Asked by 37432
Use the grouping symbols to interpret the following equation:
x/8 = (3(x + 4))/2
Which expression in the equation represents a product?
(1 point)
3(x + 4)
(3(x + 4))/2
x/8
2
x/8 = (3(x + 4))/2
Which expression in the equation represents a product?
(1 point)
3(x + 4)
(3(x + 4))/2
x/8
2
Answers
Answered by
GPT-4o mini
The expression in the equation that represents a product is \( 3(x + 4) \).
This is because a product is the result of multiplying two or more quantities together, and \( 3(x + 4) \) indicates that \( 3 \) is being multiplied by the quantity \( (x + 4) \).
Other options, like \( \frac{(3(x + 4))}{2} \), involve division and are not purely products, while \( \frac{x}{8} \) and \( 2 \) do not represent products either.
This is because a product is the result of multiplying two or more quantities together, and \( 3(x + 4) \) indicates that \( 3 \) is being multiplied by the quantity \( (x + 4) \).
Other options, like \( \frac{(3(x + 4))}{2} \), involve division and are not purely products, while \( \frac{x}{8} \) and \( 2 \) do not represent products either.
Answered by
37432
Use the grouping symbols to interpret the following equation:
x/8 = (3(x + 4))/2
Which expression in the equation represents a product?
(1 point)
3(x + 4)
(3(x + 4))/2
x/8
2
x/8 = (3(x + 4))/2
Which expression in the equation represents a product?
(1 point)
3(x + 4)
(3(x + 4))/2
x/8
2
Answered by
GPT-4o mini
The expression in the equation that represents a product is **3(x + 4)**.
This expression involves the multiplication of 3 by the quantity \( (x + 4) \). The other options either involve division or do not represent multiplication.
This expression involves the multiplication of 3 by the quantity \( (x + 4) \). The other options either involve division or do not represent multiplication.
Answered by
37432
Consider the expression [3(4^2 + 32 / 4 - 5)] . Which quotient must be found to simplify the expression?
96 / 4
48 / 4
144 / 4
32 / 4
96 / 4
48 / 4
144 / 4
32 / 4
Answered by
GPT-4o mini
To simplify the expression \(3(4^2 + 32 / 4 - 5)\), we need to focus on the part inside the parentheses, particularly \(32 / 4\).
This means the quotient that must be found to simplify the expression is:
**32 / 4**
After evaluating \(32 / 4\), we would proceed with the simplification of the entire expression.
This means the quotient that must be found to simplify the expression is:
**32 / 4**
After evaluating \(32 / 4\), we would proceed with the simplification of the entire expression.
Answered by
37432
Consider the expression [3(4^2 + 32 / 4 - 5)] .
Which quotient must be found to simplify the expression?
96 / 4
48 / 4
144 / 4
32 / 4
Which quotient must be found to simplify the expression?
96 / 4
48 / 4
144 / 4
32 / 4
Answered by
GPT-4o mini
To simplify the expression \(3(4^2 + 32 / 4 - 5)\), we need to evaluate the quotient \(32 / 4\).
So, the correct answer is:
**32 / 4**
Calculating \(32 / 4\) gives us \(8\), which will be used in the simplification of the expression inside the brackets.
So, the correct answer is:
**32 / 4**
Calculating \(32 / 4\) gives us \(8\), which will be used in the simplification of the expression inside the brackets.
Answered by
37432
Consider the expression ([15 + (-5)] + 6)/2 What is the result of the first simplification that would need to take place, according to the order of operations?
Answered by
GPT-4o mini
To simplify the expression \(\frac{[15 + (-5)] + 6}{2}\) according to the order of operations (parentheses first, then addition/subtraction, and finally division), the first simplification takes place within the parentheses:
1. **Calculate \(15 + (-5)\)**:
\[
15 + (-5) = 15 - 5 = 10
\]
So, the result of the first simplification that needs to take place is:
**10**
After this step, the expression becomes \(\frac{[10 + 6]}{2}\).
1. **Calculate \(15 + (-5)\)**:
\[
15 + (-5) = 15 - 5 = 10
\]
So, the result of the first simplification that needs to take place is:
**10**
After this step, the expression becomes \(\frac{[10 + 6]}{2}\).
Answered by
37432
Consider the expression ([15 + (-5)] + 6)/2
What is the result of the FIRST SIMPLIFICATION that would need to take place, according to the order of operations?
What is the result of the FIRST SIMPLIFICATION that would need to take place, according to the order of operations?
Answered by
GPT-4o mini
In the expression \(\frac{[15 + (-5)] + 6}{2}\), the first simplification according to the order of operations occurs inside the innermost parentheses:
1. **Calculate \(15 + (-5)\)**:
\[
15 + (-5) = 15 - 5 = 10
\]
So, the result of the **first simplification** is:
**10**
After this first step, the expression would then simplify to \(\frac{[10 + 6]}{2}\).
1. **Calculate \(15 + (-5)\)**:
\[
15 + (-5) = 15 - 5 = 10
\]
So, the result of the **first simplification** is:
**10**
After this first step, the expression would then simplify to \(\frac{[10 + 6]}{2}\).
Answered by
37432
Consider the following expression: (4 + (-6) * 2)/(-(- 3^2). What is the simplified denominator?
Answered by
GPT-4o mini
To simplify the denominator of the expression \((4 + (-6) * 2)/(-(-3^2))\), we need to focus on the part \(-(-3^2)\).
Let's break it down step by step:
1. **Calculate \(3^2\)**:
\[
3^2 = 9
\]
2. **Apply the negative sign**:
\[
-3^2 = -9
\]
3. **Apply the negative sign again**:
\[
-(-9) = 9
\]
Thus, the simplified denominator is **9**.
Let's break it down step by step:
1. **Calculate \(3^2\)**:
\[
3^2 = 9
\]
2. **Apply the negative sign**:
\[
-3^2 = -9
\]
3. **Apply the negative sign again**:
\[
-(-9) = 9
\]
Thus, the simplified denominator is **9**.
Answered by
37432
that's incorrect
remember what happens when there are negative signs inside and outside o the parentheses
remember what happens when there are negative signs inside and outside o the parentheses
Answered by
GPT-4o mini
Apologies for the confusion in my previous response. Let’s clarify the simplification of the denominator \(-(-3^2)\).
1. **Calculate \(3^2\)**:
\[
3^2 = 9
\]
2. **Apply the first negative sign**:
\[
-3^2 = -9
\]
3. **Now apply the negative sign outside the parentheses**:
\[
-(-9) = 9
\]
Therefore, the correct step should be:
- The expression \(-(-3^2)\) resolves to \(9\) because you negate a negative number.
Now, let's clarify your point about negative signs. When there are negatives, the double negative indeed results in a positive. So the interpretation is correct that \(-(-9) = 9\).
The simplified denominator is **9**.
Thank you for your patience, and I appreciate you bringing this to my attention!
1. **Calculate \(3^2\)**:
\[
3^2 = 9
\]
2. **Apply the first negative sign**:
\[
-3^2 = -9
\]
3. **Now apply the negative sign outside the parentheses**:
\[
-(-9) = 9
\]
Therefore, the correct step should be:
- The expression \(-(-3^2)\) resolves to \(9\) because you negate a negative number.
Now, let's clarify your point about negative signs. When there are negatives, the double negative indeed results in a positive. So the interpretation is correct that \(-(-9) = 9\).
The simplified denominator is **9**.
Thank you for your patience, and I appreciate you bringing this to my attention!
Answered by
37432
the answer isnt 9
Answered by
GPT-4o mini
Let's go through the calculation step by step carefully to clarify:
The expression we are evaluating is:
\[
-(-3^2)
\]
1. **Calculate \(3^2\)**:
\[
3^2 = 9
\]
2. **Apply the first negative sign**:
\[
-3^2 = -9
\]
3. **Now apply the negative sign outside**:
\[
-(-9) = 9
\]
However, I understand you might be referring to how you can represent it as a whole if parentheses were involved. In cases where someone might interpret the operation differently due to nested negatives, please clarify.
If the expression actually was misrepresented, such as within parentheses involving the negative:
If we were to reconsider \(-(-3^2)\) but only read **as** it is written and involve parentheses, like so:
Here’s another interpretation, if it was expressed differently, like:
\[
-(3^2) = -9
\]
Could you specify what exactly the correct expression structure should be if it's not clear from the earlier notation? With just \(-(-3^2)\) and the calculations shown earlier, it resolves into **9**, but I'm open if using a different parenthetical arrangement changes the context you're looking for. Thank you!
The expression we are evaluating is:
\[
-(-3^2)
\]
1. **Calculate \(3^2\)**:
\[
3^2 = 9
\]
2. **Apply the first negative sign**:
\[
-3^2 = -9
\]
3. **Now apply the negative sign outside**:
\[
-(-9) = 9
\]
However, I understand you might be referring to how you can represent it as a whole if parentheses were involved. In cases where someone might interpret the operation differently due to nested negatives, please clarify.
If the expression actually was misrepresented, such as within parentheses involving the negative:
If we were to reconsider \(-(-3^2)\) but only read **as** it is written and involve parentheses, like so:
Here’s another interpretation, if it was expressed differently, like:
\[
-(3^2) = -9
\]
Could you specify what exactly the correct expression structure should be if it's not clear from the earlier notation? With just \(-(-3^2)\) and the calculations shown earlier, it resolves into **9**, but I'm open if using a different parenthetical arrangement changes the context you're looking for. Thank you!