answer:Since line XY is a diameter, arc XY measures 180 degrees. Arc RT is formed by angle RST, which is an inscribed angle. The measure of an inscribed angle is half the measure of the arc it forms. Therefore, the measure of arc RT is: 180 degrees / 2 = 90 degrees

answer:To convert the given equation into slope-intercept form (y = mx + b), we need to isolate y on one side of the equation. Step 1: Distribute -3 to the terms inside the parentheses. 4 - 6 = -3x + 36 -2 = -3x + 36 Step 2: Add 2 to both sides of the equation. -2 + 2 = -3x + 36 + 2 0 = -3x + 38 Step 3: Divide both sides of the equation by -3 to isolate x. 0 / -3 = (-3x + 38) / -3 0 = x - 38/3 x = 38/3 Step 4: Substitute the value of x back into the original equation to find the value of y. 4 - 6 = -3(38/3 - 12) -2 = -3(38/3 - 12) -2 = -3(38/3 - 36/3) -2 = -3(2/3) -2 = -2 Therefore, the slope-intercept form of the equation is -2 = -3x + 36. The answer is -2 = -3x + 36

answer:The given problem is close to a convex optimization problem. Here's how you can approach it: 1. **Convex Reformulation:** If n=|I|, the number of indices in I, then the following problem is convex: begin{array}{ll} text{maximize} & sum_{kin K} left( prod_{iin I} a_{ik}+b_{ik} right)^{1/n} text{subject to} & a_{ik} x_{ik} + b_{ik} in [0,1] ~ forall i,k & x_{ij} in [0,1] ~ forall i,k end{array} The 1/n exponents turn the products into concave geometric means, making the objective function convex. 2. **Heuristic for the Original Problem:** If you need to solve the original problem without the exponents, consider the following heuristic: a. Start with the unweighted version of the problem, where w_kequiv 1 for all k. b. Solve the unweighted problem and obtain a current solution. c. Define weights w_k based on the current solution: w_k triangleq left(prod_{iin I} a_{ik} x_{ik} + b_{ik} right)^{1-1/n} d. Solve the weighted problem with these weights. e. Repeat steps c and d until convergence. This heuristic may not guarantee convergence, but it provides a practical approach to approximate the original problem.

answer:The given equation can be simplified by combining the logarithms on the left side since they have the same base: log (x+24) + log (5x+24) = log (-25x-21) Using the logarithmic property log(a) + log(b) = log(ab), we get: log((x+24)(5x+24)) = log(-25x-21) This implies: (x+24)(5x+24) = -25x-21 Expanding and simplifying the equation: 5x^2 + 144x + 576 = -25x - 21 Bringing all terms to one side: 5x^2 + 144x + 25x + 597 = 0 5x^2 + 169x + 597 = 0 Now, we factor the quadratic equation or use the quadratic formula to find the solutions: x = frac{-169 pm sqrt{169^2 - 4 cdot 5 cdot 597}}{2 cdot 5} x = frac{-169 pm sqrt{28561 - 11940}}{10} x = frac{-169 pm sqrt{16621}}{10} Hence, the real solutions are: x = frac{1}{10} left(-169 - sqrt{16621}right), quad x = frac{1}{10} left(-169 + sqrt{16621}right)