a circle passes through the points o(0,0), a(8,4) and b(6,6). show that oa is a diameter of the circle and find the equation of the circle

Answers

Answer 1

9514 1404 393

Answer:

  (x -4)² +(y -2)² = 20

Step-by-step explanation:

The circle is the circumcircle of triangle OAB. Then OA will be a diameter if angle OBA is a right angle. We can check that by looking at the slopes of AB and BA.

  B-O = (6, 6)-(0, 0) = (6, 6)   ⇒   slope = Δy/Δx = 6/6 = 1

  A-B = (8, 4) -(6, 6) = (2, -2)   ⇒   slope = -2/2 = -1

These slopes have a product of -1, so OB ⊥ BA. The hypotenuse (OA) of ΔOBA is the diameter of the circle.

Then the midpoint of the hypotenuse is the center of the circle.

  C = (O +A)/2 = ((0, 0) +(8, 4))/2 = (4, 2)

The equation is ...

  (x -h)² +(y -k)² = r² . . . . . circle with center (h, k) and radius r

The radius is the distance from O to C, so is ...

  r² = 4² +2² = 20

and the equation of the circle is ...

  (x -4)² +(y -2)² = 20 . . . . equation of the circle

A Circle Passes Through The Points O(0,0), A(8,4) And B(6,6). Show That Oa Is A Diameter Of The Circle

Related Questions

What three-dimensional figure is represented by the net shown below?
A cube
B square pyramid
C rectangular prism
D rectangular pyramid

Answers

Answer:

C

Step-by-step explanation:

The net, if you imagine it folded up, will look like a long box.

Because all the dimensions are not equal, the figure cannot be a cube. Both square and rectangular pyramids have 5 faces, unlike this net.

A net of a rectangular prism, however, will have different dimensions for [tex]l[/tex] and [tex]w[/tex], and have 6 faces. So, the answer is C, rectangular prism.

Good luck ^^

The three-dimensional figure represented by the net shown below is a rectangular prism.

Option C is the correct answer.

What is a prism?

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

From the figure,

We see that it is an open rectangular prism.

All the open sides are rectangular in shape.

If we fold all the sides it will form a rectangular prism.

Thus,

The three-dimensional figure represented by the net shown below is a rectangular prism.

Learn more about prism here:

https://brainly.com/question/12649592

#SPJ2

Which expression can go in the blank to make this equation true
-4.5 + 4.4 + ? = 0

Answers

Answer:

+ 0.1

Step-by-step explanation:

So, first, we will add together -4.5 + 4.4, which equals -0.1. Then, we need to add the positive value of that to make it 0, so we add 0.1. I Hope This Helps :)

Two small planes start from the same point and fly in opposite directions. The first plane is flying 25 mph slower than the second plane. In 2 hrs, the planes are 470 mi apart. Find the rate of each plane.

Answers

Answer:

105 mph = rate of first plane

130 mph = rate of second plane

Step-by-step explanation:

Let r = rate of first plane

then r + 25 = rate of second plane

2r = distance of first plane

2(r + 25) = distance of second plane

2r + 2(r + 25) = 470

2r + 2r + 50 = 470

4r = 420

r = 105 mph

r + 25 = 130 mph

Choose all of the statements that correctly compare the two functions shown.

Alec's rate of savings is greater than Beth's.

entific

Alec and Beth are saving at the same rate.

Alec started with more money than Beth

mulas

Time

maining

:19:23

Beth started with more money than Alec,

de les

At 10 days, Alec will have $1 more than Beth in savings,

Answers

Answer:

b, c and e

Step-by-step explanation:

Given

See attachment for functions

Required

Select all statements that contain both functions

First, calculate the rate (slope) of both functions.

This is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

For Alec's

[tex](x_1,y_1) = (0,3)[/tex]

[tex](x_2,y_2) = (2,9)[/tex]

So, the slope is:

[tex]m = \frac{9 - 3}{2 - 0}[/tex]

[tex]m = \frac{6}{2}[/tex]

[tex]m =3[/tex]

For Beth's

[tex](x_1,y_1) = (5,17)[/tex]

[tex](x_2,y_2) = (12,38)[/tex]

So, the slope is:

[tex]m = \frac{38 - 17}{12 - 5}[/tex]

[tex]m = \frac{21}{7}[/tex]

[tex]m =3[/tex]

Beth and Rec have the same slope. Hence, they save at the same rate.

Next, determine the amount they started with.

This implies that we calculate y when x = 0

From Alec's graph.

[tex](x,y) = (0,3)[/tex]

Alec's initial savings is 3

For Beth's savings, we make use of slope formula.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex](x_1,y_1) = (5,17)[/tex]

[tex](x_2,y_2) = (0,y)[/tex]

So, we have:

[tex]3 =\frac{y - 17}{0 - 5}[/tex]

[tex]3 =\frac{y - 17}{ - 5}[/tex]

[tex]y - 17 = -15[/tex]

[tex]y = 17 -15[/tex]

[tex]y = 2[/tex]

Beth's initial savings is 2

Hence, Alec started with more money

Next, is to determine who has more money after 10 days.

Since they save at the same rate, the difference in their savings after any number of days will be the difference in their initial savings.

The difference (d) is calculated as:

[tex]d = 3 - 2[/tex]

[tex]d = 1[/tex]

Hence, Alec will have $1 more than Beth after 10 days

Answer:

its bc and e or Alec and Beth are saving at the same rate. Alec started with more money than Beth. and At 10 days, Alec will have $1 more than Beth in savings.

Step-by-step explanation:

help me for a brianly

Answers

Answer:

32 yd²

Step-by-step explanation:

because 8 • 4 is 32 so it's 32 yd²

Answer:

A = 32 yds^2

Step-by-step explanation:

We know the formula for the area of a rectangle is

A = lw  where l is the length and w is the width

A = 4 yds * 8 yds

A = 32 yds^2

What is the slope of the line 4x + 2y = 8?
А 2
b -2
c 1/2
d -1/2

Answers

Answer:

x = -1/2y+2

Step-by-step explanation:

4x+2y=8

Step 1: Add -2y to both sides.

4x+2y+−2y=8+−2y

4x=−2y+8

Step 2: Divide both sides by 4.

4x/4 = -2y+8/4

x = -1/2y+2

Hope this helps!

Fernando and Maria are at opposite sides of a park. They plan to meet later at a fountain that is located somewhere between them. Maria will arrive at the fountain first, before Fernando even leaves his starting location. The ratio of Maria's starting location to the fountain to Fernando's starting place is 5:3. What is the location of the fountain? Round to the nearest tenth, if necessary. ( ,

Answers

Answer: the fountain is located at point (-1,-0.5)

Step-by-step explanation:

Answer: (-1 , -0.5)

Step-by-step explanation:

i’ll give brainliest please help it's due in 30 min

Answers

Answer: √8
Explanation: x=(5/√8) x (√8 √8)

Help please!!! I can’t figure it out

Answers

9514 1404 393

Answer:

  C. ... 3 1/4 cups

Step-by-step explanation:

The problem statement tells you that the other measures are combined. That means you're looking for an expression like ...

  3/8 × ((3 2/3) +(2 1/4) +(2 3/4))

This eliminates choices B and D.

If you look at the numbers in parentheses, you see that the 1/4 and 3/4 will have a sum of 1, so the only fraction in the sum will be 2/3. This eliminates choice A.

The only viable answer choice is C.

__

If you like, you can check to see that answer C is correct.

  (3/8)(8 2/3) = (3/8)(26/3) = 26/8 = 3 2/8 = 3 1/4

PLEASE HELP !! ILL GIVE BRAINLIEST !!

Answers

Answer:

jkh and ihk

Step-by-step explanation:

Answer:

<JHK and IHK

Step-by-step explanation:

Please help me ASAP really need help!!!

Answers

Answer:

2.7

Step-by-step explanation:

the scale factor should be consistant as you scale up and down. So you can divide 4.59 by its corresponding side of 1.7 in order to get the scale factor of 2.7. When repeated with the other sides this number should remian consitant.  

for triangle ABC with sides a,b and c the law of cosines states
c^2=
in which of the following cases must the law of cosines be used to solve a triangle?
ASA SSS SAS SSA

Answers

Option C is correct. The law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)

For a triangle, ABC with sides a, b, and c respectively, the law of cosines is used on such a triangle if there is a presence of an angle between any two sides.

For example, if angle C is between the sides a and b, the equivalent cosine rule will be expressed as:

[tex]c^2 = a^2 + b^2 + 2ab cos C[/tex]

Hence the law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)

Learn more here: https://brainly.com/question/20880990

Find the area of the shaded region

Answers

Answer:

A = 35cm^2

Hope this helps :)


If Sherry saves one-eighth of her paycheck and places it in a savings account, and each paycheck is $450,
then how much does she save?


Answers

Answer:

$56.25

Step-by-step explanation:

450/8=56.25

A farmer used 204 feet of fencing to enclose a garden in the shape of a rectangle. If the length of the garden is twice the width, what is the width of the garden?
A) 34ft
B) 40.8ft
C) 51ft
D) 68ft
E) 81.6ft

Answers

Answer:

A

Step-by-step explanation:

Area=L+L+B+B

L=2

B=1

So, L+L+B+B=6

204/6=34

So, it's 34 ft, which is A.

Find the equation for the following parabola. Vertex 0,0. Focus 2,0.

Answers

Answer:

8x

Step-by-step explanation:

Answer:

Hi there! The equation for this parabola is y^2=8x.

Press the button without the slightest hesitation! :)

Step-by-step explanation:

Correct for Acellus! :)

PLEASE HELP ME THIS IS URGENT I HAVE 6 MINUTES PLEASEE

Answers

Answer:

1 goes to 2

2 goes to 4

3-goes to 1

and 4 goes to 3

Step-by-step explanation:

You apply for a job and have to take a drug test. You are curious about the error rate for the test so you do some research. You find a study where 47 out of 382 test results using this test were wrong (either a false positive or a false negative). The company that produces the drug test claims that less than 14% of the test results are wrong. Test if this seems accurate.

Answers

Answer:

Test statistic  Z = -1.0

 |Z| = |-1.0| < 1.96 at 0.05 level of significance.

The null hypothesis is accepted

The company that produces the drug test claims that less than 14% of the test results are wrong

Step-by-step explanation:

Step(i):-

Given that the population proportion P = 14% =0.14

Given that the sample size 'n' = 382 tests

Given that find a study where 47 out of 382 test results using this test were wrong (either a false positive or a false negative).

Sample proportion

                        [tex]p = \frac{x}{n} = \frac{47}{382} = 0.1230[/tex]

Null hypothesis: H₀ : P = 0.14

Alternative Hypothesis:H₁ : P≠ 0.14

Step(ii):-

Test statistic

              [tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }[/tex]

         [tex]Z = \frac{0.1230-0.14}{\sqrt{\frac{0.14 X0.86}{382} } }[/tex]

       Z = - 1.0

     |Z| = |-1.0| < 1.96 at 0.05 level of significance.

Final answer:-

The null hypothesis is accepted

The company that produces the drug test claims that less than 14% of the test results are wrong

               

Sonya measured her pet mouse from the tip of its nose to the tip of its tail. Her mouse is fourteen hundredths of a meter long. Which of the following expresses this length as a decimal? A 0.014 0.14 C1.4 14.00​

Answers

Answer:

A 0.014

Hope this helps!!!!

Calculate the number of edges of the solid. Given it has 8 faces; 4 hexagons & 4 triangles

Answers

Answer:

20 Edges

Step-by-step explanation:

As this figure shows only 10 edges..so to meet the given condition (8 faces; 4 hexagons & 4 triangles) same figure is present at the back making total of 20 Edges.

-5.225 as a mixed number.

Answers

Answer:

-5 9/40

Step-by-step explanation:

5/8
6 ft
9 ft
Find the area of the shape

Answers

Answer:

33.75 or rounded to the nearest tenth: 33.8

D 2. Squares, rectangles, and rhombi åre types of trapezoids.
True
O
False

Answers

Answer:

false

Step-by-step explanation:

The residents of a certain dormitory have collected the following data: People who live in the dorm can be classified as either involved in a relationship or uninvolved. Among involved people, 15 percent experience a breakup of their relationship every month. Among uninvolved people, 15 percent enter into a relationship every month. What is the steady-state percentage of residents who are uninvolved

Answers

Answer:

the steady-state percentage of residents who are uninvolved is 0.5

Step-by-step explanation:

 Given the data in the question;

let N represent total number of people in the dormitory

I represent  people involved in a relationship

and U represent people uninvolved in a relationship.

so

N = I + U

I = N - U ------ let this be equation 1

Rate of Uninvolved = U/N

now, given that rate of break ups B = 15% every month = 0.15

rate of entering into relationship  R = 15% every month = 0.15

Now, the steady state condition is;

RU = BI ------- let this be equation 2

such that uninvolved rate is constant.

we input equation 1 into 2;

RU = B( N - U  )

we divide both sides by N

RU/N = B( N/N - U/N  )

RU/N = B( 1 - U/N  )

U/N = B / (B + R)

so we substitute

U/N = 0.15 / (0.15 + 0.15)

U/N = 0.15 / 0.3

U/N = 0.5

Therefore, the steady-state percentage of residents who are uninvolved is 0.5

Question 2 of 10
What is the solution to this equation?
x - 16 = -8
A. x= 8
B. x = -8
C. x = 24
D. x= -24

Answers

A. X= 8
X-16=-8
X= -8+16
X=8
A explanation for this add 16 to negative 16 to move it -8 plus 16 equals 8 your left with X=8

Use the information in the figure to determine the height of the pole.

Answers

(x + 5)^2 + (x/2 + 6)^2 = (30)^2

Take it from here.

Answer:

pole height = 29 ft

Step-by-step explanation:

x² = 30² - (1/2x + 6)² = 30² - (1/4x² + 6x + 36) = 900 - 1/4x² - 6x - 36

combine like terms:

x² = -1/4x² - 6x + 864

1 1/4x² + 6x - 864 = 0

divide both sides of the equation by 1 1/4:

x² + 4.8x - 691.2 = 0

(x - 24)(x + 28.8) = 0

x = 24 ft

pole height = 24 + 5 = 29 ft

The bell on the clock tower rings every 15 minutes. If the bell has rung 24 times, how many minutes have passed?

Amber chose A. How did she get that answer?

Answers

Answer 360min = 15 days

Work:
Bell rings every 15 min
It ringed 24 times

15 min x 24 = 360min = 15 days

Samantha makes $8.00 an hour babysitting. With the money Samantha earns babysitting, she plans to buy herself a MP3 player that costs $154.00.

Which inequality represents the number of hours Samantha would have to babysit in order to have enough money to buy the MP3 player?

A youth group takes a bus to the movie theater. The cost of a drink is $2.25, the cost of popcorn is $3.45, and the cost of a ticket is $7.00. Each student gets a ticket, a drink, and popcorn. The bus rental costs $100.

If the total cost of the trip is $252.40, how many people went?

Sandra surveyed 15 of her friends to find the number of badges and stickers they owned.


Based on the distribution of data, which observation is correct?


The mean number of stickers is about 1.3 times the mean number of badges.

The mean number of stickers is about 1.3 times the mean number of badges.

The mean number of stickers is about 0.78 times the mean number of badges.

The mean number of stickers is about 0.78 times the mean number of badges.

The mean number of badges is greater than the mean number of stickers because the tallest column is farther right.

The mean number of badges is greater than the mean number of stickers because the tallest column is farther right.

The median number of badges is greater than the median number of stickers because the tallest column is farther right.

The median number of badges is greater than the median number of stickers because the tallest column is farther right.

Answers

Answer:

8h ≥ 154

Step-by-step explanation:

Mark me Brainllest

30 POINT REWARD!!! (haha I need to write 20 characters so that why this is here ps. please help)

Answers

Answer

Sorry, I need points to ask more question.

find the length of the side (x)

Answers

Answer:

C) x = 3.7

Step-by-step explanation:

sin 41° = x/5.6

0.6561 = x/5.6

x = 3.7

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