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study help
mathematics
college algebra graphs and models
Questions and Answers of
College Algebra Graphs And Models
The table lists data that are exactly linear. (a) Find the slope-intercept form of the line that passes through these data points. (b) Predict y when x = -2.7 and 6.3. Decide if these calculations
Solve each inequality numerically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth when appropriate. (VII-T).x - 5.5 ≤ 0
Solve the equation (to the nearest tenth) (a) Symbolically, (b) Graphically, and (c) Numerically. 6x8 = -7x + 18
How can you recognize a symbolic representation (formula) of a linear function? How can you recognize a graph or table of values of a linear function?
The percentage of smartphone revenues that were due to iPhones is shown in the table at the top of the next column.(a) Use the four oldest data points to find a linear function f that models these
Cars A and B are traveling in the same direction. Their distances in miles north of St. Louis after x hours are computed by the functions fA and fB, respectively. The graphs of fA and fB are shown in
Solve the equation (to the nearest tenth) (a) Symbolically, (b) Graphically, and (c) Numerically. 3(π - x) + √₂ = 0
A person is riding a bicycle. The graph shows the rider's distance y in miles from an inter- state highway after x hours.(a) How fast is the bicyclist traveling? (b) Find the slope-intercept form of
Solve the inequality. Approximate the endpoints to the nearest thousandth when appropriate. 5.1x2√3 - 1.7x -
Solve the equation (to the nearest tenth) (a) Symbolically, (b) Graphically, and (c) Numerically. √3(2- #x) + x = 0
Solve the equation (to the nearest tenth) (a) Symbolically, (b) Graphically, and (c) Numerically. 5- 8x = 3(x-7) + 37
The graph shows the amount of water in a 100-gallon tank after x minutes have elapsed.(a) Is water entering or leaving the tank? How much water is in the tank after 3 minutes? (b) Find both the x-
Solve the inequality. Approximate the endpoints to the nearest thousandth when appropriate. #x - 5.12 = √2x - 5.7(x - 1.1)
Write each percentage in decimal form. (a) -5.5% (b) -1.54% (c) 120% (d) 3 20
Write each percentage in decimal form. (a) 95% (b) 0.321% (c)-175% (d) -%
In 2005 the average annual tuition and fees for attending a private college or university was $21,000. This cost rose to about $32,000 in 2015, as illustrated in the figure. (a) Find the
Write each percentage in decimal form. (a) 35% (b) -0.07% (c) 721% (d) 10
Solve the inequality. Approximate the endpoints to the nearest thousandth when appropriate. 5 < 4x - 2.5
Solve the inequality. Approximate the endpoints to the nearest thousandth when appropriate. 2x85
Solve each inequality numerically. Write the solution set in set-builder or interval notation, and approximate endpoints to the nearest tenth when appropriate. 1.5(x – 0.7) +15x< 1 -
The cost of driving a car includes both fixed costs and mileage costs. Assume that insurance and car payments cost $350 per month and gasoline, oil, and routine maintenance cost $0.29 per
Explain how you determine whether a linear function is increasing, decreasing, or constant. Give an example of each.
The table lists U.S. demand for green building materials in billions of dollars for selected years.(a) Let x represent the number of years after 2010. Find a formula in slope-intercept form for a
The following table shows mobile device usage by Black Friday shoppers from 2010 to 2015. The middle column lists the percentages of online site traffic due to mobile devices (rather than PCs), and
In 2011 online sales were $192 billion, and in 2014 they were $249 billion.(a) Find a linear function S that models these data. Write S (x) in slope-intercept form. (b) Interpret the slope of
The Celsius C and Fahrenheit F scales are related by C = 5/9(F= 32). These scales have the same temperature reading at a unique value where F = C. Find this temperature.
The table lists the number of bank- ruptcies filed in thousands for selected years.(a) Make a scatterplot of the data. (b) Find a formula in point-slope form for a linear function f that models the
The table lists average tuition and fees in dollars at private colleges for selected years.(a) Make a scatterplot of the data. (b) Find a formula in point-slope form for a linear function f that
As the altitude increases, both the air temperature and the dew point decrease. As long as the air temperature is greater than the dew point, clouds will not form. Typically, the air temperature T
Write each percentage in decimal form. (a) -4.7% (b) -0.01% (c) 500% (d) 40
The table lists the annual hours worked by the average worker in Europe for selected years.(a) Let x represent the number of years after 1970. Find a formula in slope-intercept form for a linear
Suppose the Fahrenheit temperature x miles above ground level is given by the formula T(x) = 85 - 19x. (a) Use the intersection-of-graphs method to esti- mate the altitudes where the temperature
U.S. Music Albums Sold In 2007 music sales were 500 million albums and in 2015 sales were 240 million albums.(a) Find the slope-intercept form for a line passing through the points (2007, 500) and
Distance Function f computes the distance y in miles between a car and the city of Omaha after x hours, where 0 ≤ x ≤ 6. The graphs of f and the horizontal lines y = 100 and y = 200 are shown in
Write each decimal form in percent form. (a) 0.97 (b) -0.04 (c) 10 (d) 10
Write each decimal form in percent form. (a) 0.37 (b) -0.095 (c) 1.9 (d) 20
Toyota Vehicle Sales In 1998 Toyota sold 1.4 mil- lion vehicles and in 2007 it sold 2.3 million vehicles.(a) Find the point-slope form for a line passing through the points (1998, 1.4) and (2007,
(a) Is the graph a horizontal line? (b) Why does the calculator screen appear as it does? Graph y = 1024x + 1 in [0, 3, 1] by [-2,2,1].
Write each decimal form in percent form. (a) -0.121 (b) 1.4 (c) 3.2 (d) 4 4
A rectangle is determined by the stated conditions. Find the slope-intercept form of the four lines that outline the rectangle. Vertices (0,0), (2,2), and (1,3)
Solve the given equation for the specified variable. A = LW for W
Write each decimal form in percent form. (a) 0.001 (b) 12 (c) 1.01 (d) -1% 8
A rectangle is determined by the stated conditions. Find the slope-intercept form of the four lines that outline the rectangle. Vertices (4,0), (0,4), (0, -4), and (-4, 0)
Graph the lines y = 1/2x and y = -x in the standard viewing rectangle. (a) Do the lines appear to be perpendicular?(b) Graph the lines in the following viewing rectangles.Do the lines appear to be
U.S. Social Gaming Social gaming revenues (via the Internet) in billions of dollars from 2010 to 2015 were modeled by R(x) = 0.86x + 1.2, where x represents years after 2010.(a) Interpret the slope
A rectangle is determined by the stated conditions. Find the slope-intercept form of the four lines that outline the rectangle. Vertices (1, 1), (5, 1), and (5,5)
Overweight Americans If trends continue, the past and future percentages of the population who are overweight can be estimated by W(x) = x + 45, where x represents years after 1980. (a)
Solve the given equation for the specified variable. E = IR + 2 for R
Solve the given equation for the specified variable. P = 2L + 2W for L
The number of active Facebook users increased from 100 million in 2008 to 1 billion in 2015. (a) Find a formula for a linear function U that models this growth in millions of users, where x is
A rectangle is determined by the stated conditions. Find the slope-intercept form of the four lines that outline the rectangle. Vertices (1, 1) and (2, 3); the point (3.5, 1) lies on a side of the
The cost of K-12 education per student was $2200 in 1978 and increased to $10,300 in 2008. (a) Find a formula for a linear function C that models this cost in dollars, where x is years after
Video Sharing In 2006 about 33% of Americans reported watching online videos via sharing sites such as YouTube and Vimeo. By 2011 this number increased to 71%.(a) Find a formula for a linear function
Solve the given equation for the specified variable. H 10 HTC + HMT + MTT = S
Solve the given equation for the specified variable. V = 2mrh + #² for h
Graph y = 1000x + 1000 in the standard window. (a) Is the graph a vertical line? (b) Why does the calculator screen appear as it does?
Solve the given equation for the specified variable. 3x + 2y = 8 for y
Solve the given equation for the specified variable. A = bh for h {
In 2005 consumers used credit and debit cards to pay for 40% of all purchases. This percentage was 55% in 2011.(a) Find a linear function P that models the data. (b) Estimate when this
Solve the given equation for the specified variable. 5x - 4y = 20 for y
Solve the given equation for the specified variable. y = 3(x-2) + x for x
Find the line of least-squares fit for the given data points. What is the correlation coefficient? Plot the data and graph the line. (-1,-1), (1,4), (2,6)
Find the line of least-squares fit for the given data points. What is the correlation coefficient? Plot the data and graph the line. (-2, 2), (1,0), (3,-2)
In 2011 subscription and streaming music sales were $0.6 billion and in 2016 they increased to $2.4 billion. Use a linear function to predict the years when these music sales might be between $3.12
The equation of a line is written in standard form. (a) Solve the equation for y. (b) Write a formula f(x) for a function whose graph is the given line. 2x + y = 8
The following data are exactly linear.(a) Find a linear function f that models the data. (b) Solve the inequality f(x) > 2.25. x y 0 2 -1.5 4.5 4 10.5 6 16.5
Solve the given equation for the specified variable. y = 4 (8-2x) for x
Complete the following. (a) Conjecture whether the correlation coefficient r for the data will be positive, negative, or zero. (b) Use a calculator to find the equation of the least- squares
The table lists the percentage P of the female population who had college degrees in selected years.(a) Find a linear function P that models the data. (b) Estimate when this percentage was between
The equation of a line is written in standard form. (a) Solve the equation for y. (b) Write a formula f(x) for a function whose graph is the given line. 3x - y = 5 3х у =
A sales associate receives between 6% and 8% of the selling price of a personal tablet. If the selling price of a personal tablet varies between $80 and $200, find the range for the sales associate's
Complete the following. (a) Conjecture whether the correlation coefficient r for the data will be positive, negative, or zero. (b) Use a calculator to find the equation of the least- squares
In Denver, on the 77th day (March 17) the sun rises at 7:00 A.M., and on the 112th day (April 21) the sun rises at 6:00 A.M. Use a linear function to estimate the days when the sun rises between 6:10
Suppose that an aluminum can is manufactured so that its radius r can vary from 1.99 inches to 2.01 inches. What range of values is possible for the circumference C of the can? Express your answer by
In Boston, on the 90th day (March 30) the sun rises at 6:30 A.M., and on the 129th day (May 8) the sun rises at 5:30 A.M. Use a linear function to estimate the days when the sun rises between 5:45
The following data are exactly linear.(a) Find a linear function f that models the data. (b) Solve the inequality 2 ≤ f(x) ≤ 8. 1 2 0.4 3.5 3 45 6.6 9.7 12.8
Complete the following. (a) Conjecture whether the correlation coefficient r for the data will be positive, negative, or zero. (b) Use a calculator to find the equation of the least- squares
The table lists the number N of tab- lets, such as the iPad, sold worldwide in millions for selected years .x.(a) Find a linear function N that models the data. (b) Estimate when this number is
The equation of a line is written in standard form. (a) Solve the equation for y. (b) Write a formula f(x) for a function whose graph is the given line. 2x - 4y = -1
The equation of a line is written in standard form. (a) Solve the equation for y. (b) Write a formula f(x) for a function whose graph is the given line. 7x + 3y = -4
Complete the following. (a) Conjecture whether the correlation coefficient r for the data will be positive, negative, or zero. (b) Use a calculator to find the equation of the least- squares
Suppose that a square picture frame has sides that vary between 9.9 inches and 10.1 inches. What range of values is possible for the perimeter P of the picture frame? Express your answer by using a
The equation of a line is written in standard form. (a) Solve the equation for y. (b) Write a formula f(x) for a function whose graph is the given line. -9x + 8y = 9
The equation of a line is written in standard form. (a) Solve the equation for y. (b) Write a formula f(x) for a function whose graph is the given line. -2x - 6y = 3
The following table shows mobile device usage by Black Friday shoppers from 2010 to 2015. The middle column lists the percentages of online site traffic due to mobile devices (rather than PCs), and
The following table shows mobile device usage by Black Friday shoppers from 2010 to 2015. The middle column lists the percentages of online site traffic due to mobile devices (rather than PCs), and
The following table shows mobile device usage by Black Friday shoppers from 2010 to 2015. The middle column lists the percentages of online site traffic due to mobile devices (rather than PCs), and
Airline Travel The table lists the numbers of airline passengers in millions at some of the largest airports in the United States during 2002 and 2006.(a) Graph the data by using the 2002 data for
The following table shows mobile device usage by Black Friday shoppers from 2010 to 2015. The middle column lists the percentages of online site traffic due to mobile devices (rather than PCs), and
In the late 1920s Edwin P. Hubble (1889-1953) determined both the distance to several galaxies and the velocity at which they were receding from Earth. Four galaxies with their distances in
The following table shows mobile device usage by Black Friday shoppers from 2010 to 2015. The middle column lists the percentages of online site traffic due to mobile devices (rather than PCs), and
The U.S. per capita (per person) income can be modeled by f(x) = 1550 (x - 2011) + 50,000, where x is the year. Determine the year when the per capita income might be $62,400.
Describe how to numerically solve the linear inequality ax + b ≤ 0. Give an example.
Tuition and fees x years after 2000 at private colleges can be modeled by f(x) = 1080x + 16,200. Use f(x) to determine when tuition and fees might reach $37,800.
If you multiply each part of a three-part inequality by the same negative number, what must you make sure to do? Explain by using an example.
During the 1980s, sales of compact discs surpassed vinyl record sales. From 1985 to 1990, sales of compact discs in millions can be modeled by the formula f(x) = 51.6(x - 1985) + 9.1. whereas sales
The median age A in the United States during year x, where 2000 x 2050, is projected to be A(x) = 0.07 x 104.7. Use A (x) to estimate when the median age may reach 37 years.
Explain how a linear function, a linear equation, and a linear inequality are related. Give an example.
A rectangular window has a length that is 18 inches more than its width. If its perimeter is 180 inches, find its dimensions.
In 2000 the population density of the United States was 80 people per square mile, and in 2011 it was 88 people per square mile. Use a linear function to estimate when the U.S. population density
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