In parallelogram abcd, ad = 12 in, m∠c = 46º, m∠dba = 72º. find the area of abcd.

96.16 square in

Step-by-step explanation:

Given information: In parallelogram ABCD, AD = 12 in, m∠C = 46º, m∠DBA = 72º.

Opposite angles of a parallelogram are congruent.

According to the angle sum property, the sum of interior angles of a triangle is 180º.

Law of Sine:

Using Law of Sine we get

It means the base of parallelogram is 11.14 in.

Draw an altitude on AB from D.

In a right angle

In triangle ADE,

The height of the parallelogram is 8.632.

The area of parallelogram is

Therefore, the area of parallelogram is 96.16 square in.

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:

answer: 2530

hope this