Asked by 37432
Which of the following is an equation with one constant, two coefficients, and three terms?
3x - 4 = 5y
3x - 4y = 5x
3x - 4 = 5y
3x - 4y = 5x
Answers
Answered by
GPT-4o mini
To determine which of the given options is an equation with one constant, two coefficients, and three terms, let's analyze both equations.
1. **3x - 4 = 5y**
- This can be rearranged to: \(3x - 5y - 4 = 0\).
- It has three terms: \(3x\), \(-5y\), and \(-4\).
- Coefficients: \(3\) (for \(x\)) and \(-5\) (for \(y\)).
- Constant: \(-4\).
2. **3x - 4y = 5x**
- This can be rearranged to: \(3x - 5x - 4y = 0\) or \(-2x - 4y = 0\).
- It has three terms when written in standard form as: \(-2x\), \(-4y\), and \(0\).
- Coefficients: \(-2\) (for \(x\)) and \(-4\) (for \(y\)).
- There is no constant term other than \(0\) here.
From this analysis, the first equation **3x - 4 = 5y** contains one constant (\(-4\)), two coefficients (\(3\) and \(-5\)), and meets the requirement of three terms.
Therefore, the answer is:
**3x - 4 = 5y**.
1. **3x - 4 = 5y**
- This can be rearranged to: \(3x - 5y - 4 = 0\).
- It has three terms: \(3x\), \(-5y\), and \(-4\).
- Coefficients: \(3\) (for \(x\)) and \(-5\) (for \(y\)).
- Constant: \(-4\).
2. **3x - 4y = 5x**
- This can be rearranged to: \(3x - 5x - 4y = 0\) or \(-2x - 4y = 0\).
- It has three terms when written in standard form as: \(-2x\), \(-4y\), and \(0\).
- Coefficients: \(-2\) (for \(x\)) and \(-4\) (for \(y\)).
- There is no constant term other than \(0\) here.
From this analysis, the first equation **3x - 4 = 5y** contains one constant (\(-4\)), two coefficients (\(3\) and \(-5\)), and meets the requirement of three terms.
Therefore, the answer is:
**3x - 4 = 5y**.
Answered by
GPT-4o mini
Let's break down the expression you provided:
\[
z + \frac{6}{3^2} - (2 \times 3) + 5.
\]
To simplify the expression, we'll evaluate each part:
1. Calculate \(3^2\):
\[
3^2 = 9.
\]
2. Calculate \(\frac{6}{3^2}\):
\[
\frac{6}{3^2} = \frac{6}{9} = \frac{2}{3}.
\]
3. Calculate \(-(2 \times 3)\):
\[
-(2 \times 3) = -6.
\]
Now substituting these values back into the expression:
\[
z + \frac{2}{3} - 6 + 5.
\]
Next, we simplify the constants:
- Combine \(-6\) and \(5\):
\[
-6 + 5 = -1.
\]
So now we have:
\[
z + \frac{2}{3} - 1.
\]
Now, let's express \(-1\) in terms of a fraction for easier manipulation:
\[
-1 = -\frac{3}{3}.
\]
This gives us:
\[
z + \frac{2}{3} - \frac{3}{3} = z + \frac{2 - 3}{3} = z - \frac{1}{3}.
\]
Thus, there is no specific denominator in the overall expression if we are looking for a denominator separate from the fraction itself.
However, if we are focusing specifically on the fraction \(\frac{6}{3^2}\) we evaluated, that fraction's denominator is \(9\).
Since the original options you provided were **8** and **26**, they do not directly correspond to what we've simplified, but it seems you might be looking for confirmation about the identification of terms within the expression primarily involving the fractions.
To summarize:
- From \(\frac{6}{3^2}\), the simplified denominator is **9**, not from the options given.
If you have any more specific questions or if there's a different way you'd like this to be interpreted, please let me know!
\[
z + \frac{6}{3^2} - (2 \times 3) + 5.
\]
To simplify the expression, we'll evaluate each part:
1. Calculate \(3^2\):
\[
3^2 = 9.
\]
2. Calculate \(\frac{6}{3^2}\):
\[
\frac{6}{3^2} = \frac{6}{9} = \frac{2}{3}.
\]
3. Calculate \(-(2 \times 3)\):
\[
-(2 \times 3) = -6.
\]
Now substituting these values back into the expression:
\[
z + \frac{2}{3} - 6 + 5.
\]
Next, we simplify the constants:
- Combine \(-6\) and \(5\):
\[
-6 + 5 = -1.
\]
So now we have:
\[
z + \frac{2}{3} - 1.
\]
Now, let's express \(-1\) in terms of a fraction for easier manipulation:
\[
-1 = -\frac{3}{3}.
\]
This gives us:
\[
z + \frac{2}{3} - \frac{3}{3} = z + \frac{2 - 3}{3} = z - \frac{1}{3}.
\]
Thus, there is no specific denominator in the overall expression if we are looking for a denominator separate from the fraction itself.
However, if we are focusing specifically on the fraction \(\frac{6}{3^2}\) we evaluated, that fraction's denominator is \(9\).
Since the original options you provided were **8** and **26**, they do not directly correspond to what we've simplified, but it seems you might be looking for confirmation about the identification of terms within the expression primarily involving the fractions.
To summarize:
- From \(\frac{6}{3^2}\), the simplified denominator is **9**, not from the options given.
If you have any more specific questions or if there's a different way you'd like this to be interpreted, please let me know!
Answered by
GPT-4o mini
It seems like we are interpreting the expression incorrectly in my previous responses. Let's clarify the expression step by step, specifically looking for the simplified denominator within the full expression you provided:
The expression is:
\[
z + \frac{6}{3^2} - (2 \times 3) + 5
\]
Breaking it down:
1. **Calculate \(3^2\):**
\[
3^2 = 9
\]
2. **Find \(\frac{6}{3^2}\):**
\[
\frac{6}{3^2} = \frac{6}{9} = \frac{2}{3}
\]
3. **Calculate \(-(2 \times 3)\):**
\[
-(2 \times 3) = -6
\]
4. **Now put it all together:**
The expression combines to:
\[
z + \frac{2}{3} - 6 + 5
\]
Simplifying the constants:
\[
-6 + 5 = -1
\]
Thus, we have:
\[
z + \frac{2}{3} - 1
\]
To express \(-1\) in fraction form:
\[
-1 = -\frac{3}{3}
\]
So the expression becomes:
\[
z + \frac{2}{3} - \frac{3}{3} = z + \frac{2 - 3}{3} = z - \frac{1}{3}
\]
Now, regarding the denominator, the key fractional part of the expression was \(\frac{6}{9}\), which simplifies to \(\frac{2}{3}\). This means that the only denominator we derived from fractions in the expression is \(3\).
However, since your question refers to options **A. 8** and **B. 26**, it seems we need to assess if these choices correspond to some other context possibly related to denominators or other components in a broader format.
To clarify:
- **Any individual denominator** derived from parts of this expression was **9** from the very first fraction (which simplifies further to 3) as analyzed.
Since neither 8 nor 26 correspond to the denominator of the fraction part, if those numbers have a specific context or if you want the expression evaluated for any other parameters, please provide further details.
Otherwise, the direct answer does not align with either option presented.
The expression is:
\[
z + \frac{6}{3^2} - (2 \times 3) + 5
\]
Breaking it down:
1. **Calculate \(3^2\):**
\[
3^2 = 9
\]
2. **Find \(\frac{6}{3^2}\):**
\[
\frac{6}{3^2} = \frac{6}{9} = \frac{2}{3}
\]
3. **Calculate \(-(2 \times 3)\):**
\[
-(2 \times 3) = -6
\]
4. **Now put it all together:**
The expression combines to:
\[
z + \frac{2}{3} - 6 + 5
\]
Simplifying the constants:
\[
-6 + 5 = -1
\]
Thus, we have:
\[
z + \frac{2}{3} - 1
\]
To express \(-1\) in fraction form:
\[
-1 = -\frac{3}{3}
\]
So the expression becomes:
\[
z + \frac{2}{3} - \frac{3}{3} = z + \frac{2 - 3}{3} = z - \frac{1}{3}
\]
Now, regarding the denominator, the key fractional part of the expression was \(\frac{6}{9}\), which simplifies to \(\frac{2}{3}\). This means that the only denominator we derived from fractions in the expression is \(3\).
However, since your question refers to options **A. 8** and **B. 26**, it seems we need to assess if these choices correspond to some other context possibly related to denominators or other components in a broader format.
To clarify:
- **Any individual denominator** derived from parts of this expression was **9** from the very first fraction (which simplifies further to 3) as analyzed.
Since neither 8 nor 26 correspond to the denominator of the fraction part, if those numbers have a specific context or if you want the expression evaluated for any other parameters, please provide further details.
Otherwise, the direct answer does not align with either option presented.
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