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
let's solve these pattern and flow diagram problems. Question 8 8.1 Given the flow diagram below: Determine the values of a and b. The rule for the flow diagram is: (Input × 2) + 3 = Output. Step 1: Determine the value of a. The input for a is 4. a = (4 × 2) + 3 a = 8 + 3 a = 11 Step 2: Determine the value of b. The output for b is 15. (b × 2) + 3 = 15 Subtract 3 from both sides: b × 2 = 15 - 3 b × 2 = 12 Divide by 2: b = (12)/(2) b = 6 a = 11, b = 6 8.2 The rule of a pattern is given as: Output = (Input × 3) - 2 8.2.1 Calculate the output when the input is 5. Step 1: Substitute Input = 5 into the given rule. Output = (5 × 3) - 2 Output = 15 - 2 Output = 13 13 8.2.2 Write the rule as a number sentence in terms of n. Step 1: Replace "Input" with n and "Output" with a variable like y or simply "Output". Output = (n × 3) - 2 This can be written more concisely as: Output = 3n - 2 Output = 3n - 2 8.2.3 Explain how this rule is similar to: Output = 3n - 2 The rule Output = (Input × 3) - 2 is similar to Output = 3n - 2 because in algebra, the multiplication symbol (×) between a number and a variable (like 3 × n) is often omitted and written as 3n. Also, the variable n is used to represent the "Input". The rules are identical. "Input" is replaced by the variable n, and 3 × n is written as 3n. Send me the next one 📸