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 for parts (B) and (C). Part (B): Find the values of x and y Step 1: Find the value of x. Angles PQR and RQS are angles on a straight line PS, so their sum is 180^. PQR + RQS = 180^ Substitute the given expressions for the angles: 2x + (3x + 15^) = 180^ Combine like terms: 5x + 15^ = 180^ Subtract 15^ from both sides: 5x = 180^ - 15^ 5x = 165^ Divide by 5: x = (165)/(5) x = 33 Step 2: Find the value of y. First, calculate PQR using the value of x: PQR = 2x = 2(33^) = 66^ The sum of angles in a triangle is 180^. For PQR: RPQ + PQR + PRQ = 180^ Substitute the known angle values: 70^ + 66^ + y^ = 180^ Add the known angles: 136^ + y^ = 180^ Subtract 136^ from both sides: y^ = 180^ - 136^ y = 44 The values are x = 33, y = 44. Part (C): Factorize the expression 2x + xy + 6 + 3y Step 1: Group the terms. Group the first two terms and the last two terms: (2x + xy) + (6 + 3y) Step 2: Factor out the common factor from each group. From the first group, factor out x: x(2 + y) From the second group, factor out 3: 3(2 + y) Now the expression is: x(2 + y) + 3(2 + y) Step 3: Factor out the common binomial factor (2 + y). (2 + y)(x + 3) The factored expression is (x+3)(y+2). Send me the next one 📸