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2x^2 +11

Step-by-step explanation:

f(x) = 3x^2 +2

g(x) = x^2 -9

f(x) - g(x) = 3x^2 +2 - (x^2 -9)

 Distribute the minus sign

        = 3x^2 +2 -x^2 +9

    Combine like terms

         = 2x^2 +11

2x² + 11

Step-by-step explanation:

f(x) - g(x)

(3x² + 2) - (x² - 9)

Rearrange.

3x² - x² + 2 + 9

Add or subtract like terms.

2x² + 11

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

300pi

step-by-step explanation: