No problem, I'll help you with each question and explain the correct answers. Let's go through them one by one:
1. To simplify the expression 13[6^2�€(5^2-4^2)+9], you need to follow the order of operations (PEMDAS/BODMAS). First, calculate the values within the parentheses: 5^2 = 25 and 4^2 = 16. Then, subtract: 25 - 16 = 9. Next, calculate the exponent: 6^2 = 36. Finally, multiply 36 by 9: 36 * 9 = 324. Multiply the result by 13: 13 * 324 = 4212. The correct answer is D. 4212. So, B. 585 is incorrect.
2. To simplify the expression 6xyz/2xz, you can divide the common factors. Canceling out the common factors, you'll get 6y/2 = 3y. So, the correct answer is C. 3y. Therefore, B. 3xyz is incorrect.
3. The expression that shows how many yards the running back had before those two runs is 78 - 5 - 7. This represents the total yardage of the game minus the last two runs. Therefore, the correct answer is A. 78 - 5 - 7. So, A. 78 - 5 - 7 is correct.
4. To find the value of X/yz if x = -2, y = -3, and z = -4, substitute the values into the expression. So, (-2)/(-3*-4) = (-2)/(12) = -1/6. The correct answer is D. -1/6. So, D. -1/6 is correct.
5. The product 4.56 x 4.5 is a multiplication of two decimal numbers. Since decimals can be expressed as fractions, the product is rational. Therefore, the correct answer is A. The product is rational. So, A. The product is rational is correct.
6. To determine which sum or product is rational, you need to know that the sum or product of rational numbers will always result in a rational number. In this case, the options that result in rational numbers are: C. 4 + 6 and D. 3.15 x 4.6. Therefore, the correct answers are C and D. So, A. ƒÎx6 and B. �ã3+�ã5 are incorrect.
7. Molli divided $3.96 by 9 to find out how much she paid per apple. When you divide the total cost by the number of apples, you get the cost per apple. Therefore, the correct answer is A. In order to find out how much she paid per apple. So, A. In order to find out how much she paid per apple is correct.
I hope this helps! If you have any further questions, feel free to ask.