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 answers to your questions. 1) Complete the rule and calculate N. Step 1: Determine the rule from the given input and output values. Let the input be x and the output be y. From the table: For (2, 3): y = 3 when x = 2. For (5, 18): y = 18 when x = 5. For (10, 43): y = 43 when x = 10. For (13, 58): y = 58 when x = 13. Let's assume a linear rule of the form y = ax + b. Using (2, 3) and (5, 18): 3 = 2a + b (Equation 1) 18 = 5a + b (Equation 2) Subtract Equation 1 from Equation 2: 18 - 3 = (5a + b) - (2a + b) 15 = 3a a = (15)/(3) a = 5 Substitute a = 5 into Equation 1: 3 = 2(5) + b 3 = 10 + b b = 3 - 10 b = -7 The rule is y = 5x - 7. This means "Input number × 5 - 7". The missing operation in the flow diagram is × 5. Step 2: Calculate N using the rule. For Input 9, the output is N. N = 5 × 9 - 7 N = 45 - 7 N = 38 The completed rule is: Input number × 5 - 7. The value of N is 38. 2) The rule for the table below is: Input: 1, Output: 3 Input: 2, Output: 5 Input: 3, Output: 7 Input: 4, Output: 9 Step 1: Test each option with the given input and output values. • Option 1: Input number × 2 + 3 For Input 1: 1 × 2 + 3 = 5 (Incorrect, should be 3) • Option 2: Input number × 2 + 1 For Input 1: 1 × 2 + 1 = 3 (Correct) For Input 2: 2 × 2 + 1 = 5 (Correct) For Input 3: 3 × 2 + 1 = 7 (Correct) For Input 4: 4 × 2 + 1 = 9 (Correct) • Option 3: Input number × 3 + 2 For Input 1: 1 × 3 + 2 = 5 (Incorrect, should be 3) • Option 4: Input number × 2 - 1 For Input 1: 1 × 2 - 1 = 1 (Incorrect, should be 3) Step 2: Select the correct option. The correct rule is option 2. The rule is Input number × 2 + 1. 3) Use the rule below to determine the output value if the input value is 3. Rule: "input value × 5 - 4" Input value = 3 Step 1: Substitute the input value into the rule. Output value = 3 × 5 - 4 Step 2: Calculate the output value. Output value = 15 - 4 Output value = 11 Your answer of "output value = 14" is ❌ Incorrect. The correct output value is 11. Send me the next one 📸