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mathematics
college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
Multiply or divide as indicated. 12x - 20 5x 6 9x - 15
Add or subtract as indicated. 4 x + 3 X x - 3 18 x²-9
Multiply or divide as indicated. a² - 1 4a 2 1 - a
Linear programming is a method for finding the optimal (best possible) solution that meets all the conditions for a problem such as the following. A factory can have no more than 200 workers on a shift, but must have at least 100 and must manufacture at least 3000 units at minimum cost. How
Linear programming is a method for finding the optimal (best possible) solution that meets all the conditions for a problem such as the following. A factory can have no more than 200 workers on a shift, but must have at least 100 and must manufacture at least 3000 units at minimum cost. How
Butch and Peggy want to pick up the mess that their grandson, Grant, has made in his playroom. Butch could do it in 15 min working alone. Peggy, working alone, could clean it in 12 min. How long will it take them if they work together? Butch Peggy Rate 1 15 1 12 Time
Write each rational expression in lowest terms. x² - 81 9-x
Write each rational expression in lowest terms. (a − 3)(x + y) (3- a) (x - y)
The weight of a bass varies jointly as its girth and the square of its length. (Girth is the distance around the body of the fish.) A prize-winning bass weighed in at 22.7 lb and measured 36 in. long with a 21-in. girth. How much (to the nearest tenth of a pound) would a bass 28 in. long with an
Graph each rational function. Give the equations of the vertical and horizontal asymptotes. g(x) = 1 X
Add or subtract as indicated. За a+1 a + 2a 3
Add or subtract as indicated. 2х 3x + x+4 x-7
Graph each rational function. Give the equations of the vertical and horizontal asymptotes. g(x)= 2 X
Lou can groom a customer’s dogs in 8 hr, but it takes his business partner, Janet, only 5 hr to groom the same dogs. How long will it take them to groom the dogs if they work together? Lou Janet Rate 1 - 100 8 1 5 Time Working Together X X Fractional Part of the Job Done
Graph each rational function. Give the equations of the vertical and horizontal asymptotes. f(x) 1 x-2
Write each rational expression in lowest terms. (8-p) (x + 2) (p-8)(x-2)
Jerry and Kuba are laying a hardwood floor. Working alone, Jerry can do the job in 20 hr. If the two of them work together, they can complete the job in 12 hr. How long would it take Kuba to lay the floor working alone? (Let x = the time it would take Kuba working alone.) Jerry Kuba Time Rate
The weight of a trout varies jointly as its length and the square of its girth. One angler caught a trout that weighed 10.5 lb and measured 26 in. long with an 18-in. girth. Find the weight (to the nearest tenth of a pound) of a trout that is 22 in. long with a 15-in. girth.
The collision impact of an automobile varies jointly as its mass and the square of its speed. Suppose a 2000-lb car traveling at 55 mph has a collision impact of 6.1. What is the collision impact (to the nearest tenth) of the same car at 65 mph?
Add or subtract as indicated. 11x - 13 2x - 3 3x - 1 2х - 3
Write each rational expression in lowest terms. 5k - 10 20 - 10k
Graph each rational function. Give the equations of the vertical and horizontal asymptotes. g(x) = -2 x-1
Graph each rational function. Give the equations of the vertical and horizontal asymptotes. f(x) = 1 x + 2
Add or subtract as indicated. 13x - 5 4x 1 I x - 2 4x 1 -
Write each rational expression in lowest terms. 7x21 63 21x
Mrs. Disher can grade a set of tests in 5 hr working alone. If her student teacher Mr. Howes helps her, it will take 3 hr to grade the tests. How long would it take Mr. Howes to grade the tests if he worked alone? (Let x = the time it would take Mr. Howes working alone.) Mrs. Disher Mr.
Add or subtract as indicated. 17y + 3 9y + 7 -10y - 18 9y + 7
The force needed to keep a car from skidding on a curve varies inversely as the radius of the curve and jointly as the weight of the car and the square of the speed. If 242-lb of force keeps a 2000-lb car from skidding on a curve of radius 500 ft at 30 mph, what force (to the nearest tenth of a
Write each rational expression in lowest terms. a - b2 a + b?
Add or subtract as indicated. 4x + 1 3x + 2 -2x - 3 3x + 2
The average number of vehicles waiting in line to enter a parking area is modeled by the functionwhere x is a quantity between 0 and 1 known as the traffic intensity. For each traffic intensity, find the average number of vehicles waiting (to the nearest tenth).(a) 0.1 (b) 0.8 (c) 0.9(d) What
Graph each rational function. Give the equations of the vertical and horizontal asymptotes. g(x) = - 1 x + 3
Write each rational expression in lowest terms. p² + q² p² - q²
Dixie can paint a room in 3 hr working alone. Trixie can paint the same room in 6 hr working alone. How long after Dixie starts to paint the room will it be finished if Trixie joins her 1 hr later?
The number of long-distance phone calls between two cities during a certain period varies jointly as the populations of the cities, p1 and p2, and inversely as the distance between them, in miles. If 80,000 calls are made between two cities 400 mi apart, with populations of 70,000 and
Howard can wash a car in 30 min working alone. Raj can do the same job in 45 min working alone. How long after Howard starts to wash the car will it be finished if Raj joins him 5 min later?
Perform the indicated operations. 2 (x +5)² it
Solve each formula for the specified variable. = h(b + B) for b (mathematics)
The area of a triangle varies jointly as the lengths of the base and height. A triangle with base 10 ft and height 4 ft has area 20 ft2. Find the area of a triangle with base 3 ft and height 8 ft. 4 ft! 10 ft Area: 20 ft²
Add or subtract as indicated. 3r 10r² - 3rs s² + 2r 2r² + rss²
Solve each formula for the specified variable. n S = (a + €)d for n (mathematics)
Simplify each complex fraction. 3 t 4 t +2 -7
If Dr. Dawson rides his bike to his office, he averages 12 mph. If he drives his car, he averages 36 mph. His time driving is 1/4 hr less than his time riding his bike. How far is his office from home?
Graph each inequality or compound inequality.2x + 5y > 10
Write each formula using the “language” of variation. For example, the formula for the circumference of a circle, C = 2πr, can be written as“The circumference of a circle varies directly as the length of its radius.”P = 4s, where P is the perimeter of a square with side of length s
Simplify each complex fraction. 2 m-3n 1 3n-m
Chris can do a job in 9 hr, while Dana can do the same job in 5 hr. How long would it take them to do the job if they worked together?
Solve each formula for the specified variable. E R+r e r for r (engineering)
Graph each inequality or compound inequality.x - y ≥ 3 and 3x + 4y ≤ 12
Solve each formula for the specified variable. y x + 2 a-x for x (mathematics)
Write each formula using the “language” of variation. For example, the formula for the circumference of a circle, C = 2πr, can be written as“The circumference of a circle varies directly as the length of its radius.”where V is the volume of a sphere with radius r FA 4 +le
Simplify each complex fraction. 3 2 P 9 9q² - 4p² qP
Write each formula using the “language” of variation. For example, the formula for the circumference of a circle, C = 2πr, can be written as“The circumference of a circle varies directly as the length of its radius.”d = 2r, where d is the diameter of a circle with radius r
In biology, the rational functiongives the growth rate g of a population for x units of available food.(a) What amount of food (in appropriate units) would produce a growth rate of 3 units of growth per unit of food?(b) What is the growth rate if no food is available? g(x) 5x 2+x
The rate of the current in a stream is 3 mph. Nana’s boat can travel 36 mi downstream in the same time that it takes to travel 24 mi upstream. Find the rate of her boat in still water.
Solve each system. 4x - y = -7 5x + 2y = 1
Consider the equation 5x - 3y = 8.(a) Write y as a function ƒ of x, using function notation ƒ(x).(b) Find ƒ(1).
Solve each formula for the specified variable. D= R 1 + RT for R (banking)
Solve each system. x + y = 2z = -1 2x = y + z = -6 3x + 2y3z = -3
Write each formula using the “language” of variation. For example, the formula for the circumference of a circle, C = 2πr, can be written as“The circumference of a circle varies directly as the length of its radius.” A = ½-bh, where A is the area of a triangle with base b and height h
Write each formula using the “language” of variation. For example, the formula for the circumference of a circle, C = 2πr, can be written as“The circumference of a circle varies directly as the length of its radius.”S = 4πr2, where S is the surface area of a sphere with radius r
Biologists collected a sample of 600 fish from West Okoboji Lake on May 1 and tagged each of them. When they returned on June 1, a new sample of 800 fish was collected and 10 of these had been previously tagged. Use this experiment to determine the approximate fish population of West Okoboji Lake.
Simplify each complex fraction. ج xi-y - - -X
Consider the relation y = -√2x + 2.(a) Does it define a function?(b) Give its domain and range.
Solve each formula for the specified variable. R= D 1 - DT for D (banking)
Solve each equation. 1 t + 4 1 + 2 || 3 2t + 8
What is the constant of variation in each of the variation equations in Exercises 19–24?Data from in Exercises 19–24Write each formula using the “language” of variation. For example, the formula for the circumference of a circle, C = 2πr, can be written as“The circumference of a circle
Write each formula using the “language” of variation. For example, the formula for the circumference of a circle, C = 2πr, can be written as“The circumference of a circle varies directly as the length of its radius.”where V is the volume of a cone with radius r and height h V = r²h, 3 T
Solve each system. x + 2y + z = 5 x = y + z = 3 2x + 4y + 2z = 11
The current in a simple electrical circuit is inversely proportional to the resistance. If the current is 80 amps when the resistance is 30 ohms, find the current when the resistance is 12 ohms.
Solve each equation. -5m m+1 + m 3m + 3 56 6m + 6
The water content of snow is affected by the temperature, wind speed, and other factors present when the snow is falling. The average snow-to-liquid ratio is 10 in. of snow to 1 in. of liquid precipitation. This means that if 10 in. of snow fell and was melted, it would produce 1 in. of liquid
SimplifyWrite the answer with only positive exponents. Assume that all variables represent nonzero real numbers. m-4n² m²n-3 m³n-11 m-²n5
Perform the indicated operations. (3y2 - 2y + 6) - (-y² + 5y + 12)
Solve each equation. 4x + 3 5r+5 8x + 2 10x + 5
The force of the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the velocity. If a wind blowing at 40 mph exerts a force of 50-lb on a surface of 500 ft2, how much force will a wind of 80 mph exert on a surface of 2 ft2?
Use proportions to solve each problem mentally. In a mathematics class, 3 of every 4 students are girls. If there are 28 students in the class, how many are girls? How many are boys?
What is meant by the constant of variation in a direct variation problem? If we were to graph the linear equation y = kx for some nonnegative constant k, what role would k play in the graph?
Use proportions to solve each problem mentally. In a certain southern state, sales tax on a purchase of $1.50 is $0.12. What is the sales tax on a purchase of $9.00?
Write a variation equation for each situation. Use k as the constant of variation.A varies directly as b.
Write a variation equation for each situation. Use k as the constant of variation.W varies directly as f.
Solve each equation. 2 k - 1 4k + 1 k²1 -1 k+1
The water content of snow is affected by the temperature, wind speed, and other factors present when the snow is falling. The average snow-to-liquid ratio is 10 in. of snow to 1 in. of liquid precipitation. This means that if 10 in. of snow fell and was melted, it would produce 1 in. of liquid
Perform the indicated operations. (4f + 3) (3f - 1)
Solve each equation. r r-2 8 ²-4 -1 r+2
Solve each equation. 5 x + 2 + 3 x + 3 X x2+5x+6
Write a variation equation for each situation. Use k as the constant of variation.h varies inversely as t.
On a U.S. map, the distance between Seattle and Durango is 4.125 in. The two cities are actually 1238 mi apart. On this same map, what would be the distance between Chicago and El Paso, two cities that are actually 1606 mi apart?
Write a variation equation for each situation. Use k as the constant of variation.p varies inversely as s.
Find each of the following for the polynomial functions f(x) = x² + 2x-3, g(x) = 2x³ 3x² + 4x 1, (b) (g- f)(x) (c) (f+g) (-1) (a) (f + g)(x) and h(x) = x². (d) (foh)(x)
Decide whether each of the following is an expression or an equation. Simplify the one that is an expression, and solve the one that is an equation. (a) 4 + || (b) + -
Graph the rational functionGive the equations of the vertical and horizontal asymptotes. f(x) 2 x + 1
On a world globe, the distance between New York and Cairo, two cities that are actually 5619 mi apart, is 8.5 in. On this same globe, how far apart are Madrid and Rio de Janeiro, two cities that are actually 5045 mi apart? NORTH TEARTEL JCERK
On a world globe, the distance between San Francisco and Melbourne, two cities that are actually 7856 mi apart, is 11.875 in. On this same globe, how far apart are Mexico City and Singapore, two cities that are actually 10,327 mi apart? NORTH TEARTEL JCERK
According to a law from physics,Find A if B = 30 and C = 10. 1 A || 1 B + C С'
On a U.S. map, the distance between Reno and Phoenix is 2.5 in. The two cities are actually 768 mi apart. On this same map, what would be the distance between St. Louis and Jacksonville, two cities that are actually 919 mi apart?
Write a variation equation for each situation. Use k as the constant of variation.M varies directly as the square of d.
In banking and finance, the formulagives present value at simple interest. If P = 600, M = 750, and R = 0.125, find T. P = M 1 + RT
To estimate the deer population of a forest preserve, wildlife biologists caught, tagged, and then released 42 deer. A month later, they returned and caught a sample of 75 deer and found that 15 of them were tagged. Based on this experiment, how many deer lived in the forest preserve?
Factor each polynomial completely.2x2 - 13x - 45
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