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All Textbook Solutions for Precalculus (MindTap Course List)
Plot the points -3,2,4,-2,3,1,0,-2, and -1,-2.The table shows the numbers N in thousands of cellular telecommunication service employees in the United States from 2005 through 2014, where t represents the year. Sketch a scatter plot of the data. Source: CTIA-The Wireless AssociationFind the distance between the points 3,1 and -3,0.Show that the points 2,-1,5,5, and 6,-3 are vertices of a right triangle.Find the midpoint of the line segment joining the points -2,8 and 4,-10.A football quarterback throw a pass from the 10 yard line, 10 yards from the sideline. A wide receiver catches the pass on the 32 - yard line, 25 yards from the same sideline. How long is the pass?7CP8CPAn ordered pair of real numbers can be represented in a plane called the rectangular coordinate system or the __________ plane.The x- and y-axes divide the coordinate plane into four ___________.The _________ ________ is derived from the Pythagorean Theorem.Finding the average values of the respective coordinates of the two endpoints of a line segment in a coordinate plane is also known as using the ______ ______.Plotting Points in the Cartesian Plane In Exercises 5 and 6, plot the points. 2,4,3,-1,-6,2,-4,0,-1,-8,1.5,-3.5Plotting Points in the Cartesian Plane In Exercises 5 and 6, plot the points. 1,-5,-2,-7,3,3,-2,4,0,5,23,527EFinding the Coordinated of a Point In Exercises 7 and 8, find the coordinates of the point. The point is on the x-axis and 12 units to the left of the y-axis.9EDetermining Quadrants for a Point In Exercises 9-14, determine the quadrants in which x,y could be located. x0 and y011EDetermining Quadrants for a Point In Exercises 9-14, determine the quadrants in which x,y could be located. x0 and y=7Determining Quadrants for a Point In Exercises 9-14, determine the quadrants in which x,y could be located. x+y=0,x0,y0Determining Quadrants for a Point In Exercises 9-14, determine the quadrants in which x,y could be located. xy0Sketching a Scatter Plot In Exercises 15 and 16, sketch a scatter plot of the data shown in the table. The table shows the number y of Wal-Mart stores for each year x from 2008 through 2014. Source: Wal-Mart Stores, Inc.16EFinding a Distance In Exercises 17-22, find the distance between the points. -2,6,3,-6Finding a Distance In Exercises 17-22, find the distance between the points. 8,5,0,20Finding a Distance In Exercises 17-22, find the distance between the points. 1,4,-5,-1Finding a Distance In Exercises 17-22, find the distance between the points. 1,3,3,-2Finding a Distance In Exercises 17-22, find the distance between the points. 12,43,2,-122EVerifying a Right Triangle In Exercises 23 and 24, a find the length of each side of the right triangle, and b show that these lengths satisfy the Pythagorean Theorem.Verifying a Right Triangle In Exercises 23 and 24, a find the length of each side of the right triangle, and b show that these lengths satisfy the Pythagorean Theorem.Verifying a Polygon In Exercises 25-28, show that the points form the vertices of the polygon. Right triangle: 4,0,2,1,-1,-5Verifying a Polygon In Exercises 25-28, show that the points form the vertices of the polygon. Right triangle: -1,3,3,5,5,127EVerifying a Polygon In Exercises 25-28, show that the points form the vertices of the polygon. Isosceles triangle: 2,3,4,9,-2,7Plotting, Distance, and Midpoint In Exercises 29-36, a plot the points, b find the distance between the pints, and c find the midpoint of the line segment joining the points. 6,-3,6,530EPlotting, Distance, and Midpoint In Exercises 29-36, a plot the points, b find the distance between the pints, and c find the midpoint of the line segment joining the points. 1,1,9,732EPlotting, Distance, and Midpoint In Exercises 29-36, a plot the points, b find the distance between the pints, and c find the midpoint of the line segment joining the points. -1,2,5,4Plotting, Distance, and Midpoint In Exercises 29-36, a plot the points, b find the distance between the pints, and c find the midpoint of the line segment joining the points. 2,10,10,2Plotting, Distance, and Midpoint In Exercises 29-36, a plot the points, b find the distance between the points, and c find the midpoint of the line segment joining the points. -16.8,12.3,5.6,4.936EFlying Distance An airplane flies from Naples, Italy, in a straight line to Rome, Italy, which is 120 kilometers north and 150 kilometers west of Naples. How far does the plane fly?38ESales The Coca-Cola Company had sales of 35,123 million in 2010 and 45,998 million in 2014. Use the Midpoint Formula to estimate the sales in 2012. Assume that the sales followed a linear pattern. Source: The Coca-Cola CompanyRevenue per Share The revenue per share for Twitter, Inc. was 1.17 in 2013 and 3.25 in 2015. Use the Midpoint Formula to estimate the revenue per share in 2014. Assume that the revenue per share followed a linear pattern. Source: Twitter, Inc.Translating Points in the Plane In Exercises 41-44, find the coordinates of the vertices of the polygon after the given translation to a new position in the plane.42ETranslating Points in the Plane In Exercises 41-44, find the coordinated of the vertices of the polygon after the given translation to a new position in the plane. Original coordinates of vertices: -7,-2,-2,2,-2,-4,-7,-4 Shift: eight units up, four units to the rightTranslating Points in the Plane In Exercises 41-44, find the coordinated of the vertices of the polygon after the given translation to a new position in the plane. Original coordinate of vertices: 5,8,3,6,7,6 Shift: 6 units down, 10 units to the leftMinimum Wage Use the graph below, which shows the minimum wages in the United States in dollars from 1950 through 2015. Source: U.S Department of Labor a Which decade shows the greatest increase in the minimum wage? b Approximate the percent increases in the minimum wage from 1985 to 2000 and from 2000 to 2015. c Use the percent increase from 2000 to 2015 to predict the minimum wage In 2030. d Do you believe that your prediction in part c is reasonable? Explain.Exam Scores The table shows the mathematics entrance test scores x and the final examination scores y in an algebra course for a sample of 10 students. x 22 29 35 40 44 48 53 58 65 76 y 53 74 57 66 79 90 76 93 83 99 aSketch a scatter plot of the data. bFind the entrance test score of any student with a final exam score in the 80 s. cDoes a higher entrance test score imply a higher final exam score? Explain.True or False? In Exercise 47-50, determine whether the statement is true or false. Justify your answer. If the point x,y is in Quadrant II, then the point 2x,-3y is in Quadrant III.48ETrue or False? In Exercise 47-50, determine whether the statement is true or false. Justify your answer. The points -8,4,2,11, and -5,1 represent the vertices of an isosceles triangle.50EThink About It When plotting points on the rectangular coordinate system, when should you use different scales for the x- and y- axes? Explain.Think About It What is the y-coordinate of any point on the x-axis? What is the x-coordinate of any point on the y-axis?53EUsing the Midpoint Formula Use the result of Exercise 53 to find the endpoint x2,y2 of each line segment with the given endpoint x1,y1 and midpoint xm,ym. a x1,y1=1,-2 xm,ym=4,-1 b x1,y1=-5,11 xm,ym=2,455E56EProof Prove that the diagonals of the parallelogram in the figure intersect at their midpoints.58E59E60EDetermine whether a 3,-5 and b -2,26 lie on the graph of y=14-6x.2CP3CP4CP5CP6CP7CP8CP9CP1E2E3E4E5E6ESkills and Applications Determining Solution Points: In Exercises 7-14, determine whether each point lies on the graph of the equation. Equation Points y=x+4 a 0,2 b 5,38E9E10E11E12E13ESkills and Applications Determining Solution Points: In Exercises 7-14, determine whether each point lies on the graph of the equation. Equation Points 2x2+5y2=8 a 6,0 b 0,415E16E17E18E19E20E21ESkills and Applications Identifying x- and y-Intercepts: In Exercises 19-22, identifying x- and y-intercepts of the graph. Verify your results algebraically. y2=4-x23E24E25E26E27E28E29EFinding x- and y-intercepts: In Exercises 23-32, find the x- and y-intercepts of the graph of the equation. y=x4-2531E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59ESkills and Applications Using Technology: In Exercises 57-66, use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. y=x2+x-261E62E63E64E65E66E67E68E69E70E71E72E73E74E75E76E77E78E79E80ESkills and Applications Depreciation: A hospital purchases a new magnetic resonance imaging MRI machine for 1.2 million. The depreciated value y reduced value after t years is given by y=1,200,000-80,000t, 0t10. Sketch the graph of the equation.Skills and Applications Depreciation: You purchase an all-terrain vehicle ATV for 9500. The depreciated value y reduced value after t years is given by y=9500-1000t, 0t6. Sketch the graph of the equation.Skills and Applications Geometry: A regulation NFL playing field of length x and width y has a perimeter of 34623 or 10403 yards. a Draw a rectangle that gives a visual representation of the problem. Use the specified variables to label the sides of the rectangle. b Show that the width of the rectangle is y=5203-x and its area is A=x5203-x. c Use the graphing utility to graph the area equation. Be sure to adjust your window settings. d From the graph is part c, estimate the dimensions of the rectangle that yield a maximum area. e Use your schools library, the internet, or some other reference source to find the actual dimensions and area of a regulation NFL playing field and compare your findings with the results of part d.84ESkills and Applications Population Statistics The table shows the life expectancies of a child at birth in the United States for selected years from 1940 through 2010. Source: U.S. National Center for Health Statistics Year Life Expectancy, y 1940 62.9 1950 68.2 1960 69.7 1970 70.8 1980 73.7 1990 75.4 2000 76.8 2010 78.7 The model for the life expectancy during this period is y=63.6+0.97t1+0.01t, 0t70 where y represents the life expectancy that t is the time in years, with t=0 corresponding to 1940. a Use a graphing utility to graph the data from the table and the model in the same viewing window. How well does the model fit the data? Explain. b Determine the life expectancy in 1990 both graphically and algebraically. c Use the graph to determine the year when life expectancy was approximately 70.1. Verify your answer algebraically. d Find the y-intercept of the graph of the model. What does it represent in the context of the problem? e Do you think this model can be used to predict the life expectancy of a child 50 years from now? Explain.86E87EExploration True or false? In Exercises 87-89, determine whether the statement is true or false. Justify your answer. The graph of a linear equation can have either no x-intercepts or only one intercept.89E90E91ECheckpoint Sketch the graph of each linear equation. a. y=3x+2 b. y=3 c. 4x+y=52CP3CP4CP5CPCheckpoint An accounting firm determines that value V in dollars of a copier t years after its purchase is given by V=300t+1500. Interpret the y-intercept and slope of this line.7CPCheckpoint The sales for Foot Locker were approximately 6.5billion in 2013 and 7.2 billion in 2014. Repeat Example 8 using this information Source: Foot Locker EXAMPLE 8 Predicting Sales The sales for NIKE were approximately 25.3 billion in 2013 and 27.8 billion in 2014. Using only this information, write a linear equation that gives the sales in terms of the year. Then predict the sales in 2017. Source: NIKE Inc.1E2E3E4E5E6E7E8E9E10ESkills and Applications Sketching Lines In Exercises 11 and 12, sketch the lines through the point with the given slopes on the same set of coordinate axes. Point (2,3) Slope (a)0(b)1(c)2(d)312E13ESkills and Applications Estimating the Slope of a Line In Exercises 13 and 14, estimate the slope of the line.Skills and Applications Graphing a Linear Equation In Exercise 15-24, find the slope and y-intercept if possible of the line. Sketch the line. y=5x+316E17E18E19E20E21E22E23E24E25E26ESkills and Applications Finding the Slope of a Line through Two Points In Exercises 25-34, find the slope of the line passing through the pair of points. (3,2),(1,6)28E29E30E31E32E33E34ESkills and Applications Using the Slope and a Point In Exercises 35-42, use the slope of the line and point on the line to find three additional points through which the line passes. There are many correct answers. m=0,(5,7)36E37E38E39ESkills and Applications Using the Slope and a Point In Exercises 35-42, use the slope of the line and point on the line to find three additional points through which the line passes. There are many correct answers. m=14,(3,4)41E42E43E44E45E46E47E48ESkills and Applications Using the point-Slope Form In Exercises 43-54, find the slope-intercept form of the equation of the line that has the given slope and passes through the given point. Sketch the line. m=12,(2,3)50E51E52E53E54E55E56E57E58ESkills and Applications Finding an Equation of a Line In Exercises 55-64, find an equation of the line passing through the pair of points. Sketch the line. (2,12),(12,54)60E61E62E63E64E65E66E67E68E69E70E71E72E73ESkills and Applications Finding Parallel and Perpendicular Lines In Exercises 73-80, find equations of the lines that pass through the given point and are a parallel to and b perpendicular to the given line. x+y=7,(3,2)75ESkills and Applications Finding Parallel and Perpendicular Lines In Exercises 73-80, find equations of the lines that pass through the given point and are a parallel to and b perpendicular to the given line. 5x+3y=0,(78,34)77E78E79E80E81E82E83E84ESkills and Applications Using Intercept Form In Exercises 81-86, use the intercept form to find the general form of the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts (a,0) and (0,b) is xa+yb=1,a0,b0. Pointofline:(1,2)xintercept:(c,0),c0yintercept:(0,c),c086E87ESkills and Applications Sales The graph shows the sales in billions of dollars for apple Inc. in the years 2009 through 2015. (Source:AppleInc.) a Use the Slopes of the line segments to determine the years in which the sales showed the greatest increase and the least increase. b Find the slopes of the line segment connecting the points for the years 2009 and 2015. c Interpret the meaning of the slope in part b in the context of the problem.Skills and Applications Road Grade You are driving on a road that as a 6 uphill grade. This means that the slope of the road is 6100. Approximate the amount of vertical change in your position when you drive 200 feet.Skills and Applications Road Grade From the top of a mountain road, a surveyor horizontal measurements y, as shown in the table x and y are measured in feet. x 300 600 900 1200 y -25 -50 -75 -100 x 1500 1800 2100 y -125 -150 -175 a Sketch a scatter plot of the data. b Use a straightedge to sketch the line that you think best fits the data. c Find an equation for the line you sketched in part b. d Interpret the meaning of the slope of the line in part c in the context of the problem. e The surveyor needs to put up a road sign that indicated the steepness of the road. For example, a surveyor would put up a sign that states 8 grade on a road with a downhill grade that has a slope of 8100. What should the sign state for the road in this problem?Skills and Applications Rate of Change In Exercises 91 and 92, you are given the dollar value of a product in 2016 and the rate at which the value of the product is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value v of the product in terms of the year t. Let t=16 represent 2016. 2016 value Rate 3000 150 decrease per year92E93E94ESkills and Applications Depreciation A sandwich shop purchases a used pizza oven for 875. After 5 years, the oven will have to be discarded and replaced. Write a linear equation giving the value V of the equipment during the 5 years it will be in use.96E97E98E99E100E101E102EExploration Right Triangle Explain how you can use slope to show that the points A(1,5),B(3,7), and C(5,3) are the vertices of a right triangle.104E105E106E107E108E109E110E111E112E113E114ECheckpoint Determine whether the relation represents y as a function of x. a. b. Input, x 0 1 2 3 4 Output, y 4 2 0 2 4Checkpoint Determine whether each equation represents y as a function of x. a.x2+y2=8 b. y4x2=36Checkpoint Let f(x)=103x2. Find each function value. a.f(2) b. f(4) c. f(x1)Example 4 A Piecewise-Defined Function Evaluate the function when x=1,0, and 1. f(x)={x2+1,x0x1,x0 Checkpoint Evaluate the function given in Example 4 when x=2,2, and 3.Checkpoint Find all real values of x for which f(x)=0, where f(x)=x216.Checkpoint Find the values of x for which f(x)=g(x), where f(x)=x2+6x24 and g(x)=4xx2.7CP8CPCheckpoint A second baseman throws a baseball toward the first baseman 60 feet away. The path of the baseball is given by the function f(x)=0.004x2+0.3x+6 where fx is the height of the baseball in feet and x is the horizontal distance from the second baseman in feet. The first baseman can reach 8 feet high. Can the first baseman catch the baseball without jumping?10CP