Two secants are drawn from an exterior point A. Secant AC first intersects the circle at point B and secant AE .If AB10, AD12,and AC24,
the length of DE ?

DE = 8 units.

Step-by-step explanation:

By the External Secants Theorem

AC * AB = AE * AD

24 * 10 = AE * 12

AE =  240 / 12 = 20

So DE = AE - AD = 20 -12 = 8.

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: