The vertices of △XYZ are X(4, 5), Y(4, 13), and Z(8, 9). Find an equation of the circle circumscribed about △XYZ.


An equation is ???


NEEED HELPPP PLEASEEE

Answers

Answer 1

Answer:

The equation of the circle is (x - 4)² + (y - 9)² = 4²

Explanation:

The center radius form of the equation of the circle is (x - h)² + (y - k)² = r²

Therefore, given the coordinates of the vertices of the inscribed triangle, we have points on the circumference includes;

X(4, 5), Y(4, 13), Z(8, 9)

Hence, we have;

(4 - h)² + (5 - k)² = r² = h²- 8·h - 10·k + k² + 41..........(1)

(4 - h)² + (13 - k)² = r² = h² - 8·h + k² - 26·k +185.....(2)

(8 - h)² + (9 - k)² = r² = h² - 16·h -18·k + k² +145.........(3)

Subtracting equation (1) from (2), we have;

-(16·k -144) = 0

∴ 16 k = 144

k = 9

Subtracting equation (1) from (3), we have;

-(8·h + 8·k - 104) = 0

Which gives;

8·h + 8·k - 104 = 0, where k = 9 gives

8·h + 8×9 - 104 = 0

8·h - 32 = 0

h = 32/8 = 4

Plugging in the values of h and k in equation (3), we have;

(8 - 4)² + (9 - 9)² = r²

4² = r²

∴ r = 4

The equation of the circle is (x - 4)² + (y - 9)² = 4².


Related Questions

How did Liu Bang improve China's government?
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He maintained a powerful centralized bureaucracy.
He gave local officials full power over their provinces.
He created harsh laws to force citizens to behave correctly.

Answers

Answer:

He maintained a powerful centralized bureaucracy.

Explanation:

Thats pretty much his whole thing.

where does the river erode sediment?

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Streams erode sediment from their banks. They pick up and transport sediments.

Two ways that modern golf is different then the original (folk) golf are: *
10 points
a. In golf today lowest score wins, folk golf highest score wins.
b. Irish golfers were not permitted to play in Scotland until 1926, and caddies did not exist.
c. Early Scottish courses were laid out on dunes and the game was relatively inexpensive to play.
d. golf balls were smaller than today, and tournament winners were given sheep for their farms.
e. early games were timed, and were sometimes played in villages too.

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Answer:

C

Explanation:

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which material gives the soil its high fertility

Answers

Answer:

humus

Explanation:

Humus is one of the organic matter that helps soil fertile.

Answer:

Your answer is D. humus

Explanation:

hope it helps

Explain how increased ocean temperatures increases the strength of hurricanes

Answers

Answer:

The rising of warm, moist air from the ocean helps to power the storm. Two other factors may also be contributing to the rising intensities of hurricanes. First, warm air holds more water vapor than cold air—and the rising air temperatures since the 1970s have caused the atmospheric water vapor content to rise as well.

Explanation:

Answer:

Warmer ocean waters mean more fuel to create stronger Hurricaines.

Explanation:

Hurricaines start with the evaporation of warm ocean waters. A rise in ocean temperatures will result more water vapor being evaporated into the air which causes an increase in hurricaines and make them more severe. Just a 1 degree rise in Fahrenheit can result in an incease wind speed of 15-20 mph. Hope this helps!

Surface temperature of 25 ∘C, which is 15 ∘C higher than the middle-latitude city mentioned in Part A. Vertical soundings reveal an environmental lapse rate of 6.5 ∘C per kilometer and indicate that the tropopause is encountered at 16 kilometers. What is the air temperature at the tropopause?

Answers

Answer:

at an altitude of 16 kilometers the temperature of tropopause is -79° C.

Explanation:

Given that:

The surface temperature = 25° C

Vertical constant environmental Lapse Rate ( Change in temperature with height) = 6.5° C/km

Altitude of tropopause = 16 kilometers

It is pertinent to understand that as we move higher up to the tropopause ; temperature decreases.

SO;  we need to  subtract the change in temperature from surface temperature

Thus; Air temperature at tropopause = Surface temperature - (Change in temperature till the altitude of tropopasue)

Air temperature at tropopause =  Surface temperatue - (Lapse Rate × Altitude)

Air temperature at tropopause =  25° C - (6.5 ° C/km  ×  16 km)

Air temperature at tropopause =  25° C -  104° C)

Air temperature at tropopause = -79° C

Thus; at an altitude of 16 kilometers the temperature of tropopause is -79° C.

Which events took place during the Copernican revolution, when most people started to believe in a heliocentric model of the solar system? Check three options.
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2.) Copernicus rediscovered Aristarchus’s heliocentric model.
3.) Hawking proposed theories that increased curiosity about space.
4.) Scientists checked, confirmed, refined, and mathematically proved ideas.
5.) Newton’s theories of gravity increased understanding of the movement of planets.

Answers

Answer:

2 , 3 and 5

Explanation:

Hawking proposed theories that increased curiosity about space.     true

Scientists checked, confirmed, refined, and mathematically proved ideas.     true  

Newton's theories of gravity increased understanding of the movement of planets                true

10:Three types of map projections discussed in this unit are:

projection

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Answers

cylindrical map projections , conic map projections , & azimuthal map projections.

Match the mountain range with its type of formation​

Answers

Answer:

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Explanation:

Hope that Helped!

Answer:

Aleutian : oceanic- oceanic

Himalayas : continental- continental

Grand Tetons: fault-block

Andes: oceanic- continental

Explanation:

A P E X

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Answers

Answer: waxing~ Wax as an intransitive verb means to grow in size, where

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Explanation:

In this excerpt from the Emancipation Proclamation, which phrase or sentence supports the claim that President Lincoln did not want the slaves to take up arms against their former masters?

A. I do order and declare that all persons held as slaves within said designated States, and parts of States, are, and henceforward shall be free; and that the Executive government of the United States, including the military and naval authorities thereof, will recognize and maintain the freedom of said persons.
B. And I hereby enjoin upon the people so declared to be free to abstain from all violence, unless in necessary self-defence;
C. And I further declare and make known, that such persons of suitable condition, will be received into the armed service of the United States to garrison forts, positions, stations, and other places, and to man vessels of all sorts in said service.
D. And upon this act, sincerely believed to be an act of justice, warranted by the Constitution, upon military necessity, I invoke the considerate judgment of mankind, and the gracious favor of Almighty God.

Answers

Answer:

the answer is B................

Answer:

B

Explanation:

I am 99.99% sure it's B.

PLZ HURRY!!!! Analyze the map below and answer the question that follows.

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Image courtesy of NASA


Look at the map above. Which of the following statements is true?


A.

Number 3 is the Pacific Ocean.

B.

Number 4 is the Orinoco River.

C.

Number 2 is the Strait of Magellan.

D.

Number 3 is the Amazon River.


Please select the best answer from the choices provided

A

B

C

D

Answers

Answer:

D

Explanation:

The answer is D.

Answer: D or 4

Explanation:

Got it on EDGE 2021

But actually its right -_-

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Answers

Answer:

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The evolution can be based on the genes or the offspring of the generations.

Modern people have developed a craze and trend of new tastes that have arisen in the person unlawfully of wildlife or the attractiveness of the country. It has lessened to some extent as a result of increased education and appreciation for wild creatures.

Many regulations have been created across the globe to assist and conserve feral creatures owing to the risk of them becoming extinct as a consequence of human actions such as deforestation and illegal wildlife hunting. To combat the issue, zoos and other conservation centers have been developed.

To know more about the extinction of wild animals and the appearance of modern humans, refer to the link below:

https://brainly.com/question/5076508

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Answers

Answer:

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Explanation:

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Answers

Answer:

k =x + 9/x

Explanation:: Idk hopefully this helps if not im sorry :/

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Answers

Answer:

A

Explanation:

A. Today, female rabbis are ordained within all branches of Progressive Judaism, while in mainstream Orthodox Judaism, women cannot become rabbis. => Answer A is just half true / half false about Judaism.

B. In most of the world today, Jewish houses of worship are known as Synagogues. => Answer B is true about Judaism.

C. Celebrating Easter means Jewish people are celebrating the resurrection of Christ, which is opposite of what Jews actually believe in. => Answer C is true about Judaism.

D. "Kosher" is a term used to describe food that complies with the strict dietary standards of traditional Jewish law.  => Answer C is true about Judaism.

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Answers

The correct answer is B. Elevation

Explanation

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Answer:

elevation is right anwers

Explanation:

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Answers

Answer:

They Both contain eukaryotic cells. They both contain membrane-bound organelles such as the nucleus, mitochondria, endoplasmic reticulum, golgi apparatus, lysosomes, and peroxisomes.

Explanation:

Hope this works!

Answer:

I'm not sure what exactly you are looking for, but here's a list of possible answers.

Explanation:

1. Nucleus

2. Mitochondria

3.Endoplasmic Reticulum

4. Golgi Apparatus

5. Lysosomes

6. Peroxisomes.

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Answers

Answer:

Pollution

Explanation:

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Answers

Answer:

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The updrafts / rising / hot and descending / falling / cold of the mantle can explain the movement of the plates, acting as a kind of "stimulating roller" that moves them.

Explanation:

When they move, they cause earthquakes or tsunamis in large bodies of water, when they converge and collide with each other, it may be that they form both mountains and volcanoes, in the event that they have a conduit that connects said geographic feature with the hot magma or mantle.

And if divergent movements happen they could also be caused by earthquakes, tsunamis, and even geographic divisions or neocontinent formations.

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can U give me the definition on ur own words pls!!

Answers

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A place is connected by similar characteristics is called

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Answer:A region is an area with similar characteristics. Those characteristics can be physical, natural, human, or cultural.

Explanation:

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Answers

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Drivers must understand that traffic laws _______ them and should be supported and followed.

Answers

Answer:

that traffic laws protect them

traffic laws protect them

What is a custom or tradition practiced here in the United States? (not
religious)

Answers

Answer:

The 4th of July

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A
Compaction
(B
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D
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Answers

Answer:     B

Explanation:

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Which event convinced Cuba to seek help from the Soviet Union?

Answers

Answer:

With the U.S. Castro and his regime became in important cold ally for the soviets. The soviet union was providing military, economic and political assistance to cuba

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Explanation:

hope this helps :)

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Answers

Answer:

A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail.

Explanation:

Answer:

comets are like asteroids , but they are a snowballs of frozen gases. they are and up of dust and things that can melt. comets have a tail cause they melt due to the sun's heat.

Explanation:

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