help me, please......

Problem 1

Imagine placing the nonpencil part of your compass at the center of both hexagons. Extend the compass so the pencil reaches the right-most point on the larger hexagon. Then sweep a full 360 degrees to form a circle. This surrounds the larger hexagon to form what is called the circumcircle. The circumradius is 6+6 = 12 feet.

If we know the circumradius r = 12 and the number of sides n = 6, then we can find the area of the larger regular hexagon using this formula

[tex]A = 0.5n*r^2*\sin(360/n)[/tex]

Your calculator must be in degree mode. This formula only works for regular polygons.

Let's use that formula to calculate the area of the larger regular hexagon.

[tex]A = 0.5n*r^2*\sin(360/n)\\\\A = 0.5*6*12^2*\sin(360/6)\\\\A \approx 374.122974[/tex]

Then do the same for the smaller regular hexagon that has circumradius of r = 6 this time. We still have n = 6 sides.

[tex]A = 0.5n*r^2*\sin(360/n)\\\\A = 0.5*6*6^2*\sin(360/6)\\\\A \approx 93.530744[/tex]

Now subtract the areas

374.122974-93.530744 = 280.59223

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Problem 2

The formula we use here is

[tex]A = 0.25n*s^2*\cot(180/n)[/tex]

where

Let's use that formula to calculate the area of the larger regular pentagon. It has side lengths of s = 8

[tex]A = 0.25n*s^2*\cot(180/n)\\\\A = 0.25*5*8^2*\cot(180/5)\\\\A = 0.25*5*8^2*\cot(36)\\\\A = 0.25*5*8^2*\frac{1}{\tan(36)}\\\\A \approx 110.110554\\\\[/tex]

The larger regular pentagon has area of roughly 110.110554 square cm.

Repeat those steps for the smaller pentagon where each side is now s = 6. Keep n = 5 the same.

[tex]A = 0.25n*s^2*\cot(180/n)\\\\A = 0.25*5*6^2*\cot(180/5)\\\\A = 0.25*5*6^2*\cot(36)\\\\A = 0.25*5*6^2*\frac{1}{\tan(36)}\\\\A \approx 61.937186\\\\[/tex]

Now subtract the two areas to get the area of the shaded green region.

110.110554 - 61.937186 = 48.173368

Answer:

2

Step-by-step explanation:

Answer:

there are 144 students in total

Answer:25

Step-by-step explanation:

 f(x) = x² - 5x + 1f(-3) = (-3)² - 5(-3) + 1f(-3) = 25

Answer:

4

Step-by-step explanation:

callie and her 4 friends so you have to include callie which makes 5 people. 20/5 is 4 :)

Answer:

5 Each

Step-by-step explanation

There are 4 girls and they want to share so break the 20 in 5 4 times then u get 20 bck

Answer:

2%

Step-by-step explanation:

m = 100(.5)^(1/35) = 98       so   2 % is gone after 1 day

Answer:

X=Y since x and y are alternating angles

Step-by-step explanation:

2.

an isometry means the distance between any two points in the original space is the same as the distance between them in the second space.

rotation and translation are such isometries. they leave the original shape or curve unchanged in its inner structure but move it around.

so, the shapes in this question are visibly an isometry. the size and structure of the pre-image is the same as for the image. only its position changed.

4.

(x, y) -> (x-3, y+5) means that every point of the shape or curve is moved (translated) 3 units to the left (the x coordinate is decreased) and 5 units up (the y coordinate is increased).

6.

(x, y) -> (x+7, y-2) -> (x-3, y+2)

this means that first every point of the shape or curve is moved (translated) 7 units to the right and 2 units down, and then 3 units to the left and 2 units up.

in the end this means that every point moved 4 units to the right (no up or down changes, as the intermediate changes canceled each other out).

[tex]~~~~~2^{x+1} = 3^x\\\\\implies \ln \left(2^{x+1}\right) = \ln\left(3^x \right)\\\\\\\implies (x+1) \ln 2 = x \ln 3\\\\\\\implies \dfrac{x+1}x = \dfrac{\ln 3}{\ln 2}\\\\\\\implies 1+ \dfrac 1x = \dfrac{\ln 3}{\ln 2}\\\\\\\implies \dfrac 1x = \dfrac{\ln 3 }{ \ln 2}-1\\\\\\\implies \dfrac 1x = \dfrac{ \ln 3 - \ln 2}{\ln 2}\\\\\\\implies x = \dfrac{\ln 2}{\ln 3 - \ln 2}\\\\\\\implies x \approx 1.7095\\\\\\[/tex]

Answer:

Step-by-step explanation:

103.8 seconds

68.11024 inches

Answer:

Your number written in expanded form is:

0.8

+ 0.01

+ 0.007

Answer:

0.8

+ 0.01

+ 0.007

Step-by-step explanation:

I think

Answer:

(6, 5)

Step-by-step explanation:

Coordinates are written in the form (x, y), where x is the x-axis value that the point is in, in this case 6, and where y is the y-axis value, in this case 5.

Answer:

the answer would be (6,5)

Answer:

Around 31.4

Step-by-step explanation:

The circumference formula of a circle is C=2[tex]\pi[/tex]r. Plug the radius in which is 5. 5 times 2 is 10. 10 times pi would be around 31.4

The factorization of the given expression, 3x² - 10x + 8, is expressed completely as: (x - 2)(3x - 4).

Given the expression, 3x² - 10x + 8, to factorize, follow the steps below:

Find two factors that will give you -10 when you add them and also give you 24 when you multiply them. Let's use -6 and -4.

3x² - 6x - 4x + 8

(3x² - 6x) - (4x + 8)

3x(x - 2) - 4(x - 2)

(x - 2)(3x - 4)

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Answer:

2 and 3

Step-by-step explanation:

Answer:

Domain: All real numbers

Range: y≤5

Step-by-step explanation:

Domain: All real numbers (it can be all x values)

Range: y≤5  (the y values can be 5 or less.)

Answer:

......

Step-by-step explanation:

[tex] 5x = 95[/tex]

[tex] \displaystyle{ \frac{5x}{5} = \frac{95}{5} }[/tex]

[tex]x = 19[/tex]

Answer:

19

__________________________________________________________

Divide 95 by 5

[tex]\frac{95}{5} = 19[/tex]

Now we know that x is 19, solve the whole problem optionally.

[tex]5 * 19 = 95[/tex]

__________________________________________________________

Answer: Circle

Solve for area

A≈86.66in²

C Circumference

Using the formulas

A=πr2

C=2πr

Solving forA

A=C2

4π=332

4·π≈86.65987in²

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

These two angles are related by the supplement of corresponding angles. So they add to 180.

Equation

<1 + <2 = 180

2x + 4 + 8x - 14 = 180

Givens

<1 = 2x + 4

<2 = 8x - 14

Solution

<1 + <2 = 180                Substitute the givens into this equation

2x + 4 + 8x - 14 = 180  Combine like terms

2x + 8x + 4 - 14 = 180  

10x - 10 = 180               Add 10 to both sides

10x-10+10 = 180+10     Combine

10x = 190                      Divide by 10

10x/10 = 190/10

x = 19

Answer: x = 19

A function assigns the values. The translation of the function f(x) when it is moved 2 units up is (5ˣ+2).

A function assigns the value of each element of one set to the other specific element of another set.

Given the function, f(x)=5ˣ. Now, if the function is needed to be translated by 2 units, then +2 is needed to be added to the overall value of f(x). Therefore, the function will become,

f(x) = 5ˣ

f(x) = 5ˣ + 2

Hence, the translation of the function f(x) when it is moved 2 units up is (5ˣ+2).

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Answer:

Kings and hearts

Step-by-step explanation:

Two events are said to be mutually exclusive if they cannot occur at the same time:

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Reason:

For choice A, the LCD is 30 since

We get 30 from the fact that 5*6 = 30. Notice 2/3 and 1/6 already have the LCD of 6. We could rewrite the 2/3 into 4/6 to help show this better. Effectively we want to find the LCD of 4/6, 1/6, 1/5

Cross choice A off the list because we want an LCD of 45 instead of 30.

--------------------

Choice B is the answer because

What we can do is find the LCD of 2/3 and 1/9 to get 9. The 2/3 turns into 6/9. This means we need to find the LCD of 6/9, 1/9, and 1/15

Multiply the two unique denominators to get 9*15 = 135, then divide by the GCF 3 to get 135/3 = 45.

Recall that LCD(x,y) = (x*y)/GCF(x,y)

--------------------

We can stop here since we know choice B is the answer.

But if you wanted to continue, then the LCD of 2/3, 1/5 and 1/3 is 3*5 = 15. This rules out choice C.

Choice D can be ruled out because the LCD is 27*7 = 189.

Answer:

C , third choice

Step-by-step explanation:

SAS
Side AE Congruent to Side EC simple as that

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Answer:

45%

Step-by-step explanation:

216/480

216 ÷ 480

= 0.45

0.45 × 100

= 45%

Answer:

306 m

Step-by-step explanation:

distance between her house and the third point:

280 - 10 = 270 m

distance between the third point  and the beach:

164 - 20 = 144 m

We have a right triangle ,then we can apply the Pythagorean theorem:

[tex]\text{the distance between her house and the beach} =\sqrt{\left( 270\right)^{2} +\left( 144\right)^{2} } = 306\ m[/tex]