You have a cake that is 10 inches in diameter. You expect 12 people to share it, so you cut it into 12 equal slices. Before you get a chance to serve the cake, 12 more people arrive! So, you decide to cut a concentric circle in the cake so that you will have 24 pieces. How far from the center of the cake should the circle cut be made so that all 24 people get the same amount of cake?

Answers

Answer 1

Answer:

3.5355 inches

Step-by-step explanation:

Area should be same the concentric circle and rest piece .

let's consider the radius of concentric circle as r

so it's area is π r²

area of whole circle is π (5)" ( because diameter is 10 inches)

so the area of rest piece is π (5)² - π r²

π (5)² - π r² = π r²

5² = 2r²

r² = 25/2

r = √(25/2)

r = 3.5355 inches


Related Questions

Given x^2 -4x+4 is a factor of the polynomial 2x^4 - 11x^3 +68x-80, completely factor the polynomial using algebraic methods.​

Answers

Answer:

2x^4-11x^3+68x-80

2x^4-4x^3-7x^3+14x^2-14x^2+28x+40x-80

2x^3(x-2)-7x^2(x-2)-14x(x-2)+40(x-2)

(x-2)(2x^3-7x^2-14x+40)

(x-2)(2x^3-4x^2-3x^2+6x-20x+40)

(x-2)(2x^2(x-2)-3x(x-2)-20(x-2))

(x-2)(x-2)(2x^3-3x-20)

(x-2)(x-2)(2x^2+5x-8x-20)

(x-2)(x-2)(x(2x+5)-4(2x+5))

(x-2)(x-2)(2x+5)(x-4)

(x-2)^2(2x+5)(x-4)

Find the point that is a solution for y=6x+8

Answers

Answer:

(-8/6, 0) is the answer

first is the absicca and the second is the ordinate

I will give you brainliest if you answer the question!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

A=95 miles per hour
B=95 Miles per hour as well
Both are going the same speed
Bro train a is going 80km an hour and train b is going 95km an hour, just saying ‍♂️

5
Which list shows these numbers in order from least to greatest?
37
26
-5.17, 133,
6
5
37
А
26
5
-5.17,
33
B -5.17,
26
5
37
6
33
C
26
S
-5.17)
133,
37
6
D
-5.17, 252
133,
37
6
5

Answers

Answer:

D

Step-by-step explanation:

Find the value of f(-7).

Answers

Answer:

f(-7) = -4

Step-by-step explanation:

We want to find the value of the function when x = -7

The y value of the function when x= -7 is -4

f(-7) = -4

Answer:

f(-7)=-4

Step-by-step explanation:

If you look at the x, in this case -7, and follow it down to where it stops on the parabola, you will see that it's y value is -4.

What are the x-intercepts of the polynomial function
g(x) = (2x-8)(x+1)(9 – 3x)2 ?
(Hint: There should be three of them!)

Answers

Answer:

The x intercepts are x = 4, x = -1, and x = 3.

Step-by-step explanation:

[tex]g(x)=(2x-8)(x+1)(9-3x)^{2}\\(2x-8)(x+1)(9-3x)^{2}=0\\2x-8-0\\2x=9\\x=4\\x+1=0\\x=-1\\9-3x=0\\3x=9\\x=3\\[/tex]

7 + 5x = 2x + 25
step by step pls:(

Answers

Answer:

x = 6

Step-by-step explanation:

7 + 5x = 2x + 25

first subtract 7 from both sides to isolate 5x on the left

5x = 2x + 18

then subtract 2x from both sides to isolate all of the x terms to one side

3x = 18

then divide 18 by 3 to solve for x

x = 6

hope this helped!! :)

Answer:

i got you, i wrote it out and all gimme brilliantness

Step-by-step explanation:

You have 5814 meters of rope you need to cut into 27 sections how many 27 meters secton of rope will you be able to create and how much rope will be left over as waste

Answers

Answer:

215 sections of rope that measure 27 meters in length, and you also have 9 meters of rope left

Step-by-step explanation:

we have 5,814 meters of rope and we are told to calculate the number of 27 meters sections that we can cut:

you have to divide 5,814 meters by 27 meters = 215.333

that means that you have 215 sections of rope that measure 27 meters in length, and you also have 9 meters of rope left (0.333 x 27 = 9)

77th term for -10,-8,-6

Answers

9514 1404 393

Answer:

 142

Step-by-step explanation:

The first term of this arithmetic sequence is -10. The common difference is -8-(-10) = 2. The n-th term is ...

  an = a1 +d(n -1)

  an = -10 +2(n -1) = 2n -12

Then the 77th term is ...

  a77 = 2(77) -12 = 154 -12

  a77 = 142

The 77th term is 142.

if a+b=34 then what is 4a-8ba+9a

Answers

Answer:

12x:12x=1:

1 TRUE

Step-by-step explanation:


The selling price of an item is $520. It is marked down by 10%, but this sale price is still marked up
from the cost of $360. Find the markup from cost to sale price.

Answers

Answer:

108

Step-by-step explanation:

trust me

tim bought 3 hat for 120/-. how much can he buy from 180/-

ASAP plz

Answers

Answer: 16

Step-by-step explanation:

Tim can buy 4 caps and will left with Rs.20 to spare

What is the unitary method?

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here tim can buy 3 hats from Rs.120 thus each hat cost Rs.40

Thus price of 4 hats is Rs.160 and he will be left with Rs.20 to spare.

Hence, Tim can buy 4 caps and will left with Rs.20 to spare

Learn more about the unitary method here:

https://brainly.com/question/22056199

#SPJ2

What is the image of the point (7,-5) after a rotation of 270° counterclockwise
about the origin?

Answers

Answer:

(-5, -7)

Step-by-step explanation:

if you rotate the point by 270 degrees counterclockwise, you get (5,-7) and I'm guessing image is another way to say reflection so after it is reflected then the point would be (-5,-7)

(-7,5) is the correct answer because 270 degrees counter clockwise is y,-x

What is 10-6(-8c+9) simplified

Answers

Answer:

-32c + 36

Step-by-step explanation:

10-6(-8c+9)

4(-8c+9)

4 × -8c = -32c

4 × 9 = 36

-32c + 36

A college information pamphlet provides some statistics about the students and the professors to help high school seniors decide if they want to attend the college. The pamphlet lists the ratio of students to professors as 18 to 1. If there are 702 students at the college, how many professors are there?

Answers

Answer:

39

Step-by-step explanation:

Setting up your problem and solving:

In the question it says the ratio is students to professors right? So 18 to 1.

Write that down: Students to Professors is 18 to 1.

We know that there are 702 students in that college correct?

Write that down: 702 students in the college

We are trying to find how many professors there are so...let's do that.

Number 1:

Set your equation: have your fraction bar and equal sign like this: --- = ---

On the top, we have 1 so... 1/? = ?/?

On the other top we have the x...: 1/? = x/?

Why? Because we do not know the total of professors there are so that is X.

We put the number 1 on the other side because we know that there is only 1 out of 18 professors to students.

Number 2:

On the bottom, we will have 18...: 1/18 = x/?

On the other bottom we have 702...: 1/18 = x/702

Why? Because we know that there is a total number of 18 to 1 students on the ratio and a real total of 702 students.

Number 3.

Now you have your equation set up: 1/18 = x/702

The next step is yours: cross multiple, divide on the bottom or top or find the comparison.

I'm going to divide by the bottom okay? so.. 18/702

Set that up.

(702/18)

702/18 is 39!

SO in the end there is a total of 39 professors!

'x=39'

Hoped this helped! :)

4. Given that a * b = ab- evaluate
(4marks)
(i) 4*8
(ii) 2* (4 * 8)​

Answers

Answer:

(i) 4*8 = 32

(ii) 2* (4 * 8) = 64

Step-by-step explanation:

(i) 4*8

4 × 8 = 32

(ii) 2* (4 * 8)

2 × (4 × 8)

2 × (32)

2 × 32 = 64

-TheUnknownScientist

Answer:

(i) 4*8 = 32

(ii) 2(4*8) = 2*32 = 64

what is the measure of <x​

Answers

Answer:

x = 104°

Step-by-step explanation:

180-76=104

z = 104°

z and x are vertical from each other, therefore, z = x

Hmmm this is gonna be a long process

Find the inequality represented by the graph

Answers

Answer:

y ≥ 1/2x

Step-by-step explanation:

Given the following inequality, we know that y must be greater than or equal to x because the line is not dashed, and is shaded above the line.

Now to find the equation just pretend that this is just a normal linear equation, and solve for the equation.

So since the y intercept is 0, and there is a rise of 1 for a run of 2 or 1 unit up every two units to the right, the corresponding linear equation is y = 1/2x.

Now since this is an inequality where y is greater than or equal to x.

y = 1/2x → y ≥ 1/2x

What does a equal? (b = 3√2)

Answers

9514 1404 393

Answer:

  a = √2

Step-by-step explanation:

Triangle EFG is an isosceles right triangle, so the ratios of side lengths are ...

  1 : 1 : √2

That is, we have ...

  3a/6 = 1/√2

Multiplying by 2 gives ...

  a = 2/√2

  a = √2

please tell me the answer

Answers

Answer:

It shifts left

I hope this helps you with your algebra

to my calculations the anwser is it shifts left

How many feet are traveled by a person riding once around the merry -go-round ? Clare says, " The radius of the merry -go-round is about 4 feet , so the distance around the edge is about 8π feet. " Andre says , " The diameter of the merry-go-round is about 4 feet, so the distance around the edge is about 4π feet."

Answers

if this is a question about who is correct Clair is correct

Can some please help I’m stuck :(

Answers

Answer:

"I Only" is the correct answer

Step-by-step explanation:

Given inequality is:

-10>3x-6

In order to check which numbers are solution to the given inequality, we will put each number one by one in the inequality. If the inequality is true after putting the number, the number is the solution of the inequality.

So,

I . -10

Putting -10 in the inequality

[tex]-10>3x-6\\-10>3(-10)-6\\-10>-30-6\\-10> -36[/tex]

The inequality results in true after putting x=-10 so -10 is the solution of inequality.

II. 5

Putting 5 in the inequality

[tex]-10>3x-6\\-10>3(5)-6\\-10>15-6\\-10>9[/tex]

The equality doesn't hold true for x=5 so 5 is not the solution of the problem.

III. -1

Putting -1 in the equation

[tex]-10>3x-6\\-10>3(-1)-6\\-10>-3-6\\-10>-9[/tex]

Inequality doesn't hold true for x=-1 so it is not the solution of the inequality.

Hence,

"I Only" is the correct answer as only -10 is the solution of inequality.

Quadratic functions 2. Did I do it right

Answers

Yea you did, good job

a line has a slope of 8 and a y intercept of 9 what is its equation in slope intercept form

Answers

Answer:

y= 8x +9

Step-by-step explanation:

Slope-intercept form:

y= mx +c, where m is the slope and c is the y-intercept.

Given that the slope is 8, m= 8.

Substitute m= 8 into the equation:

y= 8x +c

Given that the y-intercept is 9, c= 9.

Substitute c= 9 into the equation:

y= 8x +9

Thus, the equation of the line is y= 8x +9.

Worksheet

1. −3|2x + 6| = −12

2. |x − 2| + 10 = 12

Answers

Answer:

1.

-3|2x+6|=-12
|2x+6|=4

2x+6=4

2x+6=-4

x1=-5, x2=-1

2.

|x-2|+10=12
|x-2|=12-10
|x-2|=2

x-2=2

x-2=-2

x1=0, x2=4

If a television was 20% off and the amount of the discount was $200 what would the original price be?

Answers

Answer:

The original price of the television would be 1000$

7+3²+(12-8)÷2x4
i really need help

Answers

Answer:

3/2 :D have a good day

Step-by-step explanation:

7+9+(-4)÷2(4)

=(7+9-4)/8

=3/2

someone help me with this plz!!

Answers

84/100 = 21/25 I believe

100 writen as a perfect square

Answers

Answer:

10^2.

Step-by-step explanation:

100 is a perfect square of 10.

sqrt (100)

= 10.

Hope this helped!

which of the following is the angle bisector theorem?​

Answers

Answer:

The answer is B!

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Doing this for the other person to get the crown because they also help me :3

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