Question

which expression is equivalent to \\((-11x^2 + 1.4x - 3) + (4x^2 - 2.7x + 8)\\)?
a. \\(-7x^2 - 1.3x + 5\\)
b. \\(-7x^2 + 1.3x + 5\\)
c. \\(7x^2 - 1.3x + 5\\)
d. \\(7x^2 + 1.3x + 5\\)

Explanation:

Step1: Combine like terms for \(x^2\) terms

We have \(-11x^2 + 4x^2\). Combining these, we get \((-11 + 4)x^2 = -7x^2\).

Step2: Combine like terms for \(x\) terms

We have \(1.4x - 2.7x\). Combining these, we get \((1.4 - 2.7)x = -1.3x\)? Wait, no, wait the original problem: Wait, the first polynomial is \(-11x^2 + 1.4x - 3\) and the second is \(4x^2 - 2.7x + 8\)? Wait, no, looking at the options, the \(x\) term in the options is \(1.3x\) or \(-1.3x\)? Wait, maybe I misread. Wait the problem is \((-11x^2 + 1.4x - 3)+(4x^2 - 2.7x + 8)\). Let's recalculate:

For \(x^2\) terms: \(-11x^2 + 4x^2 = -7x^2\)

For \(x\) terms: \(1.4x - 2.7x = -1.3x\)? But the options have \(1.3x\) or \(-1.3x\)? Wait the options:

A: \(-7x^2 - 1.3x + 5\)

B: \(-7x^2 + 1.3x + 5\)

C: \(7x^2 - 1.3x + 5\)

D: \(7x^2 + 1.3x + 5\)

Wait, maybe the first polynomial is \(-11x^2 + 1.4x - 3\) and the second is \(4x^2 - 2.7x + 8\)? Wait, no, maybe the second polynomial is \(4x^2 - 2.7x + 8\)? Wait, let's do the constant terms: \(-3 + 8 = 5\).

Now, \(x\) terms: \(1.4x - 2.7x = -1.3x\)? But option A is \(-7x^2 - 1.3x + 5\), option B is \(-7x^2 + 1.3x + 5\). Wait, maybe I made a mistake. Wait, maybe the first polynomial is \(-11x^2 + 1.4x - 3\) and the second is \(4x^2 - 2.7x + 8\)? Wait, no, maybe the second polynomial is \(4x^2 - 2.7x + 8\), but let's check the \(x\) terms again. Wait, 1.4x - 2.7x = -1.3x, so the \(x\) term is -1.3x. Then the constant term is -3 + 8 = 5. The \(x^2\) term is -11x^2 + 4x^2 = -7x^2. So combining all: \(-7x^2 - 1.3x + 5\), which is option A. Wait, but let's check again. Wait, maybe the second polynomial is \(4x^2 - 2.7x + 8\), but maybe the first polynomial is \(-11x^2 + 1.4x - 3\) and the second is \(4x^2 - 2.7x + 8\). So:

\(x^2\): -11 + 4 = -7

\(x\): 1.4 - 2.7 = -1.3

constant: -3 + 8 = 5

So the expression is \(-7x^2 - 1.3x + 5\), which is option A.

Wait, but let's check the options again. Option A is \(-7x^2 - 1.3x + 5\), option B is \(-7x^2 + 1.3x + 5\), option C is \(7x^2 - 1.3x + 5\), option D is \(7x^2 + 1.3x + 5\). So the correct answer is A.

Answer:

A. \(-7x^2 - 1.3x + 5\)