#### Transcript Section 5.1.4

• Click to edit Master text styles – Second level Section 5.1.4 • Third level – Fourth level » Fifth level How Can I Use Systems #5-44 How Tall is Harold • Click to edit Master text styles Dinah –and Jamal Second level were eating as they came • Third into Algebra 4 level class from lunch. Someone had – Fourth level left a book on the floor and they tripped. As » Fifth level they each hit the floor, the food they were carrying went flying across the room directly toward Harold who was showing off his latest dance moves. #5-44 How Tall is Harold • Click to edit Master text styles • As Jamal and Dinah watched in horror, Jamal’s – Second level cupcake •and Dinah’s sandwich splattered Harold Third level right on top–ofFourth his level head! Jamal’s cupcake flew on » Fifth level a path that would have landed on the floor 20 feet away from him if it had not hit Harold. Dinah’s sandwich flew on a path that would have landed on the floor 24 feet away from her if it had not hit Harold. Jamal’s cupcake got up 9 feet high, and Jamal’s sandwich reached a height of 6 feet before hitting Harold. #5-44 How Tall is Harold • Click to edit Master text styles • How– tall is level Harold? Show solution in as Second • Thirdas level many ways possible. – Fourth level » Fifth level Generate tables of values one for each person • Click to edit Master text styles –x Second level y x • Third level 0 0 0 level – Fourth » Fifth level 12 10 9 24 20 0 y 0 6 0 Now run the Quadratic Regression (choice 5) on your calculator; remember to store one equation in Y1 and the other in Y2 Adjust the window of your calculator • Click to edit Master text styles • Once– you each formula and you have Secondknow level • Third in level stored them Y1 and Y2, use intersect key Fourth level to find the–point of intersection. » Fifth level • What does x coordinate of POI represent? • What does y coordinate of POI represent? • Once you know each equation, use the EQV method to find x and y. 11 y 10 9 8 7 6 H 5 4 3 2 1 -1 -1 x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 J D Click of the grid and turn on each function/point series. #5-45 • Click to edit Master text styles • Your–math class wants to collect money for a field Second level trip, so it• decides Third levelto sell two kinds of candy bags. – Fourth level bag costs 4.25 for five The Chocolate Lovers » Fifth level chocolate truffles and two caramel turtle candies. The Combusting Caramel Bag costs 3.50 for eight caramel turtle candies and two chocolate truffles. How much does each chocolate truffle and caramel turtle candy cost? solution • Click to edit Master text styles • Let x– be thelevel cost of Truffles Second level • Let y be• Third the cost of Caramel Turtles – Fourth level » Fifth of levelbag write an equation: Then for each type 5𝑥 + 2𝑦 = 4.25 2𝑥 + 8𝑦 = 3.5 Solution • Click to edit Master text styles • There are several methods to solve the – Second level Third level systems• of equations you just wrote. The level following –isFourth only one way: » Fifth level • 5𝑥 + 2𝑦 = 4.25 Multiply by -2 • 2𝑥 + 8𝑦 = 3.5 Multiply by 5 solution • Click to edit Master text styles • −10𝑥 − 4𝑦level = −8.5 – Second • Third level • 10𝑥 + 40𝑦 = 17.5 – Fourth level Now combine. » Fifth level • • • • 36y=9 y=0.25 Sub in one of the original equations. 5𝑥 + 2(0.25) = 4.25 x=0.75 X=0.75 and y=0.25 • Click to edit Master text styles • Now– that you Second level know the price of each kind • Third level your work by substituting of candy, check – Fourth level your answer into the second equation: » Fifth level • 2(0.75)+8(0.25) ? 3.5 • 1.5+2 = 3.5 #5-46 Jobs • Click to edit Master text styles • Lucky you!level You are a new college graduate – Second • Third level been offered two jobs. and have already – Fourth level Each job involves exactly the same tasks, » Fifth level but the salary plans differ, as shown below. • Job A offers a starting salary of 52,000 per year with an annual increase of 3,000. • Job B starts at 36,000 per year with a raise of 11% per year. #5-46 Jobs • Click to edit Master text styles • A. Under what – Second level conditions would Job A be a • Third level better choice? When would Job B be a – Fourth level better choice? Use graphs, tables and » Fifth level equations to help you justify your answer. Solution • • • • • Click to edit Master text styles Let x– be thelevel number of years. Second level JOB A:• Third 𝑦– = 52,000 + 3000𝑥 Fourth level 𝑥 » Fifth level JOB B: 𝑦 = 36,000(1.11) Graph each… make sure to display the window you choose. graph y f(x)=52000+3000x 80000 g(x)=36000(1.11)x 60000 40000 20000 x -1 1 2 3 4 5 6 7 8 9 solution • • • • • • Click to edit Master text styles By using the – Second levelintersect key: • Third level POI=( 6.625, 71876.17) – Fourth level Fifth level What does x »coordinate of POI represent? What does y coordinate of POI represent? So up to 6 years Job A is a better option. Starting with year 7 Job B is a better option. graph y Option B earns more x>7 52000+3000x<36000(1.11)x 80000 60000 40000 20000 Option A earns more for x<6 52000+3000x>36000(1.11)x x -1 1 2 3 4 5 6 7 8 9 #5-46 Jobs • Click to edit Master text styles • B. How would – Second level you change this problem Third levelJob B is always a better slightly• so that – Fourth level choice? How could you change it so that » Fifth level Job A is always better.? If it is not possible for Job A or Job B to always be the better choice, explain why not. On your own: • Click to edit Master text styles • Review and Preview • Review your – Second level Third level • Page 234 notes. •Rewrite – Fourth level and fortify them if • # 48-53 » Fifth level needed. • Update your vocab list, if needed. • Click to edit Master text styles – Second level • Third level – Fourth level » Fifth level