The cost of 12 oranges and seven apples is $5.36. eight oranges and five apples cost $3.68. find the cost of each

12o + 7a = 5.36

8o + 5a = 3.68

How can we eliminate either the o or the a? Let's multiply the first equation by -2 and the second by 3.

-24o -14a = -10.72

24o + 15a = 11.04

Adding the two equations together...

a = 0.32

8o + 5(0.32) = 3.68

8o + 1.6 = 3.68

8o = 2.08

o = 0.26

Apples are 32 cents each and oranges are 26 cents each

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.

step-by-step explanation: