To determine the value of the given expression [tex]\(\frac{10(4-7)}{-(4-1)}\)[/tex], let's follow these steps:
1. Calculate the numerator:
- The numerator is [tex]\(10(4 - 7)\)[/tex].
- First, compute inside the parentheses: [tex]\(4 - 7 = -3\)[/tex].
- Now, multiply by 10: [tex]\(10 \times -3 = -30\)[/tex].
2. Calculate the denominator:
- The denominator is [tex]\(- (4 - 1)\)[/tex].
- First, compute inside the parentheses: [tex]\(4 - 1 = 3\)[/tex].
- Now, apply the negative sign: [tex]\(-3\)[/tex].
3. Divide the numerator by the denominator:
- The expression now is [tex]\(\frac{-30}{-3}\)[/tex].
- Dividing these: [tex]\(\frac{-30}{-3} = 10\)[/tex].
Therefore, the value of [tex]\(\frac{10(4-7)}{-(4-1)}\)[/tex] is [tex]\(10\)[/tex].
So, the correct answer is [tex]\( \boxed{10} \)[/tex].
