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 for the number patterns and flow diagram. d. i. Flow diagram The rule for the flow diagram is: Multiply the input by 5, then subtract 4. Rule: Input × 5 - 4 = Output Step 1: Calculate the missing output values. For input 11: 11 × 5 - 4 = 55 - 4 = 51 For input 7: 7 × 5 - 4 = 35 - 4 = 31 For input 2: 2 × 5 - 4 = 10 - 4 = 6 For input 5: 5 × 5 - 4 = 25 - 4 = 21 Step 2: Calculate the missing input values by reversing the rule. To reverse the rule, we add 4 to the output, then divide by 5. Reverse Rule: (Output + 4) ÷ 5 = Input For output 41: (41 + 4) ÷ 5 = 45 ÷ 5 = 9 For output 26: (26 + 4) ÷ 5 = 30 ÷ 5 = 6 ii. What are the input values? The input values are the numbers that go into the rule. The input values are 11, 7, 9, 6, 2, 5. iii. What are the output values? The output values are the numbers that come out of the rule. The output values are 51, 31, 41, 26, 6, 21. iv. What is the rule? The rule is given in the diagram. The rule is × 5 - 4. v. Number sentences Here are the number sentences for each input and its corresponding output: 11 × 5 - 4 = 51 7 × 5 - 4 = 31 9 × 5 - 4 = 41 6 × 5 - 4 = 26 2 × 5 - 4 = 6 5 × 5 - 4 = 21 vi. What will the output values be if the rule is -4 × 5? This rule means to multiply the input by 5, then subtract 4. We will use the original inputs from the flow diagram: 11, 7, 2, 5. For input 11: 11 × 5 - 4 = 55 - 4 = 51 For input 7: 7 × 5 - 4 = 35 - 4 = 31 For input 2: 2 × 5 - 4 = 10 - 4 = 6 For input 5: 5 × 5 - 4 = 25 - 4 = 21 The output values are 51, 31, 6, 21. vi. What will the output values be if the rule is +2 × 7? This rule means to multiply the input by 7, then add 2. We will use the original inputs from the flow diagram: 11, 7, 2, 5. For input 11: 11 × 7 + 2 = 77 + 2 = 79 For input 7: 7 × 7 + 2 = 49 + 2 = 51 For input 2: 2 × 7 + 2 = 14 + 2 = 16 For input 5: 5 × 7 + 2 = 35 + 2 = 37 The output values are 79, 51, 16, 37. Last free one today — make it count tomorrow, or type /upgrade for unlimited.