MA1310: Module 6 Matrix Systems, Equations, and Inequalities Lab 6.1 Equations, Inequalities, and Matrix Methods The purpose of this assessment is to help you determine whether you have a clear understanding of equations, inequalities, and matrix methods. Solve the following problems: 1. A phone company has two different phone plans from which you can choose. Plan A: $40 a month for unlimited calling Plan B: $20 a month plus $0.10 a minute Based on the information provided, solve the following problems: a. What will be the cost equation for Plan A and Plan B? b. Write an inequality that models the conditions. Solve the inequality to find out how many calls must be made to make Plan A the better deal. Show all your steps. 2. A company that manufactures aquariums has a fixed cost of $118,000. It costs $140 to produce each aquarium. The selling price is $360 per aquarium. How many aquariums does the business need to sell to break even? 3. Solve the following system of equations using elimination or matrices: x - 1y + z = 6 2x + y - 3z = -3 x - 3y + 3z = 10 4. Use the back substitution method to solve the given matrix. Begin by writing the corresponding 1 0 linear equations and then use the substitution method to solve the variables. [0 1 0 0 13 15 8 | 8 ] 1 1 5. Solve the given linear inequality and identify the correct interval notation. 7 < 5x - 23 a. (6, ) b. [-6, ) c. (-, 6) d. (-, ] 6. A basic cellular phone plan costs $16 per month for 50 calling minutes. Additional time costs $0.25 per minute. The formula C = 16 + 0.25(x - 50) gives the monthly cost for this plan for calling 1 MA1310: Module 6 Matrix Systems, Equations, and Inequalities Lab 6.1 Equations, Inequalities, and Matrix Methods minutes, where > 50. How many calling minutes are possible for a monthly cost of minimum $28 and maximum $47? a. Minimum 98 minutes and maximum 174 minutes b. Minimum 112 minutes and maximum 127 minutes c. Minimum 90 minutes and maximum 140 minutes d. Minimum 130 minutes and maximum 145 minutes Submission Requirements: Submit your response in a Microsoft Word document of the following specifications: Font: Arial; Point 12 Spacing: Double Evaluation Criteria: Your submission will be evaluated against the following criteria: Did you include appropriate steps to determine the answers to questions, wherever required? Did you submit your answers in an organized fashion that was legible and easy to follow? Did you correctly answer each question? 2