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 solutions to the problems: Step 1: Analyze the Venn diagram for Question 23. The Venn diagram shows the prime factors of 12 (F12) and y (Fy). The prime factors of 12 are 2 × 2 × 3. From the diagram, the F12 circle contains x, and the common factors (intersection) are 2, 3. So, the prime factors of 12 are x, 2, 3. For this to be 2, 2, 3, the value of x must be 2. The prime factors of y (Fy circle) include the common factors 2, 3 and additional factors 2, 3 in the Fy-only section. So, the prime factors of y are 2, 3, 2, 3. Therefore, y = 2 × 3 × 2 × 3 = 36. Step 2: Answer Question 23. a) Find the value of: (i) x: x = 2 (ii) y: y = 36 b) Find the GCF of 12 and y. The prime factors of 12 are 2^2 × 3^1. The prime factors of y=36 are 2^2 × 3^2. The GCF is the product of the lowest powers of common prime factors. GCF(12, 36) = 2^2 × 3^1 = 4 × 3 = 12 c) Find the LCM of 12 and Y. The LCM is the product of the highest powers of all prime factors. LCM(12, 36) = 2^2 × 3^2 = 4 × 9 = 36 Step 3: Answer Question 24: Find the square of the following numbers. a) 9: 9^2 = 9 × 9 = 81 b) 25: 25^2 = 25 × 25 = 625 c) 16: 16^2 = 16 × 16 = 256 Step 4: Answer Question 25: Find the square root of the following numbers. a) 144: sqrt(144) = 12 b) 196: sqrt(196) = 14 c) 441: sqrt(441) = 21 d) 400: sqrt(400) = 20 Last free one today — make it count tomorrow, or type /upgrade for unlimited.