1. How many numbers less than 10,000 are there which are divisible
by 21, 35 and 63?

31

Step-by-step explanation:

To solve this problem, we must find the lowest common multiple of 21, 35 and 63

   Find the prime factors of the number;

 Prime factors of 21  = 3 x 7

                            35 = 3 x 5

                            63 = 3 x 3 x 7

  The lcm = 3 x 3 x 5 x 7 = 315

The numbers between  1 and 10, 000 divided by these three numbers;

   First number  = 315

    Last number  = 9765

Now the total number:

      =

      = + 1

     = 30 + 1

     = 31

A relation is a set of ordered pairs.

An ordered pair has an x and y value.

The x value is ALWAYS the the FIRST number of the ordered pair.

To make it a function the X value can be mapped to ONLY one Y value.

EXAMPLE:

The point (1,4)...

1 is the X value

4 is the Y value of ordered pair.

The Y values can be the same number. so, if you need to remove one point to make a funtion, look to see which one of the X values are the same and remove one of those

EXAMPLE:

The following relation is a function.

(−1,0)(0,−3)(2,−3)(3,0)(4,5)

The following relation is not a function.

(6,10) (-7,3) (0,4) (6,-4)

see how there are two 6's for the X value. This is NOT a function!