Which value of n makes the following equation true? 3 sqrt n=8 a.2 b.16 c.24 d.512

d. 512

Step-by-step explanation:

You need to remember that:

Then, given the equation:

You can find the value of "n" that make the equation true, by solving for "n".

So, to solve for "n", you need to raise both side of the equation to power 3. Therefore, you get:

Then, the value of "n" that makes the equation true is: 512 (You can observe that this matches with the option d).

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.