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 Little, good to see you again. 1. (a) i) In the diagram, AB is parallel to CD, and EF is a transversal. The angles 5x and x+78^ are alternate exterior angles, which are equal. 5x = x+78^ Subtract x from both sides: 4x = 78^ Divide by 4: x = (78)/(4) x = (39)/(2) x = 19.5^ ii) The angles 5x and 4x+y are vertically opposite angles, which are equal. 5x = 4x+y Subtract 4x from both sides: x = y Since x = 19.5^: y = 19.5^ 1. (b) i) Simplify the expression: 2(4-3xy)-5(6-xy) Distribute the numbers into the parentheses: 8 - 6xy - 30 + 5xy Combine like terms: (8 - 30) + (-6xy + 5xy) -22 - xy The simplified expression is -22 - xy. ii) Multiply 0.00834 by 0.02 and express the answer in standard form. First, convert the numbers to standard form: 0.00834 = 8.34 × 10^-3 0.02 = 2 × 10^-2 Now, multiply them: (8.34 × 10^-3) × (2 × 10^-2) (8.34 ×