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 the questions: Question 12: Simplify the expression ((x+1)(4a^2-ax))/(x^2-4ax-4a+x). Step 1: Factor the numerator. Factor out a from the second term in the numerator: (x+1)(4a^2-ax) = (x+1)a(4a-x) Step 2: Factor the denominator. Group terms in the denominator and factor by grouping: x^2-4ax-4a+x = x^2+x - 4ax-4a = x(x+1) - 4a(x+1) = (x+1)(x-4a) Step 3: Simplify the expression. Substitute the factored forms back into the expression: ((x+1)a(4a-x))/((x+1)(x-4a)) Notice that (4a-x) = -(x-4a). ((x+1)a(-(x-4a)))/((x+1)(x-4a)) Assuming x -1 and x 4a, we can cancel out the common factors (x+1) and (x-4a): = -a The simplified expression is -a. Question 13: The sum of two consecutive even numbers is 270. Find the numbers. Step 1: Define the two consecutive even numbers. Let the first even number be x. The next consecutive even number is x+2. Step 2: Set up the equation based on their sum. x + (x+2) = 270 Step 3: Solve for x. 2x + 2 = 270 2x = 270 - 2 2x = 268 x = (268)/(2) x = 134 Step 4: Find the two numbers. The first number is x = 134. The second number is x+2 = 134+2 = 136. The two consecutive even numbers are 134 and 136. **