The equation of a circle is given as $(x + 31)^2 + (y - 23)^2 = 63$. We need to find the length of the radius of the circle to the nearest tenth.

1. Problem Description

The equation of a circle is given as $(x + 31)^2 + (y - 23)^2 = 63$. We need to find the length of the radius of the circle to the nearest tenth.

2. Solution Steps

The general equation of a circle with center $(h, k)$ and radius $r$ is given by:

$(x - h)^2 + (y - k)^2 = r^2$

Comparing the given equation $(x + 31)^2 + (y - 23)^2 = 63$ with the general equation, we can see that:

$r^2 = 63$

To find the radius $r$, we take the square root of both sides:

$r = \sqrt{63}$

Calculating the square root of 63, we get:

$r \approx 7.937$

We need to round the radius to the nearest tenth:

$r \approx 7.9$

3. Final Answer

7.9