answer:The last name of the person who said Presley was concerned that his 24-month spell as a GI would ruin his career is Beaulieu. In this case, the person is Priscilla Beaulieu, who later became Priscilla Presley after marrying Elvis Presley. She mentioned this concern in her autobiography.

answer:The cost of one adult ticket is 4.25 + 3.25 = 7.50. The total cost of two adult tickets is 2 * 7.50 = 15. The cost of one children's ticket is 4.25. The total cost of x children's tickets is x * 4.25 = 4.25x. They were given a 2 discount, so the total cost after the discount is (15 + 4.25x) - 2 = 13 + 4.25x. We are given that the total cost is 30, so we can write: 13 + 4.25x = 30. Simplifying the left side, we get: 4.25x + 13 = 30. Subtracting 13 from both sides, we get: 4.25x = 17. Dividing both sides by 4.25, we get: x = 4. The value of x is 4. 4 The answer is: 4

answer:To solve the given problem, we will explore it through two methods and then conclude with the correct option. **Method 1: Analyzing the Inequality** Given the inequality 2^{x}-2^{y} < 3^{-x}-3^{-y}, we can rearrange it to form 2^{x}-3^{-x} < 2^{y}-3^{-y}. Let's define a function f(x) = 2^{x}-3^{-x}. We need to analyze the behavior of this function to understand the relationship between x and y. 1. **Monotonicity of f(x)**: We observe that f(x) = 2^{x}-3^{-x} is monotonically increasing over the real numbers. This is because the derivative of f(x) with respect to x, which is f'(x) = ln(2) cdot 2^{x} + ln(3) cdot 3^{-x}, is always positive for all real x. This implies that if x < y, then f(x) < f(y). 2. **Applying Monotonicity**: Given f(x) < f(y), we conclude that x < y. This leads to y - x > 0. Adding 1 to both sides, we get y - x + 1 > 1. 3. **Taking the Natural Logarithm**: Since the natural logarithm function is monotonically increasing, applying it to both sides of y - x + 1 > 1 maintains the inequality. Thus, ln(y - x + 1) > ln(1) = 0. **Method 2: Verification by Example** Let's choose specific values for x and y to test the inequality and the options provided. Let x = -1 and y = 0. These values satisfy the original inequality 2^{x}-2^{y} < 3^{-x}-3^{-y}. 1. **Calculating ln(y - x + 1)**: With x = -1 and y = 0, we have ln(y - x + 1) = ln(0 - (-1) + 1) = ln(2) > 0. 2. **Calculating ln |x - y|**: Similarly, ln |x - y| = ln |-1 - 0| = ln(1) = 0. Given these calculations, we can see that option A, ln(y - x + 1) > 0, is satisfied by our analysis and example, while options B, C, and D do not align with our findings. **Conclusion** Based on the analysis and verification through an example, we conclude that the correct answer is: boxed{text{A}}.

answer:1. **Original and Modified Equations**: - Original: y = ax^2 + bx + c - Modified by replacing x with -x and adding d: y = ax^2 - bx + c + d 2. **Setting Equations Equal**: [ ax^2 + bx + c = ax^2 - bx + c + d ] 3. **Simplifying**: [ ax^2 + bx + c = ax^2 - bx + c + d implies bx = -bx + d implies 2bx = d implies x = frac{d}{2b} ] 4. **Substitute x = frac{d}{2b} into Either Equation**: [ y = aleft(frac{d}{2b}right)^2 + bleft(frac{d}{2b}right) + c = afrac{d^2}{4b^2} + frac{bd}{2b} + c = afrac{d^2}{4b^2} + frac{d}{2} + c ] Thus, the intersection point is left(frac{d}{2b}, afrac{d^2}{4b^2} + frac{d}{2} + cright). 5. **Conclusion**: The two graphs intersect at a single point with coordinates left(frac{d}{2b}, afrac{d^2}{4b^2} + frac{d}{2} + cright). The final answer is boxed: [ left(frac{d{2b}, afrac{d^2}{4b^2} + frac{d}{2} + cright)} ] The final answer is boxed{C}