For which natural values of n: n+8/19 is a proper fraction?

The natural values on n is the set

{0, 1, 2, 3,4,5,6,7,8,9,10}

Step-by-step explanation:

we know that

A proper fraction is a fraction where the numerator (the top number) is less than the denominator

so

we have

so

solve for n

subtract 8 both sides

therefore

The natural values on n is the set

{0, 1, 2, 3,4,5,6,7,8,9,10}

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.

c) yes, because of asa or aas