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
Alright r30993652 — let's do this. Here are the solutions to the problems: 1. Evaluate (36 - 8 × 4 - 15 ÷ 3)/(-3 × 3 - 8(-6 + 2)) Step 1: Evaluate the numerator using the order of operations (BODMAS/PEMDAS). 36 - 8 × 4 - 15 ÷ 3 = 36 - 32 - 5 = 4 - 5 = -1 Step 2: Evaluate the denominator using the order of operations. -3 × 3 - 8(-6 + 2) = -3 × 3 - 8(-4) = -9 - (-32) = -9 + 32 = 23 Step 3: Divide the numerator by the denominator. (-1)/(23) The evaluated expression is -(1)/(23). 2. Simplify a + b - 2a Step 1: Combine the like terms involving a. a - 2a + b = -a + b The simplified expression is b - a. 3. Find the greatest number which divides 181 and 236 and leaves a remainder of 5 in each case. Step 1: Subtract the remainder from each number to find the numbers that are perfectly divisible. 181 - 5 = 176 236 - 5 = 231 Step 2: Find the Greatest Common Divisor (GCD) of 176 and 231. Prime factorization of 176 = 2^4 × 11 Prime factorization of 231 = 3 × 7 × 11 Step 3: Identify the common prime factors and multiply them. The only common prime factor is 11. The GCD is 11. The greatest number is 11. 4. A rectangle measures 20cm by 15cm. If each dimension is increased by 2.5cm, by what percentage is: Original length (L_1) = 20 cm Original width (W_1) = 15 cm New length (L_2) = 20 + 2.5 = 22.5 cm New width (W_2) = 15 + 2.5 = 17.5 cm a) the perimeter of the rectangle increased Step 1: Calculate the original perimeter. P_1 = 2(L_1 + W_1) = 2(20 + 15) = 2(35) = 70 cm Step 2: Calculate the new perimeter. P_2 = 2(L_2 + W_2) = 2(22.5 + 17.5) = 2(40) = 80 cm Step 3: Calculate the percentage increase in perimeter. Percentage Increase = (P_2 - P_1)/(P_1) × 100\% = (80 - 70)/(70) × 100\% = (10)/(70) × 100\% = (1)/(7) × 100\% ≈ 14.29\% The perimeter is increased by approximately 14.29\%. b) the area of the rectangle increased Step 1: Calculate the original area. A_1 = L_1 × W_1 = 20 cm × 15 cm = 300 cm^2 Step 2: Calculate the new area. A_2 = L_2 × W_2 = 22.5 cm × 17.5 cm = 393.75 cm^2 Step 3: Calculate the percentage increase in area. Percentage Increase = (A_2 - A_1)/(A_1) × 100\% = (393.75 - 300)/(300) × 100\% = (93.75)/(300) × 100\% = 0.3125 × 100\% = 31.25\% The area is increased by 31.25\%. Send me the next one 📸