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
Welcome back mthaby — missed you this week. Step 1: Analyze the given information for the bottom diagram. The diagram shows an input, a first rule (unknown, marked with "?"), a second rule (× 7), and a final output. We need to find the missing rule in the first box. We have the following input-output pairs: • Input 0, Output 21 • Input 2, Output (missing) • Input 4, Output 49 • Input 5, Output 56 • Input 7, Output 70 • Input 9, Output 84 Step 2: Determine the intermediate values by reversing the second rule. The second rule is "× 7". To find the value before this rule was applied (the intermediate value), we divide the output by 7. • For Input 0, Output 21: Intermediate Value = (21)/(7) = 3. • For Input 4, Output 49: Intermediate Value = (49)/(7) = 7. • For Input 5, Output 56: Intermediate Value = (56)/(7) = 8. • For Input 7, Output 70: Intermediate Value = (70)/(7) = 10. • For Input 9, Output 84: Intermediate Value = (84)/(7) = 12. Step 3: Find the first rule by comparing inputs and intermediate values. Now we look at the relationship between the original Input and the Intermediate Value: • Input 0 Intermediate Value 3 • Input 4 Intermediate Value 7 • Input 5 Intermediate Value 8 • Input 7 Intermediate Value 10 • Input 9 Intermediate Value 12 In each case, the Intermediate Value is 3 more than the Input. 0 + 3 = 3 4 + 3 = 7 5 + 3 = 8 7 + 3 = 10 9 + 3 = 12 Therefore, the missing rule in the first box is "+3". Step 4: Calculate the missing output. Using the first rule (+3) and the second rule (× 7) for Input 2: • First, apply the "+3" rule: 2 + 3 = 5. • Next, apply the "× 7" rule: 5 × 7 = 35. The missing output is 35. The missing rule is +3. Send me the next one 📸