the radius of the bigger circle is 9cm and the area of the shaded region is twice that of the smaller circle then how long is the radius of the smaller circle ?

Answers

Answer 1

Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.

How to determine the radius of the smaller circle

In this situation we have a composite figure formed by two concentric circles, whose area ratio is presented below, in which the area is directly proportional to the square of radius:

[tex]\frac{A'}{A} = \frac{(R-r)^{2}}{r^{2}}[/tex]

2 · r² = (9-r)²

2 · r² = 81 - 18 · r + r²

r² + 18 · r - 81 = 0

The roots of the second order polynomial are r₁ = -9 + 9√2 and r₂ = -9 - 9√2. As radius is a non-negative number, the only root that is reasonable is r₁ = -9 + 9√2 (r₁ ≈ 3.728).

Given the dimensions of the composite figure, formed by two concentric circles, we conclude that the radius of the smaller circle is approximately 3.728 centimeters.

Remark

The image is missing and is thus included in the figure attached below.

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The Radius Of The Bigger Circle Is 9cm And The Area Of The Shaded Region Is Twice That Of The Smaller

Related Questions

the graph f(x) is shown below. Which function could represent the graph of f(x)?
(1) f(x)=(x+2)(x^2+3x-4)
(2) f(x)=(x-2)(x^2+3x-4)
(3) f(x)=(x+2)(x^2+3x+4)
(4) f(x)=(x-2)(x^2+3x+4)

Answers

The function which represents the graph is f(x) = (x + 2)(x² + 3x - 4). Then the correct option is 1.

What is a function?

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The graph is given below.

The value of the function is zero for the values of x are -4, -2, and 1.

Let's check which function gets satisfied.

f(x) = (x + 2)(x² + 3x - 4)

The function can be written as

f(x) = (x + 2)(x + 4)(x - 1)

Then the values of x for which the value of the function is zero.

                       f(x) = 0

(x + 2)(x + 4)(x - 1) = 0

                         x = 1, -2, -4

Then the function will be f(x) = (x + 2)(x² + 3x - 4). Then the correct option is 1.

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please helb it is very hadr

Answers

Answer:

a=15.7mm2,31.4

b=18.84in2,37.68

find the sum of 1+2-3+4+5-6+7+8-9+...+97+98-99

Answers

Answer:

Hi,

Step-by-step explanation:

Let's make group of 3 numbers

1+2-3=0

4+5-6=3

7+8-9=6

...

97+98-99=96

s=1+2-3+....+97+98-99=0+3+6+..+96=3*(0+1+2+3+...+32)

=3*(32+0)*33/2

=1584

Find the dependent value
for the graph
y = 15 - 3x
when the independent value is 2.
= [?]

Answers

The dependent value for the graph given the independent value is 9.

What is the dependent value?

The independent variable is the variable that explains the dependent variable. The dependent variable is the value that the independent variable determines.

The dependent variable is y and the independent variable is x.

y = 15 - 3(2)

y = 15 - 6

y = 9.

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evaluate for f(6), show all work

Answers

Answer:

32

Step-by-step explanation:

f(6)=6^2-4

f(6)=36-4

f(6)=32

Answer:

f(6)=32

Step-by-step explanation:f(6)=6^2 -4

f(6)=36-4

f(6)=32

the number 2.525252.... can be written as a fraction, when reduced to its lowest term, the sum of numerator and denominator is:

Answers

Answer:

Here's your answer.

Let the number be x.

Here we have to multiply with 100 on both sides.

[tex] \implies \: 100x = 252.5252 \\ \\ \implies \: 100x = 250 \ + 2.5252... \\ \\ \implies \: 100x = 250 + x \\ \\ \implies \: 99x = 250 \\ \\ \implies \: x = \frac{250}{99} [/tex]

Therefore, sum of numerator and denominator = 25099 = 349

Hope it helps you from my side

Answer:

349

Step-by-step explanation:

2.525252.... is a non-terminating and recurring number.

2.525252.... can be expressed as [tex]2.\overline {52}[/tex]

Now, we convert [tex]2.\overline {52}[/tex] as a fractional number. Lets start.

[tex]Let \: x =2.\overline {52}[/tex]........(1)

Multiply both sides of eq (1) by 100, we find:

[tex]100x =252.\overline {52}[/tex]........(2)

Subtracting (2) from (1)

[tex]100x -x=252.\overline {52}-2.\overline {52}[/tex]

[tex]\implies 99x=250[/tex]

[tex]\implies x=\frac{250}{99}[/tex]

Numerator = 250

Denominator = 99

Sum of numerator and denominator = 250 + 99 = 349

2 cups is equivalent to___ pint.

Answers

Answer:

1 pint is equal to 2 cups

Step-by-step explanation:

2 cups is equivalent to__1_ pint.

Hope This Helped

Answer:

answer is 1

Step-by-step explanation:

Find the equation of the line in slope-intercept form containing the two points: (−1,5) and )(4,−3) Leave equation in fractional form.

Answers

Answer:

y = 1.6x + 3.4

Step-by-step explanation:

We have to use the equation y = m x + c to find the equation of the line.

Here,

m ⇒ slope

c ⇒ y-intercept

First, let us find the slope.

For that, we can use the given two coordinates.

( -1 , 5 ) ⇒ ( x₁ , y₁ )

( 4 , -3 )  ⇒ ( x₂ , y₂ )

The formula to find the slope of a line is :

m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )

Let us solve now.

m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )

m = ( 5 - ( -3 ) ) ÷ ( -1 - 4 )

m = ( 5 + 3 ) ÷ -5

m = 8 ÷ -5

m = -1.6

Now let us find the y-intercept (c ) of the line.

For that, let us get one of the coordinates which are given in the question.

I'll get ( -1 , 5 ) from  that.

( -1 , 5 ) ⇒ ( x , y )

Let us solve now.

y = mx + c

5 = -1.6 × -1 + c

5 = 1.6 + c

5 - 1.6 = c

3.4 = c

Therefore,

m ⇒ -1.6

c ⇒ 3.4

So, the equation of the line is :

y = mx + c

y = 1.6x + 3.4

Which equation shows an example of the associative property of addition?

Answers

Answer:

(2+3)+4 = 2+(3+4) this is an example of associative property

Jane had $5.00, then spent $2.00. How much does she have now?

Answers

Answer:

$3.00

Step-by-step explanation:

$5.00 = 5

$2.00 = 2

5

-2

_

3

3 = $3.00

Answer:

$3.00

Step-by-step explanation:

Work out the circumference of this circle.
Give your answer in terms of pi and state its units

Answers

Answer:

14π cm

Step-by-step explanation:

Circumference of a circle given the diameter is :

πd

We simply substitute the value given in the image into our formula to find our answer:

πd = π×14 = 14π

Units will be cm as circumference is a length

This is our final answer as the question states to leave it in pi form .

Hope this helped and brainliest please

Answer:

14π cm

Step-by-step explanation:

Circumference of a circle with radius r = 2πr or 2rπ

The diameter d is twice the radius so circumference = dπ

Here d= 14 so the answer is 14π cm

An account earns annual simple interest. Find the balance of
the account.
$250 at 4% for 1 year

HELP FAST

Answers

The balance of the account which earns annual simple interest of $250 at 4% for 1 year is $260

How to find simple interest?

Principal, P = $250Interest rate, r = 4%Time, t = 1 year

Simple interest = principal × rate × time

= 250 × 4% × 1

= 250 × 0.04 × 1

= $10

Balance = Principal + Simple interest

= $250 + $10

= $260

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The mean age of a group of students is 16. John joins the group and the mean age changes to 18. How old is john ?

Answers

Answer:

John is 20 years old.

Step-by-step explanation:

Given the second mean is 18, it is equal to the first mean age plus John's unknown age. The sum is also divided by 2 because there are 2 values in the sum (1. John's age and 2. the mean, 16 yrs old).

Set up an equation: [tex]\frac{x+16}{2}=18[/tex]

multiply both sides by 2: [tex]x+16=36[/tex]

simplify: [tex]x=20[/tex]

Angela bought a bookmark in the shape of an arrow as shown below. The base and height of the triangle are both 3 inches.

Answers

The area of a 2D form is the amount of space within its perimeter. The area of the arrow is 11.25 in².

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

For the given problem, the image is given below.

The area of the arrow is,

Area =  Area of rectangle + Area of triangle

        = (1.5 in × 4.5 in) + (0.5×3×3)

        = 6.75 in² + 4.5 in²

        = 11.25 in²

Hence, the area of the arrow is 11.25 in².

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There is 1/2 of a pizza left for 4 friends to share. What fraction of a pizza will each friend get to eat?

Answers

1/8, if you want to check that answer do 1/8 times the 4 friends and that will give you the 1/2 pizza you have left

Answer:

12.5% is the answer.

Step-by-step explanation:

Question 7 of 25
All else being equal, a study with which margin of error would give you the
most confidence in the results?
O A. 13 percentage points
OB. +12 percentage points
OC. 19 percentage points
OD. 16 percentage points
SUBMIT

Answers

Answer:

+12 percentage points

Step-by-step explanation:

All options have positive percentage in themselves

So lesser marginal error should be more applicable as lower the marginal errors lower the probability of doing mistakes so higher marks .

Option B

Leah's family took a road trip to Mount Rushmore. Leah fell asleep 44% of the way through the trip. If Leah fell asleep after they had travelled 132 miles, what was the total length of the trip?

Answers

The total length of the trip 190.08 miles

How you do it is to add the 44% of 132 to 132

= (132 + (132×44%))

What is the length?

Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived.

First, you have to find out how much 44% is. Change it into decimal form (0.44) and then multiply the two together.

132 × 0.44 is 58.08 miles.

Then you add that to the rest of the trip, 132 miles.

= (132 + 58/08

=190.08

The total length of the trip was 190.08 miles.

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guys pls help me i will give brain list pls help me out
if someone could please help me i will be sending more so plsss i need help

Answers

Answer:

200

Step-by-step explanation:

In the expression 67.8046 8.264 - 243.5, all of the numbers are measured quantities and have the same units. Evaluate this expression to the correct number of significant figures.

Answers

The result of evaluating 67.8046 + 8.264 - 243.5 is -167.431

How to evaluate the expression?

The expression is given as:

67.8046 + 8.264 - 243.5

The highest number of significant figures in the expression is 6 (i.e. 67.8046)

This means that the result must be in 6 significant figures.

Next, we evaluate the expression as follows:

67.8046 + 8.264 - 243.5 = -167.4314

Approximate to 6 significant figures.

67.8046 + 8.264 - 243.5 = -167.431

Hence, the result of evaluating 67.8046 + 8.264 - 243.5 is -167.431

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The interior angles of a pentagon are 126°, 114°, y°, and 83°. Find the value of y°?

please can someone help me with the answer to this question pls
am preparing for my WASSCE(west Africa senior school certificate examination) which is going to be held tomorrow
pls can someone help me​

Answers

Answer:

217

Step-by-step explanation:

angles in a pentagon =540°

y°+126°+114°+83°=540°

y°+323°=540°

y°=540°-323°

y°=217°

These graphs depict the price and output levels of apples under perfect competition and monopoly market structures. what is the extra amount that mary would pay for apples under a monopoly instead of a perfect competition? a. $2 b. $3 c. $4 d. $5 e. $6

Answers

The extra amount that Mary would pay for apples under a monopoly instead of perfect competition is B. $3

Calculations and Parameters:

From the complete information,

There are images of the prices that can be gotten under a monopoly and the ones that can be gotten in a perfect competition by Mary.

The marginal cost which is graphed against the pound of apples and the price shows Mary would pay $15 and the marginal revenue shows that Mary would pay $12.

Hence, the difference between them, which is the extra amount to be paid would be $15-$12

=$3

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Answer:

B. 3$

Hope this helps!

Step-by-step explanation:

A jar has 9 pennies.
3 nickels, 8 dimes, and
5 quarters. A coin is chosen
at random, not replaced
then another is chosen.
Find the probability that
a quarter was chosen
followed by a penny,

Answers

Answer:

the answer to this question is 3/40

Step-by-step explanation:

if you want my explanation you ca

use a number line to find the product.

5 x (-5)

a. -25
b. 25
c. 10
d. 0

Answers

Answer: a. -25

Step-by-step explanation:

1. Multiply the numbers

5x(−5)

Solution

−25x

Emi computes the mean and variance for the population data set 87, 46, 90, 78, and 89. She finds the mean is 78. Her steps for finding the variance are shown below.


What is the first error she made in computing the variance?

Emi failed to find the difference of 89 - 78 correctly.

Emi divided by N - 1 instead of N.

Emi evaluated (46 - 78)^2 as -(32)^2.

Emi forgot to take the square root of -135.6.

Answers

The error she made is Emi evaluated (46-78)² as - (32)² is wrong.

What is variance?

Variance is calculated as the average of squared differences of the data observations from the mean.

Given data: 87, 46, 90, 78, and 89.

Here, the first Emi find the difference of 89 - 78 correctly.

Now, Emi division is also correct.

Now, Emi evaluated (46 - 78)^2 as -(32)^2 is wrong.

(46-78)² = (-32)²

Here she used the negative sign outside.

Hence, Emi evaluated (46 - 78)^2 as -(32)^2 is wrong.

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Answer:

C.) Emi evaluated (46 - 78)2 as -(32)2.

Step-by-step explanation:

Look at the set of quadrilaterals in the coordinate plane shown below.



Which statement is TRUE?


Because quadrilateral ABCD can be reflected across the x-axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

Because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .

Because quadrilateral ABCD can be reflected across the y-axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

Because quadrilateral ABCD can be reflected across the y -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .

Because quadrilateral ABCD can be reflected across the x-axis, then rotated 90° clockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

Because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° clockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .

Because quadrilateral ABCD can be reflected across the line y = x, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.Look at the set of quadrilaterals in the coordinate plane shown below.



Which statement is TRUE?


Because quadrilateral ABCD can be reflected across the x-axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

Because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .

Because quadrilateral ABCD can be reflected across the y-axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

Because quadrilateral ABCD can be reflected across the y -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .

Because quadrilateral ABCD can be reflected across the x-axis, then rotated 90° clockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

Because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° clockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .

Because quadrilateral ABCD can be reflected across the line y = x, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

Answers

The true statement about the set of quadrilaterals in the coordinate plane is B. Because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

What is a quadrilateral?

A quadrilateral is a polygon having four sides, four angles, and four vertices.

In this case, because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

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Please Help!!! Two parallel lines are cut by a transversal. What is the measure of 7?

Answers

Answer:

D. 77º

Step-by-step explanation:

Because 3 and 7 are corresponding angles and 3 = 77º, 7 also is 77º.

You deposit $4000 in an account earning 7% interest compounded continuously. How much will you have in the account in 10 years?

Answers

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &10 \end{cases} \\\\\\ A=4000e^{0.07\cdot 10}\implies A=4000e^{0.7}\implies A\approx 8055.01[/tex]

What is the greatest common factor of
15x^7y^5+5x^5y^4-20x^6y

Answers

Answer:

5x^5y

Step-by-step explanation:

A major arc will have a measure that is
O A. greater than 180°
OB. less than 180°
O C. equal to 180°

Answers


Think Major greater than 180°, Minor less than 180°. If arc equals 180° than it is a semi circle.


A.

Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6x4 – 8x2 + 3x2 + 4. Her work is shown.

Step 1: (6x4 – 8x2) + (3x2 + 4)

Step 2: 2x2(3x2 – 4) + 1(3x2 + 4)

Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?

Faelyn should realize that her work shows that the polynomial is prime.
Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) – (8x2 + 4).
In Step 2, Faelyn should factor only 2x out of the first expression.
Faelyn should factor out a negative from one of the groups so the binomials will be the same.

Answers

An accurately describes what Faelyn should do next is option B. Faelyn should realize that her work shows that the polynomial is prime.

What are prime polynomials?

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called a prime polynomials.

The polynomial 6x⁴ – 8x² + 3x² + 4 needs to be factored and the steps are:

Step 1: (6x⁴ – 8x²) + (3x² + 4)

Step 2: 2x²(3x² – 4) + 1(3x² + 4)

Since they do not have any common factor.

Faelyn should realize that her work indicates that the polynomial is prime.

Prime polynomials have integer coefficients.

An accurately describes what Faelyn should do next is option B. Faelyn should realize that her work shows that the polynomial is prime.

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