Simplify the following monomials

4) b^10

5) 15x^11y^6

6) 8y^5x + 3x

Step-by-step explanation:

b^6 + b^4 = b^10 because this is multiplication. So you have to add the degrees

(3x^3y^5)(5x^8y^1) = 15x^11y^6. This is because

3 *5 = 15.

x^3 +x^8 = x^11

y^5 + y^1 = y^6.  

You have to add the degrees since this is also multiplication.

(2y^2)(4xy^3) + 3x = 24y^5x^2. This is because

2 * 4 = 8

y^2 + y^3 = y^5

x + 0 = x

Therfore, it is (8y^5x) + 3x as the final answer.

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.

16 is the absolute value

step-by-step explanation: