An arc of a circle of radius 7cm subtends an eagle of 120degree at the centre. Find its perimeter.

Answers

Answer 1

Answer:

[tex]\dfrac{14\pi }{3}\ cm[/tex]

Step-by-step explanation:

The circumference of the circle with radius of 7 cm is

[tex]C=2\pi r\\ \\C=2\pi \cdot 7=14\pi \ cm[/tex]

An arc of a circle o subtends an angle of [tex]120^{\circ}[/tex] at the centre.

The circle has the full angle of [tex]360^{\circ},[/tex] then

[tex]14\pi \ cm - 360^{\circ}\\ \\x\ cm - 120^{\circ}[/tex]

Write a proportion:

[tex]\dfrac{14\pi }{x}=\dfrac{360}{120}\\ \\\dfrac{14\pi }{x}=\dfrac{3}{1}\\ \\14\pi =3x\\ \\x=\dfrac{14\pi }{3}\ cm[/tex]


Related Questions


m×n, when m=13 and n=12

Answers

Answer:

156

Step-by-step explanation:

13 × 12

13

×

12

=

26

130

=

156

Answer:

Step-by-step explanation:

m*n

m=13

n=12

13 * 12

156

Translate the sentence into an inequality.
The product of b and 6 is less than - 16.

Answers

Final answer:

The sentence 'The product of b and 6 is less than -16' translates to the inequality '6b < -16' in Mathematics.

Explanation:

In mathematics, translating a sentence into an inequality involves identifying the mathematical symbols and operations represented by the words in the sentence. In this case, 'the product of b and 6' translates to '6 * b' and 'is less than' translates to '<'. So, the sentence 'The product of b and 6 is less than -16' translates to the inequality '6 * b < -16' or '6b < -16' in simplified form.

Learn more about Inequalities here:

https://brainly.com/question/32625151

#SPJ3

The measure of angle 1 is 30 degrees less than twice the measure of angle 2. What is the measure of angle 1. What is the measure of angle 2

Answers

Answer:

110°

Step-by-step explanation:

the supplement of an angle is 30 degrees less than twice the measure of the angle itself. find the angle and its supplement.

Let the angle be A, then its supplement = (180 - A)

Now, since the supplement is 30 degrees less than twice the measure of the angle itself, then we'll have:

 

180 - A = 2A - 30

-3A = - 210

A, or the angle = [tex]\frac{-210}{-3}[/tex]= 70 °

Its supplement, (180 - A) = 180 - 70 = 110°

use the net to compute the surface area of three dimensional figure.​

Answers

Option C:

Surface area of the three dimensional figure is 166 unit².

Solution:

Let us find the area of the net of the figure.

Length = 7, Width = 5, Height = 4

Area of the bottom = length × width

                                = 7 × 5

                                = 35 unit²

Area of the Top =  length × width

                          = 7 × 5

                          = 35 unit²

Area of the left = width × height

                         = 5 × 4

                         = 20 unit²

Area of the right = width × height

                         = 5 × 4

                         = 20 unit²

Area of the front = length × height

                            = 7 × 4

                            = 28 unit²

Area of the back = length × height

                            = 7 × 4

                            = 28 unit²

Surface area = 35 + 35 + 20 + 20 + 28 + 28

                     = 166 unit²

Surface area of the three dimensional figure is 166 unit².

what does x equal in the function: f(-11)=5x+1

Answers

Final answer:

In the equation f(-11)=5x+1, solving for x yields x = -2.4.

Explanation:

To find what x equals in the function f(-11)=5x+1, we start by understanding that the function f(x) identifies the relation between x and f(x). In this case, f(-11) has been given the value of 5x+1. Therefore, we solve for x by setting the expression equal to f(-11).

We have the equation 5x + 1 = f(-11). Since f(-11) is given as a constant, we substitute and solve for x:

5x = -12

x = -2.4

Hence, x equals -2.4 in the function f(-11)=5x+1.

solve y= 2/3x +7 and 3y= 2x -3

Answers

Answer:

The system has no solution

Step-by-step explanation:

we have

[tex]y=\frac{2}{3}x+7[/tex] ----> equation A

[tex]3y=2x-3[/tex]

Isolate the variable y

Divide by 3 both sides

[tex]y=\frac{2}{3}x-1[/tex] ------> equation B

Compare equation A and equation B

Both lines have the same slope and different y-intercept

so

Line A and Line B are parallel lines

The lines do not intersect

therefore

The system has no solution, because both lines are parallel

see the attached figure to better understand the problem

Collin has $500 in his bank account. He starts saving $30.00 per week. Kamryn
has $750 in her bank account, and she is saving $20.00 per week. Assume
neither Collin nor Kamryn make any withdrawals.
After how many weeks will. Collin and Kamryn have the same amount of
money in their accounts?​

Answers

Answer:

x = 25

Step-by-step explanation:

You would need to start by creating an equation.  X would represent the numbers of weeks.

500 + 30x = 750 + 20x

Now get the numbers on one side.  To do this subtract 500 form each side.

30x = 250 + 20x

Next, get the variables to one side.  This can be done by subtracting 20x from each side.

10x = 250

Finally divide by 10 to get the variable by its self.

x = 25

Hope this helps.

After 25 weeks, Collin and Kamryn have the same amount of

money in their accounts.

What is linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the after x weeks, Collin and Kamryn have the same amount of money in their accounts:

Then we can frame a linear equation as per the problem:

Collin's amount of money  = 500 + 30x

Kamryn amount of money = 750 + 20x

500 + 30x = 750 + 20x

10x = 250

x = 25

Thus, after 25 weeks Collin and Kamryn have the same amount of

money in their accounts.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ2

Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. What is the solution?

Answers

Answer:

Marcos had 6 nickel coins and 9 quarter coins.

Step-by-step explanation:

We are given the following in the question:

Let x be the number of nickel coins and y be the number of quarter coins.

Marcos had 15 coins in nickels and quarters.

Thus, we can write the equation:

[tex]x + y =15[/tex]

He had 3 more quarters than nickels. We can write he equation,

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

Solving the two equations, we get,

[tex]2y = 18\\y = 9\\x + 9 = 15\\x = 6[/tex]

Thus, Marcos had 6 nickel coins and 9 quarter coins.

Final answer:

The solution to the system of equations representing Marcos's coins is x = 6 and y = 9. Hence, Marcos had 6 nickels and 9 quarters.

Explanation:

This question pertains to creating and solving a system of equations in mathematics. Given Marcos had 15 coins in nickels and quarters and considering the information that he had 3 more quarters than nickels, two equations can be formed from this. The first equation sets up the total number of coins: x + y = 15. The second equation sets ups the difference in quantity of each coin: y = x + 3.

To find the solution, substitute the second equation in for y in the first equation. This gives: x + (x + 3) = 15. Solve the equation and find x = 6. Furthermore, using x in our second equation, we get y = 6 + 3 = 9. Therefore, Marcos had 6 nickels and 9 quarters.

Learn more about System of Equations here:

https://brainly.com/question/35467992

#SPJ3

2x + 3 for x = 3

evaluate each expression for the given value of x

Answers

Answer: 9

Step-by-step explanation:

2x + 3 when x = 3

2(3) + 3

2 * 3 = 6

6 + 3 = 9

Final answer:

To evaluate the mathematical expression 2x + 3 for x = 3, substitute x = 3 into the equation to get 2(3) + 3 = 6 + 3, and then add the numbers to get 9.

Explanation:

To evaluate the expression 2x + 3 for x = 3, you would replace x with 3 in the expression, then follow the order of operations (PEMDAS/BODMAS) to solve the expression.

Here is the step-by-step breakdown:

Substitute x = 3 into the expression, this makes the expression: 2(3) + 3 = 6 + 3 Then, you add the numbers together to get: 9

So, when x = 3, the value of the expression 2x + 3 is 9.

Learn more about Substitution in Expressions here:

https://brainly.com/question/31279690

#SPJ2

solve 1/8 + 6a/5 = 3/8 + 2a/5 + 7/8

Answers

Answer:

no6666//7

Step-by-step explanation:

88../6

11/4 + 2 1/8 = solve this?

Answers

Answer:

4.875

Step-by-step explanation:

4.875 is the sum of 11/4 + 2 1/8.

If 5(3x-5) = 20, then
what is 6x -8?

Answers

Answer:

10

Step-by-step explanation:

5(3x-5)=20

3x-5=20/5

3x-5=4

3x=4+5

3x=9

x=9/3

x=3

6x-8=6(3)-8=18-8=10

Find an equation for the line with the given properties.

Parallel to the line x = -5; containing the point (6, 2)

Answers

Y-Y=m(X-X)
Y-2=-5(X-6)
Y-2=-5x+30
Y=-5x+32

Raymond has a set of 57 toy cars and decides to sell 19 of them to Joey. About how many toy cars does Raymond have left

Answers

Answer:

raymond has about 38 cars left

Step-by-step explanation:

Because raymond started off with 57 cars and he got rid of( take away) 19 you must use subtraction. 57 - 19 =38

help me plz!!!!!!!!!!!!!!!​

Answers

Answer: for the third one you use x= 55

so angle = 110

for the fourth one x= 102

angle = 100

Step-by-step explanation:

A triangle has sides with lengths of 58 feet, 62 feet, and 84 feet. Is it a right triangle

Answers

Answer:

NO

Step-by-step explanation:

84*84=7056

62*62= 3844

58*58=3364

3844+3364=7208

7208 is not equal to 7056

Ben’s living room is a rectangle measuring 10 yards x 168” by how many feet does the legs of the room exceed the width

Answers

Answer:

16 feet.

Step-by-step explanation:

Given:

Ben’s living room is a rectangle measuring 10 yards x 168.

Question asked:

How many feet does the legs of the room exceed the width ?

Solution:

By applying unitary method:

Length of rectangle = 10 yards = 30 feet (1 yard = 3 feet)

                                                                    (10 yard = [tex]3\times10 = 30)[/tex]

Breadth of  rectangle = 168 inch = 14 feet   (12 inch = 1 feet)

                                                                       (1 inch = [tex]\frac{1}{12}[/tex])

                                                                       ( 168 inch = [tex]\frac{1}{12}[/tex][tex]\times168 = 14 feet)[/tex]

By subtracting the breadth from the length of rectangle,

30 feet - 14 feet = 16 feet

Therefore,  by 16 feet, length of the room exceed the width.

A cabin has a room for 7 campers and 2 counselors. How many cabins are needed for a total of 49 campers and 14 counselors?

Answers

Answer:

7 cabins

Step-by-step explanation:

So with division, we can find out

49 campers / 7 per cabin = 7

14 counselors / 2 per cabin = 7

As we can see, both problems equal 7, which lets us see that the camp needs 7 cabins to hold all the campers and counselors

HELP ASAP PLEASE HELP ME

Answers

Answer:

She is not correct

x = -9

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180° therefore if you add all three angles in this triangle it must add up to 180°

50 - 5x + 5 - 4x + 17 - 3x = 180 add/subtract the like terms

72 - 12x = 180

- 12x = 108 divide both sides by 12

-x = 9

x = -9

The sales tax rate is 8.25%. If Sheila bought a sweater for $35, a pair of jeans for $89, and a handbag for $55, find her total cost including the sates tax. Round your answer to the nearest cent.

Answers

Answer:185,422.61

Step-by-step explanation:8.25%/100=0.0825 but since it a sale tax you add a 1 so it would be 1.0825•35=37.88•89= 337.32•55=185,422.61

Madison went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 500 mg of sodium and each frozen dinner has 700 mg of sodium. Madison purchased 2 more frozen dinners than cans of soup and they all collectively contain 7400 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.

Answers

Madison purchased 5 cans of soup and 7 frozen dinners.

Step-by-step explanation:

Given,

Quantity of sodium in each soup can = 500 mg

Quantity of sodium in each frozen dinner = 700 mg

Total quantity = 7400

Let,

Number of soup cans purchased = x

Number of frozen dinners purchased = y

According to given statement;

500x+700y=7400        Eqn 1

y = x+2        Eqn 2

Putting value of y from Eqn 2 in Eqn 1

[tex]500x+700(x+2)=7400\\500x+700x+1400=7400\\1200x=7400-1400\\1200x=6000[/tex]

Dividing both sides by 1200

[tex]\frac{1200x}{1200}=\frac{6000}{1200}\\x=5[/tex]

Putting x=5 in Eqn 2

[tex]y=5+2\\y=7[/tex]

Madison purchased 5 cans of soup and 7 frozen dinners.

Keywords: linear equation, substitution method

Learn more about substitution method at:

brainly.com/question/10710410brainly.com/question/10717746

#LearnwithBrainly

Answer:

Madison purchased 5 cans of soup and 7 frozen dinners

Step-by-step explanation:

What is the least common denominator of 1/7,2/5 and 2/3?

Answers

105 will be the least common denominator

Answer:

105 is the least common denominator

Step-by-step explanation:

Since 7, 5 and 3 are all prime.

LCM would be 7×3×5 = 105

A company provides bus trips to various events for a adults and c children. The company charges $18 for each adult and $8 for each child for a trip to an upcoming play. The bus has a maximum capacity of 40 people and the school can only spend $400 dollars on the trip. Write and solve a system of equations to determine the maximum number of adults and children that can attend the play that will satisfy these constraints.

Answers

Final answer:

To determine the maximum number of adults and children that can attend the play without exceeding the bus capacity of 40 people and the $400 budget, set up and solve a system of equations representing the capacity and budget constraints. The solution is 8 adults and 32 children.

Explanation:

We are given a situation where a company charges $18 for each adult (a) and $8 for each child (c) for a bus trip to an upcoming play, with the constraints that the bus holds a maximum of 40 people and the available budget is $400. To find the maximum number of adults and children that can attend under these constraints, we need to set up a system of equations:

For the capacity constraint: a + c = 40

For the budget constraint: 18a + 8c = 400

We can solve this system using substitution or elimination. Let's use elimination. Multiply the first equation by -8 and add it to the second equation to eliminate c:

-8a - 8c = -320

18a + 8c = 400

Adding these two equations together gives us:

10a = 80

Thus, a = 8. Plugging a = 8 back into the first equation, we get c = 32.

The maximum number of adults and children that can attend the play is 8 adults and 32 children.

Perform the following multiplication. 4.7314 × 10 = 47.314 0.47314 473.14 4,731.4

Answers

Answer:

47.314

Step-by-step explanation:

We want find the results of the multiplication,

[tex]4.7314 \times 10[/tex]

When we multiply by 10, we move the decimal point forward once.

When we divide by 10, we move the decimal point backwards once.

In this case, we are multiplying, so

[tex]4.7314 \times 10 = 47.314[/tex]

Fully answer BOTH questions a and b below.

On a recent survey, 60% of those surveyed indicated that they preferred walking to running.
a. If 540 people preferred walking, how many people were surveyed?
b. How many people preferred running?

Answers

Answer:

a. Number of people surveyed were 900.

b. 360 people preferred running.

Step-by-step explanation:

Given:

On a recent survey, 60% of those surveyed indicated that they preferred walking to running.

If 540 people preferred walking.

Now, to find a. number of people were surveyed. b. number of people preferred running.

a.

Number of people preferred walking = 540.

Percentage of people preferred walking = 60%.

Let the total number of people surveyed be [tex]x.[/tex]

Now, to get the number of people surveyed:

60% of x = 540.

[tex]\frac{60}{100} \times x=540[/tex]

[tex]0.60\times x=540[/tex]

[tex]0.60x=540[/tex]

Dividing both sides by 0.60 we get:

[tex]x=900.[/tex]

Thus, number of people surveyed = 900.

b.

Total number of people surveyed = 900.

People preferred walking = 540.

Now, to get the people preferred running we subtract people preferred walking from total number of people surveyed:

[tex]900-540[/tex]

[tex]=360.[/tex]

Thus, people preferred running = 360.

Therefore, a. Number of people surveyed were 900.

b. 360 people preferred running.

A triangle has side lengths of 3 feet and 9 feet.which is the greatest possible perimeter of the triangle

Answers

21 because you have to have at least 1 side as 3m so the other two should be 9m to have the greatest possible length

If a prison deceased by 372 prisoners each month over one year what the monthy decrease

Answers

Answer:

31 deaths per month

Step-by-step explanation:

12 months in a year

372 / 12 = 31

Make a math problem for the problem 4 divided by 1/2= 8

Answers

Answer:

if Jara has [tex]\$4[/tex] and she wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex].

How many pens she can buy.

Step-by-step explanation:

If Jara has [tex]\$4[/tex] and she wants to buy pen the wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex] .

How many pen she can buy.

[tex]Let\ Jara\ can\ buy=x\ pens\\\\each\ pen\ cost=\$\frac{1}{2}\\\\Then\ Jara\ can\ buy\ pens=\$\frac{1}{2}x\\\\\frac{1}{2}x=4\\x=8\\Jara\ can\ buy\ =8\ pens[/tex]

Describe and correct the error(s) made in each of the problems below.

1−x / (5−x)(−x)=x−1 / x(x−5)

5/s+2/5=2/s

Answers

Answer:

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]

[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]

Step-by-step explanation:

Errors in Algebraic Operations

It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them

When we change the signs of all the terms of a polynomial, the expression must be preceded by a negative sign When multiplying negative and positive quantities, if the number of negatives is odd, the result is negative. If the number of negatives is even, the result is positive. Not to confuse product of fractions with the sum of fractions. Rules are quite different

The first expression is

[tex]1-x / (5-x)(-x)=x-1 / x(x-5)[/tex]

Let's arrange into format:

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =\frac{x-1 }{ x(x-5)}[/tex]

We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]

Now for the second expression

[tex]5/s+2/5=2/s[/tex]

Let's arrange into format

[tex]\displaystyle \frac{5}{s}+\frac{2}{5} =\frac{2}{s}[/tex]

It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been

[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]

HELP! I put the formula but I don’t know the radius

Answers

Answer:

C. 8,624

Step-by-step explanation:

recall that the formula for circumference is

Circumference = 2πr  ( = given as 85 meters)

hence,

85 = 2πr

r = 85/(2π)

given h = 15m

volume of cylinder

= πr²h

= π (85/2π)² 15  (using calculator and assuming π = 3.14)

= 8628.58

Comparing with the choices, the closest choice (within rounding error) is C. 8,624

Other Questions
What is a direct result of depolarizing the presynaptic membrane of an axon terminal? Balance C2 H602+02 reacts with CO2 + H2O In New York, how must all medical expense health insurance sold to individuals or small groups be rated? If the wind velocity is 43 km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 212 km/h Hickory sold $32,000 of the inventory and has agreed to pay warranty expenses for its customers. These are expected to be $1,600 and occur evenly over the next four months (i.e., starting in June). What is the amount of Hickorys May expenses when applying the matching principle? During the translation of mRNA molecules, the new polypeptides are often directed to specific parts of the cell by the presence or absence of short sequences of amino acids called signal peptides. Which of the following would you expect to find in the polypeptides that will eventually fold to become enzymes important in the citric acid cycle? Group of answer choices A. no signal peptide B. an amino terminal signal peptide C.an internal signal peptide D.a signal anchor peptide What question did Hardy and Weinberg want to answer?mASSAateSONREESOA. Are all traits in plants controlled by genes?O. Is it possible to breed a plant to have certain traits?OC. How does allele frequency change between generations?OD. How large is the gene pool for a given organism?SUBMIT Which is an example of a living thing?O A) airOB) fireO C) fishOD) water Asa works as an order-taker at Simply Salads, a fast-food restaurant. He does not cook food, or even package the final order, but he does input the order and take payment. Asa reports directly to the shift manager, and he seldom interacts with the general manager. How would you describe the organization of Simply Salads? According to Federalist 10, increasing the population and the size of the country will:_______. a. not affect the problems of factions.b. increase the need for purely democratic governance. c. decrease the effects of factions.d. generate greater corruption in government. Which of the following scenerio is an example of where a cell may meed to preform a form of endocytosis. to get rid of waste to send out the products other parts of the organism needs. to get nutrients it needs Terri brought 1.74 meters of rope. Gracie brought 1.64 meters of rope. Who brought more rope A towns January high temperatures average 36 degrees (F) with a standard deviation of 10 degrees while in July the mean high temperature is 74 degrees and the standard deviation is 8. In which month is it more unusual to have a day with a high temperature of 55? explain Which sentence from a reflective essay contains a subject and verb error and needs to be edited?A.Either the book or the review are, in my opinion, too generous to the author.B.The documentary, including the last section, is interesting, but boring.C.Each of the main characters is, to say the least, extremely colorful.D.All of the incidents, including the final action, are too fantastic to be true. 74.) Along which punishes a man for something not wrong when he did it is called a....A. Bill of attainder B. TreasonC. FelonyD. Ex post facto Read lines 146 - 149 of Beowulf.The time was longthe space of twelve winters, that the Skylding kingendured in torment all possible cares,the fullest agony.Which statement describes how connotation is used in this passage?O A. The connotation of the word "agony" makes the passage soundlike complainingOB. The connotation of the word "endured increases the feeling ofsuffering.OC. The connotation of the word "winters" reminds readers how cold itis where the story takes place.OD. The connotation of the word "possible gives the passage a feelingof hope Amazon, the largest online retailer, has experimented with physical stores and recently bought Whole Foods. Whole Foods has almost 500 stores and gives Amazon facilities for rapid physical expansion. The general insight here is that:__________ a. to survive today, organizations need to be present in both the online and physical markets b. Amazon recognized a bargain-priced stock in Whole Foods c. people do not like buying groceries online A tree was cut down and used to make a statue 2300 years ago. What fraction of 14C that was present originally remains today? t of 14C is 5730 yr Place the butane lighter in the sink or tub and let it rest there until needed. why do we soak the lighter in the water bath? In the fictional country of Unozarica, all the airlines, buses and trains are owned by businesses not the government, but the government has oversight on them, especially for safety reasons. No one is guaranteed a job, but citizens are guaranteed income in their old age. This is an example of __________.