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tankabanditka [31]
2 years ago
7

write the standard form of the equation of the circle for which the endpoints of a diameter are (0,0) and (4,-6)

Mathematics
1 answer:
Elenna [48]2 years ago
5 0

Given:

The endpoints of a diameter are (0,0) and (4,-6).

To find:

The equation of the circle.

Solution:

The endpoints of a diameter are (0,0) and (4,-6). So, the length of the diameter is

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

d=\sqrt{(-6-0)^2+(4-0)^2}

d=\sqrt{36+16}

d=\sqrt{52}

d=2\sqrt{13}

Now, radius is half of the diameter.

r=\dfrac{2\sqrt{13}}{2}

r=\sqrt{13}

Center of the circle is the midpoint of the endpoints of a diameter.

Center=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)

Center=\left(\dfrac{0+4}{2},\dfrac{0+(-6)}{2}\right)

Center=\left(\dfrac{4}{2},\dfrac{-6}{2}\right)

Center=\left(2,-3\right)

Standard form of a circle is

(x-h)^2+(y-k)^2=r^2

where, (h,k) is center and r is radius.

The center of the circle is (2,-3) and radius is \sqrt{13}. So,

(x-2)^2+(y-(-3))^2=(\sqrt{13})^2

(x-2)^2+(y+3)^2=13

Therefore, the standard form of the circle is (x-2)^2+(y+3)^2=13.

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Answer:

20(3m-2)

Step-by-step explanation:

In order to factor, you have to look for the greatest common factor, or what the biggest number could the two numbers be divided by.

In this case, both numbers can be divided by 20, and so we put the 20 outside of the parentheses.

This leaves with 3m and -2, which are left inside the parentheses.


Hope this helps :)


8 0
3 years ago
10∙20=8∙d210•20=8•d2 .
tekilochka [14]
Is that the whole equation? Exactly from the book or paper?

5 0
3 years ago
10x(15w-11)+12 what is it help me
RUDIKE [14]
If im not wrong the answer is 150w - 98.
5 0
3 years ago
Kendra earns $11.60 per hour working at the movie theater. Each week, she donates of
stich3 [128]

Answer:

$9.86

Step-by-step explanation:

First, write both numbers in the same form. Convert 8

1

2

to a decimal.

8

1

2

= 8+

1

2

= 8+

1×5

2×5

= 8+

5

10

= 8+0.5

= 8.5

Multiply.

11.6

× 8.5

580

+ 9280

98.60

Kendra earned $98.60 last week.

Now multiply to find how much money Kendra donated to the charity last week. She earned $98.60, and she donates  

1

10

of her earnings each week.

First, write both numbers in the same form. Convert  

1

10

to a decimal.

1

10

=0.1

Multiply.

98.6

× 0.1

9.86

Kendra donated $9.86 to the charity last week.

7 0
3 years ago
in the equation 6+3y=4y+2 the variable y represents the same value. Is y= 2,3,4 or 5 the solution of this equation? Explain how
kherson [118]
6 + 3y = 4y +2
3y - 4y = 2 - 6
-y = -4
y = 4

hope that helps :)
3 0
3 years ago
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