N

raph the equation with a diameter that has endpoints at (-3, 4) and (5, -2). Label the center and at least four points on the ci

andreyandreev [35.5K]

Answer:

Equation:

${x}^{2} + {y}^{2} + 2x - 2y - 35= 0$

The point (0,-5), (0,7), (5,0) and (-7,0)also lie on this circle.

Step-by-step explanation:

We want to find the equation of a circle with a diamterhat hs endpoints at (-3, 4) and (5, -2).

The center of this circle is the midpoint of (-3, 4) and (5, -2).

We use the midpoint formula:

$( \frac{x_1+x_2}{2}, \frac{y_1+y_2,}{2} )$

Plug in the points to get:

$( \frac{ - 3+5}{2}, \frac{ - 2+4}{2} )$

$( \frac{ -2}{2}, \frac{ 2}{2} )$

$( - 1, 1)$

We find the radius of the circle using the center (-1,1) and the point (5,-2) on the circle using the distance formula:

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

$r = \sqrt{ {(5 - - 1)}^{2} + {( - 2- - 1)}^{2} }$

$r = \sqrt{ {(6)}^{2} + {( - 1)}^{2} }$

$r = \sqrt{ 36+ 1 } = \sqrt{37}$

The equation of the circle is given by:

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

Where (h,k)=(-1,1) and r=√37 is the radius

We plug in the values to get:

$(x- - 1)^2 + (y-1)^2 = {( \sqrt{37}) }^{2}$

$(x + 1)^2 + (y - 1)^2 = 37$

We expand to get:

${x}^{2} + 2x + 1 + {y}^{2} - 2y + 1 = 37$

${x}^{2} + {y}^{2} + 2x - 2y +2 - 37= 0$

${x}^{2} + {y}^{2} + 2x - 2y - 35= 0$

We want to find at least four points on this circle.

We can choose any point for x and solve for y or vice-versa

When y=0,

${x}^{2} + {0}^{2} + 2x - 2(0) - 35= 0$

${x}^{2} +2x - 35= 0$

$(x - 5)(x + 7) = 0$

$x = 5 \: or \: x = - 7$

The point (5,0) and (-7,0) lies on the circle.

When x=0

${0}^{2} + {y}^{2} + 2(0) - 2y - 35= 0$

${y}^{2} - 2y - 35= 0$

$(y - 7)(y + 5) = 0$

$y = 7 \: or \: y = - 5$

The point (0,-5) and (0,7) lie on this circle.

3 0

3 years ago

The cost of 90 kg of rice is 4500. what is the cost of 2 quintal of rice?

gayaneshka [121]

Answer:

The cost of 2 quintal of rice is $10,000.

Step-by-step explanation:

To determine the cost of 2 quintals of rice, knowing that 90 kilos of said product is worth $ 4,500, it is first necessary to establish the equivalence between quintals and kilograms. In this regard, a quintal is equivalent to 100 kilograms, so 2 quintals are equivalent to 200 kilos.

Now, to determine the cost per kilogram of rice, the following calculation is required:

4,500 / 90 = X

50 = X

Therefore, 1 kilogram of rice costs $ 50. Thus, since 200 x 50 equals 10,000, 2 quintals of rice will cost $ 10,000.

5 0

3 years ago

HELP ASAP I GIVE 15 POINTS AND BRAINLIEST

IgorC [24]

Answer:

110%

Step-by-step explanation:

if each square is a whole, then when one is filled, it's 100% . 10% of the other square is filled so you just add the two.

4 0

3 years ago

How do i factor (10x^2-25x-15)

Otrada [13]

5(2x^2 - 5x - 3) = 5(2x + 1)(x - 3)

hope this helps :)

4 0

2 years ago

What’s the correct answer

PolarNik [594]

The correct answer would most likely be option C. This is because the lowest tip was on 5, thus we can eliminate B and D.

And during this time the slope almost remained stationary, minimal change.

3 0

3 years ago