The area of sector A08 is 48x and m<AOB = 270º. Find the radius of circle O.


6 Acirde shown below.bas center C What is the area of the shaded region?​

The Area Of Sector A08 Is 48x And M&lt;AOB = 270. Find The Radius Of Circle O. 6 Acirde Shown Below.bas

Answers

Answer 1

Answer:

Step-by-step explanation:

The first one gives us everything we need except the radius, which is easy enough to solve for if you're careful with your algebra. The area of a sector of a circle is given as:

[tex]A_s=\frac{\theta}{360}*\pi r^2[/tex] where θ is the measure of the central angle of the circle. For us, that fills in as follows:

[tex]48\pi=\frac{270}{360}*\pi r^2[/tex] and manipulate it as follows:

[tex]r^2=\frac{(360)(48\pi)}{270\pi}[/tex] the π's cancel out, leaving us with simple multiplication and division to get

r = 8. Now for the next one, which is a bit more involved.

In order to find the area of the shaded part, we need to find the area of the right triangle there and subtract it from the area of the sector of the circle. First the area of the sector, which is given as:

[tex]A_s=\frac{\theta}{360}*\pi r^2[/tex] where θ again is the measure of the central angle of the circle, 90°:

[tex]A_s=\frac{90}{360}(3.1415)(10)^2[/tex] which simplifies a bit to

[tex]A_s=\frac{1}{4}(3.1415)(100)[/tex], giving us an area of

[tex]A_s=78.5375m^2[/tex]. Now onto the area of the triangle.

Since this triangle is inscribed in the circle and the circle's radius is 10, tha also gives us both the height and the base measures of the triangle. The area then is:

[tex]A_t=\frac{1}{2}(10)(10)[/tex] which is

[tex]A_t=50m^2[/tex]

Subtract that from the area of the sector to get that the shaded area is 28.5 square meters, choice A.


Related Questions

given an = -4 + (n - 1)7. what is arithmetic sequence

Answers

Answer:

Step-by-step explanation:

The given an = -4 + (n - 1)7 is already an arithmetic sequence with first term -4 and common difference 7.  A more proper form would be an = -4 + 7(n - 1).

The first five terms of this sequence are {-4, 3, 10, 17, 24}

Suppose $p$ and $q$ are inversely proportional. If $p=28$ when $q=7$, find the value of $p$ when $q=49$.

Answers

Answer:$p$ =$4 when $q=49$.

Step-by-step explanation:

If $p$ and $q$ are inversely proportional, then mathematically, they are represented as

$p$ ∝ 1/$q$

So that introducing the constant of proportionality,k becomes

$p$ =k 1/$q$

$p$ =k /$q$

When $p=28$ when $q=7$,K becomes

$p$ =k /$q$

$28=K/ $7

k=$28 x $7 =$196

Now when $q=49$.,  $p$ becomes?

$p$ =k /$q$

$p$ =$196/49$

$p$ =$4

please help am stuck on this

write the set of positive even numbers that Is less than 15 using both the notations

Answers

Answer:

Let the set be X.

X = {x ∈ N  : 2x < 15}

X = {2, 4 , 6 , 8 , 10, 12 , 14}

A certain type of bacteria is growing at an exponential rate that is modeled by the equation y=aekt, where t represents the number of hours. There are 100 bacteria initially, and 500 bacteria five hours later.

Answers

Answer:

meow meow

Step-by-step explanation:

Find the value of x when : 2^30/8^9=2^x
The line means divide
please i need step by stem explanation I already know answer

Answers

Answer:

x = -3

Step-by-step explanation:

Okay, the first thing to do is get that 8 away from the fraction. How can we do it? When you have 2³ you have 8, is the same thing, so let's do it:

2³⁰/(2³)⁹ = 2^x

When you have a number with the shape (a^x)^y, you can write it as a^(x•y), so:

(2³)⁹ = 2^3•9 = 2²⁷

Now we have:

2³⁰/2²⁷ = 2^x

When you have a division like this: (a^x)/(a^y), you can write it as a^(x-y), so:

2^(30-27) = 2^x

2^-3 = 2^x

Now you know that x = -3

determine the equation of the circle graphed below .
( help please )

Answers

Answer:

(x+5)²+(y+7)²=4

Step-by-step explanation:

just count it

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Answers

Answer:

17m-7

Step-by-step explanation:

product means multiplication so we multiply 17 times m.

17m

and 7 less than 17m is subtraction

17m-7

Answer:

17m-7

Step-by-step explanation:

m = The height

7 less than the product ( Multiply) 17 and m.

so 17m-7

HELP ME PLEASE
find the volume???

Answers

Answer:

5.24m

Step-by-step explanation:

volume of a cone = (1/3)πr²h

= (1/3)×(22/7)×1²×5

= 5.24m

The circumference of a circle is 32 centimeters. Find the radius of this circle.
a. about 201.06 cm c. about 5.09 cm
b. about 100.53 cm d. about 10.19 cm

Answers

Answer:

r≈5.09cm

Step-by-step explanation:

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franklin races bikes. in his city there are 4 lengths of race tracks. The chart shows the race tracks and each tracks length in miles
A. 1/4
B. 3/2
C. 1 3/4
D. 4/4

Franklin races 3 laps in the same lane. the total distance he raced is more than 4 1/2miles
which track does franklin race on?

Answers

Answer:

Step-by-step explanation:

1/4

PLEASE HELP
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Answers

Answer:

i think its A or C so im gonna say C if not im soooooooooooooooooo sorry <3

Step-by-step explanation:

PLS HELP IF YOU CAN!THIS IS DUE IN 30 MINUTES :(

A homeowner wants to fence in a rectangular yard space along one side of her house. The total area she can fence in is 800 square feet. Create a model to determine a possible length and width of the yard. *REMEMBER*: AREA = LENGTH times WIDTH.

Answers

Answer:

Length: 20 or 40 feet

Width: 40 or 20 feet

Step-by-step explanation:

Area = 800 = length*width = x*(60-x)= 60x - x^2

- x^2 + 60x - 800 = 0

x = 20

Or x = 40

So length can be either 20 feet or 40 feet and width can be 40 (60-20) or 20 (60-40)

PLEASE HELP!!!!
If the neighborhood holds 13 total games and all 50 athletes participate, how many 6-player games and how many 2-player games are played? Write and solve a system of equations .

Answers

Answer:

2 in a half 6 player games and 6 and half 2 player games. hope this helps

Step-by-step explanation:

There were 7 two-player games and 6 six-player games played

What are system of equation?

A collection of two or more equations that share the same variables is known as a system of equations. The values of the variables that make all of the equations in a system of equations true are the solution to the system of equations. A point of intersection on the graphs of the equations of a system is known as the solution. A system of equations' solution set is the collection of all possible answers.

Solution:

Given:

Total games = 13

Athletes participated = 50

let x denote the number of 2-player games played and

   y denotes the number of 6-player games played

Hence the equations we get are:

     x ₊ y = 13 ........eq(1)

     2x ₊ 6y = 50  this can be further reduced as

      x ₊ 3y = 25 ......eq(2)

Now, solving both the equations using elimination method then we get :

   ₋2y = ₋12

      y = 6

Here we can notice that x is eliminated.

Now substitute y value in eq(1) then we get x as 7.

Hence total 13 games were played out of which 7 two-player and 6 six-palyer games were played.

Learn more about "System of equations" here-

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A coach writes the batting order of his starting 9 out of the team of 20 on a piece of paper. How many different ways could the list be written?

Answers

Answer:

Total number of orders = 77,520

Step-by-step explanation:

Given:

Number of students on team = 20

Number of students on the starting line =9

Find:

Total number of orders

Computation:

Total number of orders = 20! / [20 - 7]!(7!)

Total number of orders = 20! / [13]!(7!)

Total number of orders = [20 x 19 x 18 x 17 x 16 x 15 x 14] / [7 x 6 x 5 x 4 x 3 x 2 x 1]

Total number of orders = 77,520

The number of different ways that the list can be written will be 167,960.

What are permutation and combination?

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

A coach writes the batting order of his starting 9 out of the team of 20 on a piece of paper.

The number of different ways that the list can be written will be

²⁰C₉ = 20! / [(20 - 9)! x 9!]

²⁰C₉ = 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11! / (11! x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

²⁰C₉ = 167,960

The number of different ways that the list can be written will be 167,960.

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need help with this Q&A 4

Answers

Answer:

y=4x + 3/4

Step-by-step explanation:

If t and m are positive, t^2 + m^2 = 64 and (t+m)^2 = 98, what is tm?

(A) 162
(B) 130
(C) 81
(D) 34
(E) 17

Answers

Answer:

17

Step-by-step explanation:

t^2 + m^2 = 64

(t+m)^2 = 98

(t+m)^2 = t^2 +2tm+ m^2

==>

t^2 +2tm+ m^2 = 98

t^2+m^2+2tm=98

64+ 2tm=98

2tm = 98 -64

2tm=34

tm= 34/2

tm = 17

Graph inequality y< -3/2x -6

Answers

Answer:

Hope this helps...have a nice day/night!!

Answer:

Step-by-step explanation:

You graph it

help help help help help help help

Answers

Answer:

D I believe

Step-by-step explanation:

I may not be correct, but i hope this helps!

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Answers

Answer:

x=58

Step-by-step explanation:

Answer:

x=26 degree

Step-by-step explanation:

x+106+48 =180 degree (sum of interior angles of a triangle is 180 degree)

x+154=180

x=180-154

x=26 degree

therefore the value of x is 26 degree.

1025 + 503 – 1412 – 7

Answers

Answer will be A :) Yw

pls help me ill give brainliest and no links ty!<3:)

Answers

T is the midpoint of PQ

PT=TQ

5x+7 = 7x-7

2x= 14

x= 14/2

x= 7

PT = 5(7)+7 = 42

Use the substitution method to solve the system of equations. Write your answer as an order pair. y=x-2 and y=-2x+7

Answers

x=3 ,y=1
i hope this helps

Answer:

The Coordinates are (3, 1)

Step-by-step explanation:

Use the substitution method to solve the system of equations.

Let y = x - 2 be Equation 1

Let y = -2x + 7 be Equation 2

We know that the coordinates are (3, 1) because we graphed the slope intercept equations in part one. Its asking to use the substitution method to prove that the coordinates (3, 1) are viable or satisfies both Equation 1 and 2.

The substitution method is nothing but substituting x and y back into the equation to prove that the coordinates are viable.

For this I'll use equation 1 first,

y = x - 2

1 = 3 - 2

So yes, the coordinates (3, 1) satisfy Equation 1

Lets check equation 2 now,

y = -2x + 7

1 = -2*3 + 7

1 = -6 + 7

This is also another equation where the coordinates (3, 1) satisfy equation 2

So this means that the coordinates (3, 1) are viable for both equations

Hope this helps!

Please give real answers with an explaination. 50 points + I will give the brainliest. No Docs/No Files/No Links only answer with explaination.

Answers

Answer:

x = 134

Step-by-step explanation:

Exterior angle = sum of opposite interior angles

                      = 90 + 44 = 134

OR

Sum of angles of triangle = 180

that is,

90 + 44 +y = 180

y = 180 - 134

 y = 46

x + y = 180                [ straight line angles ]

x + 46 = 180

x = 180 - 46 = 134

Answer:

x = 134

Step-by-step explanation:

triangle sum theorem states that the sum of all angles within a triangle is equal to 180 degrees. using this we can figure out that the missing angle in the triangle is 46.

a straight line is also equal to 180 degrees, so to find the adjacent angle, we subtract 46 from 180, and we get 134

expand and simplify pla

Answers

y = f(3f - 4g + 3) +7g(3f - 4g + 3)
= 3f^2 - 4fg + 3f + 21fg - 28g^2 + 21g
= 3f^2 + 3f + 17fg + 21g - 28g^2

Help,anyone can help me do quetion,I will mark brainlest.​

Answers

Answer:

Step-by-step explanation:

B3)  

z + 127 = 180   {linear pair}

z = 180 - 127

z = 53

y=  55    {Corresponding angles}

w + z + y =  180 {angle sum property of triangle}

w + 53 + 55 = 180

   w + 108 = 180

w = 180 -108

w = 72

x = w {Vertiaclly opposite angles}

x = 72

B4)  q +  101 = 180 {Linear pair}

               q = 180 -101

              q = 79

p = 142     {Corresponding angles}

p + s = 180        {linear pair}

142 + s = 180

        s = 180 - 142

        s = 38

s +q +r = 180          {angle sum property of triangle}

38 +  79 + r = 180

          117 + r = 180

                  r = 180 - 117

                  r = 63

y + 63 = 180 {linear pair}

y = 180 - 63

y = 117

x = q = {corresponding angles}

x = 79

A pole 11 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Jayden measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot. 11 ft 20 ft-8 ft​

Answers

Answer:

7 feet after applying the pythagorean theorem

Step-by-step explanation:

A researcher posts an online advertisement offering $25 in exchange for participation in a short study. The researcher accepts the first 10 people who respond to the advertisement. Which of the following statements is true about the sample? (1 point)

a
It is not a valid sample because it is only a short study.

b
It is a valid sample because money was offered to participants.

c
It is a valid sample because the first 10 people were selected to participate.

d
It is not a valid sample because it is not a random sample of the population.

Answers

Answer:

A

Step-by-step explanation:

The study only consisted of 10 people. 10 people are not enough to come to a concrete conclusion for a project. Hope this helps!!

Answer:

A) It is not a valid sample because it is only a short study.

A(n) _______ is part of a mathematical expression consisting of a constant, or a variable, or the product of a number and a variable, separated from other terms by an operator or a relation symbol.

Answers

Answer: Algebraic Expression *-* :)))))) Hope your day is well!!!

"Algebraic Expression" is part of a mathematical expression consisting of a constant, or a variable, or the product of a number and a variable, separated from other terms by an operator or a relation symbol.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; that can be used to indicate the logical syntax's order of operations and other features.

"Algebraic Expression" is part of a mathematical expression consisting of a constant, or a variable, or the product of a number and a variable, separated from other terms by an operator or a relation symbol.

To know more about an expression follow;

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Sofia earns $9 per hour mowing lawns. The total amount earned (t) equals the amouont earned per hour times the number of hours (h) . Which equation gives the total amount earned t if Lina works (h) hours ?

Answers

Answer:

9h

Step-by-step explanation:

Given data

Sofia earns $9 per hour mowing lawns

Let the total amount earned be t

and let the time worked be h

Hence

t= 9*h

t= 9h

The expression is 9h

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