5.7 Start Thinking. 5.7 Warm Up. 5.7 Cumulative Review Warm Up

Transcription

1 .7 Start Thinking Graph the linear inequalities < + and > 9 on the same coordinate plane. What does the area shaded for both inequalities represent? What does the area shaded for just one of the inequalities represent? Is there an area that is not shaded for either inequalit? If so, what does that area represent? Choose an ordered pair that is in the area shaded for both inequalities and plug the values into the inequalities. What happens? Choose an ordered pair that is in the area not shaded for either inequalit and plug the values into the inequalities. What happens?.7 Warm Up Graph the inequalit < > 1. < 6..7 Cumulative Review Warm Up Solve the inequalit q 1 p. ( g ) ( + 6) ( ) 6. ( ) g z + 8 > 6 Copright Big Ideas Learning, LLC Algebra 1 Resources b Chapter 187

2 Name Date.7 Practice A In Eercises 1, tell whether the ordered pair is a solution of the sstem of linear inequalities. 1. (, 1 ). (, ). ( 0, ). ( 1, ) In Eercises and 6, tell whether the ordered pair is a solution of the sstem of linear inequalities.. (, 1 ); < ( 7, ); < 0 < In Eercises 7 1, graph the sstem of linear inequalities. 7. > 8. 1 < < 9. > > 11. < < > 1 In Eercises 1 and 1, write a sstem of linear inequalities represented b the graph You can spend at most $60 on beads. A bag containing red beads costs $ per bag. A bag containing blue beads costs $ per bag. You need more bags of blue beads than bags of red beads. a. Write and graph a sstem of linear inequalities that represents the situation. b. Identif and interpret a solution of the sstem. c. Use the graph to determine whether ou can bu 9 bags of red beads and 1 bags of blue beads. 188 Algebra 1 Copright Big Ideas Learning, LLC Resources b Chapter

3 Name Date.7 Practice B In Eercises 1 and, tell whether the ordered pair is a solution of the sstem of linear inequalities., 0 ; > ( ) 1, ; < + +. ( ) In Eercises 8, graph the sstem of linear inequalities > 1 < + 1. < > > < > < 1 > 7 In Eercises 9 and 10, write a sstem of linear inequalities represented b the graph Describe and correct the error in graphing the sstem of inequalities. 1. The points ( 1, ), (, ), ( 1, 6 ) are the vertices of a shaded triangle. a. Write a sstem of linear inequalities represented b the shaded triangle. b. Find the area of the triangle. Copright Big Ideas Learning, LLC Algebra 1 Resources b Chapter 189

4 Name Date.7 Enrichment and Etension Using Linear Programming Eample: A to manufacturer wants to minimize the cost to produce two lines of to airplanes. Because of the suppl of materials, no more than 0 fling bats can be built each da, and no more than 60 fling falcons can be built each da. There are enough workers to build at least 70 to airplanes each da. It costs $1 to build a fling bat and $8 to build a fling falcon. How man fling bats and falcons should be produced to minimize the cost, while still making production on both tos? What is the minimum possible cost each da? To Airplanes Let represent the number of fling bats. (10, 60) 60 (0, 60) Let represent the number of fling falcons (0, 0) f, = ( ) ( ), f(, ) ( 0, 0 ) 1( 0) 8( 0) ( 10, 60 ) 1( 10) 8( 60) ( 0, 60 ) 1( 0) 8( 60) + $70 + $600 + $ fling bats and 60 fling falcons; Minimum Cost: $ You are treating two of our friends to the movies tonight. Your parent gives ou $70. Tickets are $7 each. At the cand counter, ou are buing snacks and drinks for our friends as the find seats. Snacks are $ each, and drinks are $.. You are tring to decide what combination of snacks and drinks are possible given the mone remaining. You can onl carr drinks on a tra b ourself. a. Write a sstem of inequalities for this situation, using for the number of snacks and for bottles of water purchased. b. Graph the sstem and find the vertices. c. Indicate on the graph what combinations of snacks and drinks are possible. Eplain our reasoning in-depth. d. Does ever point within the feasible region represent a valid solution in this contet? Wh or wh not? e. Denote one combination that is possible and one that is not. Eplain our reasoning. f. Prove each of our answers to part (e) algebraicall. Number of Fling Falcons Number of Fling Bats 190 Algebra 1 Copright Big Ideas Learning, LLC Resources b Chapter

5 Name Date.7 Puzzle Time What Do You Call The Tending Of Rabbits? Write the letter of each answer in the bo containing the eercise number. Tell whether the ordered pair is a solution of the sstem of linear inequalities. 1. ( 7, 6 ); > +. ( 8, 8 ); < 9 > + 8 E. es F. no Q. es R. no. ( 9, 10 ); + 9. (, ); > D. es E. no A. es B. no Match the sstem of inequalities with its graph.. < 1 6. > R. H. 6 C. A Copright Big Ideas Learning, LLC Algebra 1 Resources b Chapter 191