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
1. 10(x + 3) = 11(x + 1) Step 1: Expand both sides. 10x + 30 = 11x + 11 Step 2: Subtract 10x from both sides. 30 = x + 11 Step 3: Subtract 11 from both sides. 30 - 11 = x 19 = x x = 19 19 2. 11101101_2 Step 1: Write powers of 2 from right to left. 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0 128 64 32 16 8 4 2 1 1 1 1 0 1 1 0 1 Step 2: Multiply and sum. 128 × 1 + 64 × 1 + 32 × 1 + 16 × 0 + 8 × 1 + 4 × 1 + 2 × 0 + 1 × 1 128 + 64 + 32 + 0 + 8 + 4 + 0 + 1 Step 3: Add step-by-step. 128 + 64 = 192 192 + 32 = 224 224 + 8 = 232 232 + 4 = 236 236 + 1 = 237 237 (denary) 237 3. 247 (denary) Step 1: Divide by 2 and record remainders. 247 ÷ 2 = 123,\ remainder\ 1 123 ÷ 2 = 61,\ remainder\ 1 61 ÷ 2 = 30,\ remainder\ 1 30 ÷ 2 = 15,\ remainder\ 0 15 ÷ 2 = 7,\ remainder\ 1 7 ÷ 2 = 3,\ remainder\ 1 3 ÷ 2 = 1,\ remainder\ 1 1 ÷ 2 = 0,\ remainder\ 1 Step 2: Read remainders from bottom to top. 11110111_2 11110111₂ 11110111_2 4. 3x^2 - 5x - 2 = 0 Step 1: Factorise. (3x + 1)(x - 2) = 0 Step 2: Set each factor to zero. 3x + 1 = 0 or x - 2 = 0 Step 3: Solve each equation. 3x = -1 x = -(1)/(3) and x = 2 x = 2 or x = -(1)/(3) x=2\\=-(1)/(3)