Which expression represents the area of the shaded region?

Which Expression Represents The Area Of The Shaded Region?

Answers

Answer 1

Given:

A circle of radius r inscribed in a square.

To find:

The expression for the area of the shaded region.

Solution:

Area of a circle is:

[tex]A_1=\pi r^2[/tex]

Where, r is the radius of the circle.

Area of a square is:

[tex]Area=a^2[/tex]

Where, a is the side of the square.

A circle of radius r inscribed in a square. So, diameter of the circle is equal to the side of the square.

[tex]a=2a[/tex]

So, the area of the square is:

[tex]A_2=(2r)^2[/tex]

[tex]A_2=4r^2[/tex]

Now, the area of the shaded region is the difference between the area of the square and the area of the circle.

[tex]A=A_2-A_1[/tex]

[tex]A=4r^2-\pi r^2[/tex]

[tex]A=4r^2-\pi r^2[/tex]

[tex]A=r^2(4-\pi )[/tex]

Therefore, the correct option is (a).


Related Questions

There were two times as many pepperoni pizzas as cheese pizzas, plus one pizza they ordered 13 pizzas altogether how many pepperoni pizzas were there? How many cheese pizzas were there

Answers

Answer:

pepperoni pizzas = 8

cheese pizzas = 4

Step-by-step explanation:

let x = cheese pizza

2x + x + 1 = 13

3x = 13 -1

3x = 12

x = 4

pepperoni = 2x4 = 8

i light is faster then anything how did dark get there first

hello there enjoy 30 points on da house

Answers

Answer:

this just confused me so much

Step-by-step explanation:

ooooooooooooooooooo

Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!Plz Help!

Answers

Answer: n=4

Step-by-step explanation:

Given

3n-(2+n)=6

Expand Parenthesis (REMEMBER TO CHANGE SIGNS)

3n-2-n=6

Combine like terms

2n-2=6

Add 2 on both sides

2n-2+2=6+2

2n=8

Divide both sides by 2

2n/2=8/2

n=4

Hope this helps!! :)

Please let me know if you have any questions

Answer:

4

Step-by-step explanation:

4 Is the Answer because you have to multiply 4 to all the N's. Which means you have to multiply 4 by 3 which equals 12. Then 2+4=6. Then you would do 12-6=6. There's your answer. Here is the equation if it were like the problem: 12 - (2+4). I'm sure you can figure out the rest. Thanks. If you find any fault in my answer let me know! Have a good day!

Two angles are supplementary. The first angle is 3x degrees. The second angle is (2x + 25) degrees. Determine the measure of each angle.

Answers

Answer: a = 3x

b = 2x+25

180 = a + b

180 = 3x + 2x + 25

180 = 5x + 25

155 = 5x

x = 31

a = 3*31 = 93

b = 2*31 + 25 = 87

Step-by-step explanation: pls mark as branlyest

Which system of inequalities has this graph as its solution?
y 10
-10
- म
5
10
-10
OA. y < 21 - 3
y OB.y > 2 - 3
y> : +4
Ocy > 21 - 3
y < = + 4

Answers

Is this real math?!

Welp what is 103883+293883=? please helppp mah mum in city :')​

Answers

The answer is 397766 hope this helps

[tex]\huge{\mathbb{\tt { PROBLEM:}}}[/tex]

Help What is 103883+293883=?

[tex]\huge{\mathbb{\tt { ANSWER:}}}[/tex]

397766

[tex]{\boxed{\boxed{\tt { SOLUTION:}}}}[/tex]

[tex] \: \: \: 103883 \\ \frac{+293883}{ \: \: \: \: 397766} [/tex]

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

[tex]\huge{\mathbb{\tt { WHAT \: IS \: ADDITION \: ?}}}[/tex]

Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined

#CarryOnLearning

#JustEnjoyTheSummer

XxKim02xX

Can someone please help me with math

Answers

Answer:

A

Step-by-step explanation:

Hello There!

This is the formula for volume of a cylinder

[tex]V=\pi r^2h[/tex]

where r = radius and h = height

we are given the height and diameter height - 10 ft diameter - 22 ft

we are not give the radius directly but we can easily convert the diameter to the radius by dividing by 2

22/2=11 so the radius is 11

now having found the radius and height we plug in the values into the formula (note: it says leave answer in terms of pi so we will not apply pi to the final answer.)

[tex]V=\pi 11^210\\11^2=121\\121*10=1210\\V=1210\pi[/tex]

so we can conclude that the answer is A

it’s 82 :))))))))))))))))

Question in pic plz help! ~

Answers

Im gonna label the long side of a rectangle a and the smaller side b.

For the perimeter, 2a + 2b = 34

For the area, a x b = 66

if a is 11 and b is 6, the equation for perimeter would be 22 + 12 = 34.

So a = 11 and  b = 6

Answer:

Longer side = 11

Shorter side = 6

Step-by-step explanation:

L x W = 66,  then W = 66/L

2L + 2W = 34

substitute for W:

2L + 2(66/L) = 34

2L + 132/L = 34

multiply both sides of the equation by L:

2L² + 132 = 34L

divide both sides by 2:

L² + 66 = 17L

L² - 17L + 66 = 0

factor:

(L - 11)(L - 6) = 0

L = 11 or L = 6

if L = 11, then W = 6

if L = 6 then W = 11

Question is in picture

Answers

Answer:

27.5ft

Step-by-step explanation:

a² + b² = c²

Plug in what you have:

a² + 12² = 30²

Get a by itself:

a² = 30² - 12²

Simplify:

a² = 900 - 144

Simplify:

a² = 756

Simplify:

√a = √756

Then you get 27.49 and when you round you get 27.5

Write an equation in slope intercept form that represents the line shown?

Answers

Answer:

I think the answer would be Y=-2X+5

Hope it helps you *^*

What’s the opposite of -5/8

Answers

The opposite of -5/8 is 5/8.
It’s 5/8, |-5/8| = 5/8

How many solutions does the system of linear equations have? Use the drop-down menus to explain your answer.

y = 3/4x + 12
y = 4/3x
The system of linear equations will have
Choose...
no solution
exactly one solution
infanite many solutions
because the slopes of the equations are
Choose...
the same
different
, so the lines will
Choose...
not intersect at all
intercect at one point
both be the same line

Answers

Answer:

There is one equation, the slopes are different so they will intersect at one point

Step-by-step explanation:

At 5 am, the temperature was -10°F. By noon the temperature was 7°F, What Integer
represents the change in temperature from 5 am, to noon?

Answers

Answer:

The integer that represents the change in temperature is 17.

Step-by-step explanation:

HELP PLEASE

Marcus works at the grocery store. He earns 8.75 per hour. Last week he worked 6.5 hours. How much did Marcus make last week?

Answers

20 dollars bev b h h b g v v v v.

It cost Erica $9.75 for the ingredients to make 30 cupcakes. She sold them for $1.00 each. What was Erica’s total profit?

Can i please get some help, I NEED A STEP BY STEP TO FULLY UNDERSTAND THE QUESTION AND YOUR ANSWER

Answers

Answer: $20.25

Step-by-step explanation:

If each cupcake is sold for $1, then all the cupcakes are sold together for $30. Now subtract 9.75 from 30 and you get 20.25.

Hope this helps :)

Can somebody help me

Answers

Answer:

25

Step-by-step explanation:

If it has 25 miles across from the 1 hour it means that it goes 25 miles per hour.

PLEASE HELP ME PUT THEM IN ORDER

Answers

Answer

picture below of order. Not entirely

Step-by-step explanation:

Peterkin park has a square fountain with a walkway aroind it. The fountain measures 12 feet on each side. The walkway is 3 1/2 feet wide.Find the area of the walkway

Answers

Answer: 829.44 ft²

Step-by-step explanation:

Correction - The walkway is 31.2 feet wide.

To solve this, first find the area of the fountain:

Area of a square = Length * Width

= 12 * 12

= 144 ft²

The find the area of the walkway including the fountain:

= 31.2 * 31.2

= ‭973.44‬ ft²

To find the area of the walkway alone, subtract the area of the square from the area of the rectangle:

= 973.44 - 144

= 829.44 ft²

can somebody help me please

Answers

Answer:

B

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² = 4² + ([tex]\sqrt{5}[/tex] )² = 16 + 5 = 21 ( take the square root of both sides )

x = [tex]\sqrt{21}[/tex] → B

Alicia would like to know if there is a difference in the average price between two brands of shoes. She selected and analyzed a random sample of 40 different types of Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the boxplot of the sample of Brand A shoe prices shows two outliers. Alicia wants to construct a confidence interval to estimate the difference in population means.

Answers

This question is incomplete, the complete question is;

Alicia would like to know if there is a difference in the average price between two brands of shoes. She selected and analyzed a random sample of 40 different types of Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the boxplot of the sample of Brand A shoe prices shows two outliers. Alicia wants to construct a confidence interval to estimate the difference in population means.

Is the sampling distribution of the difference in sample means approximately normal?

a) Yes, because Alicia selected a random sample

b) Yes, because for each brand it is reasonable to assume that the population size is greater than ten times its sample size.

c) Yes, because the size of each sample is at least 30

d) No, because the distribution of Brand A shoes has outliers

e) No, because the shape of the population distribution is unknown.

Answer:

the sampling distribution of  the difference in sample means is approximately normal because the size of each sample is al least 30

Option (c) Yes, because the size of each sample is at least 30 ) is the correct answer.

Step-by-step explanation:

Given the data in the question;

sample size of brand A shoes [tex]n_A[/tex] = 40

sample size of brand B shoes [tex]n_B[/tex] = 33

As we can notice,

[tex]n_A[/tex] = 40 > 30

[tex]n_B[/tex] = 33 > 30

Hence, we consider both samples to be large.

Therefore, the sampling distribution of  the difference in sample means is approximately normal because the size of each sample is al least 30.

Option (c) Yes, because the size of each sample is at least 30 ) is the correct answer.

what is the distance between (3,-5), (-3,0)

Answers

Answer: 11 units

Step-by-step explanation:

-3 and 3 are 6 units apart, so that would be 6 units, and when you add the -5 into the problem, the 6 units become 11 units. Hope this helped :)

Answer:

Exact Form:

√ 61

Decimal Form:

7.81024967 …

4. Which ordered pair best represents a point
on Tia's route to the store?
F .(-5, 6)
G. (-2.5, 0)
H. (-2,5)
J. (-3.5, -3)

Answers

The third one i believe

Answer:

G. (-2.5, 0)

Step-by-step explanation:

Starting from the origin, (0, 0), go 2.5 units to the left (because it's negative) on the x-axis, and then 0 units on the y-axis. You end up on (-2.5,0).

hope this helped :)

Help please :) (asap)

Answers

x^2 - x - 6= 0

(x - 3) ( x + 2) = 0

Equating

x - 3 = 0

x = 3

x+ 2= 0

x = -2

Answer: x - 6

Step-by-step explanation:

Please help me finish this i will give brainlest :) to the first person.

Answers

Answer: 8

Step-by-step explanation:

64 ÷[4* 27 (-5^2

-5 times -5 =25

27-25=2

4*2=8

64 divided by 8= 8

8 is your answer

Jamar to the local snack shop near his school He bought 3 hotdogs and 2 bags of chips for $Kenny went to the same snack shop and bought 5 hotdogs and 6 bags of chips for $9.55 ordered 2 hotdogs and 3 bags of chips, then how much did she pay her order?

Answers

Answer:

Marcy paid $4.15

Step-by-step explanation:

Given

Represent hotdogs with x and chips with y.

So, we have:

Jamal

[tex]3x + 2y = 4.85[/tex]

Kenny

[tex]5x + 6y = 9.55[/tex]

See attachment for complete question

Required

Determine the amount for 2x and 3y

From Jamal's and Kenny's orders we have:

[tex]3x + 2y = 4.85[/tex] --- (1)

[tex]5x + 6y = 9.55[/tex] --- (2)

Multiply (1) by 3

[tex]3 * [3x + 2y = 4.85][/tex]

[tex]9x + 6y = 14.55[/tex] --- (3)

Subtract (2) and (3)

[tex]9x - 5x + 6y - 6y = 14.55 - 9.55[/tex]

[tex]9x - 5x = 5[/tex]

[tex]4x = 5[/tex]

Solve for x

[tex]x = \frac{5}{4}[/tex]

[tex]x = 1.25[/tex]

Substitute [tex]x = 1.25[/tex] in [tex]3x + 2y = 4.85[/tex]

[tex]3 * 1.25 + 2y = 4.85[/tex]

[tex]3.75 + 2y = 4.85[/tex]

Solve for y

[tex]y = \frac{4.85 - 3.75}{2}[/tex]

[tex]y = \frac{1.10}{2}[/tex]

[tex]y = 0.55[/tex]

So, the cost of 2x and 3y is:

[tex]Cost = 2x + 3y[/tex]

[tex]Cost = 2*1.25 + 3*0.55[/tex]

[tex]Cost = \$4.15[/tex]

Help me please!!!!!!!!!!!

Answers

Answer:

A reflection over the y-axis.

If an item is on sale for 60% off, that means you actually PAY _____% of the price.

Answers

Answer:

40%

Step-by-step explanation:

100-60=40

Find the value of x in the picture below. (round to nearest tenth if needed) THANK YOU FOR HELPING ME:)

Answers

Answer:

x ≈ 9.6

Step-by-step explanation:

Using Pythagoras' identity in the right triangle, that is

x² + 14² = 17²

x² + 196 = 289 ( subtract 196 from both sides )

x² = 93 ( take the square root of both sides )

x = [tex]\sqrt{93}[/tex] ≈ 9.6 (to the nearest tenth )

The simple interest on birr 400 invested for 4 months was birr 12, what is the annual (yearly) rate of interest?

Answers

Answer:

9%

Step-by-step explanation:

Given :

Principal, P = 400

Time, t = 4 months = 4/12 = 0.33333

Simple interest = 12

Simple interest = (principal * rate * time)

Rate = r

12 = (400 * r * 0.33333)

12 = 133.3333r

r = 12 / 133.3333

r = 0.090000

r = 0.09

rate = 0.09 * 100% = 9%

can someone tell me the answer to this

Answers

Answer: W=12m

Step-by-step explanation:

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