Write and solve an equation using the constant of proportionality to answer each question.
the ratio between the number of children (c) on a field trip and number of teachers (t) on the trips is 14/3. there are 70 children on the field trip. how many teachers are on the trip?

15 teachers

Step-by-step explanation:

Given:

number of children is c

number of teachers is t

= (rearrange)

t = x C

When C = 70,

t = x 70

t = 15 teachers

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.