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3 years ago

Given the conditional statement:

Mathematics

1 answer:

pogonyaev3 years ago

6 0

Seodosieodoososoeoer dodostvxdhffcoxoddoodododdododod

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If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. First, find

Evgesh-ka [11]

Answer:

The equation of the circle is $(x+3)^2+(y-5)^2 = 17$

Step-by-step explanation:

The complete question is

If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. First, find the midpoint of the diameter, which is the center of the circle. Then find the radius, which is the distance from the center to either endpoint of the diameter. Finally use the center-radius form to find the equation.

Find the center-radius form of the circle having the points (1,4) and (-7,6) as the endpoints of a diameter.

Consider that, if both points are the endpoints of a diameter, the center of the circle is the point that is exactly in the middle of the two points (that is, the point whose distance to each point is equal). Given points (a,b) and (c,d), by using the distance formula, you can check that the middle point is the average of the coordinates. Hence, the center of the circle is given by

$(\frac{1-7}{2}, \frac{4+6}{2}) = (-3,5)$ .

We will find the radius. Recall that the radius of the circle is the distance from one point of the circle to the center. Recall that the distance between points (a,b) and (c,d) is given by $\sqrt[]{(a-c)^2+(b-d)^2}$ . So, let us use (1,4) to calculate the radius.

$r = \sqrt[]{(1-(-3))^2+(4-5)^2} = \sqrt[]{17}$ .

REcall that given a point $(x_0,y_0)$ . The equation of a circle centered at the point $(x_0,y_0)$ is

$(x-x_0)^2+(y-y_0)^2 = r^2$

In our case, $(x_0,y_0)=(-3,5)$ and $r=\sqrt[]{17}$ . Then, the equation is

$(x-(-3))^2+(y-5)^2 = (x+3)^2+(y-5)^2 = 17$

4 0

3 years ago

Makakaanswer neto may brainlest,follow,5 star,at 1 heart step-by-step explenaition po ah thank you

shusha [124]

3/4 + 1/2
multiply 1/2 denominator and numerator by 2 to match 3/4
= 3/4 + 2/4 = 5/4 (copy same denominator add numerator)

2/6 + 1/3
divide 2/6 denominator and numerator by 2 to match 1/3
= 1/3 + 1/3 = 2/3 (copy same denominator add numerator)

5/9 + 2/3
multiply 2/3 denominator and numerator by 3 to match 5/9
= 5/9 + 6/9 = 11/9 (copy same denominator add numerator)

6/9 -1/5
cross multiply 6x5 - 1x9 for numerator
for denominator multiply 9x5
=30/45 - 9/45= 21/45
divide num and den by 3
=7/15

5/8-1/3
cross multiply 5x3-1x8 for numerator
multiply 8x3 for denominator
= 15/24 -8/24 =7/24

7 0

2 years ago

What is 2(3x+15) - (8+2x) simplified

Olin [163]

Answer:

4x+22

Step-by-step explanation:

Brainliest?

3 0

3 years ago

Read 2 more answers

For my little cousin:

Mars2501 [29]

Answer:

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Please help I don’t understand this

horrorfan [7]

Answer:

C) 17

Step-by-step explanation:

Using the rule

A^2 + B^2 = C^2

8^2 + 15^2 = x^2

64 + 225 = x^2

x^2 = 289

x= _/-289

x = 17

3 0

3 years ago