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
You're on a roll — here are the solutions for questions 8 and 9: 8. Determine the value of: (8^2 (9^2 - 3^2))/(4^2 × 6^2) Step 1: Calculate the squares of the numbers. 8^2 = 64 9^2 = 81 3^2 = 9 4^2 = 16 6^2 = 36 Step 2: Substitute these values into the expression. (64 (81 - 9))/(16 × 36) Step 3: Perform the subtraction in the parenthesis. 81 - 9 = 72 Step 4: Substitute the result back into the expression. (64 × 72)/(16 × 36) Step 5: Simplify the expression. We can simplify by cancelling common factors: (64 × 72)/(16 × 36) = ((16 × 4) × (36 × 2))/(16 × 36) Cancel 16 from the numerator and denominator, and 36 from the numerator and denominator: = 4 × 2 = 8 The correct option is B. 8 9. Work out the value of the square of 2 (4)/(5). Step 1: Convert the mixed number to an improper fraction. 2 (4)/(5) = ((2 × 5) + 4)/(5) = (10 + 4)/(5) = (14)/(5) Step 2: Square the improper fraction. ((14)/(5))^2 = (14^2)/(5^2) Step 3: Calculate the squares of the numerator and the denominator. 14^2 = 196 5^2 = 25 Step 4: Write the result as a mixed number. (196)/(25) Divide 196 by 25: 196 ÷ 25 = 7 with a remainder of 196 - (7 × 25) = 196 - 175 = 21. So, the mixed number is 7 (21)/(25). The correct option is A. 7 (21)/(25) What's next? Send 'em!