Final answer:
None of the provided options a), b), c), or d) are equivalent to the original expression -34 ÷ (-8/12). After simplifying, the correct answer is 'None of the above' as the simplified expression equates to 51.
Step-by-step explanation:
The student asked which expression is equivalent to -34 ÷ (-8/12). To find the equivalent expression, we can simplify the division of the negative numbers and the fraction. As both numbers being divided are negative, we know that the result will be positive based on the rule that when two negative numbers are divided or multiplied, the answer has a positive sign.
Let's simplify the fraction -8/12. We can both divide the numerator and the denominator by their greatest common divisor, which is 4, to get -2/3. Now the division is -34 ÷ (-2/3). Dividing by a fraction is the same as multiplying by its reciprocal. So, this becomes -34 x (-3/2), which simplifies to 34 x 3/2, or 51. Therefore, none of the provided options a), b), c), or d) are equivalent to the original expression. The correct answer must be option d), which is 'None of the above'.