answer:To convert the quadratic equation x^{2}-6x+7=0 into the form left(x+aright)^{2}=b, we follow these steps: 1. First, we isolate the quadratic and linear terms on one side: [x^{2}-6x=-7] 2. Next, we complete the square. To do this, we take half of the coefficient of x, which is -6, divide it by 2 to get -3, and then square it to get 9. We add and subtract this number on the left side, but since we want to keep the equation balanced, we only need to add it to the right side: [x^{2}-6x+9=-7+9] 3. This simplifies to: [left(x-3right)^{2}=2] Therefore, the quadratic equation x^{2}-6x+7=0 in the form left(x+aright)^{2}=b is correctly transformed to left(x-3right)^{2}=2. Hence, the correct answer is boxed{D}.

answer:To find the volume of a triangular pyramid, we first need to find the area of the base triangle and then use the pyramid height to calculate the volume. The area of a triangle is given by the formula: Area = (base * height) / 2 For the base triangle of the pyramid: Base length (b) = 4.5 m Height (h) = 6 m Area of the base triangle = (4.5 m * 6 m) / 2 Area of the base triangle = 27 m² / 2 Area of the base triangle = 13.5 m² Now that we have the area of the base triangle, we can find the volume of the pyramid using the formula: Volume = (Base Area * Height of Pyramid) / 3 Height of the pyramid (H) = 8 m Volume of the pyramid = (13.5 m² * 8 m) / 3 Volume of the pyramid = 108 m³ / 3 Volume of the pyramid = 36 m³ Therefore, the volume of the triangular pyramid is boxed{36} cubic meters (m³).

answer:1. Consider the binomial expansion of (1 + i)^{99}: [ (1 + i)^{99} = sum_{r=0}^{99} binom{99}{r} i^r ] 2. Notice that the terms involving i alternate between the real part and the imaginary part because i^2 = -1. 3. Specifically, the real part of the expression comes from the even powers of i. Therefore, we write: [ text{Real Part} = sum_{k=0}^{49} binom{99}{2k} (-1)^k ] 4. Next, we can simplify (1 + i)^{99} algebraically using De Moivre's Theorem. Notice: [ (1+i)^{99} = left( sqrt{2} e^{i pi/4} right)^{99} = 2^{49.5} e^{99 i pi/4} ] [ = 2^{49.5} left( e^{25 i pi + 24.75 i pi/4} right) ] Recall that e^{2 pi i k} = 1 for any integer k, hence: [ = 2^{49.5} e^{24.75 i pi/4} ] 5. Simplifying the angle, we get: [ 99pi/4 = 24pi + 3pi/4 rightarrow e^{i(99 pi / 4)} = e^{i 3 pi / 4} = -frac{1}{sqrt{2}} + i cdot frac{1}{sqrt{2}} ] 6. Therefore, the expanded form is: [ (1 + i)^{99} = 2^{49.5} left( -frac{1}{sqrt{2}} + i cdot frac{1}{sqrt{2}} right) = -2^{49} + 2^{49} i ] 7. The real part of (1 + i)^{99} is: [ text{Real Part} = -2^{49} ] 8. Comparing both results for the sum of the binomial coefficients and the real part of the expanded expression: [ sum_{k=0}^{49} binom{99}{2k} (-1)^k = -2^{49} ] # Conclusion: The value of the sum is boxed{text{B}}

answer:To solve this problem, we can treat the two tour guides as a single entity when they stand next to each other, and then we will multiply by the number of ways they can arrange themselves within this entity. 1. First, consider the two tour guides as one entity. This gives us a total of 5 tourists + 1 entity = 6 entities to arrange in a row. The number of ways to arrange these 6 entities is the permutation of 6 out of 6, which is P(6,6). The formula for permutations is P(n,r) = frac{n!}{(n-r)!}. Since r = n in this case, P(6,6) = 6! = 720. 2. Next, we consider the arrangement of the two tour guides within their entity. There are 2 tour guides to arrange, so we use the permutation formula again, P(2,2) = 2! = 2. 3. To find the total number of different ways the two tour guides can stand next to each other, we multiply the number of ways to arrange the 6 entities by the number of ways the two tour guides can arrange themselves within their entity. This gives us 720 times 2 = 1440. Therefore, the number of different ways the two tour guides can stand next to each other is boxed{1440}.