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college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
Ben bought 8.5 gal of gasoline and paid $33.32. What is the price of gasoline per gallon?
Simplify each expression, using only positive exponents in the answer. a2 - -4b-2 3b - ба
A van traveling from Atlanta to Detroit averages 50 mph and takes 14-hr to make the trip. How far is it from Atlanta to Detroit?
Which equation can be solved using cross products of the proportion? Explain. Then solve each equation. Equation A: Equation B: 12 X - 1 12 x + 3 5 x-1 8 x - 3
Suppose that the given expressions are denominators of rational expressions. Find the least common denominator (LCD) for each group of denominators.3a - 3b, a2 + ab - 2b2, (a - b)2
Write each rational expression in lowest terms. 12x² - 4x - 5 8x² - 6x - 5
Solve each equation. 1 -10 + x + 4 3 3(x² - 16)
Kellen’s boat travels 12 mph. Find the rate of the current of the river if she can travel 6 mi upstream in the same amount of time she can go 10 mi downstream. Downstream Upstream Distance 10 6 Rate Time 12 + x 12- X
Sara gives horseback rides at Shadow Mountain Ranch. A 2.5-hr ride costs $50.00. What is the price per hour?
Greg paddles his canoe at a rate of 4 mph. If the rate of a stream is x mph, what is an expression that represents his rate in miles per hour when traveling each direction?(a) Upstream (b) Downstream
Write each rational expression in lowest terms. a³ + b³ a + b
Add or subtract as indicated. 8 7 + 3t
Kasey can travel 8 mi upstream in the same time it takes her to go 12 mi downstream. Her boat goes 15 mph in still water. What is the rate of the current? (Let x = the rate of the current.) Downstream Upstream Distance Rate Time 15-x
Simplifying a complex fraction by Method 1 is a good way to review the methods of adding, subtracting, multiplying, and dividing rational expressions. Method 2 gives a good review of the fundamental property of rational numbers.Refer to the following complex fraction, and work Exercises in
The volume of a can of tomatoes is directly proportional to the height of the can. If the volume of the can is 300 cm3 when its height is 10.62 cm, find the volume to the nearest whole number of a can with height 15.92 cm. TOMATOES 10.62 cm
Add or subtract as indicated. 5 X + 9 4x
Solve each equation. X x - 3 + 4 x + 3 18 x2 x²-9 ||
The force required to compress a spring is directly proportional to the change in length of the spring. If a force of 20 newtons is required to compress a certain spring 2 cm, how much force is required to compress the spring from 20 cm to 8 cm? 20 cm 18 cm 20 newtons 8 cm ?
The pressure exerted by a certain liquid at a given point is directly proportional to the depth of the point beneath the surface of the liquid. The pressure at 30 m is 80 newtons. What pressure is exerted at 50 m?
Simplifying a complex fraction by Method 1 is a good way to review the methods of adding, subtracting, multiplying, and dividing rational expressions. Method 2 gives a good review of the fundamental property of rational numbers.Refer to the following complex fraction, and work Exercises in
Write each rational expression in lowest terms. r-s ES - EA
Solve each equation. 2x x - 3 + 4 x + 3 || -24 x²-9
Write each rational expression in lowest terms. 2c²2cd60d² 2c²12cd 10d²
Solve each equation. 1 x +4 + X x - 4 -8 x² - 16
Add or subtract as indicated. 5 12х²у 11 бху
For a body falling freely from rest (disregarding air resistance), the distance the body falls varies directly as the square of the time. If an object is dropped from the top of a tower 576 ft high and hits the ground in 6 sec, how far did it fall in the first 4 sec? 576 ft
Add or subtract as indicated. 7 18a³b² 2 9ab
In his boat, Sheldon can travel 30 mi downstream in the same time that it takes to travel 10 mi upstream. If the rate of the current is 5 mph, find the rate of the boat in still water.
In his boat, Leonard can travel 24 mi upstream in the same time that it takes to travel 36 mi downstream. If the rate of the current is 2 mph, find the rate of the boat in still water.
Simplifying a complex fraction by Method 1 is a good way to review the methods of adding, subtracting, multiplying, and dividing rational expressions. Method 2 gives a good review of the fundamental property of rational numbers.Refer to the following complex fraction, and work Exercises in order.Go
Write each rational expression in lowest terms. 3s² - 9st - 54t² 3s² - 6st - 72t²
Solve each equation. 5 x - 4 x² - 1 + 4 3 x 1x²5x
On his drive from Montpelier, Vermont, to Columbia, South Carolina, Victor averaged 51-mph. If he had been able to average 60-mph, he would have reached his destination 3-hr earlier. What is the driving distance between Montpelier and Columbia? Actual Trip Alternative Trip Distance Rate Time X 60
Add or subtract as indicated. 4 3 15a4b5 20a²b6 +
Solve each equation. 5 p² + 3p + 2 3 p²-4 1 p²-p-2
Write each rational expression in lowest terms. 2xy + 2xw+y+w 2xy + y 2xw - w
Add or subtract as indicated. 2r 3s 7p³q4 14p^q
Solve each equation. 5x+14 x² - 9 -2 - 2x² - 5x + 2 x² - 9 + 2x + 4 x 3
Write each rational expression in lowest terms. 7-b b-7
Add or subtract as indicated. 4t 5s 9a8b7 27a4b³ +
The frequency of a vibrating string varies inversely as its length. That is, a longer string vibrates fewer times in a second than a shorter string. Suppose a piano string 2 ft long vibrates at 250 cycles per sec. What frequency would a string 5 ft long have?
Write each rational expression in lowest terms. r - 13 13 - r
Mary drove from her apartment to her parents’ house. She averaged 60 mph because traffic was light. On the return trip, which took 1.5 hr longer, she averaged only 45 mph on the same route. What is the distance between Mary’s apartment and her parents’ house?
Solve each equation. 4x - 7 4x² - 9 -2x² + 5x - 4 4x² - 9 + x + 1 2x + 3
The current in a simple electrical circuit varies inversely as the resistance. If the current is 20 amps when the resistance is 5 ohms, find the current when the resistance is 7.5 ohms.
Match each function in Column I with its type in Column II. I (a) f(x) = 3x - 4 10 (b) f(x) = (c) f(x) = x² + 2x - 8 (d) f(x) = x³ II A. quadratic function B. cubing function C. rational function D. linear function
Add or subtract as indicated. 1 a362 2 3 + aªb a5b7
The amount of light (measured in foot-candles) produced by a light source varies inversely as the square of the distance from the source. If the illumination produced 1 m from a light source is 768 foot-candles, find the illumination produced 6 m from the same source. m
On the first part of a trip to Carmel traveling on the freeway, Marge averaged 60 mph. On the rest of the trip, which was 10 mi longer than the first part, she averaged 50 mph. Find the total distance to Carmel if the second part of the trip took 30 min more than the first part.
Write each rational expression in lowest terms. x² - y² y - x
Which graph has vertical and horizontal asymptotes? What are their equations? A. ملال * B. 0 C. 0 D.
Add or subtract as indicated. 5 | درا + la t4u7 tu t¹⁰u
During the first part of a trip on the highway, Jim and Annie averaged 60 mph. In Houston, traffic caused them to average only 30 mph. The distance they drove in Houston was 100 mi less than their distance on the highway. What was their total driving distance if they spent 50 min more on the
A body mass index from 27 through 29 carries a slight risk of weight-related health problems, while a BMI of 30 or more indicates a great increase in risk. Use your own height and weight and the information in Example 7 to determine your BMI and whether you are at risk.Data from in Example 7
Add or subtract as indicated. 5 5 12x³y² 18x4y5 +
Kelli lives in an off-campus apartment. When she rides her bike to campus, she arrives 36 min faster than when she walks. If her average walking rate is 3 mph and her average biking rate is 12 mph, how far is it from her apartment to campus? Bike Walk Distance Rate Time X 12
For a constant area, the length of a rectangle varies inversely as the width. The length of a rectangle is 27 ft when the width is 10 ft. Find the width of a rectangle with the same area if the length is 18 ft.
Solve each equation. 2 k² + k-6 + 1 k²-k-2 4 k² + 4k + 3
Write each rational expression in lowest terms. ac-ad + be - bd ad - bc + bd ac
Simplifying a complex fraction by Method 1 is a good way to review the methods of adding, subtracting, multiplying, and dividing rational expressions. Method 2 gives a good review of the fundamental property of rational numbers.Refer to the following complex fraction, and work Exercises in
Over a specified distance, rate varies inversely as time. If a Dodge Viper on a test track goes a certain distance in one-half minute at 160 mph, what rate is needed to go the same distance in three-fourths minute?
Write each rational expression in lowest terms. x² - 4 2-x
Graph each rational function. Give the equations of the vertical and horizontal asymptotes. f(x) = 3 X
Graph each rational function. Give the equations of the vertical and horizontal asymptotes. f(x) = 2 X
If a vat of acid can be filled by an inlet pipe in 10-hr and emptied by an outlet pipe in 20-hr, how long will it take to fill the vat if both pipes are open?
Add or subtract as indicated. 1 x - 1 x 1 I
Write each rational expression in lowest terms. m² -n² n - m
A printer can complete a large job in 8 hr using a new machine. Using an older machine requires 24 hr to do the same job. How long would it take to complete the job using both machines?
The force with which Earth attracts an object above Earth’s surface varies inversely as the square of the distance of the object from the center of Earth. If an object 4000 mi from the center of Earth is attracted with a force of 160 lb, find the force of attraction if the object were 6000 mi
For a given interest rate, simple interest varies jointly as principal and time. If $2000 left in an account for 4 yr earned interest of $280, how much interest would be earned in 6 yr?
A chef can finish a catering job in 6 hr. His student can do the same job in 12 hr. How long will it take them to do the job if they work together?
Add or subtract as indicated. 3 x - 3 1 X
A routine activity such as pumping gasoline can be related to many of the concepts studied in this text. Suppose that premium unleaded costs $3.75 per gal. Work Exercises in order.Use the information from Exercise 69 to find the slope of the line on which the two points lie.Data from in Exercise
An inlet pipe can fill an artificial lily pond in 60 min, while an outlet pipe can empty it in 80 min. Through an error, both pipes are left open. How long will it take for the pond to fill?
The amount of heating oil produced (in gallons per day) by an oil refinery is modeled by the rational functionwhere x is the amount of gasoline produced (in hundreds of gallons per day). Suppose the refinery must produce 300 gal of heating oil per day to meet the needs of its customers.(a) How much
Multiply or divide as indicated. (6x + 5)(x-3) (x - 1)(x − 3) - ÷ (2x + 7)(x+9) (x - 1)(x + 9)
Add or subtract as indicated. a a-b b b - a
A routine activity such as pumping gasoline can be related to many of the concepts studied in this text. Suppose that premium unleaded costs $3.75 per gal. Work Exercises in order.0 gal of gasoline cost $0.00, while 1 gal costs $3.75. Represent these two pieces of information as ordered pairs of
Suppose that Hortense and Mort can clean their entire house in 7 hr, while their toddler, Mimi, can mess it up in only 2 hr. If Hortense and Mort clean the house while Mimi is at her grandma’s and then start cleaning up after Mimi the minute she gets home, how long does it take from the time Mimi
The force required to keep a 2000-lb car that is going 30 mph from skidding on a curve, where r is the radius of the curve in feet, is given by(a) What radius must a curve have if a force of 450 lb is needed to keep the car from skidding?(b) As the radius of the curve is lengthened, how is the
Multiply or divide as indicated. (2x+3)(x-4) (x − 4)(x+2) (x+8)(x-4) (x-4) (x + 8)
Add or subtract as indicated. W W-2 1 N M-Z W
Multiply or divide as indicated. (x+3)(x − 6) (x-4) (x + 2) (x + 5)(x-4) (x+3)(x-6)
The maximum load of a horizontal beam that is supported at both ends varies directly as the width and the square of the height and inversely as the length between the supports. A beam 6 m long, 0.1 m wide, and 0.06 m high supports a load of 360 kg. What is the maximum load supported by a beam 16 m
Add or subtract as indicated. 3 1 + 2-tt-2
A winery has a vat to hold Zinfandel. An inlet pipe can fill the vat in 9 hr, and an outlet pipe can empty it in 12 hr. How long will it take to fill the vat if both the outlet and the inlet pipes are open?
The percent of deaths caused by smoking is modeled by the rational functionwhere x is the number of times more likely a smoker is to die of lung cancer than a nonsmoker. This is the incidence rate. For example, x = 10 means that a smoker is 10 times more likely than a nonsmoker to die of lung
Multiply or divide as indicated. (x + 2)(x + 1) (x+3)(x + 4) (x+3)(x-2) (x + 2)(x+1)
Add or subtract as indicated. 2 4-x + 5 x - 4
Add or subtract as indicated. 1 x + 1 1 x-1
Multiply or divide as indicated. 4x 8x + 4 14x + 7 6
A routine activity such as pumping gasoline can be related to many of the concepts studied in this text. Suppose that premium unleaded costs $3.75 per gal. Work Exercises in order.Write the slope-intercept form of the equation of the line on which the two points lie. 1331
Add or subtract as indicated. -2 x - 1 + 2 x + 1
A routine activity such as pumping gasoline can be related to many of the concepts studied in this text. Suppose that premium unleaded costs $3.75 per gal. Work Exercises in order.Using function notation, if ƒ(x) = ax + b represents the line from Exercise 71, what are the values of a and b?Data
Multiply or divide as indicated. (7k+ 7) = 4k + 4 5
Add or subtract as indicated. 15 2 + y2 + 3у У + 5 у +3
A routine activity such as pumping gasoline can be related to many of the concepts studied in this text. Suppose that premium unleaded costs $3.75 per gal. Work Exercises in order.Why does the equation from Exercise 72 satisfy the conditions for direct variation? In the context of variation, what
A routine activity such as pumping gasoline can be related to many of the concepts studied in this text. Suppose that premium unleaded costs $3.75 per gal. Work Exercises in order.How is the value of a from Exercise 72 related to gasoline in this situation? With relationship to the line, what do we
Add or subtract as indicated. I - zx I + X 4 2 I - X 4x
Multiply or divide as indicated. p² - 25 4p 2 5-P
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