Mrs gee has 24 carpet squares. How should she arrange them so she has the smallest perimeter?

The interior angle of a regular polvgon is 9 times the size of its exterior angle

Thepotemich [5.8K]

<h3>Answer: 20 sides</h3>

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Work Shown:

x = exterior angle

9x = interior angle

interior + exterior = 180

9x+x = 180

10x = 180

x = 180/10

x = 18

n = number of sides

n = 360/x

n = 360/18

n = 20

There are 20 sides to the regular polygon.

Side notes:

The formula to determine n only works for regular polygons.
A polygon with 20 sides is known as an icosagon.
Any pair of adjacent interior and exterior angles are supplementary. They add to 180 degrees.

3 0

1 year ago

A fruit stand has 200 apples. They order 19 bags with 12 apple each. They sell 42 bags that have 8 apples each. The owner says t

solniwko [45]

Answer:

The owner's estimate is reasonable. They ordered about 240 apples and sold about 320 so they should have about 80 fewer apples than they started with.

Step-by-step explanation:

Given that:

Number of apples already available with Owner = 200

Number of bags of apples ordered with 12 apples each = 19

Number of apples ordered = 12 $\times$ 19 = 228

OR

Rounding off 19 to 20:

Number of apples ordered = 12 $\times$ 20 = 240

Around 240 apples were ordered.

Number of bags of apples with 8 apples each, sold = 42

Number of apples sold = 42 $\times$ 8 = 336

Rounding off 42 to 40, number of apples sold = around 320

Therefore, 80 more apples were sold than that of apples bought.

So, according to the estimate, there will be 80 fewer apples left than they started with.

Correct answer is:

The owner's estimate is reasonable. They ordered about 240 apples and sold about 320 so they should have about 80 fewer apples than they started with

4 0

2 years ago

On your tenth birthday, you received 500 which you invested at 9.5% interest, compounded annually. your investment is worth $250

igomit [66]

Compounded once a year: A=P(1+r)^t
2500=500(1+0.095)^t
1.095^t=5
because the unknown number is an exponent, use log to find the unknown:
log(1.095^t)=log5
tlog1.095=log5
t=log5/log1.095
use your calculator, t=17.734
so this person is about 28 years old.

6 0

2 years ago

Find the nth term of the sequence 7,25,51,85,127

olya-2409 [2.1K]

Let a (n) denote the n-th term of the given sequence.

Check the forward differences, and denote the n-th difference by b (n). That is,

b (n) = a (n + 1) - a (n)

These so-called first differences are

b (1) = a (2) - a (1) = 25 - 7 = 18

b (2) = a (3) - a (2) = 51 - 25 = 26

b (3) = a (4) - a (3) = 85 - 51 = 34

b (4) = a (5) - a (4) = 127 - 85 = 42

Now consider this sequence of differences,

18, 26, 34, 42, …

and notice that the difference between consecutive terms in this sequence b is 8:

26 - 18 = 8

34 - 26 = 8

42 - 34 = 8

and so on. This means b is an arithmetic sequence, and in particular follows the rule

b (n) = 18 + 8 (n - 1) = 8n + 10

for n ≥ 1.

So we have

a (n + 1) - a (n) = 8n + 10

or, replacing n + 1 with n,

a (n) = a (n - 1) + 8 (n - 1) + 10

a (n) = a (n - 1) + 8n + 2

We can solve for a (n) by iteratively substituting:

a (n) = [a (n - 2) + 8 (n - 1) + 2] + 8n + 2

a (n) = a (n - 2) + 8 (n + (n - 1)) + 2×2

a (n) = [a (n - 3) + 8 (n - 2) + 2] + 8 (n + (n - 1)) + 2×2

a (n) = a (n - 3) + 8 (n + (n - 1) + (n - 2)) + 3×2

and so on. The pattern should be clear; we end up with

a (n) = a (1) + 8 (n + (n - 1) + … + 3 + 2) + (n - 1)×2

The middle group is the sum,

$\displaystyle 8\sum_{k=2}^nk=8\sum_{k=1}^nk-8=\frac{8n(n+1)}2-8=4n^2+4n-8$

so that

a (n) = a (1) + (4n ² + 4n - 8) + 2 (n - 1)

a (n) = 4n ² + 6n - 3

4 0

3 years ago

Help a girl out ?? i'm confused as to solve this

Rom4ik [11]

Answer:

(5 1/2 miles, $12.50)

Step-by-step explanation:

Looking at the graph, identify as best you can the coordinates of the point at which the two graphs cross. I read (5 1/2 miles, $12.50).

3 0

3 years ago