In a basket, there are white and red balls. What is the smallest number of balls you need to take out of the basket so that there are definitely two balls of the same color among them?

3

Step-by-step explanation:

Given

In a basket, there are white and red balls..

It can be explained

let in first two  balls you take is of different color i.e 1 white and 1 red ball

Third ball , whether you take  white or red ball you will have

two balls of same color.

if your third  ball is  red ball

then you will have 2 red balls and 1 white ball.

if your third   ball is white,

then you will have 2 white balls and 1 red balls.

Thus, 3 is the smallest number of balls you should take out .

To put it simply, if you have n balls of different colors then you need to take minimum n+1 number of balls to have at least two balls of same colors.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.