Here are the answers to each of the questions:
Question 1: To solve the equation \( -6x = 48 \) for \( x \), you need to isolate \( x \). This can be done by dividing both sides by \( -6 \).
Correct Response: divide by −6 (or divide by negative 6)
Question 2: To solve the equation \( x^{12} = 6 \) for \( x \), you need to take the 12th root of both sides, which is equivalent to raising both sides to the power of \( \frac{1}{12} \). However, among the given options, dividing by 12 allows you to isolate \( x \) in terms of exponentiation.
Correct Response: divide by 12
Question 3: To solve the equation \( 52x = -18 \):
- Divide both sides by \( 52 \): \( x = \frac{-18}{52} = \frac{-9}{26} \)
This can be simplified, but assuming the standard choice form, it does not match one of the options directly, but can be approximated.
Correct Response: no exact option given, if negative fraction is acceptable, it can be approximated as \( −\frac{1}{20} \), which would generally be accepted as the closest match given options.
Question 4: To solve the equation \( -x^{2.9} = -3 \):
- Multiply both sides by -1: \( x^{2.9} = 3 \)
- Solve for \( x \) by taking the 2.9th root of both sides.
Correct Response for this would result in: \( x = 3^{\frac{1}{2.9}} \), which is not listed, but the closest answer option being \( 8.7 \) or the option would be based on numerically converting it.
Question 5: To solve the equation \( 85x = -10 \):
- Divide both sides by \( 85 \): \( x = \frac{-10}{85} = \frac{-2}{17} \)
Given the options, \( \frac{-1}{16} \) would not be correct based on basic calculation.
Correct Response: similarly, look for the accurate one based on your needs but none exactly match.
If you need any clarifications on how to approach these questions or changes on assistance, feel free to ask!
5 answers