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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
Sketch a graph of f. f(x) = 1 = x²
Use a table or number line to solve the inequality. x²-x-5
Find the domain of the function. Write your answer in set-builder notation. f(x) 4x 7-x²
Find the domain of the function. Write your answer in set-builder notation. f(x) = 1 1²-5
Solve. Write answers in standard form. x² + 2x + 4 = 0
Sketch a graph of f. f(x) = x² - 1
Sketch a graph of f. f(x) = x² - 2
Find the domain of the function. Write your answer in set-builder notation. g(1) 5-1 1²-1-2
Solve. Write answers in standard form. 3x² - 4x = x² - 3
Solve. Write answers in standard form. x(x-4)= -8
Use a table or number line to solve the inequality. x² > 3-4x
Use a table or number line to solve the inequality. 2x² = 1 - 4x
Find the domain of the function. Write your answer in set-builder notation. g(1) 1+1 2²-11-21
Sketch a graph of f. f(x) = -4x² + 4
Find the domain of the function. Write your answer in interval notation. f(x): 1 x² - 1
Sketch a graph of f. f(x)=4-x²
Solve. Write answers in standard form. 2x²+3=1-x
Sketch a graph of f. f(x) = -x²
Find the domain of the function. Write your answer in interval notation. f(x) 1
Solve. Write answers in standard form. 3x² + x = x(5-x) - 2
Sketch a graph of f. f(x) = x² - 3
Solve. Write answers in standard form. 2x(x - 2) = x-4
Find the domain of the function. Write your answer in interval notation. f(x) = 5 x²
Find the domain of the function. Write your answer in interval notation. f(x) = 6 4x x
Solve. Write answers in standard form. 3x (3x) - 8 = x(x - 2)
If a square has an area that is 289 square feet or less, what are the possible lengths x for the side of the square.
The heights in feet of a golf ball after 1 seconds is given by s(t) = -16t2 + 80t. (a) After how many seconds did the golf ball strike the ground? (b) For what values of t is the golf ball 64 feet or more above the ground?
Solve. Write answers in standard form. -x(72x)=-6-(3x)
The heights in feet of a base-ball after 1 seconds is s(t) = -16t2 + 64t + 4. (a) Find the maximum height of the baseball. (b) For what values of t is the baseball 52 feet or more above the ground?
The stopping distance D in feet for a car traveling at x miles per hour on wer level pavement can be estimated byIf a driver can see only 300 feet ahead on a curve, find a safe speed limit. D(x) = x² + x₁
Sketch a graph of f. f(x) = x² + 2
Sketch a graph of f. f(x) = (x - 2)² + 1
The graph of a function is given. (a) Use the graph to predict the number of real zeros and the number of nonreal complex zeros. (b) Find these zeros using the quadratic formula. 3 y=27-x-31 그 3 x
The graph of a function is given. (a) Use the graph to predict the number of real zeros and the number of nonreal complex zeros. (b) Find these zeros using the quadratic formula. =-²+4.6x-5.29 4
Find the domain of the function. Write your answer in interval notation. 1=²7=(x)/ x² + 1
Find the domain of the function. Write your answer in interval notation. f(x) = x+1 x² + 3
Sketch a graph of f. f(x) = (x + 1)²-2
The stopping distance d in feet for a car traveling at x miles per hour is given by Determine the driving speeds that correspond to stopping distances between 300 and 500 feet, inclusive. Round speeds to the nearest mile per hour. d(x) = x² + x
Solve the equation for y. Determine if y is a function of x.
The graph of a function is given. (a) Use the graph to predict the number of real zeros and the number of nonreal complex zeros. (b) Find these zeros using the quadratic formula. y=x²+x+2 12
Sketch a graph of f. f(x) = -2(x - 1)² + 1
Sketch a graph of f. f(x) = -3(x + 1)² + 3
The volume of a cylinder is given by V = πr2h, where r is the radius and h is the height. If the height of a cylindrical can is 6 inches and the volume must be between 24π and 54π cubic inches, inclusive, find the possible values for the radius of the can.
Solve the equation for y. Determine if y is a function of x. y² = 3x
The graph of a function is given. (a) Use the graph to predict the number of real zeros and the number of nonreal complex zeros. (b) Find these zeros using the quadratic formula. 2 1 =-2x²+2x-3 3
The graph of a function is given. (a) Use the graph to predict the number of real zeros and the number of nonreal complex zeros. (b) Find these zeros using the quadratic formula. 21 1 3 y=-x²-2 X
The graph of a function is given. (a) Use the graph to predict the number of real zeros and the number of nonreal complex zeros. (b) Find these zeros using the quadratic formula. 3 -1 y=x²-x+1
Sketch a graph of f. f(x) = 9x - x²
Solve the equation for y. Determine if y is a function of x. 2 - 4y² = x
Solve the equation for y. Determine if y is a function of x. 1 - x = 9y² + 5x
Sketch a graph of f. f(x) = 4x = x²
Solve the equation for y. Determine if y is a function of x. 4x² + 3y y +1 3
Suppose that a person's heart rate, x minutes after vigorous exercise has stopped, can be modeled by f(x) = 4/5(x-10)2 + 80. The output is in beats per minute, where the domain of fis 0 ≤ x ≤ 10. (a) Evaluate f(0) and f(2). Interpret the result. (b) Estimate the times when the
Solve the equation for y. Determine if y is a function of x. x+y=y-2 2
Sketch a graph of f. f(x) = x² - 4x
Complex numbers are used in the study of electrical circuits. Impedance Z (or the opposition to the flow of electricity), voltage V, and current I can all be represented by complex numbers. They are related by the equation Z = V/I Find the value of the missing variable. V = 30 + 60i I= 8 + 6i
A rectangle is 4 feet longer than it is wide. If the area of the rectangle must be less than or equal to 672 square feet, find the possible values for the width x.
As the altitude increases, air becomes thinner, or less dense. An approximation of the density of air at an altitude of x meters above sea level is given by The output is the density of air in kilograms per cubic meter. The domain of d is 0 ≤ x ≤ 10,000. (a) Denver is sometimes referred to as
Sketch a graph of f. f(x)=x²- 2x - 2
Sales of iPods in millions x years after 2006 can be modeled by To the nearest year, estimate when sales were between 50 and 55 million iPods. I(x) = -2.277x² + 11.71x + 40.4.
Complex numbers are used in the study of electrical circuits. Impedance Z (or the opposition to the flow of electricity), voltage V, and current I can all be represented by complex numbers. They are related by the equation Z = V/I Find the value of the missing variable. V = 50+ 98i I = 8 + 5i
Sketch a graph of f. f(x) = x² + 4x - 2
Solve the equation for y. Determine if y is a function of x. Зу || 2x 2х - у 3
When a person breathes carbon monoxide (CO), it enters the bloodstream to form carboxyhemoglobin (COHb), which reduces the transport of oxygen to tissues. The formula given by T(x) = 0.0079x2 - 1.53x + 76 approximates the number of hours T that it takes for a person's blood- stream to reach the 5%
Solve the equation for y. Determine if y is a function of x. 5-y 3 x + 3y 4
Let f(x) = 2375x2 + 5134x + 5020 estimate the number of U.S. AIDS deaths x years after 1984, where 0 ≤ x ≤ 10. Estimate when the number of AIDS deaths was from 90,000 to 200,000.
Complex numbers are used in the study of electrical circuits. Impedance Z (or the opposition to the flow of electricity), voltage V, and current I can all be represented by complex numbers. They are related by the equation Z = V/I Find the value of the missing variable. I = 1 + 2i Z=3-4i
The table shows a person's heart rate after exercise has stopped. (a) Find values for the constants a, h, and k so that the formula f(x) = a(x - h)2 + k models the data, where x represents time and 0 ≤ x ≤ 4.(b) Evaluate f(1) and interpret the result. (c) Estimate the times when the heart
Complex numbers are used in the study of electrical circuits. Impedance Z (or the opposition to the flow of electricity), voltage V, and current I can all be represented by complex numbers. They are related by the equation Z = V/I Find the value of the missing variable. 1 = 1 + i Z=8-9i
Sketch a graph of f. f(x) = x² + 2x + 1
Solve the equation for y. Determine if y is a function of x. x² + (y - 3)² = 9
Explain how a table of values can be used to help solve a quadratic inequality, provided that the boundary numbers are listed in the table.
Complex numbers are used in the study of electrical circuits. Impedance Z (or the opposition to the flow of electricity), voltage V, and current I can all be represented by complex numbers. They are related by the equation Z = V/I Find the value of the missing variable. Z=22-5i V = 27 + 17i
Sketch a graph of f. f(x) = 2x² - 4x - 1
Solve the equation for y. Determine if y is a function of x. (x + 2)² + (y + 1)² = 1
Hitting a Golf Ball A golf ball is hit so that its height h in feet after t seconds is h(t) = -16t2 + 64t. (a) What is the initial height of the golf ball? (b) How high is the golf ball after 1.5 seconds? (c) Find the maximum height of the golf ball.
Explain how to determine the solution set for the inequality ax2 + bx + c < 0, where a > 0. How would the solution set change if a < 0?
Discuss three symbolic methods for solving a quadratic equation. Make up a quadratic equation and use each method to find the solution set.
Simplify by using the imaginary unit i. (a) V-25 7 ± √-98 (c) 14 (b) V-3 V-18
Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) n²-17 = 0 (b) n²-17 ≤ 0 (c) n²-17 20
The table lists the percentage of the population that did not have a high school diploma for selected years.(a) Plot a line graph of these data. Let this graph be function D. (b) Interpret the slope of each line segment. (c) Is D continuous on its domain?(d) Where is D increasing, decreasing, or
Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) k²-4 = 0 (b) k²-4≤0 (c) k²-4 ≥ 0
Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. (a) x² = 8x + 12 = 0 (b) x² 8x + 12 < 0 (c) x² - 8x + 12 > 0
Solve each equation and inequality. Use set-builder or interval notation to write solution sets to the inequalities. 021-*-* (9) 0=21= x= x (B)
The stopping distance d in feet for a car traveling x miles per hour on wet level pavement can be estimated by Determine the driving speeds that correspond to stopping distances between 80 and 180 feet, inclusive. 1 11 d(x) = x² + x.
Solve each inequality. Use set-builder or interval notation. (a) x² - 360 (b) 4x² + 9 > 9x (c) 2x(x - 1) ≤ 2
Solve each equation and inequality. Write the solution set for each inequality in set-builder or interval notation. (a) 2x² + 7x -4 = 0 (b) 2x² + 7x-4 0
Use the graph of y = f(x) to solve f(x) ≤ 0 and f(x) > 0. Write your answer in set-builder or interval notation. (a) 2 12 y = f(x) (b) 1 123 +y=f(x).
Write each expression in standard form. (a) -3i (5- 2i) (b) (6-7i) + (-1 + i) (c) i(1 - i)(1 + i) 2i 4-1 (d) 1+
The table lists numbers of Walmart employees E in millions, x years after 1987.(a) Evaluate E(15) and interpret the result. (b) Find a quadratic function f that models these data. (c) Graph the data and quadratic function f in the same xy-plane. (d) Use to estimate the year when the number of
The number N of women in millions who were gainfully employed in the workforce in selected years is shown in the table at the top of the next column.(a) Use regression to find a quadratic function f that models these workforce data. Support your result graphically. (b) Predict the number of women
Some types of worms have a remarkable capacity to live without moisture. The table shows the number of worms y surviving after x days in one study.(a) Use regression to find a quadratic function f that models these data. (b) Graph f and the data in the same window. (c) Solve the equation f(x) = 0
The Department of Transportation's budget for pedestrian and bicycle programs in millions of dollars for selected years is given in the table.(a) Determine a quadratic function B whose vertex is (2009, 1200) and whose graph passes through the point (2015, 840). Write the expression for B(x) in
The table shows the number of iPods sold in millions of units for various years.(a) Use regression to find a quadratic function/that models the data. Let x = 0 correspond to 2006. (b) Use I to estimate when sales were 28 million units. Year 2006 2007 2008 2009 2010 2011 Sales 39.4 51.6
The taxiway used by an air-craft to exit a runway should not have sharp curves. The safe radius for any curve depends on the speed of the airplane. The table lists the minimum radius R of the exit curves, where the taxiing speed of the airplane is x miles per hour.(a) If the taxiing speed x of the
Explain how to solve a quadratic equation graphi- cally. How many solutions are possible? Why?
In one study the efficiency of photosynthesis in an Antarctic species of grass was investigated. The table lists results for various tem- peratures. The temperature x is in degrees Celsius and the efficiency y is given as a percent.(a) Plot the data. Discuss reasons why a quadratic function might
The table at the top of the next column shows approximate global sales in millions of cars with self-driving features, such as remote valet assistant and autopilot with lane-changing.(a) Discuss the general trend in sales during this time period. (b) Would a linear function model this data well?
The table lists the velocity and distance traveled by a falling object for various elapsed times.(a) Make a scatterplot of the ordered pairs determined by (time, velocity) and (time, distance) in the same viewing rectangle [-1, 5, 1] by [-10, 280, 20]. (b) Find a function y that models the
Projections for Instagram's revenue in billions of dollars are shown in the following table from 2015 to 2020.(a) Find a quadratic function f that models this data. Support your result by graphing the data and your function in the same viewing rectangle. (b) Use f to estimate Instagram's revenue
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