Final answer:
The correct answer is d. None of the above. None of the provided options are equivalent to the expression (-13)^2 + 34 + 44 - \sqrt{3}, as their evaluated results do not match the original expression's evaluation. Therefore, the correct option is d. None of the above.
Step-by-step explanation:
The student is asked to select expressions equivalent to the given expression (-13)^2 + 34 + 44 - \sqrt{3}. To find equivalent expressions, we can evaluate the original expression and then compare the results with the options provided.
Firstly, evaluate (-13)^2 which equals 169. Then add 34 to get 203, and further add 44 to obtain 247. The square root of 3 is approximately 1.732, so by subtracting it from 247, we get approximately 245.268.
Now, let's evaluate the options:
- a. (-1/3)^2 is 1/9, 3/4 is 0.75, and 4/4 is 1. Adding these up gives 1/9 + 0.75 + 1 = 1.861. This is not equivalent.
- b. (-1/3)^2 is 1/9, 3/4 is 0.75, and 2/2 is 1. Adding these gives 1/9 + 0.75 + 1 = 1.861. This is also not equivalent.
- c. (-1/3)^2 is 1/9, 1 is 1, and 2 is 2. Adding these gives 1/9 + 1 + 2 = 3.111. This is not equivalent.
None of the options a, b, or c are equivalent to the original expression. Therefore, the correct option is d. None of the above.