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.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: