A hockey fan collects hockey pucks used in professional games. She has 12 pucks already in her collection. She has a friend that works at the stadium tha can get her 3 new pucks each month. How many months will it take for her collection to have 18 pucks answer key?

it will take 6 months for her collection to have 18 pucks.

Step-by-step explanation:

Let x represent the number of months it will take for her collection to have 18 pucks.

She has 12 pucks already in her collection. She has a friend that works at the stadium that can get her 3 new pucks each month. This means that the number of pucks that she would have after x months is expressed as

12 + 3x

For her to get 18 pucks, the expression would be

12 + 3x = 18

3x = 18 - 12

3x = 6

x = 6/3

x = 2

18a

step-by-step explanation:

simply because it is. it's the highest common factor

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.