What is the radius for the circle given by the equation?

Mathematics

1 answer:

alisha [4.7K]3 years ago

7 0

Use:

$(a-b)^2=a^2-2ab+b^2\qquad(*)$

$x^2+y^2-6y-12=0\ \ \ \ |+12\\\\x^2+y^2-6y=12\\\\x^2+y^2-2y\cdot3=12\ \ \ \ |+3^2\\\\x^2+\underbrace{y^2-2\cdot y\cdot3+3^2}_{(*)}=12+3^2\\\\x^2+(y-3)^2=21\\\\\boxed{k=3}$

You might be interested in

Over the period of a year, Sam’s net worth increased. Which of the following could be true?

MAXImum [283]

Answer:

Sam's assets increased by more than his liabilities.

Step-by-step explanation:

7 0

2 years ago

One positive number is one-fifth of another number. the difference of the two numbers is 84. find the numbers.

seraphim [82]

Answer: The numbers are: " 21 " and " 105 " .
___________________________________________________
Explanation:
___________________________________________________
Let "x" be the "one positive number:

Let "y" be the "[an]othyer number".

x = 1/5 (y)
___________________________________________________
Given that the difference of the two number is "84" ; and that "x" is (1/5) of "y" ; we determine that "x" is smaller than "y".

So, y − x = 84 .

Add "x" to each side of this equation; to solve for "y" in terms of "x" ;

y − x + x = 84 + x ;

y = 84 + x ;
___________________________________________________
So, we have:

x = (1/5) y ;

and: y = 84 + x ;

Substitute "(1/5)y" for "x" ; in "y = 84 + x " ; to solve for "y" ;

y = 84 + [ (1/5)y ]

Subtract " [ (1/5)y ] " from EACH SIDE of the equation ;

y − [ (1/5)y ] = 84 + [ (1/5)y ] −  [ (1/5)y ] ;

to get:

[ (4/5)y ] = 84 ;

       ↔    (4y) / 5 = 84 ;

        → 4y = 5 * 84 ;

      Divide EACH SIDE of the equation by "4" ;
to isolate "y" on one side of the equation; and to solve for "y" ;

           4y / 4 = (5 * 84) / 4 ;

                 y = 5 * (84/4) = 5 * 21 = 105 .

   y = 105 .
___________________________________________________
Now, plug "105" for "y" into:
___________________________________________________
Either:
___________________________________________________
x = (1/5) y ;

OR:

y = 84 + x ;
___________________________________________________
to solve for "x" ;
___________________________________________________
Let us do so in BOTH equations; to see if we get the same value for "x" ; which is a method to "double check" our answer ;
___________________________________________________
Start with:

x = (1/5)y

    → (1/5)*(105) = 105 / 5 = 21 ; x = 21 ;

___________________________________________________
So, x = 21; y = 105 .
___________________________________________________
Now, let us see if this values hold true in the other equation:
___________________________________________________
y = 84 + x ;

105 = ? 84 + 21 ?

105 = ? 105 ? Yes!
___________________________________________________
The numbers are: " 21 " and "105 " .
___________________________________________________

6 0

3 years ago

What is the measure of angle z in this figure?

ASHA 777 [7]

Answer:

z = 137°

Step-by-step explanation:

$z^{o} =(180-43)^{o} =137^{o}$