How many multiples of $8$ are between $100$ and $500$?

There are 50 multiples of 8 between 100 and 500

Step-by-step explanation:

1. We need to find out the multiple of 8 closest and higher than 100.

80, 88, 96, 104, 112, 120 It's 104

2. We need to find out the multiple of 8 closest and lower than 500.

480, 488, 496, 504, 512, 520It's 496

3. Now, we use 104 and 496, this way:

(496 - 104)/8 + 1 =

392/8 + 1 =

49 + 1 = 50

There are 50 multiples of 8 between 100 and 500

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.

sine

step-by-step explanation: