Quadrilateral ABCD has vertices at A(3,−2), B(4,3), C(−2,0), and D(−3,−5). Quadrilateral A B C D in the plane with the given coordinates. © 2019 StrongMind. Created using GeoGebra. Which answers prove that quadrilateral ABCD is a parallelogram? Select all that apply. slope of AB¯¯¯¯¯¯¯¯=slope of DC¯¯¯¯¯¯¯¯; AD¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ AB¯¯¯¯¯¯¯¯∥DC¯¯¯¯¯¯¯¯ and AD¯¯¯¯¯¯¯¯∥BC¯¯¯¯¯¯¯¯ ∠A is supplementary to ∠B; ∠A≅∠C AD¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ slope of AD¯¯¯¯¯¯¯¯=slope of BC¯¯¯¯¯¯¯¯; AD¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯

The quadrilateral ABCD is a parallelogram as, slope of AB = slope of DC = 5, and slope of AD = slope of BC = 0.5.

Step-by-step explanation:

Quadrilateral ABCD has vertices at A(3,−2), B(4,3), C(−2,0), and D(−3,−5).

So, the slope of AB =

Now, the slope of BC =

The slope of CD =

Finally, the slope of DA =

Therefore, the quadrilateral ABCD is a parallelogram as, slope of AB = slope of DC = 5, and slope of AD = slope of BC = 0.5. (Answer)

Note: A quadrilateral to be a parallelogram the slope of each pair of opposite sides must be the same.

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).