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 question 3: a) Step 1: Write the sentence as an algebraic equation. "Half a number, x, plus 17 is equal to 97" translates to: (x)/(2) + 17 = 97 Step 2: Subtract 17 from both sides of the equation. (x)/(2) + 17 - 17 = 97 - 17 (x)/(2) = 80 Step 3: Multiply both sides by 2 to solve for x. (x)/(2) × 2 = 80 × 2 x = 160 The value of x is 160. b) Step 1: Write the sentence as an algebraic equation. "Double a number, y, plus 4 is equal to -4" translates to: 2y + 4 = -4 Step 2: Subtract 4 from both sides of the equation. 2y + 4 - 4 = -4 - 4 2y = -8 Step 3: Divide both sides by 2 to solve for y. (2y)/(2) = (-8)/(2) y = -4 The value of y is -4. c) Step 1: Write the sentence as an algebraic equation. "Four times a number, z, is one more than 59" translates to: 4z = 59 + 1 4z = 60 Step 2: Divide both sides by 4 to solve for z. (4z)/(4) = (60)/(4) z = 15 The value of z is 15. d) Step 1: Write the sentence as an algebraic equation. "The square of an integer, p, is 21 less than 121" translates to: p^2 = 121 - 21 p^2 = 100 Step 2: Take the square root of both sides to solve for p. Remember that an integer can be positive or negative. sqrt(p^2) = sqrt(100) p = ± 10 The value of p is 10 or -10. What's next?