Question 1: If the distance between \( (x, 3) \) and \( (7,9) \) is 10 , where \( x>0 \), then \( x \) is equal to

To solve for \( x \), we can use the distance formula, which is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). Here, the distance \( d \) is 10, \( (x_1, y_1) \) is \( (x, 3) \), and \( (x_2, y_2) \) is \( (7, 9) \). Plugging these into the formula gives us: \[ 10 = \sqrt{(7 - x)^2 + (9 - 3)^2} \] \[ 10 = \sqrt{(7 - x)^2 + 6^2} \] \[ 10 = \sqrt{(7 - x)^2 + 36} \] Squaring both sides results in: \[ 100 = (7 - x)^2 + 36 \] \[ 64 = (7 - x)^2 \] Taking the square root of both sides gives us two possible equations: \[ 7 - x = 8 \quad \text{or} \quad 7 - x = -8 \] Solving these gives \( x = -1 \) (which we discard since \( x > 0 \)) and \( x = 15 \). Thus, the solution is: \[ x = 15 \]