A box is filled with green marbles, red marbles, and blue marbles. The ratio of red marbles to green marbles is 3:1. The ratio of green marbles to all of the marbles in the box is 2:11. Write each of the following ratios using the symbol. The ratio of red marbles to blue marbles.

Red:green = 3:1, not 3:2

r:g = 3:1, so g:r = 1:3 = 2:6

r:t = 2:11 = 6:33

g:r:t = 2:6:33

now just read off the ratios.

r:t = 6:33 = 2/11

b:t = 1 - (g:t - r:t) = 25/33

b:g = 25/2

r:b = 6/25

Step-by-step explanation:

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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.

2 x t divided by n

step-by-step explanation: