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3 years ago

Express answer in exact form. Show all work for full credit.

Mathematics

2 answers:

konstantin123 [22]3 years ago

7 0

Answer:

1.5 pi in.^2 - 2 & 1/4 sqrt 3 in.^2

Step-by-step explanation:

First, since the hexagon is a regular polygon, then each of the 6 equilateral triangles in the hexagon has all sides of 3 inches. This means that the radius of the circle is equal to 3 inches.

To find the area of the circle: A = pi * r^2 --> A = 9 pi in.^2.

Next, find the area of the sector: 60o (o = degree sign) divided by 360o --> 60/360 = 1/6 --> 1/6 times area of circle (9 pi) =

1.5 pi in.^2.

Then, find the area of one of the equilateral triangles by using the formula for the area of an equilateral triangle:

A = 1/4 * s^2 * sqrt 3 --> A = 1/4 * 3^2 * sqrt 3 --> A = 2 & 1/4 sqrt 3.

Finally, to find the area of the segment, do the area of the sector minus the area of the triangle:

<u>1.5 pi in.^2 - 2 & 1/4 sqrt 3 in.^2</u> (this is the exact answer; for it to be an approximate answer, you would actually do the equation).

<em>Hope this helps! :)</em>

Mekhanik [1.2K]3 years ago

3 0

The chord length is the same as the radius, so R^2 = 9.
Area = (1/2)(9)(pi/3 - sqrt(3)/2) = (3/4) (2 pi - 3 sqrt(3))

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A corporate team-building event costs $2 for every attendee. Write an equation that shows the relationship between the attendees

nasty-shy [4]

Answer:

y = 2x

Step-by-step explanation:

1. attendee = x

2. cost = y

3. for each attendee [x], you have $2 of cost, so for each 1 x, you have 2 as result

4. Thus, y = 2x

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2 years ago

Refer to the accompanying TI-83/84 Plus calculator display of a 95% confidence interval. The sample display results from using a

nikklg [1K]

Answer:

The confidence interval is $22.805$

Step-by-step explanation:

We have given,

The Z interval (23.305,25.075)

Mean $\bar{x}=23.69$

Sample n=30

To find : The confidence interval?

Solution :

We know, The confidence interval is in the format of

$\bar{x}-E$

E denotes the margin of error,

$E=\frac{U-L}{2}$

Where, U is the upper limit U=25.075

L is the lower limit L=23.305

$E=\frac{25.075-23.305}{2}$

$E=\frac{1.77}{2}$

$E=0.885$

Substitute the value of E and $\bar{x}$ in the formula,

$23.69-0.885$

$22.805$

Therefore, The confidence interval is $22.805$

8 0

3 years ago

Help me with geometry plzzzzzzzzzzzzzzzzzzzz

Natalija [7]

Answer:

x = 17

Step-by-step explanation:

A triangle's sum is 180 degrees, hence

6x + 10 + x + 17 + 4x - 34 = 180.

11x + 10 + 17 - 34 = 180

11x - 7 = 180

11x = 187

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3 0

2 years ago

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3 years ago

Find all solutions to

BARSIC [14]

Answer:

x= 0 , $\frac{1}{14}$ , $\frac{-1}{12}$

Step-by-step explanation:

Given, equation is $\sqrt[3]{15x-1}$ + $\sqrt[3]{13x+1}$ = $4\sqrt[3]{x}$ . →→→ (1)

Now, by cubing the equation on both sides, we get

( $\sqrt[3]{15x-1}$ + $\sqrt[3]{13x+1}$ )³ = ( $4\sqrt[3]{x}$ )³

⇒ (15x-1) + (13x+1) + 3× $\sqrt[3]{15x-1}$ × $\sqrt[3]{13x+1}$ ( $\sqrt[3]{15x-1}$ + $\sqrt[3]{13x+1}$ ) = 64 x.

⇒ 28x + 3× $\sqrt[3]{15x-1}$ × $\sqrt[3]{13x+1}$ ( $4\sqrt[3]{x}$ ) = 64x.

(since from (1), $\sqrt[3]{15x-1}$ + $\sqrt[3]{13x+1}$ = $4\sqrt[3]{x}$ )

⇒ 12× $\sqrt[3]{15x-1}$ × $\sqrt[3]{13x+1}$ ( $\sqrt[3]{x}$ )= 36x.

⇒ 3x = $\sqrt[3]{(15x-1)(13+1)(x)}$ .

Now, once again cubing on both sides, we get

(3x)³ = ( $\sqrt[3]{(15x-1)(13+1)(x)}$ )³.

⇒ 27x³ = (15x-1)(13x+1)(x).

⇒ 27x³ = 195x³ + 2x² - x

⇒ 168x³ + 2x² - x = 0

⇒ x(168x² + 2x -1) = 0

⇒ by, solving the equation we get ,

x = 0 ; x = $\frac{1}{14}$ ; x = $\frac{-1}{12}$

therefore, solution is x= 0 , $\frac{1}{14}$ , $\frac{-1}{12}$

7 0

3 years ago