How many positive integers less than 20 have an odd number of distinct factors?

Solution:

we have been asked to find

How many positive integers less than 20 have an odd number of distinct factors?

No prime numbers will have an odd number of distinct factors because those numbers are divisible by 1 and itself.

So the options to check are

4,6,8,9,10,12,14,15,16,18

The factors are as below

So we have 4,9 and 16. But we will add 1 also because it has one and only one factor.

So the numbers are 1,4,9,16.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

(w – 2.5)(w + 2.5)

(–4v – 9)(–4v + 9)

step-by-step explanation: