Which scenario, when graphed, would produce a nonlinear function? A. a graph comparing weekly savings (y) to Adam saving $10 each week (x) B. a graph comparing total amount saved (y) to when Mark saves $10 each week (x) C. a graph comparing total amount saved (y) to when Sally saves 15% of her weekly salary (x) D. a graph comparing weekly savings (y) to when Joseph saves 50% as much money as each previous week (x)

C

Step-by-step explanation:

First of all, the ones that say "each" means it is probably going to be a linear function, because that means the slope will be the same and it will be linear. If it says "each" it is referring to the x in the slope intercept form: y= mx + b. X is the slope, b is the y intercept, and m is the amount you're multiplying by. So A and B are out. For c, we do not know if her weekly salary is the same each week so that means that it would probably be nonlinear since we don't know that its constant. Just to be sure, we can check D. If he saves 50% as much money as the previous week, that means that it will always be half of the last one which means it is linear. Sally's scenario is non-linear because we cannot confirm that her weekly salary is the same each week.

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.

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