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
1. Values for which the expression is not defined Step 1: Identify when the expression is undefined. A rational expression is undefined when its denominator is equal to zero. The given expression is (m+1)/(3m^2 - 2m - 5). Set the denominator to zero: 3m^2 - 2m - 5 = 0 Step 2: Solve the quadratic equation for m. We can factor the quadratic equation. We need two numbers that multiply to 3 × -5 = -15 and add to -2. These numbers are -5 and 3. Rewrite the middle term: 3m^2 - 5m + 3m - 5 = 0 Factor by grouping: m(3m - 5) + 1(3m - 5) = 0 (3m - 5)(m + 1) = 0 Set each factor to zero to find the values of m: 3m - 5 = 0 3m = 5 m = (5)/(3) m + 1 = 0 m = -1 The expression is not defined for m = -1 and m = (5)/(3). The correct option is D. D. -1 and (5)/(3) 2. Finding the value of p Step 1: Use the trigonometric identity ^2 p + ^2 p = 1. Given p = (7)/(25) and 0^ < p < 90^. Substitute the value of p into the identity: ^2 p + ((7)/(25))^2 = 1 ^2 p + (49)/(625) = 1 Step 2: Solve for p. Subtract (49)/(625) from both sides: ^2 p = 1 - (49)/(625) ^2 p = (625)/(625) - (49)/(625) ^2 p = (625 - 49)/(625) ^2 p = (576)/(625) Take the square root of both sides: p = sqrt((576)/(625)) Since 0^ < p < 90^, p is in the first quadrant, so p must be positive. p = sqrt(576)sqrt(625) p = (24)/(25) The correct option is B. B. (24)/(25) What's next? 📸