Write a proof for the biconditional using the conditional and converse. A triangle is equilateral if and only if all the side lengths of the triangle are equal.

see below

Step-by-step explanation:

Hypothesis (p): A triangle is equilateral

Conclusion (q): The side lengths are equal

Conditional (p → q): If a triangle is equilateral, then its side lengths are equal.

The conditional statement is TRUE

Converse (q → p): If the side lengths of a triangle are equal, then it is equilateral.

The converse statement is TRUE

Since p → q   and  q → p are both TRUE, then it is biconditional.

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: