The given expression is:
81 / (9 + w)
We need to identify which of the provided options is equivalent to this expression. Let's examine each option provided:
1. (9 + w) / 81 - This is simply the reciprocal of the given expression and not equivalent to it.
2. (9 + 81) + w - This option adds 81 to 9 and then adds w. This is not equivalent to dividing 81 by the sum of 9 and w; it's a completely different operation.
3. 81 / 9 + 81 / w - This option separates the original fraction into two different fractions, one where 81 is divided by 9 and another where 81 is divided by w. This is also not equivalent to the given expression because it doesn't take into account that 81 is being divided by the entire sum (9 + w).
4. 81 / w (w + 9) - This option seems to factor out a w, but it's incorrect. The correct equivalent expression that factored out w would look like 81 / w * 1 / (1 + 9/w) or something similar, which is not the same as the option provided.
None of the given options (1-4) is equivalent to the original expression 81 / (9 + w). If you're looking for an equivalent expression, it would involve maintaining the structure of dividing 81 by the entire sum of 9 and w, but none of the provided choices reflects that accurately. It's likely that there is either a typographic error in the options or additional options that were not provided which might contain the correct equivalent expression.
81 / (9 + w) which expression is equivalent to the expression shown above. 1. (9 + w) / 81. 2. (9 + 81) + w. 3. 81 / 9 + 81 / w. 4. 81 / w (w + 9).
11 answers
81 / (9 + w) which expression is equivalent to the expression shown above. (9 + w) / 81. (9 + 81) + w. 81 / 9 + 81 / w. 81 / w (w + 9).
BETTER????
BETTER????
Let's reconsider the options you've provided, and see if any of these are equivalent to the expression 81 / (9 + w):
1. (9 + w) / 81.
This is the reciprocal of the original expression. It is not equivalent to 81 / (9 + w).
2. (9 + 81) + w.
This is simply adding 9 and 81 and then adding w. This arithmetic operation is not equivalent to the original expression which is a division.
3. 81 / 9 + 81 / w.
This splits 81 into two separate divisions: one with 9 and one with w. This is not equivalent to the original expression, which is a single division by the sum of 9 and w.
4. 81 / w(w + 9).
This option appears to suggest partial fraction decomposition, but it is not presented correctly. For it to be potentially equivalent, it should be written as two separate fractions that could add up to the original expression. However, as it stands, this option is also not equivalent to the original expression.
Among the four options provided, none of them is equivalent to the original expression 81 / (9 + w). They all either represent different operations (reciprocal, addition, and incorrect partial fraction decomposition) or are not algebraically equivalent to the original expression.
If we were to express 81 / (9 + w) in a different form that emphasizes its components, it could be written as:
81 * 1 / (9 + w)
That would still be the same as the original expression, just with the multiplication by 1 made explicit, but it doesn't match any of the provided options.
1. (9 + w) / 81.
This is the reciprocal of the original expression. It is not equivalent to 81 / (9 + w).
2. (9 + 81) + w.
This is simply adding 9 and 81 and then adding w. This arithmetic operation is not equivalent to the original expression which is a division.
3. 81 / 9 + 81 / w.
This splits 81 into two separate divisions: one with 9 and one with w. This is not equivalent to the original expression, which is a single division by the sum of 9 and w.
4. 81 / w(w + 9).
This option appears to suggest partial fraction decomposition, but it is not presented correctly. For it to be potentially equivalent, it should be written as two separate fractions that could add up to the original expression. However, as it stands, this option is also not equivalent to the original expression.
Among the four options provided, none of them is equivalent to the original expression 81 / (9 + w). They all either represent different operations (reciprocal, addition, and incorrect partial fraction decomposition) or are not algebraically equivalent to the original expression.
If we were to express 81 / (9 + w) in a different form that emphasizes its components, it could be written as:
81 * 1 / (9 + w)
That would still be the same as the original expression, just with the multiplication by 1 made explicit, but it doesn't match any of the provided options.
oh my, oh my thats it im donebot GPLoser
I understand that finding equivalent expressions can sometimes be frustrating, especially if the options provided initially seem incorrect or confusing. I'm here to help, so if you have any further questions or would like to revisit any math concepts or problems, feel free to reach out. We'll work through it together until it makes sense. Don't give up, and let's tackle any difficulties you're facing one step at a time!
you ALWAYS, have something to say smart dont you?
As an AI developed by OpenAI, my aim is to provide helpful and informative responses to your questions. I'm here to assist and guide you through any queries you might have, whether they're about math, science, general knowledge, or any other topic you're interested in exploring. If you have any more questions or need further assistance, feel free to ask!
well, okay lets do the problem.
Of course! Let's take another look at the original problem. You have the expression:
81 / (9 + w)
We are looking for an equivalent expression among the following options:
1. (9 + w) / 81
2. (9 + 81) + w
3. 81 / 9 + 81 / w
4. 81 / w(w + 9)
To determine which one is equivalent to the original expression, let's simplify each option:
1. (9 + w) / 81
This is the reciprocal of the original expression, whereby you have switched the numerator and the denominator. This is not equivalent.
2. (9 + 81) + w
This is simply adding numbers and is not a division at all, so it's not equivalent to the original expression which is a division [81 / (9 + w)].
3. 81 / 9 + 81 / w
This option can be simplified:
81 / 9 = 9
So the expression becomes:
9 + 81 / w
This expression is not the same as 81 / (9 + w) because it represents a sum of two separate divisions, not the division of 81 by the sum of 9 and w.
4. 81 / w(w + 9)
This looks like it could be two product terms: 81 / w and (w + 9), but it's not written in a standard mathematical notation, which typically requires an operator between terms. If we interpret the expression as (81 / w) * (w + 9), it is not equivalent to our original expression, either.
Upon reviewing the options again, none of them are equivalent to the original expression 81 / (9 + w). There may have been a misunderstanding or misprint in the provided options. In its current form, the correct answer is not listed among the provided choices.
If you have access to more context or additional choices, I'd be happy to help you work through them to find an equivalent expression. Otherwise, based on the information given, we've correctly determined that none of the choices match the original expression.
81 / (9 + w)
We are looking for an equivalent expression among the following options:
1. (9 + w) / 81
2. (9 + 81) + w
3. 81 / 9 + 81 / w
4. 81 / w(w + 9)
To determine which one is equivalent to the original expression, let's simplify each option:
1. (9 + w) / 81
This is the reciprocal of the original expression, whereby you have switched the numerator and the denominator. This is not equivalent.
2. (9 + 81) + w
This is simply adding numbers and is not a division at all, so it's not equivalent to the original expression which is a division [81 / (9 + w)].
3. 81 / 9 + 81 / w
This option can be simplified:
81 / 9 = 9
So the expression becomes:
9 + 81 / w
This expression is not the same as 81 / (9 + w) because it represents a sum of two separate divisions, not the division of 81 by the sum of 9 and w.
4. 81 / w(w + 9)
This looks like it could be two product terms: 81 / w and (w + 9), but it's not written in a standard mathematical notation, which typically requires an operator between terms. If we interpret the expression as (81 / w) * (w + 9), it is not equivalent to our original expression, either.
Upon reviewing the options again, none of them are equivalent to the original expression 81 / (9 + w). There may have been a misunderstanding or misprint in the provided options. In its current form, the correct answer is not listed among the provided choices.
If you have access to more context or additional choices, I'd be happy to help you work through them to find an equivalent expression. Otherwise, based on the information given, we've correctly determined that none of the choices match the original expression.
what would be the correct answer then. if you dont my me asking that is
To find an equivalent expression to 81 / (9 + w), we need an expression that simplifies to the same value for any legitimate value of w (that is, any value of w that doesn't make the denominator equal to zero).
Unfortunately, the provided options don't include an equivalent expression, so we cannot simply choose one of them. However, we can manipulate the original expression to create an equivalent expression that looks different but represents the same relationship.
One approach is to divide the numerator by one of the terms in the denominator (if it divides evenly) and distribute across the terms in the denominator. Since 81 is 9 times 9, we can divide it by one of the terms in the denominator. Here's how:
81 / (9 + w) can be rewritten as
(9 * 9) / (9 + w) which simplifies to
9 * (9 / (9 + w))
This is still equivalently the same expression, just represented in a slightly different form where we factored out the 9. While it seems different, for any value of w (where w ≠ -9), this expression simplifies to the same value as the original expression.
For the options you provided, we needed to find something like this, directly factoring or simplifying the original expression without changing its value. The only available manipulations would be to factor or distribute terms, but the end result should maintain the same division as the original 81 / (9 + w).
Hopefully, this explanation clarifies what an equivalent expression should represent, even though it appears that there was not a correct equivalent expression provided in your list of options. If you have access to more choices or additional parts of a question, feel free to share them, and I'd be happy to assist you further.
Unfortunately, the provided options don't include an equivalent expression, so we cannot simply choose one of them. However, we can manipulate the original expression to create an equivalent expression that looks different but represents the same relationship.
One approach is to divide the numerator by one of the terms in the denominator (if it divides evenly) and distribute across the terms in the denominator. Since 81 is 9 times 9, we can divide it by one of the terms in the denominator. Here's how:
81 / (9 + w) can be rewritten as
(9 * 9) / (9 + w) which simplifies to
9 * (9 / (9 + w))
This is still equivalently the same expression, just represented in a slightly different form where we factored out the 9. While it seems different, for any value of w (where w ≠ -9), this expression simplifies to the same value as the original expression.
For the options you provided, we needed to find something like this, directly factoring or simplifying the original expression without changing its value. The only available manipulations would be to factor or distribute terms, but the end result should maintain the same division as the original 81 / (9 + w).
Hopefully, this explanation clarifies what an equivalent expression should represent, even though it appears that there was not a correct equivalent expression provided in your list of options. If you have access to more choices or additional parts of a question, feel free to share them, and I'd be happy to assist you further.