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
Morning black — let's get this done. To determine the values of A and K, we will use the conditions given: the lines are perpendicular, and one line passes through a specific point. Step 1: Find the slopes of both lines. The general form of a linear equation is Ax + By + C = 0, and its slope m is given by m = -(A)/(B). For the first line: Ax + 3y - 6 = 0 The slope m_1 = -(A)/(3). For the second line: 5x + 7y - k = 0 The slope m_2 = -(5)/(7). Step 2: Use the condition that the lines are perpendicular. If two lines are perpendicular, the product of their slopes is -1. m_1 · m_2 = -1 Substitute the slopes: (-(A)/(3)) · (-(5)/(7)) = -1 (5A)/(21) = -1 Multiply both sides by 21: 5A = -21 Divide by 5: A = -(21)/(5) Step 3: Use the condition that the line 5x + 7y - k = 0 passes through the point (4,3). Substitute x=4 and y=3 into the equation of the second line: 5(4) + 7(3) - k = 0 20 + 21 - k = 0 41 - k = 0 Add k to both sides: k = 41 The values are A = -(21)/(5) and K = 41. The values are A = -(21)/(5), K = 41. Send me the next one 📸