A flow diagram shows a rule that transforms input values into output values. Some input and output values are missing. Determine the input values, the output values, and the rule.

Question

Asked on April 28, 2026Mathematics

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.

Accepted Answer · 2026-04-28T14:26:38.611Z

Here are the solutions based on the flow diagram: i. What are the input values? Step 1: Identify the given input values from the diagram. The given input values are 5, 2, 7, 11. Step 2: Use the rule to find the missing input values. The rule is "multiply by 5, then subtract 4". So, if x is the input and y is the output, the rule is y = 5x - 4. We have output values 26 and 41 with missing inputs. For output 26: 5x - 4 = 26 5x = 26 + 4 5x = 30 x = (30)/(5) x = 6 For output 41: 5x - 4 = 41 5x = 41 + 4 5x = 45 x = (45)/(5) x = 9 The complete list of input values is 5, 2, 6, 9, 7, 11. The input values are: 5, 2, 6, 9, 7, 11 ii. What are the output values? Step 1: Identify the given output values from the diagram. The given output values are 26, 41. Step 2: Use the rule to find the missing output values. The rule is y = 5x - 4. For input 5: y = 5(5) - 4 = 25 - 4 = 21 For input 2: y = 5(2) - 4 = 10 - 4 = 6 For input 7: y = 5(7) - 4 = 35 - 4 = 31 For input 11: y = 5(11) - 4 = 55 - 4 = 51 The complete list of output values is 21, 6, 26, 41, 31, 51. The output values are: 21, 6, 26, 41, 31, 51 iv. What is the rule? The rule shown in the flow diagram is to multiply the input by 5, then subtract 4. The rule is: Multiply by 5, then subtract 4 (or x 5x - 4) v. Number sentences Based on the input and output values and the rule y = 5x - 4: 5 × 5 - 4 = 21 5 × 2 - 4 = 6 5 × 6 - 4 = 26 5 × 9 - 4 = 41 5 × 7 - 4 = 31 5 × 11 - 4 = 51 vi. What will the output values be if the rule is -4 × 5? Step 1: Interpret the new rule. The rule is given as -4 × 5. This simplifies to -20. So, the new rule is to multiply the input by -20. Let x be the input, the new rule is y = -20x. Step 2: Use the input values from the original diagram (5, 2, 6, 9, 7, 11) with the new rule. For input 5: y = -20 × 5 = -100 For input 2: y = -20 × 2 = -40 For input 6: y = -20 × 6 = -120 For input 9: y = -20 × 9 = -180 For input 7: y = -20 × 7 = -140 For input 11: y = -20 × 11 = -220 The output values will be: -100, -40, -120, -180, -140, -220 Send me the next one 📸

Accepted Answer · 2026-04-28T14:26:38.611Z

Here are the solutions based on the flow diagram: i. What are the input values? Step 1: Identify the given input values from the diagram. The given input values are 5, 2, 7, 11. Step 2: Use the rule to find the missing input values. The rule is "multiply by 5, then subtract 4". So, if x is the input and y is the output, the rule is y = 5x - 4. We have output values 26 and 41 with missing inputs. For output 26: 5x - 4 = 26 5x = 26 + 4 5x = 30 x = (30)/(5) x = 6 For output 41: 5x - 4 = 41 5x = 41 + 4 5x = 45 x = (45)/(5) x = 9 The complete list of input values is 5, 2, 6, 9, 7, 11. The input values are: 5, 2, 6, 9, 7, 11 ii. What are the output values? Step 1: Identify the given output values from the diagram. The given output values are 26, 41. Step 2: Use the rule to find the missing output values. The rule is y = 5x - 4. For input 5: y = 5(5) - 4 = 25 - 4 = 21 For input 2: y = 5(2) - 4 = 10 - 4 = 6 For input 7: y = 5(7) - 4 = 35 - 4 = 31 For input 11: y = 5(11) - 4 = 55 - 4 = 51 The complete list of output values is 21, 6, 26, 41, 31, 51. The output values are: 21, 6, 26, 41, 31, 51 iv. What is the rule? The rule shown in the flow diagram is to multiply the input by 5, then subtract 4. The rule is: Multiply by 5, then subtract 4 (or x 5x - 4) v. Number sentences Based on the input and output values and the rule y = 5x - 4: 5 × 5 - 4 = 21 5 × 2 - 4 = 6 5 × 6 - 4 = 26 5 × 9 - 4 = 41 5 × 7 - 4 = 31 5 × 11 - 4 = 51 vi. What will the output values be if the rule is -4 × 5? Step 1: Interpret the new rule. The rule is given as -4 × 5. This simplifies to -20. So, the new rule is to multiply the input by -20. Let x be the input, the new rule is y = -20x. Step 2: Use the input values from the original diagram (5, 2, 6, 9, 7, 11) with the new rule. For input 5: y = -20 × 5 = -100 For input 2: y = -20 × 2 = -40 For input 6: y = -20 × 6 = -120 For input 9: y = -20 × 9 = -180 For input 7: y = -20 × 7 = -140 For input 11: y = -20 × 11 = -220 The output values will be: -100, -40, -120, -180, -140, -220 Send me the next one 📸

A flow diagram shows a rule that transforms input values into output values. Some input and output values are missing. Determine the input values, the output values, and the rule.

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A flow diagram shows a rule that transforms input values into output values. Some input and output values are missing. Determine the input values, the output values, and the rule.

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