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.
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You're on a roll — here are the solutions for Task II: 1. The table is already completed in the image provided. 2. Find: *a) 3^2 + 5^2 Step 1: Calculate the squares. 3^2 = 9 5^2 = 25 Step 2: Add the results. 9 + 25 = 34 34 *b) sqrt(49) Step 1: Find the square root of 49. sqrt(49) = 7 7 3. Simplify the following expressions. *a) (2x + 3) + (x - 5) Step 1: Remove the parentheses. 2x + 3 + x - 5 Step 2: Combine like terms. (2x + x) + (3 - 5) = 3x - 2 3x - 2 *b) (3x^2 - 2x + 1) - (x^2 + x - 4) Step 1: Remove the parentheses, distributing the negative sign to the second expression. 3x^2 - 2x + 1 - x^2 - x + 4 Step 2: Combine like terms. (3x^2 - x^2) + (-2x - x) + (1 + 4) = 2x^2 - 3x + 5 2x^2 - 3x + 5 *c) 2(x + 4) - 3(x - 2) Step 1: Distribute the numbers into the parentheses. 2x + 8 - 3x + 6 Step 2: Combine like terms. (2x - 3x) + (8 + 6) = -x + 14 -x + 14 4. Solve the following equations. *a) 2x + 5 = 17 Step 1: Subtract 5 from both sides of the equation. 2x + 5 - 5 = 17 - 5 2x = 12 Step 2: Divide both sides by 2. (2x)/(2) = (12)/(2) x = 6 x = 6 *b) 3(x - 2) = 15 Step 1: Divide both sides by 3. (3(x - 2))/(3) = (15)/(3) x - 2 = 5 Step 2: Add 2 to both sides of the equation. x - 2 + 2 = 5 + 2 x = 7 x = 7 Drop the next question!