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Given a circle with a central angle of 80° and a radius of 27 cm, determine which of the following statements are true. Select all that apply!

A. The area of the sector is 81 π


B. The area of the circle is 729 π


C. The circumference of the circle is 27 π


D. The arc length of the sector is 12π

Answers

Answer 1

Answer:

[tex]\checkmark \text{B. The area of the circle is } 729\pi,\\\checkmark \text{D. The arc length of the sector is } 12\pi[/tex]

Step-by-step explanation:

Area of a circle with radius [tex]r[/tex]: [tex]r^2\pi[/tex]

Circumference of a sector with radius [tex]r[/tex]: [tex]2r\pi[/tex]

Area of sector with angle [tex]\theta[/tex]:  [tex]r^2\pi\cdot \frac{\theta}{360}[/tex].

Arc length of sector with angle [tex]\theta[/tex]: [tex]2r\pi\cdot \frac{\theta}{360}[/tex]

Using these equations, we get the following information:

Area of circle: [tex]27^2\pi=729\pi[/tex]

Circumference of a circle: [tex]2\cdot 27\cdot \pi=54\pi[/tex]

Area of sector: [tex]27^2\pi\cdot \frac{80}{360}=162\pi[/tex]

Arc length of sector: [tex]2\cdot 27\cdot \pi \cdot \frac{80}{360}=12\pi[/tex]


Related Questions

- True or False: When you multiply fractions, you need common denominators.
True
False

Answers

Answer: true

Step-by-step explanation:

Answer:

Multiplication of fractions do not require the same denominator, or the bottom number of the fraction, like addition and subtraction does. Instead, you would simply multiply the denominators and the top numerators.

Determine algebraically the equation of the line passing through the points (0, -5) and (4, -9)

Answers

Answer:

y = -1x -5

Step-by-step explanation:

y2 - y1 / x2 - x1

-9 - (-5) / 4 - 0

-4 / 4

-1

y = -1x + b

-5 = -1(0) + b

-5 = 0 + b

b = -5

y = -1x -5

Rewrite the expression in the form y^n​

Answers

Step-by-step explanation:

y^3/4×y^1/3y(3/4+1/3)y^2/3

stay safe healthy and happy.

Answer:

y^13/12 or y^1 1/12

Step-by-step explanation:

Convert the fractions to compatible bases. In this case, you can multiply the 3/4 by 3 making it 9/12, and multiply the 1/3 by 4 making it 4/12. If you add these now compatible fractions, you get 13/12. The base remains the same, I hope this helps!

-3
Which expression is equivalent to
21n^-3m^5/3p^-5?

Answers

Answer:

IM NOT SURE WHAT

Step-by-step explanation:

HELLPPPP MEEE NEEDD HELP ¶∆¶

Find the RATIO and the EXACT VALUE of the given Cos B.​

Answers

Answer:   5/13

=================================

Work Shown:

cos(angle) = adjacent/hypotenuse

cos(B) = BC/AB

cos(B) = 5/13

A circle has an arc with a measure of 120 degrees and a lenght of 3π cm. What is the diameter of the circle

Answers

Answer:

9 cm

Step-by-step explanation:

Arc length = θ/360 × 2πr

A circle has an arc with a measure of 120 degrees and a lenght of 3π cm. What is the diameter of the circle

Hence,

3π = 120/360 × 2πr

Diameter = 2r

3π = 1/3 × 2πr

Cross Multiply

9π = 2πr

2r = 9π/π

Note that :

Diameter = 2r

Hence,

Diameter = 9 cm

FIND ANGLE ADB
the number is 116 on top

Answers

Answer:

[tex]m\angle ADB=58^{\circ}[/tex]

Step-by-step explanation:

For an angle with a point on the circle, the measure of that angle is equal to half the measure of the arc it forms. Since angle ADB forms an arc AB that measures [tex]116^{\circ}[/tex], the measure of angle ADB equals [tex]\frac{116}{2}=\boxed{58^{\circ}}[/tex]

Step-by-step explanation:

ADB=116/2(inscribed angle is half of it's arc)

58°

stay safe healthy and happy...

What's the surface area for all these??

Answers

Answer:

the surface area of the square is "378"

Step-by-step explanation:

2×(9×9 + 9×6 + 9×6) = 378

the figure below. help me please ​

Answers

It’s C, i just did it and i got 90% of them right. It’s C.
Part b it is c the 592pi cm3

The young mathematician is presented with this problem: (13 + 7) x (5 - 3) / 4 x (1 + 1) = Which operation would the young mathematician do first?

The division
The subtraction
Those inside parentheses
The multiplication

Answers

Those inside the parentheses. Rember pemdas or Parentheses Exponets Multiple Divide Add Subtract in that order from left to right

Find surface area of right cone with diameter of 12 meters and a slant height of 9 meters

Answers

C ^^^ !!!!!! aahhahahahahhahahahaha

Find the probability of drawing either a Queen or a Heart from a standard deck of cards.
A) 0
B)17/52
C) 1/4
D)4/13

Answers

Answer:

17/52 (Answer B)

Step-by-step explanation:

There are four queens and 13 hearts.  The probability of drawing a Queen is thus 4/52 (= 1/13); that of drawing a Heart is 13/52 (= 1/4).  

The probability of drawing either is 1/13 + 1/4, or 4/52 + 13/52, or 17/52 (Answer B)

Which one is equivalent? Ez points

Answers

Answer: B: -4 by -4 by -4

Step-by-step explanation: When a number is to be used with a negative exponent, the number is to be multiplied by however many times the number says to multiply it, and whether the exponent is positive or negative determines the numbers being multiplied, whether they should be negative or positive. (Sorry, I'm not good at wording this, I'll provide an example below.);

4^-3 means that you multiply four three times, but the exponent is also negative, so it would make each of the base numbers negative.

-4 by -4 by -4

The volume of a sphere of radius 3 cm is
(A)
9x cm
(B)
18.t cm
(C)
27 cm
(D)
36 cm

Answers

Answer:

3^3 = 27

27 * 3.14 = 84.78

84.78 * 4/3 = 113.04 is your answer.

Formula of volume of sphere is:

4/3 x π(3.14 or 22/7 whatever they tell you to use for pi) x r^3(your radius being cubed)

You get your radius by finding out what is half of your diameter or your given radius.


what is the result?? Show explanation.

A. 4⁵
B. 4¹
C. 4-¹
D. 4-⁵​

Answers

Answer:

4^-5

Step-by-step explanation:

4^-3 = 1/4^3

1/4^3 · 1/^2 = 1/4^5 which is the same as 4^-5

Mhmhmhmhmhmhmhmhmhmhmhmhmhmhmhmhmhmhmhhm that would be D

Evaluate √ 20.

A: 4. 47
B: 4
C: 5
D: 10

Answers

Answer:

It would be A. 4.47

Look at the picture!

Answers

Answer:

6 3/8 pounds (also 6.375 pounds)

Step-by-step explanation:

2 2/3 + 1 5/6 + 1 7/8 = x

8/3 + 11/6 + 15/8 = x

(multiply each fraction by to create the denominator 24)

8/3 x 8/8 = 64/24

11/6 x 4/4 = 44/24

15/8 x 3/3 = 45/24

64/24 + 44/24 = 108/24

108/24 + 45/24 = 153/24

153/24 = 6.375 = 6 3/8

Give the other person brainliest!


They answered one of my questions before

what is oral traditions? don’t copy word to word from the internet

Answers

Answer:

, hope u understand and happy

Answer:

Oral traditions are things that have been passed down from generations, such as folktales, pieces of art, stories, and more

Step-by-step explanation:

Plz help me i am stuck

Answers

Given:

The two statements.

To find:

The probability of an impossible event.

The probability of a certain event.

Solution:

Formula for probability is:

[tex]P=\dfrac{\text{Possible favorable outcomes}}{\text{Total number of outcomes}}[/tex]

For an impossible event, the possible favorable outcomes is 0. So,

[tex]P=\dfrac{0}{\text{Total number of outcomes}}[/tex]

[tex]P=0[/tex]

For a certain event (sure event), the possible favorable outcomes is equal to total number of outcomes. So,

[tex]P=\dfrac{\text{Total number of outcomes}}{\text{Total number of outcomes}}[/tex]

[tex]P=1[/tex]

Therefore, an event that is impossible has probability 0 and an event that is certain has probability 1.

5b^2+39b=8 please solve and explain why

Answers

Step-by-step explanation:

5b²+39b=8

<=> 5b²+39b-8=0

(5b-1)(b+8)=0

b = ¹/5 or b = -8

b=-8 and b=1/5.

Answer:

Solution given:

5b²+39b=8

5b²+39b-8=0

try to do middle term factorization.

it needs 40 while multiplication and 39 when subtraction.

it is 40-1 and 40*1

now

doing middle term factorization

5b²+(40-1)b-8=0

5b²+40-b-8=0

take common from each 2 term

5b(b+8)-1(b+8)=0

again take common and keep remaining in another brackets

(b+8)(5b-1)=0

either

b=-8

or

b=1/5

A cone has a height of 10 millimeters and a radius of 6 millimeters. What is its volume? Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

Answers

Answer:[tex]376.80\ mm^3[/tex]

Step-by-step explanation:

Given

The height of the cone is [tex]h=10\ mm[/tex]

The radius of the cone is [tex]r=6\ mm[/tex]

Volume of cone is given by

[tex]V=\dfrac{1}{3}\pi r^2h[/tex]

Insert the values

[tex]\Rightarrow V=\dfrac{1}{3}\times 3.14\times 6^2\times 10\\\\\Rightarrow V=376.80\ mm^3[/tex]

Thus, the volume of the cone is [tex]376.80\ mm^3[/tex]

please help i keep getting the wrong answers

Answers

Answer:

10 inches

Step-by-step explanation:

Surface Area = π R² + π R L [ L is Slant Height ]

200 π = π (10)² + π (10) L

200 π = π (100) + π (10) L

200 π - 100 π = 10 π L

100 π = 10 π L

100 π / 10 π = L

10 = L

L = 10 inches

Hope this Helps......

[tex]\huge{ \mathrm{  \underline{ Answer} \:  \:  ✓ }}[/tex]

Given terms :

Surface area (a) = 200 π

radius = 10 inches

Now, we know

[tex] \large\boxed{\mathrm{surface \: \: area = \: \pi r(l + r) }}[/tex]

[tex]200\pi = \pi \times 10 \times (10 + l)[/tex]

[tex] \dfrac{200\pi}{10\pi} = 10 + l[/tex]

[tex]20 = 10 + l[/tex]

[tex]l = 10 \: in[/tex]

(note : " l " represents slant height.)

Therefore, Measure of slant height (l) :

[tex] \huge \boxed{10 \: \: in \: }[/tex]

_____________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

What is the value of 8?

Answers

Answer:

40320

Step-by-step explanation:

8! is equal to 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 , which equal 40320

Answer:

40320

Step-by-step explanation:

An exclamation point denotes a factorial, so multiply all the numbers less than or equal to  8  until you get to  1

[tex]8*7*6*5*4*3*2*1=40320[/tex]

whats this shape help I'm struggling

Answers

Answer: It is a rectangle.

Step-by-step explanation: 2 rectangles of different sizes are being in top of each other.

What is the area in square centimeters of the triangle below?

Answers

Answer:

45cm2

Step-by-step explanation:

10x7(base x height)=70

70/2=45

please answer these questions. only use the power of one to solve it. if u answer it right il give brainlest and ill make another question which u can get 50 points for free. pls answer no links or random answers.

Answers

Answer:

9a) 6 1/5

b) 6 4/7

c) 1 1/0

d) 4 1/8

e) 1 1/3

f) 3 1/6

10a) 15 years old

b) 14 1/6 years old

11) 8/3 = 2 2/3

7/5 = 1 2/5

2 2/3 + 1 2/5 = 4 1/15

12a) They ate 3 11/12 pizzas

b) They ate 1 1/3 more cheese pizzas than veg

if 20 men can finish a piece of work in 30 days how many additional numbers of mains will be employed to finish the work in 24 days​

Answers

Answer:

Step-by-step explanation:

no of days                                                   no of men

30                                                                         20

24                                                                             20

30/24=x/20

24 x=30*20

24x=600

x=600/24

x=25

therefore  5 more men are needed to complete the work in 24 days                

WILL MARK BRAINLIEST!!!
Jamie is going on a trip to visit her grandparents. The airline allows each suitcase to hold 50 pounds. She has already packed clothes and other things that weigh a total of 26 pounds. The inequality p + 26 ≤ 50 can be used to see how much more she can pack in the suitcase.

Why is this problem written as an inequality instead of an equation?

Answers

Answer:

Because the airline allows each suitcase to hold up to 50 pounds, and it doesn't force them to hold exactly 50 pounds

Answer:

Step-by-step explanation:

b/c she doesn't have to have exactly 50 pounds,  she can have any were from 0 to 50 pounds  in each suit case.   They are not going to charge her more, if she only brings 49 pounds :DDDD  It's the same charge up to and including 50 pounds.  If she brings 51 pounds then maybe she would get charged more :P    But not for 50 pounds or less .  :)  Make sense?

which inequality is graphed in blue

Answers

The inequality graphed in blue is y<-3x-2

Trigonometry help please! Show work thank you !

Answers

Answer:

Step-by-step explanation:

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