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Fed [463]
3 years ago
14

Find an equation of the circle whose diameter has endpoints , 6−2 and , −4−4 .

Mathematics
1 answer:
MrRissso [65]3 years ago
4 0
If you need just the answer, it's in bold at the bottom. Otherwise, the process for how I got there is below. 

In order to find the equation, we first find the midpoint. This will give us the center of the two endpoints. Then, we do the distance formula to find how many units there are between the endpoints and cut it in half to find the radius. After, we plug in the new information into the equation format of the circle. 

Midpoint = ( \frac{x_{1}+ x_{2} }{2},  \frac{ y_{1} + y_{2} }{2} )

So plug in the ordered pairs given to get: 

Midpoint = ( \frac{6-4}{2},  \frac{-2-4}{2})
Midpoint = ( \frac{2}{2},  \frac{-6}{2})
Midpoint = (1, - 3)

This is your center.

Now for the distance between the endpoints. 

Distance = √((X₂ - X₁)² + (Y₂ - Y₁)²)
Distance = √((-4 - 6)² + (-4 - (-2))²)
Distance = √((- 10)² + (- 2)²)
Distance = √(100 + 4)
Distance = √104 which simplifies to 2√26

So the distance between the two endpoints (the diameter) is 2√26 units long. We divide this by 2 and get the measurement of the radius. The radius is √26 units long. 

Now we plug in to the equation of a circle:

(x - h)² + (y - k)² = r² 

The center of the circle is represented by the ordered pair (h, k) and the radius is represented by r. 

So your equation becomes:
(x - 1)² + (y + 3)² = (√26)²

Which simplifies to your final answer:

(x - 1)² + (y + 3)² = 26

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Need help!!! Worth 13 points!
alisha [4.7K]
All you have to do is plug in the given values for a and b.

0.9a - 1.5b = ?

a = 15
b = 3

0.9 (15) - 1.5 (3)

= 13.5 - 4.5

= 9

Note:

•Integers are whole numbers.
For ex: 1, 2, 3, 4...

•Decimals have a period in between 2 numbers
For ex: 0.1, 0.2, 0.3

Sometimes when it’s concerning significant digits then decimals could also be
1.0, 2.0, 3.0 ... I wouldn’t worry about this right now until you get into higher years



3 0
3 years ago
Solve 4(2x - 1) - 3 = 9(x - 4). (1 point)
DiKsa [7]

Answer:

x = 29

Step-by-step explanation:

First we will expand the equation using the rule

x(y - z) = xy - xz

Thus,

4(2x - 1) - 3 = 9(x - 4)

is equal to

8x - 4 - 3 = 9x - 36

Simplify:

8x - 7 = 9x - 36

Add 36 to both sides:

8x + 29 = 9x

Therefore,

x = 29

4 0
3 years ago
HELP ASAP. please show work. the plane of a room in the picture. the scale is 2 inches: 6 feet. what is the actual length, width
lina2011 [118]

Answer:

Actual Length: 27 feet - Actual Width: 15 feet - Actual Area: 405 feet

Step-by-step explanation:

First, to find the length, you have to divide 9 by 2 to get 4.5 and then multiply it by 6 to get the actual amount of feet. Then you divide 5 by 2 and multiply the quotient by 6 to get the actual width. Then, you take the actual length (27 feet) and multiply it by the actual width (15 feet) and you get an area of 405 feet

8 0
3 years ago
Hey can you please help me posted picture of question
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