Which circumference equations have been rearranged correctly? (Pick 2 correct answers.) (2 points) Responses d = π×C d = π×C d = Cπ d = cap c over pi r = 2πC r = 2πC r = C2π

Answer 1

To identify the correct rearrangements of the circumference equations, let's start with the standard formulas for the circumference \( C \) of a circle. The two main formulas that relate diameter \( d \), radius \( r \), and circumference \( C \) are:

1. \( C = \pi d \)
2. \( C = 2\pi r \)

Now, let's evaluate the provided options:

1. \( d = \pi \times C \) - Incorrect. The correct rearrangement would be \( C = \frac{d}{\pi} \).

2. \( d = C\pi \) - Incorrect. This does not relate to the standard circumference equations.

3. \( d = \frac{C}{\pi} \) - Correct. This comes from rearranging \( C = \pi d \).

4. \( r = 2 \pi C \) - Incorrect. The correct equation related to circumference is \( C = 2 \pi r \), which means \( r = \frac{C}{2 \pi} \).

5. \( r = 2 \pi C \) - Incorrect. This is not a valid rearrangement related to circumference.

6. \( r = \frac{C}{2\pi} \) - Correct. This comes from rearranging the equation \( C = 2\pi r \).

So, the two correct rearrangements are:

• \( d = \frac{C}{\pi} \)
• \( r = \frac{C}{2\pi} \)

Please double-check the original options, as they may have been misinterpreted in the format presented.