Three student teams collected 65 books for the school library. the first team collected 10 fewer books than the second team and the third team collected 30% of the number of books collected by first and second teams together. how many books did each team collect?

me!

Team 1 - x

Team 2 - y

Team 3 - z

x = y - 10

z =0.3(x+y)

x + y + z = 65

(y-10) + y + (0.3(x+y)) = 65

(y-10) + y + (0.3((y-10)+y)) = 65

y-10+y+(0.3(y-10)+0.3y)=65

2y-10+(0.3y-3+0.3y)=65

2y-10+0.6y-3=65

2.6y-13=65

2.6y=78

0.2y=6

2y=60

y=30 which is Team 2's books

x = y - 10

x=20-10

x=10 which is Team 1's books

z = 0.3(x+y)

z = 0.3(20+10)

z = 9 which is Team 3's books

Team 1 - 10

Team 2 - 20

Team 3 - 9

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.

yes

step-by-step explanation: