Stacy wants to build a patio with a small, circular pond in her backyard. the pond will have a 6-foot radius. she also wants to install tiles in the remaining area of the patio. the length of the patio is 13 feet longer than the width. if the cost of installing tiles is $1 per square foot, and the cost of installing the pond is $0.62 per square foot, then which of the following inequalities can be used to solve for the width, x, of the patio, if stacy can spend no more than $536 on this project? a.) $1x^2 + $13x - $13.68 $536 b.) $0.62x^2 + $8.06x - $13.68 $536 c.) $1x^2 + $13x - $58.32 $536 d.) x^2 + $13x - $13.68 $536

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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