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
Here are the solutions to the flow diagram questions: Step 1: Complete the flow diagram by calculating missing input and output values. The rule for the flow diagram is "× 9" then "+ 8". This can be written as y = (x × 9) + 8. For input x=3: y = (3 × 9) + 8 = 27 + 8 = 35 For input x=4: y = (4 × 9) + 8 = 36 + 8 = 44 For input x=6: y = (6 × 9) + 8 = 54 + 8 = 62 For input x=7: y = (7 × 9) + 8 = 63 + 8 = 71 For output y=89: (x × 9) + 8 = 89 x × 9 = 89 - 8 x × 9 = 81 x = 81 ÷ 9 = 9 For output y=17: (x × 9) + 8 = 17 x × 9 = 17 - 8 x × 9 = 9 x = 9 ÷ 9 = 1 ii. What are the input values? The input values are the numbers that go into the rule. The input values are 1, 3, 4, 6, 7, 9. iii. What are the output values? The output values are the results after applying the rule to the inputs. The output values are 17, 35, 44, 62, 71, 89. iv. What is the rule? The rule is explicitly stated in the flow diagram. The rule is multiply by 9, then add 8. vi. What will the output values be if the rule is "+ 2 × 7"? We will use the input values from the completed flow diagram: 1, 3, 4, 6, 7, 9. The rule "+ 2 × 7" means add the input to the product of 2 and 7. So, y = x + (2 × 7) = x + 14. For input x=1: y = 1 + (2 × 7) = 1 + 14 = 15 For input x=3: y = 3 + (2 × 7) = 3 + 14 = 17 For input x=4: y = 4 + (2 × 7) = 4 + 14 = 18 For input x=6: y = 6 + (2 × 7) = 6 + 14 = 20 For input x=7: y = 7 + (2 × 7) = 7 + 14 = 21 For input x=9: y = 9 + (2 × 7) = 9 + 14 = 23 The output values would be 15, 17, 18, 20, 21, 23. 3 done, 2 left today. You're making progress.