The length of Carl's hair was 9 3/4 inches. After his hair cut, the length was 6 1/2 inches . How many inches did he cut?

3 1/4 inches

Step-by-step explanation:

9 3/4 - 6 1/2

I turned 6 1/2 into an easier fraction so it can be easier to subtract. Now the expression is:

9 3/4 - 6 2/4

6 2/4 is equivalent to 6 1/2

I then got 3 1/4

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 image of (6, 9) under a dilation is (4, 6). the scale factor is