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
Hey AthanusMulwa, good to see you again. Here are the solutions to your problems: 1. Solve the following simultaneous equation using elimination: x + y = 10 (1) x - y = 2 (2) Step 1: Add equation (1) and equation (2) to eliminate y. (x + y) + (x - y) = 10 + 2 2x = 12 Step 2: Solve for x. (2x)/(2) = (12)/(2) x = 6 Step 3: Substitute the value of x into equation (1) to find y. 6 + y = 10 y = 10 - 6 y = 4 The solution is x=6, y=4. 2. In a shooting range, the target is placed 320 m away from the shooting point. If the bullet took 2(1)/(2) seconds to hit the target, what was the average speed of the bullet? Step 1: Identify the given values. Distance (d) = 320 m Time (t) = 2(1)/(2) s = 2.5 s Step 2: Use the formula for average speed. Average Speed = DistanceTime Average Speed = 320 m2.5 s Step 3: Calculate the average speed. Average Speed = 128 m/s The average speed of the bullet was 128 m/s. 3. On a given map with scale of 1:600, a rectangular shape was measuring 6 cm by 2.5 cm. Find the actual area of the rectangular shape in square metres. Step 1: Convert the map dimensions to actual dimensions using the scale 1:600. Actual length = Map length × Scale factor Actual length = 6 cm × 600 = 3600 cm Actual width = Map width × Scale factor Actual width = 2.5 cm × 600 = 1500 cm Step 2: Convert the actual dimensions from centimeters to meters. (1 m = 100 cm) Actual length in meters = 3600 cm100 cm/m = 36 m Actual width in meters = 1500 cm100 cm/m = 15 m Step 3: Calculate the actual area in square meters. Actual Area = Actual length × Actual width Actual Area = 36 m × 15 m Actual Area = 540 m^2 The actual area of the rectangular shape is 540 m^2. 4. Solve (2x - 6)/(3) = (x - 4)/(4) Step 1: Cross-multiply to eliminate the denominators. 4(2x - 6) = 3(x - 4) Step 2: Distribute the numbers on both sides of the equation. 8x - 24 = 3x - 12 Step 3: Gather x terms on one side and constant terms on the other side. 8x - 3x = -12 + 24 5x = 12 Step 4: Solve for x. x = (12)/(5) x = 2.4 The solution is x = (12)/(5) or 2.4. 5. Factorise 4y - 144 Step 1: Find the greatest common factor (GCF) of the terms 4y and 144. The GCF of 4 and 144 is 4. Step 2: Factor out the GCF from the expression. 4y - 144 = 4(y - 36) The factorised expression is 4(y - 36). Send me the next one 📸