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. Problem 42: The diagram shows a triangle LMN inscribed in a circle with center O. Since LN passes through the center O, LN is the diameter of the circle. An angle inscribed in a semicircle is a right angle, so LMN = 90^. Step 1: Set up the equation for the sum of angles in LMN. The sum of angles in a triangle is 180^. LNM + NLM + LMN = 180^ Substitute the given values: LNM = (x+15)^, NLM = (x-5)^, and LMN = 90^. (x+15) + (x-5) + 90 = 180 Step 2: Solve for x. 2x + 10 + 90 = 180 2x + 100 = 180 2x = 180 - 100 2x = 80 x = (80)/(2) x = 40 The value of x is 40. The correct option is B. B. 40^ Problem 43: Given vectors a = 3 \\ 2 and b = -1 \\ 4 . We need to find (1)/(2)a - b. Step 1: Calculate (1)/(2)a. (1)/(2)a = (1)/(2) 3 \\ 2 = (3)/(2) \\ (2)/(2) = 1.5 \\ 1 Step 2: Calculate (1)/(2)a - b. (1)/(2)a - b = 1.5 \\ 1 - -1 \\ 4 = 1.5 - (-1) \\ 1 - 4 = 1.5 + 1 \\ -3 = 2.5 \\ -3 The correct option is A. A. 2.5 \\ -3 Problem 44: Calculate the magnitude of the vector 2i - 3j. Step 1: Identify the components of the vector. A vector v = xi + yj has components x and y. For the vector 2i - 3j, we have x = 2 and y = -3. Step 2: Calculate the magnitude using the formula |v| = sqrt(x^2 + y^2). |2i - 3j| = sqrt((2)^2 + (-3)^2) = sqrt(4 + 9) = sqrt(13) The magnitude of the vector 2i - 3j is sqrt(13). sqrt(13) Send me the next one 📸