A man has x matches in a matchbox. On Monday he uses one-quarter of the matches
On Tuesday he uses five more. How many
matches has he used? How many has he left?

Used: 1/4x +5

Left: 3/4x -5

Step-by-step explanation:

Monday: 1/4 of the x matched

1/4x are used

Tuesday: uses 5 more

1/4x +5 are used

Total used 1/4x +5

To find what is left, take what was started with x, and subtract what was used

Left: x - (1/4x+5)

        x - 1/4x -5

         3/4x -5

the third picture

step-by-step explanation:

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.