Draw the following regular polygons inscribed in a circle:

square

pentagon

hexagon

octagon

decagon

For each polygon, include the following information in the paragraph box below:

What was the central angle you used to locate the vertices? Show your calculation.

What is the measure of each interior angle of the polygon? Show your calculation.

Answer the questions below.

What is the relationship between the central angle and the interior angle?


As the number of sides increases, how do the angles change?

Answer:

Step-by-step explanation:

We'll start with going form exponential to radical, since it may be easier to follow. For example,

[tex]x^{\frac{4}{3}[/tex] can be written, in radical form, as

[tex]\sqrt[3]{x^4}[/tex]. What happens is that the denominator of the fraction serves as the index (the number that sits in the bend of the radical) and the numerator serves as the power on the variable (or number, if that's the case). Let's look at another one:

[tex]4^{\frac{2}{3}[/tex] becomes

[tex]\sqrt[3]{4^2}=\sqrt[3]{16}=\sqrt[3]{8*2}=2\sqrt[3]2}[/tex]

And you can go the other way with it. For example,

[tex]\sqrt[5]{x^4}[/tex] becomes

[tex]x^{\frac{4}{5}[/tex], etc. Get it?

Answer:

When you're given a problem in radical form, you may have an easier time if you You can rewrite every radical as an exponent by using the following property — the top ... For example, 643/2 is easier if you write it as (641/2)3 = 83 = 512 rather than (643)1/2,  Rewrite the entire expression using rational exponents.

Answer:

x = -72

Step-by-step explanation:

-72 + 8 = -64

The third square root of -64 is -4

Answer:

Step-by-step explanation:

We'll call the 2 numbers x and y. Starting with the last part of that first sentence "one number is 10 times the other number" can be written, in algebraic form:

y = 10x

Now on to the first statement about the numbers: "twice their sum" is 2(x + y) and "equals their product" is = xy. Putting that all together:

2(x + y) = xy and we know that y = 10x so

2(x + 10x) = x(10x) and

[tex]2(11x)=10x^2[/tex] and

[tex]10x^2-22x=0[/tex] and

x(10x - 22) = 0 so

x = 0 or 10x - 22 = 0 which makes

x equal to [tex]\frac{22}{10}=2.2[/tex]

So x = 2.2 and y = 22.

Answer:

Rs 968

Step-by-step explanation:

Given :-

To Find :-

Solution :-

We know CI as ,

> CI = P ( 1 + R/100)ⁿ

> CI = Rs 800 ( 1 + 10/100)²

> CI = Rs 800 × 11/10 × 11/10

> CI = Rs 968 .

Answer:

It's letter D.

Step-by-step explanation:

3.14÷60×50= 2.61 but you have to opposite remember if the number is a little number you have to opposite and that is the answer 6.2 but do not joy like this . so the real answer is 62

Answer:

Units

Step-by-step explanation:

From the value above 478.92

4 represents hundreds

7 represents tens

8 represents units

Hence the answer is units

Answer:

Step-by-step explanation:

[tex]sin^2 \ x + sin ^2 \ x + 2cos^ 2\ x = 2\\\\2sin^2 \ x + 2 cos^2 \ x = 2\\\\2 ( sin^2 \ x + cos^2 \ x ) = 2 \\\\2 \times 1 = 2 \\\\2 = 2 \\\\LHS = RHS \\\\Hence \ proved.[/tex]

profit from selling 5 oranges is 20%

Profit percentage of  selling 5 oranges, a shopkeeper gains the selling price of 1 orange is equals to 25%.

" Profit is defined as difference of cost price from selling price when the selling price of a product is greater than its cost price."

Formula used

Profit percentage = [tex]\frac{Selling price - cost price}{cost price} (100)[/tex]

According to the question,

We know that,

Selling price = cost price + profit

Substitute the given condition in the selling price formula we get,

Selling price of 5 oranges

= Cost price of 5 oranges + Selling price of 1 oranges

⇒(S.P of 5 oranges) - (S.P of 1 oranges) = C.P. of 5 oranges

⇒S.P of 4 oranges = C.P of 5 oranges

⇒[tex]\frac{S.P}{C.P}=\frac{5}{4}[/tex]

Substitute the value in the formula to get profit percentage,

Profit percentage = [tex]\frac{5-4}{4}(100)[/tex]

                              = 25%

Hence, profit percentage of  selling 5 oranges, a shopkeeper gains the selling price of 1 orange is equals to 25%.

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Answer:

Q = G

Step-by-step explanation:

We are already given that angle P = angle H

We are also given that side QP = side GH

Remember if two sides are congruent then so are their opposite angles meaning that the opposite angle of GH ( which would be angle F ) would be congruent to the opposite angle of QP ( which would be angle R )

The remaining angles would be angle q and angle g so the additional information needed would be G = Q

Answer:

the answer is A

Step-by-step explanation:

Answer:

70= (x+3)

Step-by-step explanation:

the length of the rectangle  its width by 3 inches, if the width is x,the length will be x+3. so A=LW= 70

To find= 70= (x+3)x

x= 7 or -10

Answer:

The answer should be: B

I think it's B because there are 2 cups of water (2c) and 7 bottles of water (7w) which costs $16 so that would be 2c +7w=16. Also for the other one, it's 3 cups (3c) and 8 bottles of water (8W) and the cost is $19 so that would be

3c + 8w =19

Step-by-step explanation: Hope this helps and gl :))

Answer:

0.25 feet

7.62 centimeters

3 inches

Step-by-step explanation:

Not really a clear question-

Answer:

-13 is the answer I think so but wait for others also because my could be wrong

Answer:

B

Step-by-step explanation:

Two negatives is a positive, and you want your outcome to be a positive x, therefore b is the correct answer.

Answer:

second one

A negative multiplied by a negative is a positive.

- (-x) is multiplication.

Answer:

sorry i cannot help you

Answer:

(a) is 8 x 7 x 3 = 168

(b) is 8 x 7 = 56

(b2) is weird I don't know what it's asking

Answer:

FOR LETTER A

Volume of prism (expression) = Length x Width/Breadth x Height

Volume of prism (expression) = 8 units x 7 units x 3 units = 168 cubic units

FOR LETTER B

Area of the shaded base = 8 x 7 = 56 square units

Volume of prism = Area of the shaded base x Height

Volume of prism = 56 square units x 3 units = 168 cubic units

Step-by-step explanation:

To find the volume of rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism.

Volume of rectangular prism = length × width × height

To get the area of the shaded base, when the base is in rectangular shape:

Definition: Area of rectangle is the region occupied by a rectangle within it's four sides or boundaries.

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area. But in the case of a square, since all the sides are equal, therefore, the area of the square will be equal to the square of side-length.

Area of rectangle = Length × Breadth

A = l × b

Answer:

p + 4p

5p

Step-by-step explanation:

Problems Vicki solved = p

Tamra worked 4 times as many problems as Vicki = 4 x p = 4p

total problems solved by both of them =4p + p

= 5p

Answer:

f(-5) = 7

Step-by-step explanation:

f(-5) means find the y value when x = -5

y = 7 when x = -5

Answer:

72 +72=144

180-144=36

the answer is 36°

The measure of the angle x is 36° obtained by the concept of an Isosceles triangle and interior angle sum.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know an isosceles triangle has two similar sides and angles opposite to the similar side and also measures the same.

So, By the interior angle sum concept,

72° + 72° + x = 180°.

x = 36°.

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Answer:

gradient = slope = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{rise}{run}[/tex]

Slope intercept Form equation : y = mx + b

m = slope or gradient

b = y - intercept ( where the line crosses the y = axis)

x and y = are place holders for a coordinate pair that makes the equation true

c) y = -6x + 8

The -6 is the m. It's the slope or gradient.

the + 8  is the b. It's the y- intercept.

d) y = 4

This is a horizontal line. It intercepts the y-axis at 4.

That means the 4 is the y-intercept.

There is no x. That means the slope is 0. The line rises 0 as it runs left to right.

e) y -4x= 0  

equation needs to be is standard form y = mx + b.

add 4x to both sides in order to isolate the y variable.

y = 4x + 0.

The slope or gradient is 4. The y - intercept is 0. The line crosses through the origin.

f) y -x = -8

Add x to both sides.

y = x - 8

There is one x.  That means the gradient is 1. The y-intercept is the -8

g) y + 3x = 7

Subtract 3x from both sides.

y = -3x + 7

-3 = gradient. 7 = y-intercept.

h) y + [tex]\frac{1}{2}[/tex]x = -4

Subtract [tex]\frac{1}{2}[/tex]x from each side.

y = -[tex]\frac{1}{2}[/tex]x - 4

One last thing. If you are presented with an equation without a y, the gradient is  'undefined'.

example : x = 4

This a vertical line passing through 4 on the x-axis. There is no 'b' because its not crossing the y-axis.

Why is it 'undefined' ?

As the line rises it, it does not 'run' left or right. [tex]\frac{rise}{0}[/tex] . Zero can never, ever be in the denominator. Denominators can't be zero. That is why we say it's 'undefined'.

Hope this helps.

Answer:

1) 25

2) 2

3) f(g(1)) = 42

Step-by-step explanation:

1) Given that f(x) = 4x^2  + 9

If x = -2

f(-2) = 4(-2)^2 + 9

f(-2) = 4(4) + 9

f(-2) = 16 + 9

f(-2) = 25

2) Given that f(x) = 4x - 6

y = 4x - 6

Replace y  with x

x = 4y - 6

MAke y the subject of the forfmula

4y = x+ 6

y = (x+6)/4

SInce x = 2

f^(-1)(2) = (2+6)/4

f^(-1)(2) = 8/4 = 2

3) If f(x) = 6x and g(x) = x+6

f(g(x)) = f(x+6)

f(x+6) = 6(x+6)

Since x = 1

f(g(1)) = 6(1+6)

f(g(1)) = 6(7)

f(g(1)) = 42

Answer:

3(y+6)=30

3y + 18 = 30

18 - 30 = 3y

12 = 3y

12/3 = y

4 = y

or

y = 4

Answer:

Following are the responses to the given question:

Step-by-step explanation:

For point a:

Following are the null and alternative hypotheses:

[tex]H_0 : \mu_1 \leq \mu_2\\\\H_1 : \mu_1 > \mu_2[/tex]

For point b:

By using the Excel we obtained the output of the 2 sample t-test that is defined in the attached file.  

These point estimately are the difference among the mean for the two populations:

[tex]\to \mu_{\bar{x_1}-\bar{x_2}} = \mu_{\bar{x_1}}-\mu{\bar{x_2}} ={\bar{x_1}-\bar{x_2}}=573-491=82[/tex]

Answer:

sin o = opposite/hypotenuse

sin o= 7/12

Answer:

It will take 13 months for the second phone to be less expensive than the first phone.

Step-by-step explanation:

Since Sal is trying to determine which cell phone and service plan to buy for his mother, and the first phone costs $ 100 and $ 55 per month for unlimited usage, while the second phone costs $ 150 and $ 51 per month for unlimited usage, to determine how many months will it take for the second phone to be less expensive than the first phone, the following calculation must be performed:

100 + (55 x 10) = 100 + 550 = 650

150 + (51 x 10) = 150 + 510 = 660

100 + (55 x 12) = 100 + 660 = 760

150 + (51 x 12) = 150 + 612 = 762

100 + (55 x 13) = 100 + 715 = 815

100 + (51 x 13) = 150 + 663 = 813

Therefore, it will take 13 months for the second phone to be less expensive than the first phone.

Answer:

1) 100 + 55x > 150 + 51x

2) x > 12.5

3) 13

Step-by-step explanation:

Got it right on Edge :D

Answer:

89 minutes

Step-by-step explanation:

let he talked for x minutes.

$12.79=1279 cents

1279=300+11x

11x=1279-300=979

x=89

Answer:

the answer is a

tell me if it’s rite or wrong I did the work as best as I could

f(10) is undefined.

"It is the set of points on the coordinate plane which satisfies the given function."

For given question,

We need to find the value of a function at x = 10.

We can observe that, when x = 10, the function value 2 is denoted by an open circle.

This means the function do not have value 2 when x = 10

Therefore, f(10) is undefined.

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Hello!

(6x + 9)/3 =

= 3(2x + 3)/3 =

= 2x + 3

Good luck! :)