d) As a smart consumer, you are always on the lookout for sales, coupons, and rebates. While shopping for new clothes, you notice that one particular brand of shirts is on sale for 20% off the original price. You also have a coupon for $10 off a $40 purchase. Coupons are applied after the 20% discount is taken. If each shirt originally costs $17.99, how many shirts would you need to buy to be able to use your coupon? Show your work.

3 shirts

Step-by-step explanation:

Each shirt costs originally $17.99 with a 20% discount.  This means that you are paying 80% of the original price.  The discounted price is $14.39.

$17.99 × 0.80 = $14.39

You need to buy enough shirts so that you spend at least $40.  You need to round up since you can't buy a fraction of a shirt.

40 ≤ 14.39x

40/14.39 ≤ (14.39x)/(14.39)

2.779 ≤ x

2.779 ≈ 3

You will need to buy at least 3 shirts.

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.

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.