How to find the radius of a circle using the distance formula.

Answers

Answer 1

SOLUTION:

Case: Deriving the equation of a circle isolating the radius

We know that the general equation for a circle is given as:

Method:

The distance between two points is given as:

$\begin{gathered} d=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ (x_1,y_1)\text{ is the center of the circle written as (a,b)} \\ (x_2,y_2)\text{ is any part of the circle written as (x,y)} \\ d=\text{ }\sqrt[]{(x_{}-a_{})^2+(y_{}-b_{})^2} \\ d\text{ is the distance betwe}en\text{ the center of the circle (a,b) and any parts of the circumference (x, y)} \\ \text{This means d is the radius, r} \\ r=\text{ }\sqrt[]{(x_{}-a_{})^2+(y_{}-b_{})^2} \end{gathered}$

How To Find The Radius Of A Circle Using The Distance Formula.

Related Questions

Name the similar triangles. ΔBAC ~ ΔDEF , ΔBAC ~ ΔEDF, ΔBAC ~ ΔDFE, ΔBAC ~ ΔFED

Name the similar triangles. BAC ~ DEF , BAC ~ EDF, BAC ~ DFE, BAC ~ FED

Answers

Based on the angle-angle similarity theorem (AA), the similar triangles in the image given can be named as: ΔBAC ~ ΔEDF.

What are Similar Triangles?

When two triangles have the same shape but have different sizes, it means the triangles have corresponding pairs of congruent angles and corresponding pairs of sides that are proportional to each other. The triangles are said to be similar.

The image given show two set of triangles that have two corresponding pairs of congruent angles, based on the angle-angle similarity theorem, it means that they are similar to each other.

Therefore, the similar triangles are:

ΔBAC ~ ΔEDF.

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If a/b=7/2, then 2a= ______
A) 7b
B) 4b
C) 2b
D) 14b

Answers

Answer:

Option A, 7b

Step-by-step explanation:

a/b=7/2

or, 2a=7b

Answered by GAUTHMATH

Answer:

A)7b

its yr ans.

hope it helps.

stay safe healthy and happy. ..

X square/3 - x/3 -44

Answers

Answer:

$\frac{x^2}{3} - \frac{x}{3} - 44 =\frac{(x -12)(x+ 11)}{3}$

Step-by-step explanation:

Given

$\frac{x^2}{3} - \frac{x}{3} - 44$

Required

Solve

Take LCM

$\frac{x^2 - x - 132}{3}$

Expand

$\frac{x^2 +11 x -12x- 132}{3}$

Factorize:

$\frac{x(x+11) -12(x+ 11)}{3}$

$\frac{(x -12)(x+ 11)}{3}$

Hence:

$\frac{x^2}{3} - \frac{x}{3} - 44 =\frac{(x -12)(x+ 11)}{3}$

A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet
and the volume of each large box is 22 cubic feet. A total of 22 boxes of paper were
shipped with a combined volume of 324 cubic feet. Write a system of equations that
could be used to determine the number of small boxes shipped and the number of
large boxes shipped. Define the variables that you use to write the system.

Answers

Answer:

Small Boxes: 10

Large boxes: 12

Step-by-step explanation:

A paper company needs to ship paper to a large printing business. The paper will beshipped in small boxes

Select the correct answer from each drop-down menu.If vector u=(5,-7) and v=(-11,3),2v-6u= and ||2v-6u||≈

Answers

If vector u = (5,-7), then 6u = (5*6, -7*6) = (30, -42)

If vector v = (-11, 3), then 2v = (-11*2, 3*2) = (-22, 6)

Therefore, 2v - 6u = (-22 - 30, 6 - (-42)) = (-52, 48)

||v|| si the length of vector v. If v = (x, y), then

$\mleft\Vert v\mleft\Vert=\mright?\mright?\sqrt[]{x^2+y^2}$

Replacing with the components of 2v - 6u,we get:

$\mleft\Vert2v-6u\mleft\Vert=\sqrt[]{(-52)^2+48^2}\mright?=\sqrt[]{2704+2304}=\sqrt[]{5008}=70.767\mright?$

SLOPE DIGITAL ESCAPE ROOM
I need help finding the code

Answers

By finding all the four slopes, we can see that the word is ECHA.

How to find the word?

We know that the general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

s = (y₂ - y₁)/(x₂ - x₁)

With that formula we can get the slopes.

1) Using the points (0, 3) and (2, 4).

m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.

2)Using (-1, -12) and (1, -8)

m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.

3) We have (2, -6) and (-4, -3) so:

m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H

4)we can use the points (0, 3) and (1, 1), so:

m = (1 - 3)/(1 - 0) = -2, so the letter is A

Then the word is ECHA

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Hi can anyone help me with this much appreciate j

Answers

For the given arena's tickets sales , the round of figure of all the sales to the nearest thousand is given by :

Events Nearest thousand

Dart Domination cup : $169,000Boadicea's basketball league : $40,000The Rub-a-Dub Club Reggae band : $215,000Agent Green : $65,000Britney Pitchfork : $224,000Sunshine Droops : $111,000

As given in the question,

Rules to round of nearest thousand are:

Check the near by hundred digit :

If the hundred digit is 5 or more than 5 than round up that is write next digit. If the hundred digit is less than 5 than round down.

Given is the actual ticket rates of the different events tickets sales ,round off to the nearest thousand is given by:

Events Nearest thousand

Dart Domination cup : $169,000Boadicea's basketball league : $40,000The Rub-a-Dub Club Reggae band : $215,000Agent Green : $65,000Britney Pitchfork : $224,000Sunshine Droops : $111,000

Therefore, For the given arena's tickets sales , the round of figure of all the sales to the nearest thousand is given by :

Events Nearest thousand

Dart Domination cup : $169,000Boadicea's basketball league : $40,000The Rub-a-Dub Club Reggae band : $215,000Agent Green : $65,000Britney Pitchfork : $224,000Sunshine Droops : $111,000

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In two or more complete sentences, compare the number of x-intercepts in the graph of f(x)=x2 to the number of x-intercepts in the graph of g(x)= (x+2)2 -7

Answers

Because f(x)=x^2 is the parent function of a quadratic, it has one x-intercept at (0,0), no shifts up or down. But because g(x)=(x+2)^2-7 is a quadratic being shifted 2 units to the left and most importantly 7 units down, the function will cross the x-intercept 2 times.

I hope this is the answer you were looking for!

four times the sum of the three consecutive even intergers is 240 more than six times the smallest integer.

Answers

Answer:

Step-by-step explanation:

Let's call the smallest of the three consecutive even integers "x". Since they are consecutive and even, we know that the next two integers must be "x + 2" and "x + 4".

Now we can set up the equation for the problem:

4 * (x + (x + 2) + (x + 4)) = 240 + 6x

Expanding the parentheses on the left side:

4 * (3x + 6) = 240 + 6x

Simplifying the left side:

12x + 24 = 240 + 6x

Subtracting 6x from both sides:

6x + 24 = 240

Subtracting 24 from both sides:

6x = 216

Dividing both sides by 6:

x = 36

So the smallest of the three consecutive even integers is 36, and the others are 38 and 40.

Answer is x = 36

Three even integers are
x = 36
x + 2 = 38
x + 4 = 40

Step by step

We know even integers = x, x + 2, x + 4

Our equation is

4(x + x + 2 + x + 4) = 6x + 240
Combine like terms in parentheses

4 (3x + 6) = 6x + 240
Multiply

12x + 24 = 6x + 240
Subtract 6x from both sides to combine variables

12x - 6x + 24 = 6x - 6x + 240
Simplify

6x + 24 = 240
Subtract 24 from both sides to combine constants

6x + 24 - 24 = 240 - 24
Simplify

6x = 216
Divide both sides by 6 to solve

6/6 x = 216/6

x = 36
x + 2 = 38
x + 4 = 40

Check your work using the original equation

4(x + x + 2 + x + 4) = 6x + 240

4 (36 + 36 + 2 + 36 + 4) = 6(36) + 240
Combine like terms inside parentheses

4(114) = 6(36) + 240
Multiply

456 = 456

They equal so solution is correct

Mofor has homework assignments in five subjects. He only has time to do two of
them.

Answers

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Please help answers do in 30 minutes

Answers

Answer:

The angle for x would be 45°

A straw is placed inside a rectangular box that is 4 inches by 2 inches by 10 inches, as
shown. If the straw fits exactly into the box diagonally from the bottom left corner to
the top right back corner, how long is the straw? Leave your answer in simplest
radical form.
10 in.
4 in.
2 in.

Answers

Answer:

The length of the straw in the simplest radical form is $2\sqrt{30}$ inches

Step-by-step explanation:

The length of the straw can be calculated as follow

The first step is to calculate the diagonal of the base of the rectangular box by using Pythagorean theorem

$c^{2}=a^{2}+b^{2}$

Where $c$ is the base diagonal or the hypotenuse, $a$ is the short leg, $b$ is the long leg

Substitute $2$ for $a$, $4$ for $b$ in the Pythagorean theorem

$c^{2}=2^{2}+4^{2}$

Simplify the right side of the equation

$c^{2}=4+16$

$c^{2}=20$

Take the square root of the right side to get the value of $c$

$c=\sqrt{20}$

Factor $20$ by $4$

$c=\sqrt{4\times 5}$

Substitute $2^{2}$ for 4

$c=\sqrt{2^{2}\times 5}$

Rewrite the value of $c$ in the simplest radical form

$c=2\sqrt{5}$

Since the value of $c$ is $2\sqrt{5}$, then the length of the diagonal of the base is

$2\sqrt{5}$ inches

The second step is to calculate the length of the straw by using Pythagorean theorem

$c^{2}=a^{2}+b^{2}$

Where $c$ is the diagonal from the bottom left corner to the top right back corner or the hypotenuse, $a$ is the short leg, $b$ is the long leg

Substitute $2\sqrt{5}$ for $a$, $10$ for $b$ in the Pythagorean theorem

$c^{2}=(2\sqrt{5})^{2}+10^{2}$

Simplify the right side of the equation

$c^{2}=20+100$

$c^{2}=120$

Take the square root of the right side to get the value of $c$

$c=\sqrt{120}$

Factor $120$ by $4$

$c=\sqrt{4\times 30}$

Substitute $2^{2}$ for 4

$c=\sqrt{2^{2}\times 30}$

Rewrite the value of $c$ in the simplest radical form

$c=2\sqrt{30}$

Since the value of $c$ is $2\sqrt{30}$, then the length of the diagonal from the bottom left corner to the top right back corner or the hypotenuse is

$2\sqrt{30}$ inches

Since the length of the diagonal from the bottom left corner to the top right back corner is $2\sqrt{30}$ inches, then the length of the straw is $2\sqrt{30}$ inches

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What is the value of x in the solution to this system of equations?

Answers

Answer:

x = 10/3

Step-by-step explanation:

3x = 2y + 14

y = -6x + 18

3x = 2(-6x+18) + 14

3x = -12x + 36 + 14

15x = 50

x = 50/15

x = 10/3

Answer:

10/3

Step-by-step explanation:

3x= 2y+14-------(1)

y= -6x+18------(2)

from equation (2) put y= -6x+18 into equation (1)

3x= 2(-6x+18)+14

3x= -12x+36+14

3x+12x= 50

15x= 50

dividing bothsides by 16

x = 50/15

x= 10/3

How many different ways are there to arrange the letters in the word MISSISSIPPI?

Answers

Answer: 34,650 permutations

Please give the y intercept, slope, and x intercept of y=6x−7. All of them, not just one or two!

Answers

Answer:

Slope = 6, y intercept = -7, x intercept = 7/6

Step-by-step explanation:

Slope = 6

y intercept = -7

x intercept = 7/6

3) A real estate agent sells a house for $1 500 000. The commission rate is 1.85% of the selling price. Calculate the commission. (A) $2 775 000 (B) $27 750 (C) $277 500 (D) $2 775

Answers

Answer:

B 27,750

Step-by-step explanation:

1,500,000 × 1.85 /100

= 27,750

7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

Answers

The sum of the terms is x^7+10x^4+4x^3-5x^11-10x^6

How to determine the value

To determine the value, we need to know that algebraic expressions are described as expressions that are composed of factors, constants, variables, terms and coefficients.

These algebraic expressions are also identified with the presence of arithmetic operations,

These operations are;

AdditionBracketParenthesesSubtractionMultiplicationDivision

From the information given, we have that;

7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

collect the like terms

7x^7 - 6x^7+10x^4+4x^3-5x^11-10x^6

add the like terms

x^7+10x^4+4x^3-5x^11-10x^6

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Need help please!!!!!!!

Answers

Answer:

yes ASA

Step-by-step explanation:

Catherine sells bags of popcorn at the theatre. The bags come in three sizes.
small
60g
£1.49
medium
150g
£3.99
large
250g
£5.99
Catherine thinks the medium bag of popcorn is the best value for money.
Is the medium bag of popcorn the best value for money?
Use the space below to show clearly how you get your answer

Answers

Answer:

The answer is the most reasonable one which I think large is

Step-by-step explanation:

Because it's only 100 grams more and $2 bucks seems like a good deal

iiioooooooooooooooooooooooooooooooooooooooooooooioioioioihi

Answers

There are 9 i's, 1 h, and 49 o's

Answer:

49 o's, 9 i's, and one lonely h

Step-by-step explanation:

uh...

yeah

Using the table of integrals, solve

Answers

The expression gotten from integrating the trigonometry function is -1/2cot(x)csc(x) - 1/2[ln|csc(x) - cot(x)| + c

How to integrate the trigonometry function

From the question, we have the following trigonometry function that can be used in our computation:

∫ (1/sin(x))³

Express properly

So, we have

∫ (1/sin(x))³ dx

When integrated using a graphing tool, we have

∫ (1/sin(x))³ dx = -[ln(|csc(x) + cot(x)|) + cot(x)csc(x)]/2 + c

Where C is a constant value

When expanded, we have

∫ (1/sin(x))³ dx = -1/2cot(x)csc(x) - 1/2[ln|csc(x) - cot(x)| + c

Hence, integrating the trigonometry function ∫ (1/sin(x))³ dx gives (a) -1/2cot(x)csc(x) - 1/2[ln|csc(x) - cot(x)| + c

Answers

Answer:

2.04

Step-by-step explanation:

$5.33-3.29=2.04$

Answer:

2.04

Step-by-step explanation:

5.33-3.29=2.045.33−3.29=2.04

What is the missing term?
+1 4x -3
3x 12x²?
4x - 3

Answers

Answer:

Step-by-step explanation:

41 plus 36 plus 36 is 83 is the answer for me

The length of a rectangle is 8 less than the width. The perimenter is 44 meters. Find the dimension of the rectangle

Answers

Answer:

Length = 7

Width = 15

Step-by-step explanation:

L= x

W= x-8

2x+2(x-8)=44

You start at (0,-4). You move left 1 unit and right 4 units. where do you end?

Answers

If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)

Calculating the endpoint of the point

From the question, we have the following parameters that can be used in our computation:

Start = (0, -4)

Also, we have

You move left 1 unit and right 4 units

Mathematically, this can be expressed as

(x, y) = (x - 1 + 4, y)

Substitute the known values in the above equation, so, we have the following representation

Endpoint = (0 - 1 + 4, -4)

Evaluate the expression

Endpoint = (3, -4)

Hence, the endpoint is (3, -4)

Answers

Answer:

18.9%

Step-by-step explanation:

Given data

Principal= $500

Amount=$1000

Time= 4 years

Rate= ???

The compound interest expression is given as

A=P(1+r)^t

when we make "r" the subject of formula we have

r = (A/P)^1/t - 1

substitute

r= (1000/500)^1/4 -1

r= 2^0.25 -1

r= 1.189-1

r= 0.189

Hence the rate is

=0.189*100

=18.9%

PLEASE HELP FAST!! IT IS URGENT!! Some stores print multiple coupons and advertisements on their receipts, making the receipts unusually long. A curious shopper makes the same purchase at a random sample of 10 stores and measures the length of each receipt (n inches). Here are the results: 8.25, 7.5, 5, 9.5, 12, 5.5, 9, 14, 11.5, 18 Are the conditions for cons tructing at confidence interval met?
O No, the random condition is not met.
O No, the 10% condition is not net.
O No, the Normal/large sanple condition is not met.
O Yes, the conditions for inference are met.

Answers

Answer:

No, the Normal/large sample condition is not met. A confidence interval assumes that the underlying population follows a normal distribution and that the sample size should be at least 30. Since the sample size in this case is only 10, the Normal/Large Sample condition is not met and the conditions for constructing a confidence interval are not met.

Please help!!!!!!!!!!!

Answers

Answer:

Circle on the left: 30 ft Circle in the middle: 4m Circle on the right: 10 mm

Step-by-step explanation:

I got these answers by multiplying the radius by 2. In the problem, they gave you the radius. The diameter is r*2, so that is how I got my answers.

Answer:

1. I think 30ft 2. I think 4m 3.I think 10mm

Write the polynomial f(x) that meets the given conditions.
Degree 3 polynomial with zeros of -2,4i, and -4i.

Answers

Answer:

f(x) = x^3 + 2 x^2 + 16 x + 32

or also

f(x) = k (x^3 + 2 x^2 + 16 x + 32)

Step-by-step explanation:

Given that -2, 4i and - 4i are roots, then the binomial factors to be included are:

(x - - 2) (x - 4i) (x --4i) = (x + 2) (x - 4i) (x + 4i) =

(x + 2 ) (x^2 - x 4i + x 4i - 16 i^2) = (x + 2) (x^2 + 16) =

x^3 + 16 x + 2 x^2 + 32

which in standard form reads:

x^3 + 2 x^2 + 16 x + 32

Also have in mind that the polynomial could also include a constant multiplicative factor "k".

Which are the solutions of x^2 = 19x + 1?

Answers

Answer:

x = $\frac{19+\sqrt{365}}{2}, \frac{19-\sqrt{365}}{2}$

Step-by-step explanation:

1. Move everything to one side of the equation.

x^2 - 19x - 1 = 0

2. Use the quadratic formula where a = 1, b = -19, and c = -1.

x = (-b +- sqrt(b^2-4ac)) / 2a

If you plug those numbers into that formula, you will get the result listed above

Answer:

x₁ = $\frac{19-\sqrt{365}}{2}$, x₂ = $\frac{19+\sqrt{365} }{2}$

Step-by-step explanation:

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