Mrs. simms told her class to find two consecutive even integers such that twice the lesser of two intergers is 4 less than two times the greater integer

Let the two consecutive even integers be 'x' and 'x+2'.

The lesser number is 'x' and greater number is 'x+2'

Since, twice the lesser of two integers is 4 less than two times the greater integer.

therefore, 2x = 2(x+2)-4

2x = 2x +4 -4

Therefore, x =0

Hence, x+ 2 = 2

Therefore, 0 and 2 are the required consecutive even integers.

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.

the answer is 0.071

good luck! : d