While on a walk in the countryyou pass a field full of goats and ducks After quick countyou determine there are 31 heads and 84 feet in each animal are there?

There are 11 goats and 20 ducks.

Step-by-step explanation:

Given:

While on a walk in the country you pass a field full of goats and ducks.

After quick count you determine there are 31 heads and 84 feet in each animal.

Now, to find the number of each animals.

Let the number of goats be

And let the number of ducks be

So, total number of heads:

As, the goats have 4 feets and ducks have 2.

Now, the total number of feet:

Substituting the value of from equation (1) we get:

Subtracting both sides by 62 we get:

Dividing both sides by 2 we get:

The number of goats = 11.

Substituting the value of in equation (1) we get:

The number of ducks = 20.

Therefore, there are 11 goats and 20 ducks.

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl