The reciprocal of the reciprocal of a number is

the same number, as long as the original number is different from zero.

Step-by-step explanation:

Notice that the number zero doesn't have reciprocal (division by zero is not defined). Therefore, as long as the number is different from zero, the reciprocal of the reciprocal of the number is the number itself.

Here in math terms:

Reciprocal of the number "x" (with "x" different from zero) is:

the reciprocal of this is:

where we have used that dividing a number by a rational expressions is equivalent to multiplying the number by its reciprocal.

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.