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Sagot :
Let's solve these problems step-by-step:
### Question 3:
We need to evaluate the expression [tex]\( \frac{9}{\frac{6}{-2}} \)[/tex].
1. First, compute the denominator:
[tex]\[ \frac{6}{-2} = -3 \][/tex]
2. Substitute [tex]\(-3\)[/tex] back into the main expression:
[tex]\[ \frac{9}{-3} \][/tex]
3. Finally, compute the division:
[tex]\[ \frac{9}{-3} = -3 \][/tex]
So, the answer for Question 3 is [tex]\(-3\)[/tex].
### Question 4:
We need to evaluate the complex expression step-by-step:
1. First, evaluate the expression inside the first brackets:
[tex]\[ (-2) \cdot 5 - (-3) \cdot 3 \][/tex]
Compute each multiplication:
[tex]\[ (-2) \cdot 5 = -10 \][/tex]
and
[tex]\[ (-3) \cdot 3 = -9 \][/tex]
So, the expression becomes:
[tex]\[ -10 - (-9) \][/tex]
Simplify the subtraction:
[tex]\[ -10 + 9 = -1 \][/tex]
2. Multiply the result by 2 (the outer multiplication):
[tex]\[ (-1) \cdot 2 = -2 \][/tex]
So, the intermediate result after this part is [tex]\(-2\)[/tex].
3. Next, we are given another expression, but it seems there's a small confusion in the original setup. Let's clarify it:
[tex]\[ 8 / (2 - 2) \][/tex]
Here, notice that [tex]\(2 - 2 = 0\)[/tex].
4. Since division by zero is undefined, this part of the expression cannot be evaluated:
[tex]\[ \frac{8}{0} \][/tex]
Therefore, the provided part [tex]\( 8 / (2-2) \)[/tex] results in a division by zero, so it's undefined. We can't proceed further with the calculation that involves this operation.
#### Final Evaluation:
- From the first step of Question 4, we found an intermediate result [tex]\(-2\)[/tex].
- Addition of extra term [tex]\(50\)[/tex] is done separately, ignoring the undefined division part:
The result given in the problem:
[tex]\((... \text{undefined here} = 50)\)[/tex]
We conclude:
- Our final correctly computable value up to the undefined point is [tex]\(-2\)[/tex] from intermediate steps before the undefined division error.
- We should recognize that the term involving division by zero makes final expression [tex]\(50\)[/tex] not realistically achievable in a mathematical sense.
#### Conclusions:
- Answer for Question 3: [tex]\(-3\)[/tex].
- Answer for Question 4: Undefined due to division by zero in the final steps. Intermediate computable value is, however, [tex]\(-2\)[/tex].
### Question 3:
We need to evaluate the expression [tex]\( \frac{9}{\frac{6}{-2}} \)[/tex].
1. First, compute the denominator:
[tex]\[ \frac{6}{-2} = -3 \][/tex]
2. Substitute [tex]\(-3\)[/tex] back into the main expression:
[tex]\[ \frac{9}{-3} \][/tex]
3. Finally, compute the division:
[tex]\[ \frac{9}{-3} = -3 \][/tex]
So, the answer for Question 3 is [tex]\(-3\)[/tex].
### Question 4:
We need to evaluate the complex expression step-by-step:
1. First, evaluate the expression inside the first brackets:
[tex]\[ (-2) \cdot 5 - (-3) \cdot 3 \][/tex]
Compute each multiplication:
[tex]\[ (-2) \cdot 5 = -10 \][/tex]
and
[tex]\[ (-3) \cdot 3 = -9 \][/tex]
So, the expression becomes:
[tex]\[ -10 - (-9) \][/tex]
Simplify the subtraction:
[tex]\[ -10 + 9 = -1 \][/tex]
2. Multiply the result by 2 (the outer multiplication):
[tex]\[ (-1) \cdot 2 = -2 \][/tex]
So, the intermediate result after this part is [tex]\(-2\)[/tex].
3. Next, we are given another expression, but it seems there's a small confusion in the original setup. Let's clarify it:
[tex]\[ 8 / (2 - 2) \][/tex]
Here, notice that [tex]\(2 - 2 = 0\)[/tex].
4. Since division by zero is undefined, this part of the expression cannot be evaluated:
[tex]\[ \frac{8}{0} \][/tex]
Therefore, the provided part [tex]\( 8 / (2-2) \)[/tex] results in a division by zero, so it's undefined. We can't proceed further with the calculation that involves this operation.
#### Final Evaluation:
- From the first step of Question 4, we found an intermediate result [tex]\(-2\)[/tex].
- Addition of extra term [tex]\(50\)[/tex] is done separately, ignoring the undefined division part:
The result given in the problem:
[tex]\((... \text{undefined here} = 50)\)[/tex]
We conclude:
- Our final correctly computable value up to the undefined point is [tex]\(-2\)[/tex] from intermediate steps before the undefined division error.
- We should recognize that the term involving division by zero makes final expression [tex]\(50\)[/tex] not realistically achievable in a mathematical sense.
#### Conclusions:
- Answer for Question 3: [tex]\(-3\)[/tex].
- Answer for Question 4: Undefined due to division by zero in the final steps. Intermediate computable value is, however, [tex]\(-2\)[/tex].
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