In Exercises 1–28, compute the products. Some of these may be undefined. Exercises marked should be done by using technology. The others should be done in two ways: by hand and by using technology where possible. [HINT: See Example 3.]
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- In Problems 57–68, solve each equation in the real number system. 57. x* - x + 2x? - 4x - 8 = 0 58. 2x + 3x? + 2x + 3 = 0 59. 3x + 4x? - 7x + 2 = 0 60. 2x – 3x –- 3x – 5 = 0 234 CHAPTER 4 Polynomial and Rational Functions 61. 3x – x? - 15x + 5 = 0 62. 2x - 11x² + 10x + 8 = 0 63. x* + 4x + 2r? - x + 6 = 0 64. x* - 2x + 10x? - 1&r + 9 == (0 8 +x +1 = 0 65. x 66. х + + 3x - 2 = 0 67. 2x - 19x + 57x - 64x + 20 = 0 68. 2x + x - 24x + 20x + 16 = 0arrow_forwardThe length of each of the following classes respectively is: Class A: [84.96 – 210.76] Class B: [8.5 – 20.3] Class C: [2.397 8.014] O 125.81 , 12.0 and 5.518 O 125.82, 12.0 and 5.618 O 125.80 , 11.9 and 5.617 O 125.81, 11.9 and 5.619 O 125.81, 11.9 and 5.618arrow_forwardA-1 does not exist.arrow_forward
- In Problems 99–106, analyze each polynomial function farrow_forwardNational Debt The size of the total debt owed by the UnitedStates federal government continues to grow. In fact,according to the Department of the Treasury, the debt perperson living in the United States is approximately $53,000(or over $140,000 per U.S. household). The following datarepresent the U.S. debt for the years 2001–2014. Since thedebt D depends on the year y, and each input correspondsto exactly one output, the debt is a function of the year. SoD1y2 represents the debt for each year y. Source: www.treasurydirect.govDebt (billions Debt (billionsYear of dollars) Year of dollars)2001 5807 2008 10,0252002 6228 2009 11,9102003 6783 2010 13,5622004 7379 2011 14,7902005 7933 2012 16,0662006 8507 2013 16,7382007 9008 2014 17,824 (a) Plot the points 12001, 58072, 12002, 62282, and so on ina Cartesian plane.(b) Draw a line segment from the point 12001, 58072 to12006, 85072. What does the slope of this line segmentrepresent?(c) Find the average rate of change of the debt from 2002…arrow_forwardQuestions 15: (A.SSE.A.2) * The expression 4x² – 25 is equivalent to - O (4x- 5)(x+5) (4x+5)(x - 5) (2x + 5)(2x - 5) (2x - 5)(2x - 5)arrow_forward
- create a Mathematical Model (with complete solution on how it was derived)arrow_forward21–23. Language enrollments. The line graph in Figure 2.28 shows total course enrollments in languages other than English in U.S. institutions of higher education from 1960 to 2009. (Enrollments in ancient Greek and Latin are not included.) Exercises 21 through 23 refer to this figure. 1,800,000 1,629,326 1.522.770 1,600,000 - 1,400,000 - 1347.036 1,200,000- 1,073,097 1,067,217 1,000.000 - 975.7m 963,930 883.222 1.06.603 922,439 960.588 B00,000 - 97.077 877.91 600,000 - 608,749 400.000 - 200,000 - 1960 1965 1968 | 1972 1977 1980 1983 1986 1990 1995 199 2002 2006 2009 1970 1974 Figure 2.28 Crauder, et al., Quantitative Literacy, 3e, © 2019 W. H. Freeman and Company FIGURE 2.28 Enrollments in languages other than English in U.S. institutions of higher education (2009). 21. During which time periods did the enrollments decrease? 22. Calculate the average growth rate per year in enrollments over the two periods 1960–1965 and 2006– 2009. Note that the time periods are not of the same…arrow_forwardYou need to take x= 0,1,2,3,4,5arrow_forward
- 11.4 Converting from One Uni PROBLEMS FOR SECTION 11.4 1. A recipe calls for 4 ounces of chocolate. If you make 15 batches of the recipe (for a large party), then how many pounds of chocolate will you need? a. Use multiplication or division or both to solve the chocolate problem. Explain why your method of solution makes sense in a way that children could understand. Do not use di- mensional analysis. b. Describe a number of different correct ways to write the answer to the chocolate problem. Explain briefly why these different ways of writing the answer mean the same thing. b. A car is 41 feet and in centimete your reas 7. The distan 260 kilom Make an ing brief fact tha your an your a answe than 2. A class needs 27 pieces of ribbon, each piece 2 feet, 3 inches long. How many yards of ribbon does the class need? a. Use multiplication or division or both to solve the ribbon problem. Explain why your nkes sense in a way that 8. In Ge hour they firs late 9.0 foarrow_forwardLet A = 4 5 6 7 INPUT HELP . What is the (2, 1)-entry of A-¹?arrow_forwardExercises 151–153 will help you prepare for the material covered in the next section. 151. Replace each boxed question mark with a polynomial that results in the given product. a. 3x . ? = 9x b. 2r'y² ? = 12r*y+ In Exercises 152–153, a polynomial is given in factored form. Use multiplication to find the product of the factors. 152. (x – 5)(x? + 3) 153. (x + 4)(3x – 2y)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage