In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0).
What is the area of the circle?

Select the appropriate response:

A) 3
B) 9
C) 18
D) 25

Answers

Answer 1

Answer:

18pi or 56.52 units²

Step-by-step explanation:

Radius² = (-3-0)² + (2-5)²

= 18

Area = pi × r²

3.14 × 18

56.52

Answer 2

The area of the circle is 57.

What is Circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

To find the area of the circle, we need to know the radius.

The radius can be determined using the distance formula between the center of the circle (2, -3) and the point on the circle (5, 0).

The distance formula is given by:

d =√(5 - 2)² + (0 - (-3))²

= √3²+ 3²

=√9 + 9

=√18

The radius is the distance between the center and a point on the circle, which is the square root of 18.

Now, we can calculate the area of the circle using the formula:

Area = π × radius²

Area = π ×√18²

= 18π

= 56.52

Hence, the area of the circle is 57.

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Related Questions


What is the least common multiple of 4 and 5?

Answers

Answer:

20

Step-by-step explanation:

the answer is 20 for sure

To pass science, a student must earn at least a grade of 70. How many failed this science class?

Answers

In order to pass the class kids must have a 70 or higher and looking at the graph only 5 kids did not pass the class.

Amber is trying to solve 3x^2-4x=0 using a graphical method. She therefore starts by drawing the graph of y=3x^2 on a grid she now intends to complete her method by drawing a straight line graph in the same grid. complete Ambrrs method to solve 3x^2-4x=0

Answers

You can rewrite the equation as

[tex]3x^2-4x=0 \iff 3x^2=4x[/tex]

So, you draw the graph of [tex]y=3x^2[/tex] (the parabola), and then the graph of [tex]y=4x[/tex] (the line), and see where they intersect.

Final answer:

To solve the equation 3x^2 - 4x = 0 graphically, Amber can draw the graph of y=3x^2 and a straight line that intersects the parabola. The x-values where the line intersects the parabola are the solutions to the equation.

Explanation:

To solve the equation 3x^2 - 4x = 0 using a graphical method, Amber starts by drawing the graph of y=3x^2. This is a parabola that opens upwards with a vertex at the origin (0,0). Since she wants to find the x-values that satisfy the equation, she needs to draw a line that intersects the parabola. The line should be a straight line that crosses the x-axis at the values of x that make the equation true.

To draw this line, she needs to find two points that lie on the line. Since the equation is linear, she can choose any two points to draw the line. Let's choose two points that are easy to calculate. For example, when x=0, y=9 and when x=1, y=12. Plot these two points on the graph.

Next, draw a straight line that passes through these two points. Extend the line so that it intersects the parabola. The x-values where the line intersects the parabola are the solutions to the equation 3x^2 - 4x = 0. In this case, the line intersects the parabola at x=0 and x=4/3.

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When 125 is subtracted from one third of a number the result is 2 what is the number

Answers

Answer:

381

Step-by-step explanation:

Let n be the number

When 125 is subtracted from one third of a number the result is 2

1/3n - 125 = 2

Add 125 to each side

1/3n -125+125 = 2+125

1/3n = 127

Multiply each side by 3

1/3n *3 = 127*3

n =381

Luke is x years old. Kate is half of Luke's age. Adam is 6 years younger than Kate. Adam is 4 years old. How old is Luke?

Answers

Answer: luke is twenty

Step-by-step explanation: Adam is 4 plus 6 is 10 ten times two is twenty

Answer:

luke is 20

Step-by-step explanation:

because you had 6 and 4 and multiply it by 2

I have this question about volume of spheres, can you help me out ?

Answers

Given:

The diameter of the sphere = 42 cm

To find the volume of the given sphere.

Formula:

The volume of a sphere is given by [tex]V=\frac{4}{3} \pi r^3[/tex]

The radius is given by [tex]r=\frac{d}{2}=\frac{42}{2}=21[/tex]

Volume of the sphere:

The volume of the sphere is given by

[tex]V=\frac{4}{3} (3.14)(21)^3[/tex]

Simplifying, we get;

[tex]V=\frac{4}{3}(3.14)(9261)[/tex]

Multiplying the terms, we have;

[tex]V=\frac{116318.16}{3}[/tex]

Dividing, we get;

[tex]V=38772.7[/tex]

Thus, the volume of the sphere is 38772.7 cubic cm.

(-1,-4) and (6,10) x intercept write as ordered paid

Answers

Answer:

y=2x-2 I hope this helps

Step-by-step explanation:

Slope intercept form, y=mx+b

What if you wanted a smaller margin of error in your interval for the proportion of left-handed people (say plus or minus 2%)? How many people would you need to survey in order to get a margin of error of 2% ? You can use the LaTeX: \hat{p} p ^ that you already calculated as your estimate in the sample size formula.

Answers

Answer:

The sample size n= 2500

A survey with 2500 left-handed people guarantees  the given margin error is 2%

Step-by-step explanation:

Explanation:-

The margin of error = [tex]\frac{2 S.D}{\sqrt{n} }[/tex]

here for proportions , the standard deviation (σ) = [tex]\sqrt{p(1-p)} \leq \frac{1}{2}[/tex]

[tex]Margin of error = \frac{2 S.D}{\sqrt{n} } \leq \frac{2(\frac{1}{2}) }{\sqrt{n} }[/tex]

[tex]Margin of error = \frac{1}{\sqrt{n} }[/tex]

now The necessary sample size is

[tex]n= \frac{1}{(M.E)^{2} }[/tex]

Given data the survey in order to get a margin of error of 2%

M.E = 0.02

[tex]n= \frac{1}{(0.02)^{2} } = 2500[/tex]

Conclusion:-

The sample size n= 2500

A survey with 2500 left-handed people guarantees the given margin error is 2%

A circle with radius of 5 cm sits inside a 11 cm * 11 cm rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.

Answers

Answer:

42.43  [tex]cm^{2}[/tex]

Step-by-step explanation:

Given:

A circle with a radius of 5 cm sits inside a 11 cm x 11 cm rectangle.

Question asked:

What is the area of the shaded region as shown in the figure ?

Solution:

First of all calculate area of circle and then area of rectangle:-

[tex]Area\ of\ cirle=\pi r^{2}[/tex]

                      [tex]=\frac{22}{7} \times5\times5\\ \\ =\frac{550}{7}\\ \\=78.571\ cm^{2}\\[/tex]

As here length an width both are 11 cm, we can say that this is a square.

[tex]Area\ of\ square=(Side)^{2}[/tex]

                         [tex]=11\times11=121\ cm^{2}[/tex]

Now, area of shaded region = Area of square - Area of circle

                                               = 121 - 78.571 = 42.429 [tex]cm^{2}[/tex]

Therefore, the area of the shaded region will be 42.43  [tex]cm^{2}[/tex]

Consider the matrix shown below:
What are the dimensions of A.



3 X 4

4 X 3

12

A and B

Answers

Answer:

Dimensions of a matrix:

r × c

Where r is the no. of rows and c is the no. of columns

If A has 4 rows (horizontal) and 3 columns (vertical),

Dimensions are: 4 × 3

If A has 3 rows (horizontal) and 4 columns (vertical),

Dimensions are: 3 × 4

Suppose a population of 200 crickets doubles in size every month the function f(x) equals 200×2 to the X power gives the population after X months how many crickets will there be after three years

Answers

Answer:

≈ 1.37 * [tex]10^{13}[/tex]

Step-by-step explanation:

Given the exponental function is:

F(x) =  200*[tex]2^{x}[/tex] where:

200 is initial value of crickets 2 is the base number (doubles in size every month) x is the number of months  

How many crickets will there be after three years?

3 years = 12*3 = 36 so x = 36. Substitute x into the function we have:

F(x) = 200*[tex]2^{36}[/tex] ≈ 1.37 * [tex]10^{13}[/tex]

So the number of crickets after three years is: ≈ 1.37 * [tex]10^{13}[/tex]

Answer:  There will be 1.37 x 10^13  crickets after 3 years.

Step-by-step explanation:

Hi, to answer this question we simply have to replace x in the formula by the number of months in 3 years.

f (x) = 200 (2^x)

Where x is the number of months

Since one year has 12 months,

for 3 years: 3 x 12 = 36 months

Substituting  x= 36 on the function

f (36) = 200 (2^36)

f (36) = 200 (2^x)

f(36) = 1.37 x 10^13

Feel free to ask for more if needed or if you did not understand something.

write 5/57 as a percentage and round to the nearest tenth​

Answers

Answer: 8.8%

Convert the fraction to a decimal, then multiply by  100

8.77192982  rounded to the nearest 10 is 8.8%

8.8% is the answer

The angle shown is in standard position. Select the possible measures of the angle. –450° –360° –270° –90° 90° 270° 360° 450° On a coordinate plane, 2 rays are shown. One ray is on the x-axis between quadrants 1 and 4, and the other ray is on the y-axis between quadrants 3 and 4.

Answers

Answer: a, d,f

On edge.

Step-by-step explanation:

The possible measures of the angle are -450°, -90° and 270°

What is terminal side?

An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.

In any standard position, the vertex of the angle is on the origin (0, 0) of the x and y-axis. Therefore, one side of the angle is always fixed along the positive x-axis, namely, going to the right along the axis in the 3 o'clock direction. This is called the initial side of the angle. The other side of the angle is called the terminal side.

Hence, the angles that match the figure above are the measures of the angle. That is:

-450°

-90°

270°

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The drama club members at Millie's middle school are selling tickets to the school play. Millie wants to determine the average
number of tickets sold. First, she surveyed the club members in her homeroom, and then she surveyed every third member of
the club in her physical education class. Which sampling technique should produce a more representative sample?

Answers

Answer:

Every third member of the club in her physical educations class

Step-by-step explanation:

The reasoning behind this is because if Millie surveys her club members who are hosting the school play, she wouldn't be able to get an accurate average number of tickets sold because the club member have a bias in terms of purchasing the tickets as they run the club. Meanwhile the physical education class has a more random assessment because every third person in the class may or may not have an interest in the play the same way the club would.

Answer:The answer is

Neither sample will be representative. B on edge

Step-by-step explanation:):):):):):):):):):) I GOT IT RIGHT

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 15 feet.

Answers

Answer:

The length of ladder is 17 feet .

Step-by-step explanation:

Refer the attached figure .

Let the length of ladder AC be h

We are given that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder.

So ,Perpendicular = AB = h-9

Distance from the bottom of the ladder to the building= BC = Base =15 feet.

Using Pythagoras theorem

[tex]Hypotenuse^2=Perpendicular^2+Base^2\\h^2=(h-9)^2+15^2\\h^2=h^2+81-18h+225\\18h=306\\h=\frac{306}{18}\\h=17[/tex]

Hence The length of ladder is 17 feet .

2. Simplify: *
V75x2

Answers

Answer:

√3·5x

Step-by-step explanation:

√(75x²) = √75·√x²

or          =√3√25√x²     Recognize that both 25 and x² are perfect squares.

or           =√3·5x

Question 1 (1 point)
The ordered pairs in the table below represent a linear function.
Xy
23
9 h
What is the slope of the function?
1/2
Oo oo
1/4

Answers

25 is the answer ur welcome
The answer is 25, I gotchu

(3 × 9) + (5 + 8) + (33 ÷ 3) =

Answers

Answer:

Step-by-step explanation:

(3 x 9) + (5 + 8) + (33/3) = 51

   27   +     13    +    11     = 51

Answer:

51

Step-by-step explanation:

use PEMDAS

How would you find # 3 HELP ASAP PLZZ

Answers

Answer:

24 = AE

How to find it

AB = 26 and BD = 20 find AE

Because its a rhombus point is the midpoint of BD so BE is 1/2 BD so BE is 10

Now we no longer need to use BD and instead we use BE

Now since ∠BEA is 90° we can use the Pythagorean Theorem

AB²-BE²=AE²

26²-10²=AE²

676-100=AE²

576=AE²

[tex]\sqrt{576}[/tex]=AE

24 = AE

5 2/3 x 4 1/2 make sure your anser is correct

Answers

The answer is 25.5 as a decimal, as a fraction it is 51/2.

Do ya'll know how to do this? (grade 10)

Please help im stranded :(

(15 Points)

Answers

Answer:

a.) (-16,0)(0,12)

b.) (-3,0)(0, 3/2)

Step-by-step explanation:

Plug it in for each.

y= 3/4x+12 (Lets plug in our x intercept of (x,0) and our y intercept of (0,y)

x-intercept

0=3/4x+12

-12        -12

-12=3/4x

-12/(3/4)=x

-16=x

SO, your x intercept is -16 which is point (-16, 0)

Now to do your y intercept in lets plug x in as 0 instead this time:

y = 3/4(0)+12

y = 12

Your y intercept is 12

Now for b its the same process of plugging 0 in for the values let

y-int=-2(0)-4y+6=0

                      -6  -6

                       -4y/-4=-6/-4 <- divide both sides by 4

                              y = 3/2 <- Simplified answer

y int = (0, 3/2)

x-int = -2x-4(0)+6 = 0

                       +6   +6

                       -2x = 6

                           x = 6/-2 <-- Divide both sides by -2

                           x = -3     <-- Simplify

x-int = (-3, 0)

A house was built in 1985 and cost $62000. It was sold in 2003 for $310000.
(a) Work out the 1985 price as a percentage of the 2003 price.
(b)Calculate the percentage increase in the price from 1985 to 2003.

Answers

Answer:

a) 20%

b) 400%

Step-by-step explanation:

In a) you firts do

$310000=100% what about $62000.Then cross multiply

$62000×100%=6200000÷310000=20%

In b) you first do

$62000=100% what about $248000.Then cross multiply

$248000×100=$24800000÷62000=400%

Final answer:

The 1985 cost of the house is 20% of the 2003 price. There was a 400% increase in price from 1985 to 2003.

Explanation:

To answer both parts of this question, we will use the concept of percentages.

(a) First, we calculate the 1985 price as a percentage of the 2003 price by dividing the cost of the house in 1985 by the cost in 2003, and then multiply the result by 100 to give a percentage. So we have (62000/310000)*100 = 20%. Therefore, the 1985 house cost represents 20% of the 2003 price.

(b) To calculate the percentage increase from 1985 to 2003, we take the difference in prices from 1985 to 2003, divide this by the original price in 1985, and then multiply the result by 100. So we have ((310000-62000)/62000)*100 = 400%. Hence, there was 400% increase in the price from 1985 to 2003.

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Which equation would help find the measure of

Answers

Answer:

x + 52 + 78 = 180

Step-by-step explanation:

By angle sum property of a triangle:

[tex]x + 52 + 78 = 180[/tex]

Answer: the top one x+52+78=180

the point A (6,3) maps onto A'(2,1) under a dilation with respect to the origin. what is the constant of dilation

Answers

Answer:

[tex]k = \frac{1}{3}[/tex]

Step-by-step explanation:

The coeficcient of dillation is:

[tex](6,3)[/tex]

[tex](3\cdot 2, 3\cdot 1)[/tex]

[tex]3\cdot (2,1)[/tex]

The constant of dilation is [tex]k = \frac{1}{3}[/tex].

Final answer:

To find the constant of dilation for a point A (6,3) mapping onto A\'(2,1) under dilation with respect to the origin, the coordinates are compared resulting in a constant of dilation of 1/3.

Explanation:

The question involves finding the constant of dilation when a point A (6,3) maps onto A\'(2,1) under a dilation with respect to the origin.

The constant of dilation can be found by comparing the coordinates of A with those of A\'.

For point A with coordinates (x,y) mapping to A\' with coordinates (x\',y\'), the dilation factor (k) is found by the formula k = x\'/x = y\'/y when the dilation is centered at the origin (0,0).

In this case, for the x-coordinates: k = 2/6 = 1/3, and for the y-coordinates: k = 1/3 which confirms our calculation, as the dilation factor must be consistent across both coordinates.

Therefore, the constant of dilation is 1/3.

Brian just bought 9 bags of 14 cookies each. He already had 8 cookies in a jar. How many cookies does Brian have now?

Answers

Answer: 134 cookies

Step-by-step explanation: First we want to find the total amount of cookies Brain bought. Simply multiply 14 x 9 to find the total amount of cookies bought.

14 x 9 = 126 cookies.

Since Brian already had 8 cookies in the jar, we will simply add the new amount of cookies he bought to the cookies in the jar left.

126 + 8 = 134 total cookies that Brain has now.

He bought 9*14=126 cookies. Since he already had 8 cookies, he now has 126+8=134 cookies.

An aquarium I’d 8 feet long , 5 feet wide, and 5.5 feet deep . What is the volume of the tank?

Answers

Answer:

V = 220 feet³

Step-by-step explanation:

Formula: V = LWH

(8ft) (5ft) (5.5ft) = 220 ft^3

On a Timeline a milestone 11 years in the future will be the ___ of a milestone 20 years in the future and to the ___ of a milestone 25 years in the future

Answers

On a timeline, a milestone 11 years in the future will be to the left of a milestone 20 years in the future and to the right of a milestone 25 years in the future, considering events are arranged from left (earlier) to right (later).

On a Timeline a milestone 11 years in the future will be to the left of a milestone 20 years in the future and to the right of a milestone 25 years in the future. This question revolves around understanding the sequential order of events plotted on a timeline, which is a graphical representation of events placed in a chronological sequence. A timeline is typically read from left to right, with events placed according to their date from earliest to latest. Therefore, if we are talking about the future, 11 years from now is sooner than 20 years from now, so it would be placed to the left. Similarly, it is later than 25 years from now, hence it would be to the right of the 25-year milestone.

A box contains cards that are numbered from 1 to 100. What is the probability of randomly selecting a number that is less than 12
A 1/100
B 1/12
C 11/100
D 12/100​

Answers

Answer:

c

Step-by-step explanation:

If there are 100 cards and you can only pick numbers less then 12, you then could only have a number between 1 and 11

Answer:

its c

Step-by-step explanation:

A logical argument arranged with statements and reasons.

Answers

The answer is Two column proof

A survey found that 89% of a random sample of 1024 American adults approved of cloning endangered animals. Find the margin of error for this survey if we want 90% confidence in our estimate of the percentage of American adults who approve of cloning endangered animals.

Answers

Answer:

The margin of error for the survey is 0.016

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 1024

Sample proportion:

[tex]\hat{p} = 89\% = 0.89[/tex]

We have to find the margin of error associated with a 90% Confidence interval.

Formula for margin of error:

[tex]z_{stat}\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.10} = 1.64[/tex]

Putting the values, we get:

[tex]M.E = 1.64\times (\sqrt{\dfrac{0.89(1-0.89)}{1024}})\\\\M.E=0.016[/tex]

Thus, the margin of error for the survey is 0.016

Final answer:

The margin of error for the given survey, when wanting a 90% confidence level, is approximately 1.58%. This means that the true proportion of American adults who approve of cloning endangered animals is likely to be within 1.58% above or below the survey's result of 89%.

Explanation:

The subject matter of this question is in the field of statistics, specifically exploring concepts of confidence intervals and margin of error. A 90% confidence interval implies that we are 90% certain that the true population proportion lies within the calculated range, whereas the margin of error gives us the range that this estimate might deviate from the actual value.

In your scenario, you have a sample size of 1024 adults with 89% approving cloning of endangered animals. To compute the margin of error in this case, we first need to find the standard error. The standard error (SE) for a proportion is calculated as √[P(1 - P) / n] where P is the sample proportion and n is the total sample size. Let's compute this:

SE = √[0.89(1 - 0.89) / 1024] = 0.0096

For a 90% confidence interval, the critical value from the z-table is 1.645 ((double-tail distribution). Therefore, the margin of error (E) is calculated as:

E = z * SE = 1.645 * 0.0096 = 0.01579, approximately 1.58%

To interpret this value, you could say that with 90% confidence, the true proportion of American adults in favor of cloning endangered animals is within the range of 1.58% above or below 89%.

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Match the following terms with their definitions.. 1. a subtraction 2. pay that includes overtime, commissions, and bonuses before any deductions 3. the portion the employee takes home withholding 4. free from deduction 5. an amount entered on the W-4 form that tells the employer the amount of income tax to subtract from an employee's paycheck a. net pay b. deduction c. allowance d. gross pay e. exempt A coffee shop is considering accepting orders and payments through their phone app and have decided to use public key encryption to encrypt their customers' credit card information. Is this a secure form of payment? Yes, public key encryption is built upon computationally hard problems that even powerful computers cannot easily solve.No, encryption is an issue in that case Write your own SportsCar class that extends the Car class. This new class should have the following unique protected instance variables: myColor, MyEngine that stores its engine size in liters, mySuspension - e.g., firm, soft, touring, etc., and myTires - e.g., regular, wide, low profile, etc. To utilize this SportsCar class, add the following lines to the Driver class. Note that the last four parameters ( The three inside angles (a,b and c) of a right-angled triangle are in the ratio 7:18:11the smallest angle is 35 degreesworkout angles a,b and c When ConAgra learned that stores were selling more time-saving meals and snacks when school started, it launched its "Seasons of Mom" campaign to help grocers adjust to seasonal shifts in household needs. Which of the eight possible actions to improve the quantity and quality of its marketing intelligence most likely yielded this insight? What was the code name of the planned invasion of the Japanese mainislands: which graph best represents disruptive selection Which drug is a treatment for a bacterial infection, such as strep throat?a drug that interferes with viralDNAa drug that moderates your use of sugara drug called anantibiotic 2. Carolyn drew a rhombus ABCD. Fill in the blanks.BCBCADand ABABDCandis parallel to, is equal tois not parallel to, is not equal tois parallel to, is not equal tois not parallel to, is equal to How many of the products or foods you use daily come from Asias many resources, industries, and ecosystems? Give examples of one or two Asian products or resources that are part of your daily life. What factor limits the number of eclipses per year? A study found that 1% of Social Security recipients are too young to vote. If 800 social security recipients are randomly selected find the Mean, Variance and the Standard deviation of social security recipients who are too young to vote. Present your answer in two decimal places and in order: mean, Variance, Standard deviation.