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 1

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: \[ \boxed{14.75x^2 - x - 11.75} \]

Answer 2

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 3

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.

Answer 4

boxed{\frac{59}{4}x^2 - x - \frac{47}{4}}

Answer 5

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.

Answer 6

Simplify (1/4x^2−3x+2.25)+(0.75x^2+2x−1/4) .(1 point) The sum of the polynomials is .

Answer 7

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: \[ \boxed{x^2 - x + 2} \]