To simplify the expression \( \left( -3x + 2.25 \right) + \left( 0.75x^2 + 21 \right) \), we need to combine like terms.
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Identify the terms present in both polynomials:
- From the first polynomial: \(-3x\) (a linear term) and \(2.25\) (a constant).
- From the second polynomial: \(0.75x^2\) (a quadratic term) and \(21\) (a constant).
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Organize the terms by degree:
- Quadratic term: \(0.75x^2\)
- Linear term: \(-3x\)
- Constant terms: \(2.25 + 21\)
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Combine the constant terms: \[ 2.25 + 21 = 23.25 \]
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Now, combine all the terms: \[ 0.75x^2 - 3x + 23.25 \]
So the sum of the polynomials is:
\[ 0.75x^2 - 3x + 23.25 \]