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

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.

myq-eimh-otm

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

Answers

Yesssssssssssssssssssssssssss


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

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".

the sum of 1+3+5+7+...+101=?​

Answers

Answer:

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

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.

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]

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

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

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! =)  

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

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)

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

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

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:

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 :)

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

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?

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

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

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

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)

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

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:

how many degrees is a acute angle

Answers

The answer is 90 degrees

Any angle that measures less than 90 degrees

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
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