Question
Simplify (14x2−3x+2.25)+(0.75x2+2x−14) .(1 point) The sum of the polynomials is . Incorrect Convert all fractions to decimals or decimals to fractions. Remaining Attempts : 2
Answers
Answer
Simplify (14x2−3x+2.25)+(0.75x2+2x−14) .(1 point) The sum of the polynomials is . Incorrect Convert all fractions to decimals or decimals to fractions. Remaining Attempts : 2
Answer
boxed{\frac{59}{4}x^2 - x - \frac{47}{4}}
Answer
Simplify (1/4x^2−3x+2.25)+(0.75x^2+2x−1/4) .(1 point) The sum of the polynomials is .
Answered by
GPT-4o mini
To simplify the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), let's first convert the fractions to decimals and ensure all terms are combined correctly.
1. **Separate the terms**:
- From the first polynomial: \(14x^2 - 3x + 2.25\)
- From the second polynomial: \(0.75x^2 + 2x - 14\)
2. **Combine like terms**:
- For \(x^2\) terms:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
- For \(x\) terms:
\[
-3x + 2x = -1x \quad (or -x)
\]
- For constant terms:
\[
2.25 - 14 = -11.75
\]
3. **Write the simplified polynomial**:
Combining all the results gives us:
\[
14.75x^2 - x - 11.75
\]
Thus, the sum of the polynomials is:
\[
\boxed{14.75x^2 - x - 11.75}
\]
1. **Separate the terms**:
- From the first polynomial: \(14x^2 - 3x + 2.25\)
- From the second polynomial: \(0.75x^2 + 2x - 14\)
2. **Combine like terms**:
- For \(x^2\) terms:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
- For \(x\) terms:
\[
-3x + 2x = -1x \quad (or -x)
\]
- For constant terms:
\[
2.25 - 14 = -11.75
\]
3. **Write the simplified polynomial**:
Combining all the results gives us:
\[
14.75x^2 - x - 11.75
\]
Thus, the sum of the polynomials is:
\[
\boxed{14.75x^2 - x - 11.75}
\]
Answered by
GPT-4o mini
To simplify the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we'll first combine the terms correctly.
1. **Identify the terms**:
- From the first polynomial:
- \(14x^2\)
- \(-3x\)
- \(2.25\)
- From the second polynomial:
- \(0.75x^2\)
- \(2x\)
- \(-14\)
2. **Combine like terms**:
- Combine the \(x^2\) terms:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
- Combine the \(x\) terms:
\[
-3x + 2x = -1x \quad (or simply -x)
\]
- Combine the constant terms:
\[
2.25 - 14 = 2.25 - 14 = -11.75
\]
3. **Final result**:
Putting it all together, we have:
\[
14.75x^2 - x - 11.75
\]
So, the sum of the polynomials is:
\[
\boxed{14.75x^2 - x - 11.75}
\]
If you wish to convert \(0.75\) and \(2.25\) to fractions, they become \( \frac{3}{4} \) and \( \frac{9}{4} \) respectively. Let's confirm by re-doing the calculations using fractions:
1. **Using fractions**:
- \(14x^2 - 3x + \frac{9}{4}\)
- \( \frac{3}{4}x^2 + 2x - 14\)
2. **Combine \(x^2\) terms**:
\[
14x^2 + \frac{3}{4}x^2 = \frac{56}{4}x^2 + \frac{3}{4}x^2 = \frac{59}{4}x^2
\]
3. **Combine \(x\) terms**:
\[
-3x + 2x = -1x
\]
4. **Combine constant terms**:
\[
\frac{9}{4} - 14 = \frac{9}{4} - \frac{56}{4} = -\frac{47}{4}
\]
5. **Final result**:
The sum in fraction form is:
\[
\frac{59}{4}x^2 - x - \frac{47}{4}
\]
So you can express the sum of the polynomials as:
\[
\boxed{\frac{59}{4}x^2 - x - \frac{47}{4}}
\]
Depending on the format you need (decimals or fractions), both are valid.
1. **Identify the terms**:
- From the first polynomial:
- \(14x^2\)
- \(-3x\)
- \(2.25\)
- From the second polynomial:
- \(0.75x^2\)
- \(2x\)
- \(-14\)
2. **Combine like terms**:
- Combine the \(x^2\) terms:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
- Combine the \(x\) terms:
\[
-3x + 2x = -1x \quad (or simply -x)
\]
- Combine the constant terms:
\[
2.25 - 14 = 2.25 - 14 = -11.75
\]
3. **Final result**:
Putting it all together, we have:
\[
14.75x^2 - x - 11.75
\]
So, the sum of the polynomials is:
\[
\boxed{14.75x^2 - x - 11.75}
\]
If you wish to convert \(0.75\) and \(2.25\) to fractions, they become \( \frac{3}{4} \) and \( \frac{9}{4} \) respectively. Let's confirm by re-doing the calculations using fractions:
1. **Using fractions**:
- \(14x^2 - 3x + \frac{9}{4}\)
- \( \frac{3}{4}x^2 + 2x - 14\)
2. **Combine \(x^2\) terms**:
\[
14x^2 + \frac{3}{4}x^2 = \frac{56}{4}x^2 + \frac{3}{4}x^2 = \frac{59}{4}x^2
\]
3. **Combine \(x\) terms**:
\[
-3x + 2x = -1x
\]
4. **Combine constant terms**:
\[
\frac{9}{4} - 14 = \frac{9}{4} - \frac{56}{4} = -\frac{47}{4}
\]
5. **Final result**:
The sum in fraction form is:
\[
\frac{59}{4}x^2 - x - \frac{47}{4}
\]
So you can express the sum of the polynomials as:
\[
\boxed{\frac{59}{4}x^2 - x - \frac{47}{4}}
\]
Depending on the format you need (decimals or fractions), both are valid.
Answered by
GPT-4o mini
To summarize the calculations for clarity, we have simplified the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\) step-by-step, both in decimal form and as fractions.
### Using Decimals
1. **Original Expression**:
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]
2. **Combine Like Terms**:
- \(x^2\) terms:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
- \(x\) terms:
\[
-3x + 2x = -1x \quad (or -x)
\]
- Constant terms:
\[
2.25 - 14 = -11.75
\]
3. **Final Result in Decimal**:
\[
14.75x^2 - x - 11.75
\]
### Using Fractions
1. **Convert Decimals to Fractions**:
- \(2.25 = \frac{9}{4}\)
- \(0.75 = \frac{3}{4}\)
2. **Convert the Expression**:
\[
(14x^2 - 3x + \frac{9}{4}) + (\frac{3}{4}x^2 + 2x - 14)
\]
3. **Combine Like Terms**:
- \(x^2\) terms:
\[
14x^2 + \frac{3}{4}x^2 = \frac{56}{4}x^2 + \frac{3}{4}x^2 = \frac{59}{4}x^2
\]
- \(x\) terms:
\[
-3x + 2x = -1x
\]
- Constant terms:
\[
\frac{9}{4} - 14 = \frac{9}{4} - \frac{56}{4} = -\frac{47}{4}
\]
4. **Final Result in Fraction**:
\[
\frac{59}{4}x^2 - x - \frac{47}{4}
\]
Thus, the final answer can be expressed in fractional form as:
\[
\boxed{\frac{59}{4}x^2 - x - \frac{47}{4}}
\]
You can choose either form depending on the requirement, and both represent the same polynomial.
### Using Decimals
1. **Original Expression**:
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]
2. **Combine Like Terms**:
- \(x^2\) terms:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
- \(x\) terms:
\[
-3x + 2x = -1x \quad (or -x)
\]
- Constant terms:
\[
2.25 - 14 = -11.75
\]
3. **Final Result in Decimal**:
\[
14.75x^2 - x - 11.75
\]
### Using Fractions
1. **Convert Decimals to Fractions**:
- \(2.25 = \frac{9}{4}\)
- \(0.75 = \frac{3}{4}\)
2. **Convert the Expression**:
\[
(14x^2 - 3x + \frac{9}{4}) + (\frac{3}{4}x^2 + 2x - 14)
\]
3. **Combine Like Terms**:
- \(x^2\) terms:
\[
14x^2 + \frac{3}{4}x^2 = \frac{56}{4}x^2 + \frac{3}{4}x^2 = \frac{59}{4}x^2
\]
- \(x\) terms:
\[
-3x + 2x = -1x
\]
- Constant terms:
\[
\frac{9}{4} - 14 = \frac{9}{4} - \frac{56}{4} = -\frac{47}{4}
\]
4. **Final Result in Fraction**:
\[
\frac{59}{4}x^2 - x - \frac{47}{4}
\]
Thus, the final answer can be expressed in fractional form as:
\[
\boxed{\frac{59}{4}x^2 - x - \frac{47}{4}}
\]
You can choose either form depending on the requirement, and both represent the same polynomial.
Answered by
GPT-4o mini
To simplify the expression \(\left(\frac{1}{4}x^2 - 3x + 2.25\right) + \left(0.75x^2 + 2x - \frac{1}{4}\right)\), we will first convert all decimals and fractions into a consistent format and then combine like terms.
### Step 1: Convert Decimals to Fractions
1. Convert \(2.25\) to a fraction:
\[
2.25 = \frac{9}{4}
\]
2. Convert \(0.75\) to a fraction:
\[
0.75 = \frac{3}{4}
\]
Now, the expression becomes:
\[
\left(\frac{1}{4}x^2 - 3x + \frac{9}{4}\right) + \left(\frac{3}{4}x^2 + 2x - \frac{1}{4}\right)
\]
### Step 2: Combine Like Terms
1. **Combine \(x^2\) Terms**:
\[
\frac{1}{4}x^2 + \frac{3}{4}x^2 = \left(\frac{1 + 3}{4}\right)x^2 = \frac{4}{4}x^2 = 1x^2 \text{ (or } x^2\text{)}
\]
2. **Combine \(x\) Terms**:
\[
-3x + 2x = -1x \text{ (or } -x\text{)}
\]
3. **Combine Constant Terms**:
\[
\frac{9}{4} - \frac{1}{4} = \left(\frac{9 - 1}{4}\right) = \frac{8}{4} = 2
\]
### Step 3: Put It All Together
Now we can write the simplified polynomial:
\[
x^2 - x + 2
\]
### Final Answer
Thus, the sum of the polynomials is:
\[
\boxed{x^2 - x + 2}
\]
### Step 1: Convert Decimals to Fractions
1. Convert \(2.25\) to a fraction:
\[
2.25 = \frac{9}{4}
\]
2. Convert \(0.75\) to a fraction:
\[
0.75 = \frac{3}{4}
\]
Now, the expression becomes:
\[
\left(\frac{1}{4}x^2 - 3x + \frac{9}{4}\right) + \left(\frac{3}{4}x^2 + 2x - \frac{1}{4}\right)
\]
### Step 2: Combine Like Terms
1. **Combine \(x^2\) Terms**:
\[
\frac{1}{4}x^2 + \frac{3}{4}x^2 = \left(\frac{1 + 3}{4}\right)x^2 = \frac{4}{4}x^2 = 1x^2 \text{ (or } x^2\text{)}
\]
2. **Combine \(x\) Terms**:
\[
-3x + 2x = -1x \text{ (or } -x\text{)}
\]
3. **Combine Constant Terms**:
\[
\frac{9}{4} - \frac{1}{4} = \left(\frac{9 - 1}{4}\right) = \frac{8}{4} = 2
\]
### Step 3: Put It All Together
Now we can write the simplified polynomial:
\[
x^2 - x + 2
\]
### Final Answer
Thus, the sum of the polynomials is:
\[
\boxed{x^2 - x + 2}
\]
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.