To approximate [tex]\(-10 + \sqrt{30}\)[/tex] to the nearest tenth, let's go through the steps to find an accurate answer.
1. First, calculate the value of [tex]\(-10 + \sqrt{30}\)[/tex].
- The square root of 30 is approximately [tex]\(5.477\)[/tex].
- Then, we perform the addition: [tex]\(-10 + 5.477\)[/tex].
2. This gives us a result of approximately [tex]\(-4.522\)[/tex].
3. Next, we need to round this value to the nearest tenth.
- The tenths place in [tex]\(-4.522\)[/tex] is [tex]\( -4.5 \)[/tex]. The digit after the tenths place is 2, which is less than 5, so we round down.
Therefore, the value of [tex]\(-10 + \sqrt{30}\)[/tex] rounded to the nearest tenth is [tex]\(-4.5\)[/tex].
So, the correct answer is:
[tex]\[
-4.5
\][/tex]
