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

i need help with this math question

Answers

Answer:

it is S

Step-by-step explanation:

because it is being reflected on the X-axis

Answer:

point R

Step-by-step explanation:

If you move point R across the x-axis, and then up the y-axis, you meet point Q

how many degrees is a acute angle

Answers

The answer is 90 degrees

Any angle that measures less than 90 degrees

Find the surface area of the regular pyramid

Answers

Greetings from Brazil!

[tex]4\dfrac{1}{2} =\dfrac{9}{2}[/tex]

[tex]Af1=\dfrac{b\cdot h}{2} \cdot 4\\\\\\Af1=\dfrac{\dfrac{9}{2} \cdot 4}{2} \cdot 4\\\\\\Af1=\dfrac{\dfrac{36}{2} }{2} \cdot 4\\\\\\Af1=\dfrac{18}{2} \cdot 4\\\\Af1=9\cdot 4\\\\Af1=36~m^2[/tex]

[tex]Af2=l^2\\\\Af2=(\dfrac{9}{2})^2\\\\\ Af2=\dfrac{81}{4}\\\\Af2=20,25~m^2[/tex]

[tex]At=Af1+Af2\\At=36+20,25\\At=56,25~m^2[/tex]

I hope I helped you! =)  

Which values are solutions to the inequality below? Check all that apply.

x² < 64​

Answers

Answer:

C, D, and E work,

Step-by-step explanation:

An expression is shown below:

2x3y + 8xy − 4x2y − 16y

Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)

Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

Plz help, give good answer and get brainlest!!

Answers

Answer:

Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)

answer:

2y(+4x-2x²-8)

Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

answer:

2y(x³+4x-2x²-8)

2y(x³-2x²+4x-8)

2y((x-2)+4(x-2))

2y(+4)(x-2)

Help plssss I can’t

Answers

Answer:

336 square units

Step-by-step explanation:

The formula for a triangle is 1/2 * height *base

What is 468,839 rounded to the nearest hundred thousand?

Answers

Answer:  500,000

Step-by-step explanation:

468,839 rounded to the nearest hundred thousand ( 100,000 ) would be 500,00 since its above 50 and its 68.

Hopes this helps :)

Help me please with this math problem.

Answers

Answer:

The table is a quadratic function

Step-by-step explanation:

Given

The attached table

Required

Tell if it is a quadratic function

The difference in the x values are uniform (i.e. difference of 1), so the following method can be applied.

(1) Subtract adjacent y values.

[tex]d_1=2 - 16 = -14[/tex]

[tex]d_2=-2 - 2 = -4[/tex]

[tex]d_3 = 4--2 = 6[/tex]

[tex]d_4 = 20 - 4 = 16[/tex]

(2) Subtract adjacent differences in (1) above

[tex]d_5 = d_2 - d_1 = -4 --14 = 10[/tex]

[tex]d_6 = d_3 - d_2 = 6 --4 = 10[/tex]

[tex]d_7 = d_4 - d_3 = 16 -6 = 10[/tex]

Notice the calculated differences in (2) are the same.

Hence, the table is a quadratic function

PLS HELP!!! FOR 10 POINTS SHOW WORK PLEASE

Tell whether the angles are adjacent or vertical. Then find the value of x

The angles are ? Angles
The value of x is ?

Answers

Answer:

adjacent

x = 100

Step-by-step explanation:

These two angles share a ray in common. They are adjacent.

x + 80 = 180      Subtract 80 from both sides

x =  180 - 80

x = 100

f(x) = x2. What is g(x)?




A. g(x) = 4x²
B. g(x) = (1/4x)²
C. g(x) = (1/2x)²
D. g(x) = 1/4x²

Answers

Answer:

B. g(x) = (1/4x)²

Step-by-step explanation:

g(x) experiences a horizontal stretch where 0<|a|<1

This means we can eliminate A because that would be a horizontal compression since |a|>1

B seems to work because (1/4(4))^2=1

C does not work because you'll get 2 as your y-value

D does not work because you'd be taking 1/4 of x^2 which would give you 4.

x+3.6= −4.75

Solve for x

Tell what you did to find x

Answers

Answer:

x=3.85

brainliest plssssssss

Step-by-step explanation:

Question:

x+3.6= −4.75

Step 1:

Subtract  3.6 from both sides of the equation

x+3.6-3.6=-4.75-3.6

Step 2:

Subtract the Numbers and simplify

x=3.85

There are 4 points that form a rectangle. Three of the points are: (-5 -1) (-5 3) (2<3 What are the coordinates of the fourth point?

Answers

Answer:

[tex]C = (2,-1)[/tex]

Step-by-step explanation:

Given

[tex]A = (-5,-1)[/tex]

[tex]B = (-5,3)[/tex]

[tex]D = (2,3)[/tex]

Required

The coordinate of the fourth point (C)

The given coordinates indicate the rectangle is vertical/horizontal because it has similar x and y values.

The coordinate of such rectangle can be represented as:

[tex]A = (x_1,y_1)[/tex]

[tex]B = (x_1,y_2)[/tex]

[tex]C = (x_2,y_1)[/tex]

[tex]D = (x_2,y_2)[/tex]

By comparing the general coordinates with the given coordinates, we have:

[tex]x_1 = -5[/tex] --- see A and B

[tex]y_1 = -1[/tex] --- see A and C

[tex]x_2 = 2[/tex] ---- see C and D

[tex]y_2 = 3[/tex] --- see B and D

So, we have:

[tex]C = (x_2,y_1)[/tex]

[tex]C = (2,-1)[/tex]

Answer is:

C. (2, -1)

the sum of 1+3+5+7+...+101=?​

Answers

Answer:

.......117. hope it helps

How many tons are equal to 6,000 pounds

Answers

1 ton equals 2000 pounds

so 3 tons equals 6000 pounds

Answer: 3 tons

Answer:

6,000 Pounds =

3 Tons

Step-by-step explanation:

A pound is a unit of weight commonly used in the United States and the British commonwealths. A pound is defined as exactly 0.45359237 kilograms.

A ton, also referred to as a short ton, is a unit of weight equal to 2,000 pounds. It is commonly used in the United States. Most other countries use the metric ton, or "tonne".

A study9 compared personality characteristics between adult children of alcoholics and a control group matched on age and gender. For the 29 pairs of women, the authors reported a mean of 24.8 on the well-being measure for the children of alcoholics, and a mean of 29.0 for the control group. They reported t = 2.67 for the test comparing the means. Assuming that this is the result of a dependent-samples analysis, identify the df for the t test statistic, report the P-value, and interpret.

Answers

Answer:

df.= 28

P - value = 0.0124 < 0.05

There is a difference between the mean of  the well-being measure for the children of alcoholics, and a mean of the control group.

Step-by-step explanation:

As the given test is dependent or paired test the degrees of freedom is n-1 = 20-1 = 28

The reported t = 2.67

The P value for ∝= 0.05 at  calculated t= 2.67 and 28 d.f is 0.0124 which is less than 0.05 .

The null hypothesis is rejected.

The null hypothesis is that there is no difference between the means of the two samples.

H0: u1 = u2

The alternate hypotheis is accepted that there is  difference between the means of the two samples.

Ha: u1≠ u2

There is a difference between the mean of  the well-being measure for the children of alcoholics, and a mean of the control group.

Two processes in a manufacturing line are performed manually: operation A and operation B. A random sample of 50 different assemblies using operation A shows that the sample average time per assembly is 8.05 minutes, with a population standard deviation of 1.36 minutes. A random sample of 38 different assemblies using operation B shows that the sample average time per assembly is 7.26 minutes, with a population standard deviation of 1.06 minutes.

Required:
For α = 0.10, is there enough evidence in these samples to declare that operation A takes significantly longer to perform than operation B?

Answers

Answer:

3.06

Step-by-step explanation:

The correct answer is - 3.06

Reason -

For sample A :

mean, [tex]\bar{x_{1} }[/tex] = 8.05          

Standard deviation, [tex]\sigma_{1}[/tex] = 1.36          

Size, [tex]n_{1}[/tex] = 50          

                 

For sample B :

mean, [tex]\bar{x_{2} }[/tex] = 7.26          

Standard deviation, [tex]\sigma_{2}[/tex] = 1.06          

Size, [tex]n_{2}[/tex] = 38

Now,

[tex]\bar{x_{1} }[/tex] - [tex]\bar{x_{2} }[/tex]  = 8.05 - 7.26 = 0.79

Standard deviation error, SE = √([tex]\sigma_{1}[/tex]²/[tex]n_{1}[/tex] + [tex]\sigma_{2}[/tex]²/[tex]n_{2}[/tex])  = 0.2580

Now,

Z-statistic = ([tex]\bar{x_{1} }[/tex] - [tex]\bar{x_{2} }[/tex] )/ SE

                = 0.79/0.2580

                = 3.06

⇒Z-statistic = 3.06

an expression is shown. 9,537 ÷ 33 what is the value of the expresion?

Answers

Answer:

9537÷33=289

why?

33×289=9537

A scale drawn on a map represents 1 inch to be equal to 28 miles. If two cities are 2 3/4 in. apart on the map, what is the distance between them in real life? A. 49 mi. B. 77 mi. C. 56 mi. D. 63 mi.

Answers

The answer is B.
28x2 then the remaining 3/4 equals to 21 miles so add first to inches then the remaining. 28+28+21=77

Answer: i got it right the answer is 77

Step-by-step explanation:


Sally's savings account has $238 and she is withdrawing (taking money out) $17 each week to put gas in her car. How much money will Sally have after 5 weeks?

Answers

Answer:

$153

Step-by-step explanation:

The Correct Answer for this is 153$ Because you times 17 by 5 and subtract that from 238

A professor compares the number of students at his school majoring in statistics, engineering, both, or neither.

How many items are in the sample space for a student at his school?
A. 1
B. 2
C. 3
D. 4

Answers

Answer:

Step-by-step explanation:

3

Solve by Graphing: Y=4x-3 and y=-x+2

Answers

1. The starting point is -3 then go up 4 and run 1

2. The starting point is 2 then go up one and then go one left bc it’s negative

Evaluate the polynomial for x = -2.
x² - 9x+7

Answers

Evaluate usually means simplify/solve

(-2)^2 - 9(-2) + 7
(-2)(-2) - (-18) + 7
4 + 18 + 7
= 22 + 7
= 29

Answer:

Hi! The answer to your question is [tex]29[/tex]

Step-by-step explanation:

☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆

☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

Question below in photo!! Please answer! Will mark BRAINLIEST! ⬇⬇⬇⬇⬇⬇⬇
Answer (chose the right one):
-40°
-30°
-50°
-100°

Answers

Answer:

30°

Step-by-step explanation:

∠EGD = ∠BGA

∠BGA= 30°

GIVING BRAINLIEST!!!

Which summation formula is equivalent to the one below?​

Answers

Answer:

The second summation, counting from the top.

Step-by-step explanation:

Remember the relation:

[tex]a^{-n} = \frac{1}{a^n}[/tex]

The first summation is:

4*(  (-1/2)^0 + (-1/2)^1 +  (-1/2)^2 + (-1/2)^3)

4*( 1 - 1/2 + 1/4 - 1/8) = 2.5

Now let's analyze the options.

Let's look at option A, here we only have 2 to different powers, so we never can have a summation equal to 2.5, then we can discard that option.

Let's look at the next one (B), it will be equal to:

= (1/4)*( (-2)^4 + (-2)^3 + (-2)^2 + (-2)^1) =

= (1/4)*( 16 - 8 + 4 - 2) = 2.5

Then this summation is the one equivalent to the first one.

Answer:

B

Step-by-step explanation:

edg 2021

To graduate this semester, you must pass Statistics 314; and you estimate that you have an 85% chance of passing. You need to pass Math 272 or Math 444, each of which you have an 80% chance of passing: so you will take both in hopes that you will pass at least one. Further, you must pass German 320, which you believe you have a 90% chance of passing. Assuming your chances of passing each class you take are independent, what is your probability of graduating this semester

Answers

Answer:

Probability of graduating this semester is 0.7344

Step-by-step explanation:

Given the data in the question;

let A represent passing STAT-314

B represent passing at least in MATH-272 or MATH-444

M1 represent passing in MATH-272

M2 represent passing in MATH-444

C represent  passing GERMAN-32

now

P( A ) = 0.85, P( C ) = 90, P( M1 ) = P( M2 ) = 0.8

P( B ) = P( pass at least one of either MATH-272 or MATH-444 ) = P( pass in MATH-272 but not MATH-444 ) + ( pass in MATH-444 but not in MATH 272) + P( pass both )

P( B ) =  P( M1 ) × ( 1 - P( M2 ) ) + ( 1 - P( M1 ) ) × P( M2 ) + P( M1 ) × P( M2 )

we substitute

⇒ 0.8×0.2 + 0.2×0.8 + 0.8×0.8 = 0.16 + 0.16 + 0.64 = 0.96

∴ the probability of graduating this semester will be;

⇒ P( A ) × P( B ) × P( C )

we substitute

⇒ 0.85 × 0.96 × 90

0.7344

Probability of graduating this semester is 0.7344

Rammy has saved some money for a new bicycle helmet that costs $47, but needs to save more. He writes an addition equation with a variable to represent the amount of money that he still needs to save. Which must be true about Rammy's equation

Answers

Is this the full question? 47= money saved+money needed?

Write the mix number as a fraction. 1 2/3 ||

Answers

Answer:

8/3

Step-by-step explanation:

Evaluate: show your work
Find the value of the variable.
102-8m=86

HELP. PLEASE HELP ME. I could really use your help if you evaluated it. Please and thank you :))

Answers

Answer:

this is easy. all you have to do is subtract 102 from 86 (which makes -16) and then divide by -8 (making m equal to 2).

Step-by-step explanation:

102 - 8m = 86

86 - 102 = -16

-16/-8 = 2

Answer:

Its 2 bby :)

Step-by-step explanation:

When a number (in this case it's a variable) is put next to another number we are multiplying. So 8×2=16 Lets test it out. 102-16=86

myq-eimh-otm

a.l.l
a.l.o.u.l.d

Answers

Yesssssssssssssssssssssssssss

Need help please???

Answers

Answer:

y= [tex]\frac{3}{5}x[/tex] [tex]-\frac{26}{5}[/tex]

Step-by-step explanation:

x₁    y₁                     m= slope

(2, -4)                     point-slope equation: y - y₁ = m( x - x₁)

y-(-4) = [tex]\frac{3}{5}[/tex]( x - 2)

y + 4 = [tex]\frac{3}{5} x[/tex] - [tex]\frac{6}{5}[/tex]

y = [tex]\frac{3}{5}x[/tex] - [tex]\frac{6}{5}[/tex] - [tex]\frac{20}{5}[/tex]

y = [tex]\frac{3}{5} x[/tex] - [tex]\frac{26}{5}[/tex]

Other Questions
Here are two patterns made using identical rhombuses. Without using a protractor, determine the value of a and b. Explain or show your reasoning in your workbook. Is the Rio Grande River the border between South and North America? The levels of organizations in multicellular organisms are shown below, but they are not in the correct order. Arrange the levels of organization in order from simplest to most complex. Carmen will randomly pick one marker from a bowl and one crayon from another bowl.- There are 4 green markers, 3 brown markers, and 1 purple marker.- There are 6 orange crayons and 2 yellow crayon.What is the probability of picking a brown marker and a yellow crayon? what is Otorhinolaryngologist. What were the characteristics of each party? NO LINKS THIS IS THE 4TH TIME IVE TRIEDfederalists:democratic republicans:list at least 4 for each THANK YOUU 10. Which is true of the Mycenaeans?A. They built large ornate palaces.B. They began the Trojan War.C. They placed great emphasis on trade.(This is to help some others who dont get it) All of the following statements concerning drugs and supplements are true EXCEPT:A. Many drugs and supplements are ineffective and expensive.B. Many supplements and drugs are frequently used to improve performance and appearance.C. Supplements and drugs both undergo stringent government testing.D. Supplements and drugs can both cause unwanted side effects. I need the organelle and it's role in analogy.Ive been called the storage tank. Im a sac filled with water, food, enzymes, and waste. Im big in a plant and tiny in an animal.Im like the UPS delivery person. I deliver stuff, mostly proteins. Im the fluid in the cell that fills in the space, my main purpose it to hold organelles in place.Im found only in plant cells, Im as green as can be, I make food for the plant using the suns energy. A cone has a height of 8.4 centimeters and a base with a radius of 5.2 centimeters. What is the volume of the cone?(PLEASE SOLVE IT) What are the prevailing winds from the west toward the east called?Prevailing WesterliesJet StreamGulf StreamLa Nina The invention of the internet began in 1960s after ...................Sent sputnik the first satellite into space find the area of a semi circle when the radius is 10cm.give the answer in term of pi Find the area of a rectangle that has a length of 212 units and a width of 7 units in units2.Give your answer as a mixed number. Es un crusigrama de las emociones ayuda 1. It's Bobby's birthday! He is HAPPY. 3. Lisa has a new pink bike. Her neighbour is _____. 4.Tom did not study for his Math exam. He is _____. 6. Someone stole Mark's lunch money! He is _____. 8. Tina's hamster died. She is _____. ACROSS 2. Diego and Alan are watching a horror movie. They are ____. 5. Pedro won the first prize in the Poetry contest. He is filled with _____. 7. The twins are going to Disneyworld next summer. They are _____. 9. Tom accidentaly broke his friend's new toy. He is _____ Please help A helicopter is 2,500 feet above sea level. A pirate ship sunk with buriedtreasure off the coast of Florida 125 years ago. It's depth is 3,000 feetbelow the helicopter. How many feet below sea level is the pirate ship? Evaluate.f(x)=17-5x at x=a-3 Misterio Company uses a standard costing system. During the past quarter, the following variances were computed: Variable overhead efficiency variance $ 24,000 U Direct labor efficiency variance 120,000 U Direct labor rate variance 10,400 U Misterio applies variable overhead using a standard rate of $2 per direct labor hour allowed. Two direct labor hours are allowed per unit produced. (Only one type of product is manufactured.) During the quarter, Misterio used 30 percent more direct labor hours than should have been used. Required:1. What were the actual direct labor hours worked? The total hours allowed?2. What is the standard hourly rate for direct labor? The actual hourly rate?3. How many actual units were produced? Read the excerpt from Keeshas essay about Labrador retrievers.Everyone seems to have a favorite breed of dog, but the Labrador retriever, with its many skills and natural friendliness, has always had a special place in my heart. Labradors are widely regarded as highly intelligent and loyal. Because of their personality, they are often valued as great family dogs. My uncle owns a Labrador, and its the friendliest dog Ive ever met. Because he is such a friendly dog, we often take him to the dog park. But the most fascinating thing about Labradors is their hunting skills.What sentence in this paragraph is unnecessary? A. "Labradors are known to be highly intelligent and loyal." B. "Because of their personality, they are often valued as great family dogs." C. "Because he is such a friendly dog, we often take him to the dog park." D. "But the most fascinating thing about Labradors is their hunting skills."