Mathematics, 24.09.2019 20:00 CAPEPOPPA

Acircle is centered at the point (5,-4) and passes through the point (-3,2).
the equation of this circle is (x+ 1] 2+0+ 0
.
what is?

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Answer from: liliauedt

(x-5)^2 + (y+4)^2 = 10^2

Step-by-step explanation:

We need to find the equation of the circle. First, the formula:

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

Where (h,k) is the center and r is the radius

The center is (5,-4), so we can say:

(x-5)^2 + (y+4)^2 = r^2

Now, to find the radius, we can use the distance formula to find distance between (5,4) and (-3,2).

The distance formula is $\sqrt{(y_2-y_1)^2 + (x_2-x_1)^2}$

Where

x_1 = 5

x_2 = -3

y_1 = 4

y_2 = 2

Plugging in, we get:

$\sqrt{(2+4)^2 + (-3-5)^2} \\=\sqrt{6^2 + 8^2}\\ =\sqrt{100} \\=10$

Hence, the radius is 10 and we can write the equation of circle as:

(x-5)^2 + (y+4)^2 = 10^2

Answer from: PNA

(x-5)^2+(y+4)^2=100

Step-by-step explanation:

Equation of circle having center at (h,k) :

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

Then, the equation of circle having center at (5,-4) and radius r will be:-

$(x-5)^2+(y-(-4))^2=r^2\\\\(x-5)^2+(y+4)^2=r^2$ (1)

Since, circle is passes through (-3,2).

Put x= -3 and y=-2

$(-3-5)^2+(2+4)^2=r^2\\\\\Rightarrow\ 64+36=r^2\\\\\Rightarrow\ r^2=100$

Putting value of r^2=100 in (1), we get

(x-5)^2+(y+4)^2=100

Hence, the equation of this circle is (x-5)^2+(y+4)^2=100

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

the answer is 24

step-by-step explanation:

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