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mathematics
college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
Perform the indicated operations. Express answers in lowest terms. 2q² a + b a-b 4a
Solve each formula for the specified variable. μl Mv M + m for M (electronics)
Solve each formula for the specified variable. F = GMm d² for m (physics)
Write a variation equation for each situation. Use k as the constant of variation.P varies inversely as the cube of x.
Factor each polynomial completely.100t4 - 25
Perform the indicated operations. Express answers in lowest terms. x² - 9 2x + 4 x³ - 27 4
Write a variation equation for each situation. Use k as the constant of variation.I varies jointly as g and h.
In 2016, the average ratio of teachers to students in public elementary and secondary schools was approximately 1 to 16. If a public school had 896 students, how many teachers would be at the school according to this ratio?
Suppose that in the experiment in Exercise 35, only 5 of the previously tagged deer were collected in the sample of 75. What would be the estimate of the deer population?Data from in Exercise 35To estimate the deer population of a forest preserve, wildlife biologists caught, tagged, and then
Factor each polynomial completely.8p3 + 125
Perform the indicated operations. Express answers in lowest terms. x + 4 x 2 + 2x - 10 x-2
Write a variation equation for each situation. Use k as the constant of variation.C varies jointly as a and the square of b.
At one point during the 2017–2018 NBA Season, the Indiana Pacers had won 19 of their 38 regular season games. If the team continued to win the same fraction of its games, how many games would the Pacers win for the complete 82-game season? Round the answer to the nearest whole number.
Solve each problem. If x varies directly as y, and x = 9 when y = 3, find x when y = 12.
Solve each problem. A river has a current of 4 km per hr. Find the rate of Herby’s boat in still water if it travels 40 km downstream in the same time that it takes to travel 24 km upstream. Upstream Downstream d 24 40 r X-4 t
Solve each problem. If x varies directly as y, and x = 10 when y = 7, find y when x = 50.
An article in Scientific American predicted that in the year 2050, about 23,200 of the 58,000 passenger-km per day in North America will be provided by high-speed trains. If the traffic volume in a typical region of North America is 15,000, how many passenger kilometers per day will high-speed
Solve each problem. If a varies directly as the square of b, and a = 4 when b = 3, find a when b = 2.
Biologists tagged 500 fish in a lake on January 1. On February 1, they returned and collected a random sample of 400 fish, 8 of which had been previously tagged. On the basis of this experiment, how many fish does the lake have?
Solve.3x2 + 4x = 7
Johnny’s car uses 15 gal of gasoline to travel 495 mi. He has 6 gal of gasoline in the car. He still needs to drive 600 mi. If the car continues to use gasoline at the same rate, how many more gallons will he need (to the nearest tenth)?
Solve each problem. If h varies directly as the square of m, and h = 15 when m = 5, find h when m = 7.
Suppose that in the experiment of Exercise 37, 10 of the previously tagged fish were collected on February 1. What would be the estimate of the fish population?Data from in Exercise 37Biologists tagged 500 fish in a lake on January 1. On February 1, they returned and collected a random sample of
Solve each problem. If z varies inversely as w, and z = 10 when w = 0.5, find z when w = 8.
Mike Love’s T-bird uses 6 gal of gasoline to drive 141 mi. He has 4 gal of gasoline in the car, and he still needs to drive 275 mi. If the car continues to use gasoline at the same rate, how many more gallons will he need? DA 1965 Shelby Cobra 289 CLD VS C4 Automatic Transmission 1 out of 17 built
Bruce Johnston’s Shelby Cobra uses 5 gal of gasoline to drive 156 mi. He has 3 gal of gasoline in the car, and he still needs to drive 300 mi. If the car continues to use gasoline at the same rate, how many more gallons will he need? DA 1965 Shelby Cobra 289 CLD VS C4 Automatic Transmission 1 out
In geometry, two triangles with corresponding angle measures equal, called similar triangles, have corresponding sides proportional. For example, in the figure, angle A = angle D, angle B = angle E, and angle C = angle F, so the triangles are similar. Then the following ratios of corresponding
Solve each problem. A sink can be filled by a cold-water tap in 8 min and by a hot-water tap in 12 min. How long would it take to fill the sink with both taps open? Cold Hot Rate Time Working Together X X Fractional Part of the Job Done
Simplify each expression, using only positive exponents in the answer. 1 x2 + y-2
In geometry, two triangles with corresponding angle measures equal, called similar triangles, have corresponding sides proportional. For example, in the figure, angle A = angle D, angle B = angle E, and angle C = angle F, so the triangles are similar. Then the following ratios of corresponding
Write each rational expression in lowest terms. 1²-9 3t + 9
Simplify each expression, using only positive exponents in the answer. d_ج – b_ح 1
Solve each equation. 6 + w +3 -7 w-5 -48 w22w 15 -
Machine A can complete a certain job in 2hr. To speed up the work, Machine B, which can complete the job alone in 3hr, is brought in to help. How long will it take the two machines to complete the job working together?
Write each rational expression in lowest terms. m² - 25 4m - 20
Solve each problem. If t varies inversely as s, and t = 3 when s = 5, find s when t = 5.
Solve each problem. In which one of the following does y vary inversely as x? A. y = 2x X B. y = 1/2 3 3 c. y = // D. y = x²
Simplify each expression, using only positive exponents in the answer. z_^²+z_x _( X x-¹ + y²-¹ -1
Suppose that the given expressions are denominators of rational expressions. Find the least common denominator (LCD) for each group of denominators.2t2 + 7t - 15, t2 + 3t - 10
Solve each equation. 2 r-5 + 3 22 2r + 1 2r² - 9r - 5
Solve each problem. Jane and Jessica need to sort a pile of bottles at the recycling center. Working alone, Jane could do the entire job in 9 hr, while Jessica could do the entire job in 6 hr. How long will it take them if they work together?
Solve each problem. If m varies inversely as the square of p, and m = 20 when p = 2, find m when p = 5.
Suppose that the given expressions are denominators of rational expressions. Find the least common denominator (LCD) for each group of denominators.s2 - 3s - 4, 3s2 + s - 2
Solve each problem. If a varies inversely as the square of b, and a = 48 when b = 4, find a when b = 7.
Suppose that the given expressions are denominators of rational expressions. Find the least common denominator (LCD) for each group of denominators.2y + 6, y2 - 9, y
For a particular camera, the viewing distance varies directly as the amount of enlargement. A picture that is taken with this camera and enlarged 5 times should be viewed from a distance of 250 mm. Suppose a print 8.6 times the size of the negative is made. From what distance should it be viewed?
Solve each problem. p varies jointly as q and the square of r, and p = 200 when q = 2 and r = 3. Find p when q = 5 and r = 2.
Write each rational expression in lowest terms. 2t + 6 1²-9
Solve each equation. 2 X + 4 x + 9 = 1
Simplify each expression, using only positive exponents in the answer. x-¹-y-¹ x-²-y-² -2 -2
Suppose that the given expressions are denominators of rational expressions. Find the least common denominator (LCD) for each group of denominators.9x + 18, x2 - 4, x
For a particular camera, the viewing distance varies directly as the amount of enlargement. A picture that is taken with this camera and enlarged 5 times should be viewed from a distance of 250 mm. Suppose a print 8.6 times the size of the negative is made. From what distance should it be viewed?
Solve each problem. ƒ varies jointly as h and the square of g, and f = 50 when h = 2 and g = 4. Find ƒ when h = 6 and g = 3.
Write each rational expression in lowest terms. 5s - 25 s² - 25 2
As review, add or subtract the rational numbers as indicated. Write answers in lowest terms. 3 10 + 7 15
Add or subtract as indicated. 7 61² 1 3t
Multiply or divide as indicated. w² - 16 W 3 4-w W
Perform the indicated operations. 1-2 +5-2 t-¹ - 8-1 -1 S
Evaluate. |2x + 3y - 2³ for x = -4, y = 3, and z = 6.
Add or subtract as indicated. 9 4 + x - 7 x+7
The gravitational force between two masses is given byFind M to the nearest thousandth if F = 10, G = 6.67 × 10-11, m = 1, and d = 3 × 10-6. F = GMm d²
Add or subtract as indicated. 9 x² - 6x + 9 + 2 x² - 9
Use personal experience or intuition to determine whether the situation suggests direct or inverse variation.Your age and the probability that you believe in the tooth fairy
Multiply or divide as indicated. x² - 4 x-2 x + 2 x - 4
Perform the indicated operations. 9x² + 46x + 5 3x²2x1 + x² + 11x + 30 x³ + 5x² - 6x
Perform the indicated operations. k² 6k+9 1 - 216k³ 6k² + 17k - 3 9-k²
Multiply or divide as indicated. 2²-2-6 2-6 2² - 62 2² + 2z - 15
Use personal experience or intuition to determine whether the situation suggests direct or inverse variation.The surface area of a balloon and its diameter
Solve each equation or inequality. |6x8-4 = 0
To solve the equation rp - rq = p + q for r, a student began by adding rq and then dividing by p to obtainGive the correct answer. r= p+q+rq P
Perform the indicated operations. 4a 6b - a a² - ab 2b² a² + ab + 3b²
Solve each equation or inequality. 2 -y + 3 5 12 y
Add or subtract as indicated. 6 + x +4 1 x + 2 3x x2 + 6x + 8
Solve each formula for the specified variable. F: GMm d² for G (physics)
Multiply or divide as indicated. 8 x 8 + x 16+ 2x x² - 64
Use personal experience or intuition to determine whether the situation suggests direct or inverse variation.The demand for an item and the price of the item
Perform the indicated operations. b + b C + C d
Determine whether each equation represents direct, inverse, joint, or combined variation. y= 3 X
Solve each formula for the specified variable. F = GMm d² for M (physics)
Simplify each expression. 12 r+4 11 6r+24
Multiply or divide as indicated. m³ - n³ m² -n² m² + mn + n² m+n
Use personal experience or intuition to determine whether the situation suggests direct or inverse variation.The number of hours worked by an hourly worker and the amount of money earned
Simplify each expression. 1 a a b T b b a
Solve each equation. x + 3 rẻ – 5r+4 1 X 2 x² - 4x
Solve each equation or inequality. 3x + 2 ≥ 4
Determine whether each equation represents direct, inverse, joint, or combined variation. y x 100
Solve each equation. 3x x-4 + 2 alx || 48 X x² - 4x
Solve each formula for the specified variable. 1 a 1 1 + b C for a (electricity)
Simplify each expression. 2x2 + y2 x-¹-y-¹
A triangle has area 42 m2. The base is 14 m long. Find the height of the triangle. 14 m
Solve each formula for the specified variable. 1 1 1 ===+= for b (electricity) a b c
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) 2x 3 + 4 11 2 (b) 2x X + 3 4 2
Abushieba invested some money at 4% interest and twice as much at 3% interest. His interest for the first year was $400. How much did he invest at each rate?
Solve each equation. 1 5 r || -4 p2
Determine whether each equation represents direct, inverse, joint, or combined variation.y = 10x2
Determine whether each equation represents direct, inverse, joint, or combined variation.y = 2x3
Use the the method of factoring by grouping to factor each polynomial.10x2 + 5x3 - 10y2 + 5y3
Give the domain of the following rational function using (a) Set-builder notation(b) Interval notation f(x) = x + 3 3x² + 2x - 8
Factor each trinomial. 2k² (5-y)- 7k(5 - y) + 5(5-y)
Give the domain of each rational function using (a) Set-builder notation (b) Interval notation. f(x) = -7 3x + 18
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