171S1.5p Linear Equations, Functions, Zeros and Applications August 30, 2012 MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 1: Graphs, Functions, and Models 1.1 Introduction to Graphing 1.2 Functions and Graphs 1.3 Linear Functions, Slope, and Applications 1.4 Equations of Lines and Modeling 1.5 Linear Equations, Functions, Zeros and Applications 1.6 Solving Linear Inequalities Aug 2510:04 PM Equations and Solutions An equation is a statement that two expressions are equal. To solve an equation in one variable is to find all the values of the variable that make the equation true. Each of these numbers is a solution of the equation. The set of all solutions of an equation is its solution set. Aug 309:30 AM EquationSolving Principles The Addition Principle: If a = b is true, then a + c = b + c is true. The Multiplication Principle: If a = b is true, then ac = bc is true. A linear equation in one variable is an equation that can be expressed in the form mx + b = 0, where m and b are real numbers and m ≠ 0. Equations that have the same solution set are equivalent equations. Aug 2510:09 PM Aug 2510:14 PM Zeros of Linear Functions Distance Formula The distance d traveled by an object moving at rate r in time t is given by d = rt. An input c of a function f is called a zero of the function, if the output for the function is 0 when the input is c. That is, c is a zero of f if f (c) = 0. Simple Interest I = Prt I = the simple interest ($) P = the principal ($) r = the interest rate (%) t = time (years) Aug 2510:16 PM A linear function f (x) = mx + b, with m ≠ 0, has exactly one zero. Aug 2510:20 PM 1 171S1.5p Linear Equations, Functions, Zeros and Applications August 30, 2012 1.5 Linear Equations, Functions, Zeros and Applications 134/4. Solve (6/5)y + 3 = 3/10 A formula is an equation that can be used to model a situation. We have used the motion formula, d = r • t. We have used the simpleinterest formula, I = Prt. We can use the equationsolving principles to solve a formula for a given variable. Aug 2510:22 PM 134/10. Solve 10x 3 = 8 + 10x Aug 267:01 AM 1.5 Linear Equations, Functions, Zeros and Applications 1.5 Linear Equations, Functions, Zeros and Applications 134/22. Solve 4x + 3 = 2x 7 134/37. Ocean Depth. The average depth of the Pacific Ocean is 14,040 ft. This is 8890 ft less than the sum of the average depths of the Atlantic Ocean and the Indian Ocean. The average depth of the Indian Ocean is 272 ft less than fourfifths of the average depth of the Atlantic Ocean. (Source: Time Almanac, 2010) Find the average depth of the Indian Ocean. 134/30. Solve 4(3x + 2) 7 = 3(x 2) Aug 267:01 AM Aug 267:01 AM 1.5 Linear Equations, Functions, Zeros and Applications 1.5 Linear Equations, Functions, Zeros and Applications 135/38. Where the Textbook Dollar Goes. Of each dollar spent on textbooks at college bookstores, 22.3 cents goes to the college store for profit, store operations, and personnel. On average, a college student at a fouryear college spends $ 667 per year for textbooks. (Source: National Association of College Stores) How much of this expenditure goes to the college store? 135/40. Nutrition. A slice of carrot cake from the popular restaurant The Cheesecake Factory contains 1560 calories. This is threefourths of the average daily calorie requirement for many adults. ( Source: The Center for Science in the Public Interest) Find the average daily calorie requirement for these adults. Aug 267:01 AM Aug 267:01 AM 2 171S1.5p Linear Equations, Functions, Zeros and Applications August 30, 2012 1.5 Linear Equations, Functions, Zeros and Applications 1.5 Linear Equations, Functions, Zeros and Applications 135/46. Commission vs. Salary. Juliet has a choice between receiving an $ 1800 monthly salary from Furniture by Design or a base salary of $ 1600 and a 4% commission on the amount of furniture she sells during the month. For what amount of sales will the two choices be equal? 136/52. Garden Dimensions. The children at Tiny Tots Day Care plant a rectangular vegetable garden with a perimeter of 39 m. The length is twice the width. Find the dimensions of the garden. Use this to graph, calculate perimeter and area of rectangle given the width and the relationship between length and width http://cfcc.edu/faculty/cmoore/RectangleL_aW.html Aug 267:01 AM Aug 267:01 AM 1.5 Linear Equations, Functions, Zeros and Applications 1.5 Linear Equations, Functions, Zeros and Applications 136/56. Water Weight. Water accounts for 60% of a man's weight ( Source: ga.water.usgs.gov/edu). Jake weighs 186 lb. How much of his body weight is water? 136/60. Traveling Downstream. Angelos kayak travels 14 km/hr in still water. If the rivers current flows at a rate of 2 km/hr , how long will it take him to travel 20 km downstream? Aug 267:11 AM Aug 267:12 AM 1.5 Linear Equations, Functions, Zeros and Applications 1.5 Linear Equations, Functions, Zeros and Applications 136/64. Student Loans. Dimitri's two student loans total $ 9000. One loan is at 5% simple interest and the other is at 6% simple interest. At the end of 1 yr, Dimitri owes $ 492 in interest. What is the amount of each loan? 137/76. Find the zero of the linear function: f(x) = 2x + 7. Aug 267:12 AM Solve algebraically and graphically. Aug 267:12 AM 3 171S1.5p Linear Equations, Functions, Zeros and Applications August 30, 2012 1.5 Linear Equations, Functions, Zeros and Applications 1.5 Linear Equations, Functions, Zeros and Applications 137/82. Find the zero of the linear function: f(x) = 3x + 13. In Exercises 8792, use the given graph to find each of the following: (a) the x intercept and (b) the zero of the function. 138/90. Solve algebraically and graphically. Aug 267:12 AM Aug 267:12 AM Aug 302:59 PM Aug 303:08 PM 1.5 Linear Equations, Functions, Zeros and Applications In Exercises 8792, use the given graph to find each of the following: (a) the x intercept and (b) the zero of the function. 138/92. Aug 309:07 AM Aug 267:12 AM 4 171S1.5p Linear Equations, Functions, Zeros and Applications August 30, 2012 Aug 304:22 PM Aug 304:27 PM Aug 3010:20 AM Aug 3010:35 AM 5
© Copyright 2026 Paperzz