What is the product of -2x^2 + x - 5 and x^3 - 3x - 4 ? show your work. is the product of -2x^2 + x - 5 and x^3 - 3x - 4 equal to the product of x^3 - 3x - 4 and -2x^2 + x - 5 ? explain your answer.

For this case we must find the product of the following expressions:

We must apply distributive property, that is, multiply each term:

We must bear in mind that:

If we multiply we would obtain the same result according to the commutative property of the multiplication:

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.

-3.5 degrees per hour

step-by-step explanation:

find the unit rate:

-12   1/4 degrees           12.25 degrees

= - = -3.5 degrees per hour

      3   1/2 hours               3.5 hours