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
Welcome back martinodok — been a while! Let's pick up where you left off. Step 1: Solve the pair of simultaneous equations. Given equations: 4a + 12b = 16 (1) 2a + 3b = 7 (2) Multiply equation (2) by 2 to eliminate a: 2(2a + 3b) = 2(7) 4a + 6b = 14 (3) Subtract equation (3) from equation (1): (4a + 12b) - (4a + 6b) = 16 - 14 6b = 2 b = (2)/(6) b = (1)/(3) Step 2: Substitute the value of b into equation (2) to find a. 2a + 3((1)/(3)) = 7 2a + 1 = 7 2a = 7 - 1 2a = 6 a = (6)/(2) a = 3 Step 3: Find the positive value of K. Given that (a+b) = K^2. Substitute the values of a and b: (3 + (1)/(3)) = K^2 ((9)/(3) + (1)/(3)) = K^2 (10)/(3) = K^2 Take the square root of both sides. Since we need the positive value of K: K = sqrt((10)/(3)) Rationalize the denominator: K = sqrt(10)sqrt(3) × sqrt(3)sqrt(3) K = sqrt(30)3 The positive value of K is sqrt(30)3. Send me the next one 📸