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All Textbook Solutions for College Algebra
For the following exercises, match the given linear equation with its graph in Figure 33. 69. f(x)=3x+2For the following exercises, sketch a line with the given features. 70. An x-intercept of (4,0) and y-intercept of (0,2)For the following exercises, sketch a line with the given features. 71. An x-intercept of (2,0) and y-intercept of (0,4)For the following exercises, sketch a line with the given features. 72. A y-intercept of (0,7) and slope 32For the following exercises, sketch a line with the given features. 73. A y-intercept of (0,3) and slope 25For the following exercises, sketch a line with the given features. 74. Passing through the points (6,2) and (6,6)For the following exercises, sketch a line with the given features. 75. Passing through the points (3,4) and (3,0)For the following exercises, sketch the graph of each equation. 76. f(x)=2x1For the following exercises, sketch the graph of each equation. 77. g(x)=3x+2For the following exercises, sketch the graph of each equation. 78. h(x)=13x+2For the following exercises, sketch the graph of each equation. 79. k(x)=23x3For the following exercises, sketch the graph of each equation. 80. f(t)=3+2tFor the following exercises, sketch the graph of each equation. 81. p(t)=2+3tFor the following exercises, sketch the graph of each equation. 82. x=3For the following exercises, sketch the graph of each equation. 83. x=2For the following exercises, sketch the graph of each equation. 84. r(x)=4For the following exercises, write the equation of the line shown in the graph.For the following exercises, write the equation of the line shown in the graph.For the following exercises, write the equation of the line shown in the graph.For the following exercises, write the equation of the line shown in the graph.For the following exercises, which of the tables could represent a linear function? For each that could be linear, find alinear equation that models the data.For the following exercises, which of the tables could represent a linear function? For each that could be linear, find alinear equation that models the data.For the following exercises, which of the tables could represent a linear function? For each that could be linear, find alinear equation that models the data.For the following exercises, which of the tables could represent a linear function? For each that could be linear, find alinear equation that models the data.For the following exercises, which of the tables could represent a linear function? For each that could be linear, find alinear equation that models the data.For the following exercises, which of the tables could represent a linear function? For each that could be linear, find alinear equation that models the data.For the following exercises, which of the tables could represent a linear function? For each that could be linear, find alinear equation that models the data.For the following exercises, which of the tables could represent a linear function? For each that could be linear, find alinear equation that models the data.For the following exercises, use a calculator or graphing technology to complete the task 97. If f is a linear function, f(0.1)=11.5 , and f(0.4)=5.9 , find an equation for the function.For the following exercises, use a calculator or graphing technology to complete the task. 98. Graph the function ffor a domain of [10,10]:f(x)=0.02x0.01. Enter the function in agraphing utility.For the viewing window, set the minimum value of x to be 10 and the maximum value of x to be 10.For the following exercises, use a calculator or graphing technology to complete the task 99. Graph the function f on a domain of [10,10]:f(x)=2,500x+4,000For the following exercises, use a calculator or graphing technology to complete the task 100. Table 3 shows the input, w, and output, k, for a linear function k. a. Fill in the missing values of the table. b. Write the linear function k, round to 3 decimal places.For the following exercises, use a calculator or graphing technology to complete the task 101. Table 4 shows the input, p, and output, q, for a linear function q. a. Fill in the missing values of the table. b. Write the linear function k.For the following exercises, use a calculator or graphing technology to complete the task 102. Graph the linear function f on a domain of [10,10] for the function whose slope is 18 and y-intercept is 3116. Label the points for the input values of 10 and 10.For the following exercises, use a calculator or graphing technology to complete the task 103. Graph the linear function f on a domain of [0.1,0.1] for the function whose slope is 75 and y-intercept is 22.5 .Label the points for the input values of 0.1 and 0.1.For the following exercises, use a calculator or graphing technology to complete the task 104. Graph the linear function f where f(x)=ax+b on the same set of axes on a domain of [4,4] for the following values of a andb. a. a=2;b=3 b. a=2;b=4 c. a=2;b=4 d. a=2;b=5Find the value ofx if a linear function goes throughthe following points and has the following slope: (x,2),(4,6),m=3Find the value ofy if a linear function goes throughthe following points and has the following slope: (10,y),(25,100),m=5Find the equation of the line that passes throughthe following points: (a,b) and (a,b+1)Find the equation of the line that passes throughthe following points: (2a,b) and (a,b+1)Find the equation of the line that passes throughthe following points: (a,0) and (c,d)Find the equation of the line parallel to the line g(x)=0.01x+2.01 through the point (1,2).Find the equation of the line perpendicular to the line g(x)=0.01x+2.01 through the point (1,2).For the following exercises, use the functions f(x)=0.1x+200 and g(x)=20x+0.1. 112. Find the point of intersection of the lines f and g.For the following exercises, use the functions f(x)=0.1x+200 and g(x)=20x+0.1. 113. Where is f(x) greater than g(x)? Where is g(x) greater than f(x)?At noon, a barista notices that she has 20 in hertip jar. If she makes an average of 0.50 from eachcustomer, how much will she have in her tip jar ifshe serves n more customers during her shift?A gym membership with two personal trainingsessions costs 125, while gym membership with?ve personal training sessions costs 260. What iscost per session?A clothing business finds there is a linearrelationship between the number of shirts, n, it can sell and the price, p, it can charge per shirt.In particular, historical data shows that 1,000 shirtscan be sold at a price of 30, while 3,000 shirts canbe sold at a price of 22. Find a linear equation inthe form p(n)=mn+b that gives the price p they can charge for n shirts.A phone company charges for service accordingto the formula: C(n)=24+0.1n, where n is thenumber of minutes talked, and C(n) is the monthlycharge, in dollars. Find and interpret the rate ofchange and initial value.A farmer finds there is a linear relationship betweenthe number of bean stalks, n, she plants and theyield, y, each plant produces. When she plants 30stalks, each plant yields 30 oz of beans. When sheplants 34 stalks, each plant produces 28 oz of beans.Find a linear relationship in the form y=mn+b that gives the yield when n stalks are planted.A city’s population in the year 1960 was 287,500.In 1989 the population was 275,900. Computethe rate of growth of the population and make astatement about the population rate of change inpeople per year.A town’s population has been growing linearly.In 2003, the population was 45,000, and thepopulation has been growing by 1,700 peopleeach year. Write an equation, P(t), for the population tyears after 2003.Suppose that average annual income (in dollars) forthe years 1990 through 1999 is given by the linearfunction: I(x)=1,054x+23,286 , where x is thenumber of years after 1990. Which of the followinginterprets the slope in the context of the problem? a. As of 1990, average annual income was $23,286. b. In the ten-year period from 1990-1999, averageannual income increased by a total of $1,054. c. Each year in the decade of the 1990s, averageannual income increased by $1,054. d. Average annual income rose to a level of $23,286 bythe end of 1999.When temperature is 0 degrees Celsius, theFahrenheit temperature is 32. When the Celsius temperature is 100, the corresponding Fahrenheittemperature is 212. Express the Fahrenheittemperature as a linear function of C, the Celsiustemperature, F(C). a. Find the rate of change of Fahrenheit temperaturefor each unit change temperature of Celsius. b. Find and interpret F(28) . c. Find and interpret F(40) .A company sells doughnuts. They incur a fixed cost of $25,000 for rent, insurance, and other expenses. It costs $0.25to produce each doughnut. a. Write a linear model to represent the cost C of the company as a function of x, the number of doughnuts produced. b. Find and interpret the y-intercept.A city’s population has been growing linearly. In 2008, the population was 28,200. By 2012, the population was36,800. Assume this trend continues. a. Predict the population in 2014. b. Identify the year in which the population will reach 54,000.Try it #3 There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway downthe road,it junctions with a second road, perpendicular to the first, leading to the town of Garrison. If the town ofGarrison is located 2.2 miles directly east of the town of Timpson, how far is the road junction from Timpson?Explain how to find the input variable in a word problem that uses a linear function.Explain how to find the output variable in a wordp roblem that uses a linear function.Explain how to interpret the initial value in a word problem that uses a linear function.Explain how to determine the slope in a wordproblem that uses a linear function.Find the area of a parallelogram bounded by they-axis, the line x=3, the line f(x)=1+2x, and theline parallel to f(x) passing through (2,7).Find the area of a triangle bounded by the x-axis,the line f(x)=1213x, and the line perpendicularto f(x) that passes through the origin.Find the area of a triangle bounded by the y-axis,the line f(x)=967x, and the line perpendicular to f(x) that passes through the origin.Find the area of a parallelogram bounded by thex-axis, the line g(x)=2, the line f(x)=3x, and theline parallel to f(x) passing through (6,1).For the following exercises, consider this scenario: A town’s population has been decreasing at aconstant rate. In2010 the population was 5,900. By 2012 the population had dropped 4,700.Assume this trend continues. 9. Predict the population in 2016.For the following exercises, consider this scenario: A town’s population has been decreasing at aconstant rate. In2010 the population was 5,900. By 2012 the population had dropped 4,700.Assume this trend continues. 10. Identify the year in which the population will reach 0.For the following exercises, consider this scenario: A town’s population has been increased at a constant rate. In2010 the population was 46,020. By 2012 the population had increased to 52,070. Assume this trend continues. 11. Predict the population in 2016.For the following exercises, consider this scenario: A town’s population has been increased at a constant rate. In2010 the population was 46,020. By 2012 the population had increased to 52,070. Assume this trend continues. 12. Identify the year in which the population will reach75,000.For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constantrate of 2,500 per year for 5 years. Find the linear function that models the town’spopulation P as a function of the year, t, where t isthe number ofyears since the model began.For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years. Find a reasonable domain and range for the function P.For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constantrate of 2,500 per year for 5 years. If the function P is graphed, find and interpret thex-and y-intercepts.For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years. If the function P is graphed, find and interpret the slope of the function.For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years. When will the output reached 100,000?For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years. What is the output in the year 12 years from the onset of the model?For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month for its first year. Find the linear function that models the baby’s weight, W, as a function of the age of the baby, in months, t.For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month for its first year. Find a reasonable domain and range for the function W.For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month for its first year. If the function W is graphed, find and interpret the x-and y-intercepts.For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month for its first year. If the function W is graphed, find and interpret the slope of the function.For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month for its first year. When did the baby weight 10.4 pounds?For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. Thebaby gained one-halfpound a month for its first year. What is the output when the input is 6.2? Interpretyour answer.For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2.005 until 2010. In 2005, 12,025 people were afflicted. Find the linear function that models the number of people in?icted with the common cold, C, as a function of the year, t.For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were afflicted. Find a reasonable domain and range for the function C.For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were afflicted. If the function C is graphed, find and interpret the x-and y-intercepts.For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were afflicted. If the function C is graphed, find and interpret the slope of the function.For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were afflicted. When will the output reach 0?For the following exercises, consider this scenario: The number of people afflicted with the common cold in thewinter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were afflicted. 30. In what year will the number of people be 9,700?For the following exercises, use the graph in Figure 7, which shows the profit, y, in thousands of dollars, of a companyin a given year, t, where t represents the number of years since 1980. 31. Find the linear function y, where y depends on t, the number of years since 1980.For the following exercises, use the graph in Figure 7, which shows the profit, y, in thousands of dollars, of a companyin a given year, t, where t represents the number of years since 1980. 32. Find and interpret the y-intercept.For the following exercises, use the graph in Figure 7, which shows the profit, y, in thousands of dollars, of a companyin a given year, t, where t represents the number of years since 1980. 33. Find and interpret the x-intercept.For the following exercises, use the graph in Figure 7, which shows the profit, y, in thousands of dollars, of a companyin a given year, t, where t represents the number of years since 1980. 34. Find and interpret the slope.For the following exercises, use the graph in Figure 8, which shows the profit, y, in thousands of dollars, of a companyin a given year, t, where trepresents the number of years since 1980. 35. Find the linear function y, where y depends on t, the number of years since 1980.For the following exercises, use the graph in Figure 8, which shows the profit, y, in thousands of dollars, of a companyin a given year, t, where trepresents the number of years since 1980. 36. Find and interpret the y-intercept.For the following exercises, use the graph in Figure 8, which shows the profit, y, in thousands of dollars, of a companyin a given year, t, where trepresents the number of years since 1980. 37. Find and interpret the x-intercept.For the following exercises, use the graph in Figure 8, which shows the profit, y, in thousands of dollars, of a companyin a given year, t, where trepresents the number of years since 1980. 38. Find and interpret the slope.For the following exercises, use the median home values in Mississippi and Hawaii (adjusted for inflation) shown inTable 2. Assume that the house values are changing linearly. 39. In which state have home values increased at a higher rate?For the following exercises, use the median home values in Mississippi and Hawaii (adjusted for inflation) shown inTable 2. Assume that the house values are changing linearly. 40. If these trends were to continue, what would be the median home value in Mississippi in 2010?NUMERIC For the following exercises, use the median home values in Mississippi and Hawaii (adjusted for inflation) shown in Table 2. Assume that the house values are changing linearly. If we assume the linear trend existed before 1950 and continues after 2000, the two states median house values will be (or were) equal in what year? (The answer might be absurd.)For the following exercises, use the median home values in Indiana and Alabama (adjusted for inflation) shown in Table 3. Assume that the house values are changing linearly. In which state have home values increased at a higher rate?For the following exercises, use the median home values in Indiana and Alabama (adjusted for inflation) shown in Table 3. Assume that the house values are changing linearly. If these trends were to continue, what would be the median home value in Indiana in 2010?For the following exercises, use the median home values in Indiana and Alabama (adjusted for inflation) shown in Table 3. Assume that the house values are changing linearly. If we assume the linear trend existed before 1950 and continues after 2.000, the two states median house values will be (or were) equal in what year? (The answer might be absurd.)In 2004, a school population was 1,001. By 2008the population had grown to 1,697. Assume thepopulation is changing linearly. a. How much did the population grow between theyear 2004 and 2008? b. How long did it take the population to grow from1,001 students to 1,697 students? c. What is the average population growth per year? d. What was the population in the year 2000? e. Find an equation for the population, P, of theschool t years after 2001. f. Using your equation, predict the population of theschool in 2011 .In 2003, a town’s population was 1,431. By 2007the population had grown to 2,134. Assume thepopulation is changing linearly. a. How much did the population grow between theyear 2003 and 200?? b. How long did it take the population to grow from1,431 people to 2,134 people? c. What is the average population growth per year? d. What was the population in the year 2000? e. Find an equation for the population, P of the town tyears after 2000. f. Using your equation, predict the population of thetown in 2014.A phone company has a monthly cellular plan where a customer pays a flat monthly fee and thena certain amount of money per minute used on thephone. If a customer uses 410 minutes, the monthly cost will be $71.50. If the customer uses 720 minutes,the monthly cost will be $118. a. Find a linear equation for the monthly cost of thecell plan as a function of x, the number of monthly minutes used. b. Interpret the slope and y-intercept of the equation. c. Use your equation to find the total monthly cost if687 minutes are used.A phone company has a monthly cellular data plan where a customer pays a flat monthly fee of $10 andthen a certain amount of money per megabyte (MB)of data used on the phone. If a customer uses 20 MB,the monthly cost will be $11.20. Ifthe customer uses130 MB, the monthly cost will be $1180. a. Find a linear equation for the monthly cost of thedata plan as a function of x, the number of MB used. b. Interpret the slope and y-intercept of the equation. c. Use your equation to find the total monthly cost if 250 MB are used.In 1991, the moose population in a park wasmeasured to be 4,360. By 1999, the population was measured again to be 5,880. Assume the population continues to change linearly. a. Find a formula for the moose population,P since 1990. b. What does your model predict the meme population to be in 2003?In 2003, the owl population in a park was measured to be 340. By 2007, the population was measured again to be 285. The population changes linearly. Letthe input be years since 1990. a. Find a formula for the owl population, P. Let the input be years since 2003. b. What does your model predict the owl population to be in 2012?The Federal Helium Reserve held about 16 billioncubic feet of helium in 2010 and is being depleted byabout 2.1 billion cubic feet each year. a. Give a linear equation for the remaining federalhelium reserves, R, in terms of t, the number of years since 2010. b. In 2015, what will the helium reserves be? c. If the rate of depletion doesn’t change, in what year will the Federal Helium Reserve be depleted?Suppose the world’s oil reserves in 2014 are 1,820 billion barrels. If, on average, the total reserves are decreasing by 25 billion barrels of oil each year: a. Give a linear equation for the remaining oil reserves,R, in terms of t, the number of years since now. b. Seven years from now, what will the oil reserves be? c. If the rate at which the reserves are decreasing is constant, when will the world’s oil reserves be depleted?You are choosing between two different prepaid cellphone plans. The first plan charges a rate of 26 centsper minute. The second plan charges a monthly fee of $19.95 plus 11 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?You are choosing between two different windowwashing companies. The first charges $5 per window.The second charges a base fee of $40 plus $3 perwindow. How many windows would you need tohave for the second company to be preferable?When hired at a new job selling jewelry, you aregiven two pay options: • Option A: Base salary of $17,000 a year with acommission of 12% of your sales • Option B: Base salary of $20,000 a year with acommission of 5% of your sales How much jewelry would you need to sell for optionA to produce a larger income?When hired at a new job selling electronics, you are given two pay options: • Option A: Base salary of $14,000 a year with acommission of 10% of your sales • Option B: Base salary of $19,000 a year with acommission of 4% of your sales How much electronics would you need to sell foroption A to produce a larger income?When hired at a new job selling electronics, you aregiven two pay options: • Option A: Base salary of $20,000 a year with acommission of 12% ofyour sales • Option B: Base salary of $26,000 a year with acommission of 3% of your sales How much electronics would you need to sell foroption A to produce a larger income?When hired at a new job selling electronics, you aregiven two pay options: • Option A: Base salary of $10,000 a year with acommission of 9% of your sales • Option B: Base salary of $20,000 a year with acommission of 4% of your sales How much electronics would you need to sell foroption A to produce a larger income?According to the data from Table 1, what temperature can we predict it is if we counted 20 chirps in 15 seconds?Use the model we created using technology in Example 6 to predict the gas consumption in 2011. Is this aninterpolation or an extrapolation?Describe what it means if there is a model breakdown when using a linear model.What is interpolation when using a linear model?What is extrapolation when using a linear model?Explain the difference between a positive and anegative correlation coefficient.Explain how to interpret the absolute value of acorrelation coefficient.A regression was run to determine whether there isa relationship between hours of TV watched per day (x) and number of sit-ups a person can do (y). The results of the regression are given below. Use this topredict the number of situps a person who watches 11 hours of TV can do. y=ax+b a=1.341 b=32.234 r=0.896A regression was run to determine whether there is arelationship between the diameter of a tree (x, in inches) and the tree’s age (y, in years). Theresults of the regression are given below. Use this topredict the age of a tree with diameter 10 inches. y=ax+ba=6.301b=1.044r=0.970For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related?For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related?For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related?For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related?For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related? For the following data, draw a scatter plot. If we wanted to know when the population would reach 15,000, would the answer involve interpolation or extrapolation? Eyeball the line, and estimate the answer.For the following exercises, draw a scatter plot for the data provided. Does the data appear to be linearly related? 13. For the following data, draw a scatter plot. If wewanted to know when the temperature would reach 28°F, would the answer involve interpolation or extrapolation? Eyeball the line and estimate the answer.For the following exercises, match each scatterplot with one of the four specified correlations in Figure 9 and Figure 10. 14. r = 0.95For the following exercises, match each scatterplot with one of the four specified correlations in Figure 9 and Figure 10. 15. r=0.89For the following exercises, match each scatterplot with one of the four specified correlations in Figure 9 and Figure 10. 16. r=0.26For the following exercises, match each scatterplot with one of the four specified correlations in Figure 9 and Figure 10. 17. r=0.39For the following exercises, draw a best-fit line for the plotted data.For the following exercises, draw a best-fit line for the plotted data.For the following exercises, draw a best-fit line for the plotted data.For the following exercises, draw a best-fit line for the plotted data.The U.S. Census tracks the percentage of persons 25 years or older who are college graduates. That data forseveral years is given in Table 4[14]. Determine whether the trend appears linear. If so, and assuming the trendcontinues. in what year will the percentage exceed 35%?The US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?Table 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy.For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy.For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy.For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy.For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy.For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy.For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy.Graph f(x)=0.5x+10. Pick a set of 5 orderedpairs using inputs x=2,1,5,6,9 and use linearregression to verify that the function is a good fit forthe data.Graph f(x)=2x10. Picka set of5 ordered pairs using inputs x=2,1,5,6,9 and use linear regression to verify the function.For the following exercises, consider this scenario: The profit of a company decreased steadily overa ten-year spam.The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span, (number of units sold, profit) for specific recorded years: (46,600),(48,550),(50,505),(52,540),(54,495). Use linear regression to determine a function Pwhere the profit in thousands of dollars depends onthe number of units sold in hundreds.For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year spam.The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span, (number of units sold, profit) for specific recorded years: (46,600),(48,550),(50,505),(52,540),(54,495). 35. Find to the nearest tenth and interpret thex-intercept.For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year spam.The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span, (number of units sold, profit) for specific recorded years: (46,600),(48,550),(50,505),(52,540),(54,495). Find to the nearest tenth and interpret they-intercept.For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span.The following ordered pairs shows the population and the year over the ten-year span, (population, year) for specific recorded years: (2500,2000),(2650,2001),(3000,2003),(3500,2006),(4200,2010) 37. Use linear regression to determine a function y,where the year depends on the population. Roundto three decimal places of accuracy.For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span.The following ordered pairs shows the population and the year over the ten-year span, (population, year) for specific recorded years: (2500,2000),(2650,2001),(3000,2003),(3500,2006),(4200,2010) 38. Predict when the population will hit 8,000.For the following exercises, consider this scenario: The profit of a company increased steadily over a ten-year span. Thefollowing ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten-yearspan, (number of units sold, profit) for specific recorded years: (46,250),(48,305),(50,350),(52,390),(54,410). Use linear regression to determine a function y,where the profit in thousands of dollars depends onthe number of units sold in hundreds.For the following exercises, consider this scenario: The profit of a company increased steadily over a ten-year span. Thefollowing ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten-yearspan, (number of units sold, profit) for specific recorded years: (46,250),(48,305),(50,350),(52,390),(54,410). Predict when the profit will exceed one milliondollars.For the following exercises, consider this scenario: The profit of a company decreased steadily overa ten-year span.The following ordered pairs show dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span (number of units sold, profit) for specific recorded years: (46,250),(48,305),(50,350),(52,390),(54,410). Use linear regression to determine a function y,where the profit in thousands of dollars depends onthe number of units sold in hundreds.For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span.The following ordered pairs show dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span (number of units sold, profit) for specific recorded years: (46,250),(48,305),(50,350),(52,390),(54,410). Predict when the profit will dip below the $25,000threshold.Determine whether the algebraic equation is linear. 2x+3y=7Determine whether the algebraic equation is linear. 6x2y=5Determine whether the function is increasing ordecreasing. f(x)=7x2Determine whether the function is increasing ordecreasing. g(x)=x+2Given each set of information, find a linear equationthat satis?es the given conditions, if possible. Passesthrough (7,5) and (3,17)Given each set of information, find a linear equationthat satis?es the given conditions, if possible.x-intercept at (6,0) and y-intercept at (0,10)Find the slope of the line shown in the graph.Find the slope of the line shown in the graph.Write an equation in slope-intercept form for the line shown.Does the following table represent a linear function ? If so, find the linear equation that models the data.Does the following table represent a linear function ? If so, find the linear equation that models the data.On June 1st, a company has $4,000,000 profit.If the company then loses 150,000 dollars perday thereafter in the month of June, what is thecompany’s profit nthday after June 1st?For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: 2x6y=12x+3y=1For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: y=13x23x+y=9For the following exercises, find the x-and y-intercepts of the given equation 7x+9y=63For the following exercises, find the x-and y-intercepts of the given equationFor the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pairof lines parallel perpendicular. or neither? Line 1: Passes through (5,11) and (10,1) Line 2: Passes through (1,3) and (5,11)For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pairof lines parallel, perpendicular,or neither? Line 1: Passes through (8,10) and (0,26) Line 2: Passes through (2,5) and (4,4)For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pairof lines parallel, perpendicular, or neither? Write an equation for a line perpendicular to f(x)=5x1 and passing through the point (5,20).For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pairof lines parallel, perpendicular, or neither? Find the equation of a line with a y-intercept of (0,2) and slope 12 .For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pairof lines parallel, perpendicular, or neither? Sketch a graph of the linear function f(t)=2t5.For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pairof lines parallel, perpendicular, or neither? Find the point of intersection for the 2 linearfunctions: x=y+62xy=13For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither? A car rental company offers two plans for renting a car. Plan A: 25 dollars per day and 10 cents per mile Plan B: 50 dollars per day with free unlimited mileage How many miles would you need to drive for plan B to save you money?Find the area of a triangle bounded by the y-axis, the line f(x)=102x, and the line perpendicular to f thatpasses through the origin.A town’s population increases at a constant rate. In 2010 the population was 55,000. By 2012 the population had increased to 76,000. If this trend continues. predict the population in 2016.The number of people afflicted with the common cold in the winter months dropped steadily by 50 each yearsince 2004 until 2010. In 2004, 875 people were inflicted. Find the linear function that models the number of people afflicted with the common cold C as a function of theyear, t. When will no one be afflicted?For the following exercises, use the graph in Figure 1 showing the profit, y, in thousands ofdollars, of a company ina given year, 1, where x represents years since 1980. 27. Find the linear function y, where y depends on x, the number of years since 1980.For the following exercises, use the graph in Figure 1 showing the profit, y, in thousands of dollars, of a company in a given year, 1, where x represents years since 1980. Find and interpret the y-intercept.For the following exercise, consider this scenario: In 2004, a school population was 1,700. By 2012 the population had grown to 2,500. Assume the population is changing linearly. a. How much did the population grow between the year 2004 and 2012? b. What is the average population growth per year? c. Find an equation for the population, P, of the school t years after 2004.For the following exercises, consider this scenario: In 2000, the moose population in a park was measured to be 6,500. By 2010, the population was measured to be 12,500. Assume the population continues to change linearly. Find a formula for the moose population, P.For the following exercises, consider this scenario: In 2000, the moose population in a park was measured to be 6,500. By 2010, the population was measured to be 12,500. Assume the population continues to change linearly. What does your model predict the moose population to be in 2020?For the following exercises, consider this scenario: The median home values in subdivisions Pima Central and East Valley (adjusted for inflation) are shown in Table 1. Assume that the house values are changing linearly. In which subdivision have home values increased at a higher rate?For the following exercises, consider this scenario: The median home values in subdivisions Pima Central and East Valley (adjusted for inflation) are shown in Table 1. Assume that the house values are changing linearly. If these trends were to continue, what would be the median home value in Pima Central in 2015?Draw a scatter plot for the data in Table 2. Then determine whether the data appears to belinearly related.Draw a scatter plot for the data in Table 3. If we wanted to know when the population would reach 15,000,would the answer involve interpolation or extrapolation?Eight students were asked to estimate their score on a 10-point quiz. Their estimated and actual scores are givenin Table 4. Plot the points, then sketch a line that fits the data.Draw a best-fit line for the plotted data.For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city of people 25 years or older who are college graduates is given below, by year. 38. Determine whether the trend appears to be linear.If so, and assuming the trend continues, find alinear regression model to predict the percent of unemployed in a given year to three decimal places.For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city of people 25 years or older who are college graduates is given below, by year. In what year will the percentage exceed 12%?For the following exercises, consider the data in Table 5, which shows the percent of unemployed ina city of people 25 years or older who are college graduates is given below, by year. 40. Based on the set of data given in Table 6, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city ofpeople25 years or older who are college graduates is given below, by year. 41. Based on the set of data given in Table 7, calculatethe regression line using a calculator or othertechnology tool, and determine the correlationcoefficient to three decimal places.For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span.The following ordered pairs show the population and the year over the ten-year span (population, year) for specific recorded years: (3,600,2000);(4,000,2001);(4,700,2003);(6,000,2006) 42. Use linear regression to determine a function y,where the year depends on the population, to threedecimal places of accuracy.For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs show the population and the year over the ten-year span (population, year) for specific recorded years: Predict when the population will hit 12,000.For the following exercises, consider this scenario: The population of a city increased steadily overa ten-year span. The following ordered pairs show the population and the year over the ten-year span (population, year) for specific recorded years: (3,600,2000);(4,000,2001);(4,700,2003);(6,000,2006) 44. What is the correlation coefficient for this model tothree decimal places of accuracy?For the following exercises, consider this scenario: The population of a city increased steadily overa ten-year span. The following ordered pairs show the population and the year over the ten-year span (population, year) for specific recorded years: (3,600,2000);(4,000,2001);(4,700,2003);(6,000,2006) 45. According to the model, what is the populationin 2014?Determine whether the following algebraic equationcan be written as a linear function. 2x+3y=7Determine whether the following function isincreasing or decreasing. f(x)=2x+5Determine whether the following function isincreasing or decreasing f(x)=7x+9Given the following set of information, find a linearequation satisfying the conditions, if possible. Passesthrough (5,1) and (3,9)Given the following set of information. find a linear equation satisfying the conditions, if possible.x-intercept at (4,0) and y-intercept at (0,6)Find the slope ofthe line in Figure l.Write an equation for line in Figure 2.Does Table 1 represent a linear function? If so, finda linear equation that models the data.Does Table 2 represent a linear function? If so, finda linear equation that models the data.At 6 am, an online company has sold 120 items that day. If the company sells an average of 30 items per hourfor the remainder of the day, write an expression to represent the number of items that were sold n after 6 am.For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: y=34x94x3y=8For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: 2x+y=33x+32y=5For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: Find the x-and y-intercepts of the equation 2x+7y=14.For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: Given below are descriptions of two lines. Find the slopes of Line 1 and Line 2. Is the pair of lines parallel,perpendicular, or neither? Line 1: Passes through (2,6) and (3,14) Line 2: Passes through (2,6) and (4,14)For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: Write an equation for a line perpendicular to f(x)=4x+3 and passing through the point (8,10).For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: Sketch a line with a y-intercept of (0,5) and slope 52.For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: Graph of the linear function f(x)=x+6.For the following exercises, determine whether the lines given by the equations below are parallel,perpendicular, orneither parallel nor perpendicular: For the two linear functions, find the point ofintersection: x=y+22x3y=1For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: 19. A car rental company offers two plans for rentinga car. Plan A: $25 per day and $0.10 per mile Plan B: $40 per day with free unlimited mileage How many miles would you need to drive for plan Bto save you money?For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: Find the area of a triangle bounded by the y-axis,the line f(x)=124x, and the lineperpendicularto f that passes through the origin.For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: A town’s population increases at a constant rate.In 2010 the population was 65,000. By2012 thepopulation had increased to 90,000. Assuming thistrend continues, predict the population in 2018.For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, orneither parallel nor perpendicular: The number of people afflicted with the commoncold in the winter months dropped steadily by25 each year since 2002 until 2012. In 2002, 8,040people were in?icted. Find the linear function thatmodels the number of people afflicted with thecommon cold C as a function of the year, t. Whenwill less than 6,000 people be afflicted?For the following exercises, use the graph in Figure 3, showing the profit, y, in thousands of dollars, of a companyin a given year, x, where x represents years since 1980. Find the linear function y, where y depends on x,the number of years since 1980.For the following exercises, use the graph in Figure 3, showing the profit, y, in thousands of dollars, of a company in a given year, x, where x represents years since 1980. Find and interpret the y-intercept.For the following exercises, use the graph in Figure 3, showing the profit, y, in thousands of dollars, of a company in a given year, x, where x represents years since 1980. In 2004, a school population was 1250. By 2012 the population had dropped to 875. Assume the population is changing linearly. a. How much did the population drop between the year 2004 and 2012? b. What is the average population decline per year? c. Find an equation for the population, P, of the school t years after 2004.For the following exercises, use the graph in Figure 3, showing the profit, y, in thousands of dollars, of a company in a given year, x, where x represents years since 1980. Draw a scatter plot for the data provided in Table 3. Then determine whether the data appears to be linearly related.For the following exercises, use the graph in Figure 3, showing the profit, y, in thousands of dollars, of a company in a given year, x, where x represents years since 1980. 27. Draw a best-fit line for the plotted data.For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Determine whether the trend appears linear. If so, and assuming the trend continues, find a linear regression model to predict the percent of unemployed in a given year to three decimal places.For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. In what year will the percentage drop below 4%?For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracyFor the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. Thefollowing ordered pairs shows the population (in hundreds) and the year over the ten-year span, (population, year) forspecific recorded years: (4,500,2000);(4,700,2001);(5,200,2003);(5,800,2006) Use linear regression to determine a function y, where the year depends on the population. Round to threedecimal places of accuracy.For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. Thefollowing ordered pairs shows the population (in hundreds) and the year overthe ten-year span, (population, year) forspecific recorded years: (4,500,2000);(4,700,2001);(5,200,2003);(5,800,2006) Predict when the population will hit 20,000.For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. Thefollowing ordered pairs shows the population (in hundreds) and the year overthe ten-year span, (population, year) forspecific recorded years: (4,500,2000);(4,700,2001);(5,200,2003);(5,800,2006) What is the correlation coefficient for this model?A coordinate grid has been superimposed over the quadratic path of a basketball in Figure 8 Find an equation for the path of the ball. Does the shooter make the basket?.Given the equation g(x)=13+x26x, write the equation in general form and then in standard form.Find the domain and range of f(x)=2(x47)2+811.In a separate Try It, we found the standard and general form for the function g(x)=13+x26x. Now find the y-and x-intercepts (ifany).A rock is thrown upward from the top of a 112-foot high cliff overlooking the ocean at a speed of 96 feet per second.The rock's height above ocean can be modeled by the equation H(t)=16t2+96t+112. a. When does the rock reach the maximum height? b. What is the maximum height of the rock? c. When does the rock hit the ocean?Explain the advantage of writing a quadraticfunction in standard form.How can the vertex of a parabola be used in solvingreal-world problems?Explain why the condition of a0 is imposed inthe de?nition of the quadratic function.What is another name for the standard form of aquadratic function?What two algebraic methods can be used to find thehorizontal intercepts of a quadratic function?For the following exercises, rewrite the quadratic functions in standard form and give the vertex. 6. f(x)=x212x+32For the following exercises, rewrite the quadratic functions in standard form and give the vertex. 7. g(x)=x2+2x3For the following exercises, rewrite the quadratic functions in standard form and give the vertex. 8. f(x)=x2xFor the following exercises, rewrite the quadratic functions in standard form and give the vertex. 9. f(x)=x2+5x2For the following exercises, rewrite the quadratic functions in standard form and give the vertex. 10. h(x)=2x2+8x10For the following exercises, rewrite the quadratic functions in standard form and give the vertex. 11. k(x)=3x26x9For the following exercises, rewrite the quadratic functions in standard form and give the vertex. 12. f(x)=2x26xFor the following exercises, rewrite the quadratic functions in standard form and give the vertex. 13. f(x)=3x25x1For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. y(x)=2x2+10x+12For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. f(x)=2x210x+4For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. f(x)=x2+4x+3For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. f(x)=4x2+x1For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. h(t)=4t2+6t1For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. f(x)=12x2+3x+1For the following exercises, determine whether there is a minimum or maximum value to each quadratic function. Find the value and the axis of symmetry. f(x)=13x22x+3For the following exercises, determine the domain and range of the quadratic function. f(x)=(x3)2+2For the following exercises, determine the domain and range of the quadratic function. f(x)=2(x+3)26For the following exercises, determine the domain and range of the quadratic function. f(x)=x2+6x+4For the following exercises, determine the domain and range of the quadratic function. f(x)=2x24x+2For the following exercises, determine the domain and range of the quadratic function. k(x)=3x26x9For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h,k)=(2,0),(x,y)=(4,4)For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h,k)=(2,1),(x,y)=(4,3)For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h,k)=(0,1),(x,y)=(2,5)For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h,k)=(2,3),(x,y)=(5,12)For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h,k)=(5,3),(x,y)=(2,9)For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h,k)=(3,2),(x,y)=(10,1)For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h,k)=(0,1),(x,y)=(1,0)For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. (h,k)=(1,0),(x,y)=(0,1)For the following exercises. sketch a graph of the quadratic function and give the vertex, axis of symmetry, andintercepts. 34. f(x)=x22xFor the following exercises. sketch a graph of the quadratic function and give the vertex, axis of symmetry, andintercepts. 35. f(x)=x26x1For the following exercises. sketch a graph of the quadratic function and give the vertex, axis of symmetry, andintercepts. 36. f(x)=x25x6For the following exercises. sketch a graph of the quadratic function and give the vertex, axis of symmetry, andintercepts. 37. f(x)=x27x+3For the following exercises. sketch a graph of the quadratic function and give the vertex, axis of symmetry, andintercepts. 38. f(x)=2x2+5x8For the following exercises. sketch a graph of the quadratic function and give the vertex, axis of symmetry, andintercepts. 39. f(x)=4x212x3For the following exercises, write the equation for the graphed function.For the following exercises, write the equation for the graphed function.For the following exercises, write the equation for the graphed function.For the following exercises, write the equation for the graphed function.For the following exercises, write the equation for the graphed function.For the following exercises, write the equation for the graphed function.For the following exercises. use the table of values that represent points on the graph of a quadratic function.By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.For the following exercises. use the table of values that represent points on the graph of a quadratic function.By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.For the following exercises. use the table of values that represent points on the graph of a quadratic function.By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.For the following exercises. use the table of values that represent points on the graph of a quadratic function.By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.For the following exercises. use the table of values that represent points on the graph of a quadratic function.By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.For the following exercises, use a calculator to find the answer. 51. Graph on the same set of axes the functions f(x)=x2,f(x)=2x2, and f(x)=13x2. What appearsto be the effect of changing the coefficient?For the following exercises, use a calculator to find the answer. 52. Graph on the same set ofaxes f(x)=x2,f(x)=x2+2 and f(x)=x2,f(x)=x2+5 and f(x)=x23. Whatappears to be the effect of adding a constant?For the following exercises, use a calculator to find the answer. 53. Graph on the same set of axes f(x)=x2,f(x)=(x2)2,f(x3)2, and f(x)=(x+4)2. What appears to be the effect of adding or subtractingthose numbers?For the following exercises, use a calculator to find the answer. 54. The path of an object rejected at a 45 degree anglewith initial velocity of 80 feet per second is givenby the function h(x)=32(80)2x2+x where x is thehorizontal distance traveled and h(x) is the heightin feet. Use the [TRACE] feature of your calculatorto determine the height of the object when it hastraveled 100 feet away horizontally.For the following exercises, use a calculator to find the answer. 55. A suspension bridge can be modeled by the quadratic function h(x)=0.0001x2 with 2000x2000 where x is the number of feet from the center and h(x) is height in feet. Use the [TRACE] feature of your calculator toestimate how far from the center does the bridge have a height of 100 feet.For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opensto find the domain and range of the function. 56. Vertex (1,2), opens up.For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opensto find the domain and range of the function. 57. Vertex (1,2) opens down.For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opensto find the domain and range of the function. 58. Vertex (5,11), opens down.