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
Given = (3)/(4). Step 1: Find and . We can use a right-angled triangle where = oppositeadjacent. Let the opposite side be 3k and the adjacent side be 4k for some constant k. Using the Pythagorean theorem, the hypotenuse h is: h = sqrt((3k)^2 + (4k)^2) = sqrt(9k^2 + 16k^2) = sqrt(25k^2) = 5k Now we can find and : = oppositehypotenuse = (3k)/(5k) = (3)/(5) = adjacenthypotenuse = (4k)/(5k) = (4)/(5) Step 2: Evaluate the expression 7 + 5 . Substitute the given value of and the calculated value of : 7 + 5 = 7 ((3)/(4)) + 5 ((4)/(5)) = (21)/(4) + (20)/(5) = (21)/(4) + 4 To add these fractions, find a common denominator: = (21)/(4) + (4 × 4)/(4) = (21)/(4) + (16)/(4) = (21 + 16)/(4) = (37)/(4) The value of the expression is (37)/(4).