Please help me with these math questions and show all the work so I can understand, thanks!

Lesson 7.5: Quadratic Inequalities in Two Variables NAME: Lesson 7.5: Quadratic Inequalities in Two Variables E Explore Your Understanding Assignment This assignment includes multiple choice and short answer questions. For multiple choice questions, select the best answer. Each is worth 1 mark. Marks assigned to short answer questions are Indicated for each question. Be sure to show all necessary work. y2%(x4)2+l . /l 1. The solution region of the inequality 1ncludes the points A. (1, 1), (4, 0), and (7, 1) B. (1, 3), (4, 1), and (8, 2) C. (4,2),(7,4),and(8,8) D. (41, 2), (o, 9), and (9, 1) /1 2. The points (3, 8), and (6, 8) are part of the solution region of a quadratic inequality, while (5, 9), and (7, 7) are not. The point that must also be part of the solution region is A. (4,7) B. (4,9) C. (8,6) D. (6,10) /l 3. The wording that implies a strict inequality is A The diameter can be a maximum of... B. Acceptable values cannot exceed... C. The prot was at least... D. The ball was below... /1 4. Consider the inequality y > a(xh)2 , where a, h > O . No new solutions will be added to the solution region when A. ais increased B. a is decreased C. his increased D. his decreased ADLC Mathematics 20-1 Lesson 7.5: Quadratic Inequalities in Two Variables 12 5. Graph the inequality y 2 2(x+1)2+5. ADLC Mathematics 20-1Lesson 7.5: Quadratic Inequalities in Two Variables 6. Modern cylindrical metal cans, like the one shown, are usually made from steel, and then covered with a thin layer of tin. /1 a. Write an inequality representing the amount of sheet metal that can be used to fabricate the surface of a can that is 10 cm tall. /1 b. Graph the inequality. s incruelly that would make to wiese a berean like the e ADLC Mathematics 20-1Lesson 7.5: Quadratic Inequalities in Two Variables ll c. Explain how the graph can be used to determine the minimum amount of metal required for cans of various radii. d. Solving this problem using the formula for the surface area of a cylinder is not completely accurate. {0.5 i. Explain a factor that the surface area of a cylinder does not account for. /0.5 ii. Suggest a change to a surface area of a cylinder inequality that would make it more acurately represent the amount of metal required to make a tin can like the one s own. [10 You have completed Lesson 7.5 Explore Your Understanding Assignment. Please take some time to rev1ew Unit 7 and complete the practice quiz before attempting Quiz 7. ADLC Mathematics 20-1