This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — Here are the solutions based on the provided flow diagram and questions: a.i. Complete the flow diagram: The rule is "× 9 + 8". For input 3: 3 × 9 + 8 = 27 + 8 = 35 For output 89: Let input be x. x × 9 + 8 = 89 9x = 81 x = 9 For input 4: 4 × 9 + 8 = 36 + 8 = 44 For input 6: 6 × 9 + 8 = 54 + 8 = 62 For input 7: 7 × 9 + 8 = 63 + 8 = 71 For output 17: Let input be y. y × 9 + 8 = 17 9y = 9 y = 1 The completed flow diagram values are: Inputs: 3, 9, 4, 6, 7, 1 Outputs: 35, 89, 44, 62, 71, 17 a.ii. What are the input values? The input values are 3, 9, 4, 6, 7, 1. a.iii. What are the output values? The output values are 35, 89, 44, 62, 71, 17. a.iv. What is the rule? The rule is multiply by 9 and add 8 (or × 9 + 8). a.v. Number sentences: 3 × 9 + 8 = 35 9 × 9 + 8 = 89 4 × 9 + 8 = 44 6 × 9 + 8 = 62 7 × 9 + 8 = 71 1 × 9 + 8 = 17 a.vi. What will the output values be if the rule is + 2 x 7? Assuming the rule means (input + 2) × 7, and using the input values from the flow diagram (3, 9, 4, 6, 7, 1): For input 3: (3 + 2) × 7 = 5 × 7 = 35 For input 9: (9 + 2) × 7 = 11 × 7 = 77 For input 4: (4 + 2) × 7 = 6 × 7 = 42 For input 6: (6 + 2) × 7 = 8 × 7 = 56 For input 7: (7 + 2) × 7 = 9 × 7 = 63 For input 1: (1 + 2) × 7 = 3 × 7 = 21 The output values would be 35, 77, 42, 56, 63, 21. What's next? 📸