Figure#0 has 4 tiles figure#1 has 9 tiles figure#2 has 16 figure #3 has 25 tiles figure#4 has 36 tiles figure#5 has 49 tiles how many will figure #100 have, and what is the rule that will give the number of tiles in any figure in the pattern.

The figure number and the number of tiles are related by the number the formula

t = (f + 2)^2

The number of tiles (t) equals the figure number plus 2 the result of that squared.

For example for f =1

the number of tiles is t = (n + 2) ^2 = (1 + 2)^2 = 3^2 = 9

For f = 2

The number of tiles = (n+2)^2 = (2 + 2)^2 = 4^2 = 16

For f = 3

The number of tiles = (n + 2)^2 = (3 + 2)^2 =5^2 = 25

We can be fairly confident in the formula. So what about figure 100

t = (n + 2)^2 = 102^2 = 10404 tiles.

Your next problem is figure out what this will look like.

You are going to have to do a little reading as you draw this on a piece of paper.

Go back to figure 1. There is a square in the middle of the drawing. The square consists of 4 tiles. Draw them on a piece of paper. I can't reproduce them, but it looks like every drawing has a square with (n + 1)^2 tiles in it.

Look at figure 2. There is a square in the middle of the drawing. The figure number plus 1 all squared = the number of tiles in that square. t = (f + 1)^2. You should be able to see 9 squares in that central square.

Three will give you 16 squares in the middle square.

Now there are arms coming off the square. Again each arm is related to the figure number.

In figure 1 the arm length is 2 tiles. It suggests 2*f is the number of tiles in both arms together.

Figure 2 has 3 tiles in each arm. That means that the total number of tiles used for 1 arm (f + 1) = (2 + 1) = 3

Figure 3 has 4 tiles in each arm. Total 8.

Finally all figures have 1 tile sitting on top of everything else. No more than 1 and no less than 1. Just 1.

Now we are ready to talk about figure 100.

The square in the middle was determined to be (f + 1)^2 = 101^2 = 10201

The arms were determined to be t = 2 *( f + 1) = 2 * 101 = . . . . .. . . . . .202

And there is one more square that every figure has . . . . . . . . . . . . . . . ..1

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10404

Just what we got before. If you need more, leave a note about what you need, in detail.

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

step-by-step explanation: