Solving this math problem with a mathematical explanation about the answer

1) 1²+2²+3²+4²+5²+6²+7²+8² = 204

2) here the pattern is squares form with only squares of natural number of tiles i.e) 1,4,9.....

3) floor with 10 tiles long, the number of squares = 385

   floor with 100 tiles long, the number of squares =338350

   floor with N tiles long, the number of squares = ∑ N² =

Step-by-step explanation:

We can make square only using number of tiles which are squares of natural numbers.

so, we need 1, 4, 9, 16 ..... number of tiles to form a square.

Now, if there are N number of squares along one side,

choosing 1 square at a time , we get N² number of squares

choosing 2 square at a time , we get (N-1)² number of squares

and so on...

choosing N square at a time , we get 1² number of squares

so the total number of squares = 1² + 2² +......+ N² = ∑N²

And ∑N² =  

you already gave the answer

step-by-step explanation:

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)