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 problems: 2. (a) Simplify: (3(1)/(2) + 2(1)/(4)) ÷ (5(2)/(3) - 1(1)/(2)) Step 1: Simplify the expression inside the first parenthesis. Convert mixed numbers to improper fractions and find a common denominator. 3(1)/(2) + 2(1)/(4) = (7)/(2) + (9)/(4) = (14)/(4) + (9)/(4) = (14+9)/(4) = (23)/(4) Step 2: Simplify the expression inside the second parenthesis. Convert mixed numbers to improper fractions and find a common denominator. 5(2)/(3) - 1(1)/(2) = (17)/(3) - (3)/(2) = (34)/(6) - (9)/(6) = (34-9)/(6) = (25)/(6) Step 3: Perform the division of the results from Step 1 and Step 2. To divide by a fraction, multiply by its reciprocal. (23)/(4) ÷ (25)/(6) = (23)/(4) × (6)/(25) = (23 × 6)/(4 × 25) = (138)/(100) Step 4: Simplify the fraction and convert it to a mixed number. (138)/(100) = (69)/(50) = 1(19)/(50) The simplified expression is 1(19)/(50). 2. (b) Solve for n in the equation 2n^2 = 4n. Step 1: Rearrange the equation to set it equal to zero. 2n^2 - 4n = 0 Step 2: Factor out the common term, which is 2n. 2n(n - 2) = 0 Step 3: Set each factor equal to zero and solve for n. 2n = 0 or n - 2 = 0 n = (0)/(2) or n = 2 n = 0 or n = 2 The solutions for n are n=0 or n=2. Last free one today — make it count tomorrow, or type /upgrade for unlimited.