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 problems: 1. a) Company charges: Let C be the total charge and k be the number of kilometers. The fixed charge is Sh 50. The charge per kilometer is Sh 20. The total charge can be expressed as: C = 50 + 20k 1. b) Percentage commission: Step 1: Identify the commission amount and the total sales amount. Commission received = Sh 30,000 Total sales amount = Sh 600,000 Step 2: Calculate the percentage commission. Percentage Commission = CommissionTotal Sales × 100\% Percentage Commission = (30000)/(600000) × 100\% Percentage Commission = (3)/(60) × 100\% Percentage Commission = (1)/(20) × 100\% Percentage Commission = 0.05 × 100\% Percentage Commission = 5\% 2. Gradient of a line: Step 1: Identify the coordinates of the two points. Let (x_1, y_1) = (4, 5) and (x_2, y_2) = (8, 3). Step 2: Use the gradient formula m = (y_2 - y_1)/(x_2 - x_1). m = (3 - 5)/(8 - 4) m = (-2)/(4) m = -(1)/(2) 3. Solving simultaneous equations by substitution: Given equations: 1) 2x - y = 6 2) x - y = 1 Step 1: Express x in terms of y from Equation 2. From (2): x = 1 + y (Equation 3) Step 2: Substitute Equation 3 into Equation 1. 2(1 + y) - y = 6 2 + 2y - y = 6 2 + y = 6 Step 3: Solve for y. y = 6 - 2 y = 4 Step 4: Substitute the value of y back into Equation 3 to find x. x = 1 + 4 x = 5 The solution is x=5, y=4. Solving the inequality: Given the inequality: -3 < 2x - 5 Step 1: Add 5 to all parts of the inequality. -3 + 5 < 2x - 5 + 5 2 < 2x Step 2: Divide all parts by 2. (2)/(2) < (2x)/(2) 1 < x The solution is x > 1.