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: 1. Complete the table below. The table is already completed in the image. | x | x^2 | sqrt(x) | (1)/(x) | |---|---|---|---| | 1 | 1 | 1 | 1 | | 4 | 16 | 2 | (1)/(4) | | 9 | 81 | 3 | (1)/(9) | | 16 | 256 | 4 | (1)/(16) | | 25 | 625 | 5 | (1)/(25) | 2. Find: a) 3^2 + 5^2 Step 1: Calculate the squares. 3^2 = 3 × 3 = 9 5^2 = 5 × 5 = 25 Step 2: Add the results. 9 + 25 = 34 The answer is 34. b) sqrt(49) Step 1: Find the square root of 49. sqrt(49) = 7 The answer is 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 The answer is 3x - 2. b) (3x^2 - 2x + 1) - (x^2 + x - 4) Step 1: Distribute the negative sign to the terms in the second parenthesis. 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 The answer is 2x^2 - 3x + 5. c) 2(x + 4) - 3(x - 2) Step 1: Distribute the numbers outside the parentheses. 2 × x + 2 × 4 - 3 × x - 3 × (-2) 2x + 8 - 3x + 6 Step 2: Combine like terms. (2x - 3x) + (8 + 6) = -x + 14 The answer is -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 The answer is 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 The answer is x = 7. 3 done, 2 left today. You're making progress.