You have five different varieties of flowers and you want to put 3 different varieties in each vase how many cases will you make without duplicating a vase

10

Step-by-step explanation:

Given:

There are 5 different varieties of flowers.

To place 3 different varies in each vase.

To find how many ways we can do so without duplicating a vase.

Solution:

We need to choose 3 different flowers out of 5 different variety of flowers.

In order to do so we use combination.

We can place the flowers in ways.

Thus, we can make vase in 10 different ways without duplicating a vase.

the answer is 5/3x+7/5y+7

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough