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2 years ago

Which is the equation of a circle with its center at (-4,2) and a radius of 4?

Mathematics

1 answer:

Snowcat [4.5K]2 years ago

4 0

Answer:

(x +4)^2 + (y-2)^2 = 16

Step-by-step explanation:

We can write the equation for a circle with the formula

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

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

We know the center is at (-4,2) and the radius is 4

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

(x +4)^2 + (y-2)^2 = 16

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Help math look at pic

Sloan [31]

Answer: $\Large\boxed{(-4,~-3)~\text{and}~(-2,~1)}$

Step-by-step explanation:

Given the system of equation

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

$2)~y=2x+5$

Expand the parenthesis of the 1) equation

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

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

$y=-x^2-4x-4+1$

$y=-x^2-4x-3$

Current System

$1)~y=-x^2-4x-3$

$2)~y=2x+5$

Substitute the y value of the 1) equation with the 2) equation

$2x+5=-x^2-4x-3$

Add ( x² + 4x + 3) on both sides

$2x+5+(x^2+4x+3)=-x^2-4x-3+(x^2+4x+3)$

$2x+5+x^2+4x+3=0$

Combine like terms

$x^2+2x+4x+5+3=0$

$x^2+6x+8=0$

Factorize the quadratic equation

$(x+4)(x+2)=0$

$x=-4~\text{or}~x=-2$

Substitute the x values into one of the equations to find the y value

$y=2x+5$

$y=2(-4)+5=-8+5=-3$

$y=2(-2)+5=-4+5=1$

Therefore, the two solutions are:

$\Large\boxed{(-4,~-3)~\text{and}~(-2,~1)}$

Hope this helps!! :)

Please let me know if you have any questions

8 0

1 year ago

Find the volume of the following cylinder using its net.

lord [1]

Answer:

226.08 yd 3

Step-by-step explanation:

3 0

2 years ago

(3x + 3x²) + (2x² + 2x)?

Galina-37 [17]

Answer:

=5x2+5x

Step-by-step explanation:

Let's simplify step-by-step.

3x+3x2+2x2+2x

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3 years ago

Round 0.1278 to the nearest thousandth

eduard

≈0.128 is the correct answer

5 0

3 years ago

Divide the following problem: 4/5 ÷ 37 Please give me a answer that helps.

Triss [41]

Answer:

4/185 or 0.0216...

Step-by-step explanation:

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3 years ago