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Scilla [17]
3 years ago
11

What is the center of the circle whose equation, in standard form, is (x – 5)2 + y2 = 4​

Mathematics
1 answer:
irina [24]3 years ago
3 0

Answer:

(5, 0)

Step-by-step explanation:

The center of the circle is determined by the numbers being subtracted from the corresponding variables.

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Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4
Alik [6]

Answer:

\alpha=3

Step-by-step explanation:

<u>Equation of a Circle</u>

A circle of radius r and centered on the point (h,k) can be expressed by the equation

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

We are given the equation of a circle as

3x^2+3y^2-6\alpha x+12y-3\alpha=0

Note we have corrected it by adding the square to the y. Simplify by 3

x^2+y^2-2\alpha x+4y-\alpha=0

Complete squares and rearrange:

x^2-2\alpha x+y^2+4y=\alpha

x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4

(x-\alpha)^2+(y+2)^2=r^2

We can see that, if r=4, then

\alpha+\alpha^2+4=16

Or, equivalently

\alpha^2+\alpha-12=0

There are two solutions for \alpha:

\alpha=-4,\ \alpha=3

Keeping the positive solution, as required:

\boxed{\alpha=3}

8 0
3 years ago
The sum of two numbers is 28. one number is 14 more. find the numbers
ruslelena [56]
The numbers are:  "7 " and "21 " .
_______________________________________
Explanation:
_______________________________________
The numbers are:  "x"  and "x + 14" .

x + (x + 14) = 28 .  Solve for "x" ; and then solve for "x + 14" .
_______________________________________
 → x + (x + 14) = 28 ;

Rewrite as:

 →  x + x + 14 = 28 ;

 →  1x + 1x + 14 = 28 ;

 →  2x + 14 = 28 ; 
  
 Subtract "14" from each side of the equation;
 
 →  2x + 14 − 14 = 28 <span>− 14 ;

</span> →  2x = 14  ;

Divide EACH SIDE of the equation by "2" ;
     to isolate "x" on one side of the equation; & to solve for "x" ;

 →  2x / 2 = 14 / 2 ;

 →  x = 7 . 
_________________________________________
So;  one of the numbers is:  " 7 " .

The other number is:  " x + 14 " ; which equals: " 7 + 14 = 21".

The other number is:  "21 " .
_________________________________________
The numbers are:  "7 " and "21 " .
_________________________________________
5 0
3 years ago
Problem-solving Practice
kotykmax [81]
First, what's 3 to the power of 8?
Then what's 3 to the power of 10

Now subtract them by each other for your answer
6 0
3 years ago
Read 2 more answers
Ordering real numbers least to greatest
Darina [25.2K]
Hello,


The correct order is:


-16.5, -√270, -50/30, 16 3/10


Faith xoxo
8 0
3 years ago
Read 2 more answers
The radius of a wheel is 21m.how much distance will it covers when it rotates 5 times?​
mrs_skeptik [129]

Answer:

Distance = 660 meters

Step-by-step explanation:

Given the following data;

Radius, r = 21 m

Number of revolutions = 5 times

To find the distance covered;

The distance covered in one revolution is given by the circumference of a circle.

Mathematically, circumfeence of a circle is equal to;

C = 2πr

Substituting into the formula, we have;

C = 2 * 22/7 * 21

C = 44 * 3

C = 132 meters

Next, we find the distance covered;

Distance = Circumference * Number of revolutions

Distance = 132 * 5

Distance = 660 meters

8 0
2 years ago
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