Quadrilateral abcd is a rectangle.
if ag = –7y + 5 and dg = 2y + 68, find bd.
a) 108
b) -7
c) 27
d) 54

A

Step-by-step explanation:

The diagonals of a rectangle are congruent and bisect each other, so

AC = BD

2AG = 2DG, that is

AG = DG, substitute values

- 7y + 5 = 2y + 68 ( subtract 2y from both sides )

- 9y + 5 = 68 ( subtract 5 from both sides )

-9y = 63 ( divide both sides by - 9 )

y = - 7

Hence

BD = 2(2y + 68)

     = 4y + 136

     = (4 × - 7) + 136

     = - 28 + 136

     = 108 → A

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.