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College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions

Fill in each blank so that the resulting statement is true.The slope, m, of a line through the distinct points (x1, y1) and (x2, y2) is given by the formula m =_______ .
In Exercises 1–10, find f(g(x)) and g( f(x)) and determine whether each pair of functions f and g are inverses of each other. f(x) = 4x and g(x) = X
Fill in each blank so that the resulting statement is true.We exclude from a function’s domain real numbers that result in a square root of a/an__________ number.
Fill in each blank so that the resulting statement is true.A set of ordered pairs in which each member of the set of first components corresponds to exactly one member of the set of second components is called a/an________.
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places.(5, 1) and (8, 5)
Fill in each blank so that the resulting statement is true.If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative______ of f. If f(b) < f(x) in an open interval containing b, x ≠ b, then the function value f(b) is a relative______ of f.
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places.(2, 3) and (14, 8)
Fill in each blank so that the resulting statement is true.If the function g is the inverse of the function f, then f(g(x)) =______ and g( f(x)) =________ .
Fill in each blank so that the resulting statement is true.We exclude from a function’s domain real numbers that cause division by_________ .
Fill in each blank so that the resulting statement is true.The distance, d, between the points (x1, y1) and (x2, y2) in the rectangular coordinate system is d =_______ .
Fill in each blank so that the resulting statement is true.The notation f -1 means the________ of the function f.
In Exercises 1–10, find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (-2, 1) and (2, 2)
Fill in each blank so that the resulting statement is true.(f + g)(x) =_________ .
Fill in each blank so that the resulting statement is true.The notation f(x) describes the value of________ at________ .
Fill in each blank so that the resulting statement is true.The graph of y = -f(x) is the graph of y = f(x) reflected about the_______ .
In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places.(4, -1) and (-6, 3)
In Exercises 1–30, find the domain of each function. g(x) 3 x - 4
Fill in each blank so that the resulting statement is true.The graph of an equation is symmetric with respect to the______ if substituting -x for x in the equation results in an equivalent equation.
In Exercises 1–16, use the graph of y = f(x) to graph each function g.g(x) = f(x + 1) y y = f(x) 4- (-2,2) 1- -5-4-3-2. [T (0,2) (2.2) H 1 2 3 4 5 [IIIDIICO X
In Exercises 1–12, use the graph to determinea. intervals on which the function is increasing, if any.b. intervals on which the function is decreasing, if any.c. intervals on which the function is constant, if any. -3-2- y -3- HE 1 2 3 4 5 L..... CXIXªTICIOD ||| -4- X
Fill in each blank so that the resulting statement is true.A function f has an inverse that is a function if there is no________ line that intersects the graph of f at more than one point. Such a function is called a/an__________ function.
Let a function f be the line graph connecting the data points (1, 2), (4,9), and (6,3). (a) Write the formula for a piecewise-linear function f that passes through these data points whose domain is 1 ≤ x ≤ 6. (b) Evaluate f(5). (c) Is f continuous on its domain?
Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. 3=5x 3
Solve the equation (a) Graphically, (b) Numerically, and (c) Symbolically. Then solve the related inequality. |4x7| = 5, |4x - 7| ≥ 5
The table shows equivalent temperatures in degrees Celsius and degrees Fahrenheit.(a) Plot the data with Fahrenheit temperature on the x-axis and Celsius temperature on the y-axis. What type of relation exists between the data? (b) Find a function C that receives the Fahrenheit temperature x as
The graph depicts the distance y that a person driving a car on a straight road is from home after x hours. Interpret the graph. What speeds did the car travel? Distance (miles) 2 Time (hours)
Determine the x-and y-intercepts on the graph of the equation. Graph the equation. 4x - 3y = 6
Use the intersection-of-graphs method to solve the equation. Then solve symbolically. -(x + 1)2 = 2x
Solve the linear inequality graphically. Write the solution set in set-builder notation. Approximate endpoints to the nearest hundredth whenever appropriate. 1.238x +0.998 1.23 (3.987-2.1x)
Determine the x-and y-intercepts on the graph of the equation. Graph the equation. 0.2x + 0.4y= 0.8
Solve the equation symbolically. Then solve the related inequality. |2.1x0.7| = 2.4, 2.1x -0.7 2.4
Let y vary directly with x. Complete the following. Find y when x = 1, if y = when x = 3.
Determine the x-and y-intercepts on the graph of the equation. Graph the equation. y = x= 1
Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. -4 < 55-3.1x 4 < 17
Solve the linear equation with the x-intercept method. Check your answer. Approximate the solution to the nearest thousandth whenever appropriate. 2x-4 = 0
Determine the x- and y-intercepts on the graph of the equation. Graph the equation. y = 8x-5
Solve the equation symbolically. Then solve the related inequality. 1 - X
Solve the compound linear inequality graphically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth whenever appropriate. 1.59.10.5x6.8
Find the constant of proportionality k and the undetermined value in the table if y is directly proportional to x. x y 3 7.5 5 12.5 6 15 8 ?
Solve the linear equation with the x-intercept method. Check your answer. Approximate the solution to the nearest thousandth whenever appropriate. -1-²x = = 0
Solve the equation symbolically. Then solve the related inequality. |3x| + 5 = 6, |3x| +5>6
Solve the linear equation with the x-intercept method. Check your answer. Approximate the solution to the nearest thousandth whenever appropriate. 2x = -(3x)
Determine the x-and y-intercepts on the graph of the equation. Graph the equation. y=-1.5x + 15
The table lists the actual annual cost y to drive a midsize car 15,000 miles per year for selected years X.(a) Predict whether the correlation coefficient is positive, negative, or zero. (b) Find a least-squares regression line that models these data. What is the correlation coefficient? (c)
Find the constant of proportionality k and the undetermined value in the table if y is directly proportional to x. x 1.2 4.3 5.7 3.96 14.19 18.81 ? 23.43
Let y vary directly with x. Complete the following.Find y when x = 1.3, if y = 7.2 when x = 5.2.
A driver of a car is initially 455 miles from home, traveling toward home on a straight freeway at 70 miles per hour. (a) Write a formula for a linear function f that models the distance between the driver and home after x hours. (b) Graph f. What is an appropriate domain? (c)
Solve the equation symbolically. Then solve the related inequality. |5x – 0.3| = −4, |5x – 0.3| > →4 -
Solve the equation symbolically. Then solve the related inequality. - 두 - x] S | - H =
Initially, a tank contains 20 gallons of a 30% anti-freeze solution. How many gallons of an 80% antifreeze solution should be added to the tank in order to increase the concentration of the antifreeze in the tank to 50%? 20 gal
Solve the equation symbolically. Then solve the related inequality. |x|- 10 = 25, |x-10 < 25
Solve the inequality. Write the solution in interval notation. |3x - 1| < 8
In 2012 the population of a city was 143,247, and in 2016 it was 167,933. Estimate the population in 2014.
Solve the inequality. Write the solution in interval notation. E > 1
Solve the inequality. Write the solution in interval notation. |7 - 4x = 11
Solve the inequality. Write the solution in interval notation. 6 IV
Solve the inequality. Write the solution in interval notation. |15 = x < 7
Solve the inequality. Write the solution in interval notation. |-3x + 1 ≤ 5
Suppose that one worker can shovel snow from a storefront sidewalk in 50 minutes and another worker can shovel it in 30 minutes. How long will it take if they work together?
Due to acid rain, the percentage of lakes in Scandinavia that lost their population of brown trout increased dramatically between 1940 and 1975. Based on a sample of 2850 lakes, this percentage can be approximated by the following piecewise-linear function.(a) Determine the percentage of lakes that
Suppose the tank is modified so that it has a second inlet pipe, which flows at a rate of 2 gallons per minute. Interpret the graph by determining when each inlet and outlet pipe is open or closed. Volume (gallons) 80 70 60 50 (4.45) 40 30 20 10 (16,77) (12,61), (24,69) (8.33) (28,69) 0 4 8 12 16
An athlete traveled 13.5 miles in 1 hour and 48 minutes, jogging at 7 miles per hour and then at 8 miles per hour. How long did the runner jog at each speed?
Solve the inequality. Write the solution in interval notation. |3x - 5|
The table at the top of the next column lists the cost in millions of dollars for a 30-second Super Bowl commercial for selected years.(a) Find a linear function f that models the data. (b) Estimate the cost in 2009 and compare the estimate to the actual value of $3.0 million. Did your estimate
Solve the inequality. Write the solution in interval notation. |-5-2x| > 1
Solve the inequality. Write the solution in interval notation. |9x + 1| < 10
At one time the Thames River in England supported an abundant community of fish. Pollution then destroyed all the fish in a 40-mile stretch near its mouth for a 45-year period beginning in 1915. Since then, improvement of sewage treatment facilities and other ecological steps have resulted in a
For altitudes up to 4 kilometers, moist air will cool at a rate of about 6°C per kilometer. If the ground temperature is 25°C, at what altitudes would the air temperature be from 5°C to 15°C?
The actual length of a side of a building is 52.3 feet. How accurately must an apprentice carpenter measure this side to have the relative error in the measurement be less than 0.003 (0.3%)?
The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. (a) Solve the inequality. (b) If the high and low monthly average temperatures satisfy equality, interpret the inequality. IT - 50| ≤ 22, Boston, Massachusetts
The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. (a) Solve the inequality. (b) If the high and low monthly average temperatures satisfy equality, interpret the inequality. |T- 10 = 36, Chesterfield, Canada
The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. (a) Solve the inequality. (b) If the high and low monthly average temperatures satisfy equality, interpret the inequality. |T − 61.5| ≤ 12.5, Buenos Aires, Argentina
The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. (a) Solve the inequality. (b) If the high and low monthly average temperatures satisfy equality, interpret the inequality. |T-43.5| ≤ 8.5, Punta Arenas, Chile
If a quantity is measured to be Q and its exact value is A, then the relative error in Q isIf the exact value is A = 35 and you want the relative error in Q to be less than or equal to 0.02 (or 2%), what values for Q are possible? 14
An aluminum can should have a diameter D of 3 inches with a maximum error tolerance that is less than 0.004 inch. (a) Write an absolute value statement that describes this situation. (b) Solve this inequality for D and interpret your result.
The classic iPod is 10.5 millimeters thick. Suppose that the actual thickness T of any particular iPod has a maximum error tolerance that is less than 0.05 millimeter.(a) Write an absolute value statement that describes this situation.(b) Solve this inequality for T and interpret your result.
A part for a machine must fit into a hole and must have a diameter D that is less than or equal to 2.125 inches. The diameter D cannot be less than this maximum diameter of 2.125 inches by more than 0.014 inch. (a) Write an absolute value statement that describes this situation. (b) Solve
Find the point-slope form of the line pass- ing through the given points. Use the first point as (x1, y1). (-3,4), (2,5)
Suppose that a 12-inch ruler must have the correct length L to within 0.0002 inch. (a) Write an absolute value inequality for L that describes this requirement. (b) Solve this inequality and interpret the results.
The exact perimeter P of a square is 50 feet. What measured lengths are possible for the side S of the square to have relative error in the perimeter that is less than or equal to 0.04 (or 4%)?
Find the point-slope form of the line passing through the given points. Use the first point as (x1, y1). (1,-6), (-7,5)
Find the point-slope form of the line passing through the given points. Use the first point as (x1, y1). Then convert the equation to slope-intercept form and write a formula for a function f whose graph is the line. Slope-, passing through (-5,6)
Let a ≠ 0.Solve |x| = 3.
EvaluateRound your answer to the nearest hundredth. 4+ √₂ 4-√₂
(a) Solve the equation |2x - 1| = 5.(b) Use part (a) to solve the absolute value inequalities |2x - 1| ≤ 5 and |2x - 1| > 5. Use interval notation.
Explain how to solve |ax + b| = k with k > 0 symbolically. Give an example.
Rewrite √4x2 by using an absolute value.
Explain how to use the solutions to ax + b = k with k > 0 to solve the inequalities and |ax + b| > k. Give an example. ax + b < k
Write 123,000 and 0.0051 in scientific notation.
Let a ≠ 0.Solve |x| ≤ 3.
Let δ be a positive number and let x and e be real numbers. Write an absolute value inequality that expresses that the distance between x and c on the number line is less than δ.
Let ϵ be a positive number, L be a real number, and be a function. Write an absolute value inequality that expresses that the distance between f(x) and L on the number line is less than ϵ.
Graph y = |3x - 2| by hand.
Write 6.7 x 106 and 1.45 x 10-4 in standard form.
Let a ≠ 0.Solve |x| > 3.
Let a ≠ 0.Solve |ax + b| ≤ -2.
The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. (a) Solve the inequality. (b) If the high and low monthly average temperatures satisfy equality, interpret the inequality. |T62|19, Memphis, Tennessee
The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. (a) Solve the inequality. (b) If the high and low monthly average temperatures satisfy equality, interpret the inequality. |T - 43| ≤ 24, Marquette, Michigan
The dew point decreases as altitude increases. If the dew point on the ground is 80°F, then the dew point x miles high is D = 80 - (29/5)x.(a) Determine the altitudes x where the dew point D is between 50°F and 60°F, inclusive. (b) Use an absolute value inequality to describe these
The air temperature decreases as altitude increases. If the ground temperature is 80°F, then the air temperature x miles high is T = 80 - 19x. (a) Determine the altitudes x where the air temperature T is between 0°F and 32°F, inclusive. (b) Use an absolute value inequality to describe

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