The equation of a given circle in. general form is x^2+y^2+12y+27=0. write the equation in standard form, (x-h)^2+(y-k)^2=r^2, by completing the squares in the equation. show your work in the table.

Center (h, k) = (0, 6)

Radius, r = 3 units

Step-by-step explanation:

The given equation of the circle is:

STEP I: Move the constant term to the right hand side.

To do that we subtract 27 on both the sides, we get:

STEP II: Divide the co - effecient of 'x' by 2 and square it.

Here there is no 'x' term. Its co-effecient is 0.

STEP III: Add the result on both sides.

Since, we got 0 in the previous step, there would no change in the equation

STEP IV: We repeat the process for 'y'.

Here, the co-effecient of 'y' is: 12.

Dividing by 2 and squaring it will yield:

STEP V: Adding 36 to both the sides of the equation, it becomes:

We have arrived at perfect squares.

STEP VI: Write in the form of perfect squares.

STEP VII: Compare it with the standard form.

We get: The centre of the circle: (h, k) = (0, 6) and

the radius of the circle, r = 3 units.

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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the correct answer is a) they believe they have a "just cause."

islamic terrorists justify their violent actions because they believe they have a "just cause."

every act of terrorism of islamic sects is done “in the name of allah”. that justifies their actions. islam people who commit those terrorist attacks are not afraid to die. that is why the attacks have horrible consequences. they know they are going to die and they are proud to do it because it is in the name of allah, so it is justified and is for a “good cause.”

since the very beginning of the conflict with israel, islam is fighting a “sacred war”, respecting the words stated in the qur’an. they fight against the domination of the western countries and to defend their occupied territories.