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 your questions: Find the equation passing through A(2, 4) and B(5, 13) in form y = mx + c. Step 1: Calculate the slope (m) of the line using the two given points A(x_1, y_1) = (2, 4) and B(x_2, y_2) = (5, 13). m = (y_2 - y_1)/(x_2 - x_1) m = (13 - 4)/(5 - 2) m = (9)/(3) m = 3 Step 2: Use the slope m=3 and one of the points (e.g., A(2, 4)) to find the y-intercept (c) using the equation y = mx + c. 4 = 3(2) + c 4 = 6 + c c = 4 - 6 c = -2 Step 3: Write the equation of the line in the form y = mx + c. y = 3x - 2 The equation of the line is y = 3x - 2. Solve the equation sqrt(x+2) = x. Step 1: Square both sides of the equation to eliminate the square root. (sqrt(x+2))^2 = x^2 x+2 = x^2 Step 2: Rearrange the equation into a standard quadratic form ax^2 + bx + c = 0. x^2 - x - 2 = 0 Step 3: Solve the quadratic equation by factoring. (x - 2)(x + 1) = 0 This gives two possible solutions: x - 2 = 0 x = 2 x + 1 = 0 x = -1 Step 4: Check both possible solutions in the original equation sqrt(x+2) = x to identify any extraneous solutions. For x = 2: sqrt(2+2) = sqrt(4) = 2 2 = 2 This solution is valid. For x = -1: sqrt(-1+2) = sqrt(1) = 1 1 ≠ -1 This solution is extraneous because the square root symbol sqrt() denotes the principal (non-negative) square root. The only valid solution is x = 2. What's next?