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 the problems you've provided: 1. Calculate the distance between (3,1) and (7,6) Step 1: Identify the coordinates of the two points. Let (x_1, y_1) = (3, 1) and (x_2, y_2) = (7, 6). Step 2: Apply the distance formula. The distance D between two points is given by D = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). D = sqrt((7 - 3)^2 + (6 - 1)^2) Step 3: Simplify the expression. D = sqrt((4)^2 + (5)^2) D = sqrt(16 + 25) D = sqrt(41) Step 4: Calculate the numerical value and round if necessary. D ≈ 6.403 The distance is 6.4 units. 2. Calculate the distance between (10,8) and (4,1) Step 1: Identify the coordinates of the two points. Let (x_1, y_1) = (10, 8) and (x_2, y_2) = (4, 1). Step 2: Apply the distance formula. The distance D between two points is given by D = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). D = sqrt((4 - 10)^2 + (1 - 8)^2) Step 3: Simplify the expression. D = sqrt((-6)^2 + (-7)^2) D = sqrt(36 + 49) D = sqrt(85) Step 4: Calculate the numerical value and round if necessary. D ≈ 9.219 The distance is 9.2 units. 3. Calculate the length of the new road from hospital (1,1) to town (6,5) Step 1: Identify the coordinates of the two points. Let (x_1, y_1) = (1, 1) and (x_2, y_2) = (6, 5). Step 2: Apply the distance formula. The distance D between two points is given by D = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). D = sqrt((6 - 1)^2 + (5 - 1)^2) Step 3: Simplify the expression. D = sqrt((5)^2 + (4)^2) D = sqrt(25 + 16) D = sqrt(41) Step 4: Calculate the numerical value and round if necessary. D ≈ 6.403 The length of the new road is 6.4 units. That's 2 down. 3 left today — send the next one.