Mathematics: Using the following equation, find the center and radius: x2 + 4x + y2 - 6y = -4the center is located at (-2, 3), and the radius is 3.the center is located at (2, -3), and the radius is 3.the center is located at (-2, 3), and the radius is 9.the center is located at (2, -3), and the radius is 9.

Using the following equation, find the center and

margaret8800

11.06.2020

The correct option is 1.

Step-by-step explanation:

The given equation of the circle is

x^2+4x+y^2-6y=-4

It can be written as

(x^2+4x)+(y^2-6y)+4=0

If we have an expression x^2+bx , then we have to add $(\frac{b}{2})^2$ to make it perfect square.

In first parenthesis the value of b is 4 so we will add (2)^2 .

In second parenthesis the value of b is -6 so we will add (-3)^2 .

(x^2+4x+2^2)+(y^2-6y+(-3)^2)+4-2^2-(-3)^2=0

(x+2)^2+(y-3)^2+4-4-9=0 $[\because (a+b)^2=a^2+2ab+b^2)]$

(x+2)^2+(y-3)^2-9=0

Add 9 on both the sides.

(x+2)^2+(y-3)^2=9

(x+2)^2+(y-3)^2=3^2 .... (1)

The standard form of the circle is

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

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

From (1) and (2), we get

h=-2,k=3, r=3

Therefore the center is located at (-2, 3), and the radius is 3. Option 1 is correct.

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brownkat002

07.08.2022

$3150

Step-by-step explanation:

I = P • R • T

Intrest Equals Principal Amout times Rate of Intrest times Amount of Time

P is our Principal amount of $3,000

R is our Rate of 7%

T is the time span of years

Now if we plug in the values and solve the equation we get $3150 dollars in intrest.

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