the squares is 95 in.2. Find the lengths of the sides of the two
The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in.2. Find the lengths of the sides of the two
The lengths of the sides of a right triangle are consecutive positive integers. Find these lengths.
The lengths of the sides of a right triangle are consecutive even integers. Find these lengths.
If x represents an integer, then x + 1 represents the next consecutive integer.If x represents an even integer, then x + 2 represents the next consecutive even integer.If x represents an odd integer,
If x represents an integer, then x + 1 represents the next consecutive integer.If x represents an even integer, then x + 2 represents the next consecutive even integer.If x represents an odd integer,
If x represents an integer, then x + 1 represents the next consecutive integer.If x represents an even integer, then x + 2 represents the next consecutive even integer.If x represents an odd integer,
If x represents an integer, then x + 1 represents the next consecutive integer.If x represents an even integer, then x + 2 represents the next consecutive even integer.If x represents an odd integer,
If x represents an integer, then x + 1 represents the next consecutive integer.If x represents an even integer, then x + 2 represents the next consecutive even integer.If x represents an odd integer,
If x represents an integer, then x + 1 represents the next consecutive integer.If x represents an even integer, then x + 2 represents the next consecutive even integer.If x represents an odd integer,
If x represents an integer, then x + 1 represents the next consecutive integer.If x represents an even integer, then x + 2 represents the next consecutive even integer.If x represents an odd integer,
If x represents an integer, then x + 1 represents the next consecutive integer.If x represents an even integer, then x + 2 represents the next consecutive even integer.If x represents an odd integer,
If x represents an integer, then x + 1 represents the next consecutive integer.If x represents an even integer, then x + 2 represents the next consecutive even integer.If x represents an odd integer,
If x represents an integer, then x + 1 represents the next consecutive integer.If x represents an even integer, then x + 2 represents the next consecutive even integer.If x represents an odd integer,
Decide whether each statement is true or false.Solving the literal equation A = 1/2 bh for the variable h gives h = A/2b.
Solve each equation. -2x + 3 + Vx + 3 = 3
Unknown Numbers Consider the following problem.One number is 3 less than 6 times a second number. Their sum is 46. Find the numbers.If x represents the second number, which equation is correct for
Solve each equation.|3x - 1| = 2
Match each equation in Column I with the correct first step for solving it in Column II.(x + 5)2/3 - (x + 5)1/3 - 6 = 0A. Cube each side of the equation.B. Multiply each side of the equation by x(x +
Decide whether each statement is true or false. If false, correct the right side of the equation.(–2 + 7i) – (10 - 6i) = –12 + i
Match the inequality in each exercise in Column I with its equivalent interval notation in Column II.A. (-2, 6]B. [-2, 6)C. (-∞, -6)D. [6, ∞)E. (-∞, -3) ⋃ (3,
If the length of each side of a square is decreased by 4 in., the perimeter of the new square is 10 in. more than half the perimeter of the original square. What are the dimensions of the original
Solve each equation.x2 - 29 = 0
Match the equation in Column I with its solution(s) in Column II.x + 5 = 0
Decide whether each statement is true or false.The equation 5x = 4x is an example of a contradiction.
Suppose that the quadratic equation S = 0.0538x2 - 0.807x + 8.84 models sales of new cars, where S represents sales in millions, and x = 0 represents 2000, x = 1 represents 2001, and so on. Which
Solve each equation. V3x + 4 + 5 = 2x + 1
Unknown Numbers Consider the following problem.The difference between seven times a number and 9 is equal to five times the sum of the number and 2. Find the number.If x represents the number, which
Match each equation or inequality in Column I with the graph of its solution set in Column II.|x| ≠ 7 A. + -7 B. + + -7 C. -7 D. + -7 E. + -7 F. + -7 G. -7 Н. -7 1. 1.
Decide whether each statement is true or false. If false, correct the right side of the equation.i12 = 1
Match each equation in Column I with the correct first step for solving it in Column II.(x + 5)5/2 = 32A. Cube each side of the equation.B. Multiply each side of the equation by x(x + 5).C. Raise
Carry-on rules for domestic economy-class travel differ from one airline to another, as shown in the table.Airline........................................ Size (linear
Solve each equation.3x2 - x = -1
Match the equation in Column I with its solution(s) in Column II.x – 5 = 0
Decide whether each statement is true or false.The equation 5(x - 8) = 5 x - 40 is an example of an identity.
Solve each equation. 3 -6 4х х2 — 2х |х — 2 х
If a projectile is launched vertically upward from the ground with an initial velocity of 45 ft per sec, neglecting air resistance, its height s (in feet) above the ground t seconds after projection
Solve each problem.Acid Mixture Suppose two acid solutions are mixed. One is 26% acid and the other is 34% acid. Which one of the following concentrations cannot possibly be the concentration of the
Match each equation or inequality in Column I with the graph of its solution set in Column II.|x| ≤ 7 A. + -7 B. + + -7 C. -7 D. + -7 E. + -7 F. + -7 G. -7 Н. -7 1. 1.
Decide whether each statement is true or false. If false, correct the right side of the equation.√–4 · √-9 = –6
Match each equation in Column I with the correct first step for solving it in Column II.√x + 5 = 7A. Cube each side of the equation.B. Multiply each side of the equation by x(x + 5).C. Raise each
Match the inequality in each exercise in Column I with its equivalent interval notation in Column II.A. (-2, 6]B. [-2, 6)C. (-∞, -6)D. [6, ∞)E. (-∞, -3) ⋃ (3,
If x represents the number of pennies in a jar in an applied problem, which of the following equations cannot be a correct equation for finding x?A. 5x + 3 = 11 B. 12x + 6 = -4C. 100x = 50(x +
Write the quotient 7 - 2i/2 + 4i in standard form a + bi.
Match the equation in Column I with its solution(s) in Column II.x2 = 20
Solve each equation. 12 x? - 9 3 x+ 3 2
Decide whether each statement is true or false.The solution set of 2x + 5 = x - 3 is {-8}.
If a projectile is launched vertically upward from the ground with an initial velocity of 60 ft per sec, neglecting air resistance, its height s (in feet) above the ground t seconds after projection
Solve each problem.Sale Price Suppose that a computer that originally sold for x dollars has been discounted 60%. Which one of the following expressions does not represent its sale price?A. x -
Decide whether each statement is true or false. If false, correct the right side of the equation.√–25 = 5i
Match each equation in Column I with the correct first step for solving it in Column II.A. Cube each side of the equation.B. Multiply each side of the equation by x(x + 5).C. Raise each side of the
Match each equation or inequality in Column I with the graph of its solution set in Column II.|x| ≥ 7 A. + -7 B. + + -7 C. -7 D. + -7 E. + -7 F. + -7 G. -7 Н. -7 1. 1.
Match the inequality in each exercise in Column I with its equivalent interval notation in Column II.6 ≤ xA. (-2, 6]B. [-2, 6)C. (-∞, -6)D. [6, ∞)E. (-∞,
Solve each problem.Which of the following cannot be a correct equation to solve a geometry problem, if x represents the measure of a side of a rectangle?A. 2x + 2(x + 2) = 20B. 2x + (15 + x) = -2C.
Write -4 + √-24/8 in standard form a + bi.
Fill in the blank to correctly complete each sentence.A(n)_________ is an equation that has no solution.

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