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jekas [21]
3 years ago
6

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.

Mathematics
1 answer:
bogdanovich [222]3 years ago
3 0

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 . . . . . . . . .<u> . . . . . . ..1</u>

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

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

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mars1129 [50]

Step-by-step explanation:

hope it is helpful to you

5 0
3 years ago
Read 2 more answers
Select the choice that translates the following verbal phrase correctly to algebra:
likoan [24]
The answer is <span>one halfn − 16
</span>
Let the number be n.

<span>One half of a number is (1/2n)
</span><span>decreased by 16 is (-16)

</span><span>one half of a number decreased by 16 is
1/2n - 16

Or </span><span>one halfn − 16</span>
4 0
2 years ago
A local water park has two types of season passes. Plan A costs a one-time fee of $125 for admission plus $8 for parking every t
Margarita [4]

Answer:

40+8X=50+23X

8X-23X=50-140

-15X=-90

X=-90/-15

X=7 TRIPS IS THE ANSWER.

PROOF:

140+8*6=50+23*6

140+48=50+138

188=188

4 0
3 years ago
-4/5 to the power of 2 times -3/50
Crazy boy [7]
=(-4/5)^2 * -3/50
square -4/5 first; remember -4/5^2 is the same as -4/5 * -4/5

=(-4/5 * -4/5) * -3/50
multiply -4 numerators; multiply 5 denominators

=(-4 * -4)/(5 * 5) * -3/50

=16/25 * -3/50
multiply numerators 16 & -3; multiply denominators 25 & 50

=(16 * -3)/(25 * 50)
= -48/1250

simplify by 2
= -24/625 (or -0.0384)


ANSWER: -24/625 (or -0.0384)

Hope this helps! :)
6 0
3 years ago
Read 2 more answers
Use the given scale factor in the side length of the scale drawing to determine the side links of the real object
ozzi

Answer:

A. side a is 7 inches long, side b is 6 inches long,and side c is 3 inches long

Step-by-step explanation:

Here is the complete question. Please find attached a diagram showing the scaled and real drawing

Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object

A. side a is 7 inches long, side b is 6 inches long,and side c is 3 inches long

B. side a is 30 inches long, side b is 25 inches long, and side c is 20 inches long

C. side a is 40 inches long, side b is 35 inches long,and side c is 20 inches long

D. side a is 175 inches long,side b is 150 inches long, and side c is inches long

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

The scaled drawing is an enlarged image of the original triangle.

It is enlarged at a ratio of 5:1

original dimensions

a = 35/5 = 7

b = 30 / 5 = 6

c = 15/5 = 3

7 0
2 years ago
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