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Simora [160]
3 years ago
13

Find the center and radius of the circle with the given equation. Then select the correct graph of the equation.

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

Answer:

Step-by-step explanation:

In order to find the center and the radius of this circle, you have to complete the square on it. And only for the x-terms, because the y term is squared and there is no other y term. We'll get to that in a second.

Take half the linear x-term, square it and add it to both sides. Our linear term is 10. Half of 10 is 5, and 5 squared is 25. We add 25 to both sides:

The reason we do this is to create a perfect square binomial inside that set of parenthesis. Simplifying the right side as well gives us:

This tells us that the center is (-5, 0). Remember when I said we would get back to the y terms? Because there was only a y-squared and no other y terms, that is the same as writing the equation as

The radius is the square root of the constant. So the radius is 6.

D is the graph you want.

You might be interested in
A+b=180<br> A=-2x+115<br> B=-6x+169<br> What is the value of B?
natulia [17]
The answer is:  " 91 " .   
___________________________________________________
                    →    " B = 91 " .
__________________________________________________ 

Explanation:
__________________________________________________
Given:  
__________________________________________________
    "  A +  B = 180 " ;

  "A =  -2x + 115 " ;   ↔  A =  115 − 2x ;  

  "B = - 6x + 169 " ;  ↔  B = 169 − 6x ;  
_____________________________________________________
METHOD 1)
_____________________________________________________
Solve for "x" ; and then plug the solved value for "x" into the expression given for "B" ; to  solve for "B"
_____________________________________________________

(115 − 2x) + (169 − 6x) = 

  115 − 2x + 169 − 6x = ?

→ Combine the "like terms" ;  as follows:

      + 115 + 169 = + 284 ; 

 − 2x − 6x = − 8x ; 
_________________________________________________________
And rewrite as:

 " − 8x + 284 " ; 
_________________________________________________________
   →  " - 8x + 284 = 180 " ; 

Subtract:  "284" from each side of the equation:

  →  "  - 8x + 284 − 284 = 180 − 284 " ; 

to get:

 →  " -8x = -104 ; 

Divide EACH SIDE of the equation by "-8 " ; 
    to isolate "x" on one side of the equation; & to solve for "x" ; 

→ -8x / -8 = -104/-8 ; 

→  x = 13
__________________________________________________________
Now, to find the value of "B" :
__________________________________________________________
  "B = - 6x + 169 " ;  ↔  B = 169 − 6x ;  

↔  B = 169 − 6x ;  

         = 169 − 6(13) ;   ===========> Plug in our "solved value, "13",  for "x" ;

         = 169 − (78) ; 

         = 91 ;

   B   = " 91 " .
__________________________________________________
The answer is:  " 91 " . 
____________________________________________________
     →     " B = 91 " . 
____________________________________________________
Now;  let us check our answer:
____________________________________________________
               →   A + B = 180 ;  
____________________________________________________
Plug in our "solved answer" ; which is "91", for "B" ;  as follows:
________________________________________________________

→  A + 91 = ? 180? ;  

↔  A = ? 180 − 91 ? ; 

→  A = ?  -89 ?  Yes!
________________________________________________________
→  " A =  -2x + 115 " ;   ↔  A =  115 − 2x ;  

Plug in our solved value for "x"; which is: "13" ; 

" A = 115 − 2x " ; 

→  A = ? 115 − 2(13) ? ;

→  A = ? 115 − (26) ? ; 

→  A = ? 29 ? Yes!
_________________________________________________ 
METHOD 2)
_________________________________________________
Given:  
__________________________________________________
    "  A +  B = 180 " ;

  "A =  -2x + 115 " ;   ↔  A =  115 − 2x ;  

  "B = - 6x + 169 " ;  ↔  B = 169 − 6x ; 

→  Solve for the value of "B" :
_______________________________________________________
 A + B = 180 ;  

→ B = 180 − A ; 

→ B = 180 − (115 − 2x) ; 

→ B = 180 − 1(115 − 2x) ;  ==========> {Note the "implied value of "1" } ; 
__________________________________________________________
Note the "distributive property" of multiplication:__________________________________________________  a(b + c)  = ab +  ac ;  <u><em>AND</em></u>:
  a(b − c)  = ab − ac .________________________________________________________
Let us examine the following part of the problem:
________________________________________________________
              →      " − 1(115 − 2x)  " ; 
________________________________________________________

→  "  − 1(115 − 2x) " = (-1 * 115) − (-1 * 2x) ;

                                =  -115 − (-2x) ;
                         
                                =  -115  +  2x ;        
________________________________________________________
So we can bring down the:  " {"B = 180 " ...}"  portion ; 

→and rewrite:
_____________________________________________________

→  B = 180 − 115 + 2x ; 

→  B = 65 + 2x ; 
_____________________________________________________
Now;  given:   "B = - 6x + 169 " ;  ↔  B = 169 − 6x ; 

→ " B =  169 − 6x  =  65 + 2x " ; 
______________________________________________________
→  " 169 − 6x  =  65 + 2x "

Subtract "65" from each side of the equation;  & Subtract "2x" from each side of the equation:

→  169 − 6x − 65 − 2x  =  65 + 2x − 65 − 2x ; 

to get:

→   " - 8x + 104 = 0 " ;
 
Subtract "104" from each side of the equation:

→   " - 8x + 104 − 104 = 0 − 104 " ;

to get: 

→   " - 8x = - 104 ;

Divide each side of the equation by "-8" ; 
   to isolate "x" on one side of the equation; & to solve for "x" ; 

→  -8x / -8  = -104 / -8 ; 

to get:

→  x =  13 ; 
______________________________________________________

Now, let us solve for:  " B " ;  → {for which this very question/problem asks!} ; 

→  B = 65 + 2x ;  

Plug in our solved value, " 13 ",  for "x" ; 

→ B = 65 + 2(13) ; 

        = 65 + (26) ;  

→ B =  " 91 " .
_______________________________________________________
Also, check our answer:
_______________________________________________________
Given:  "B = - 6x + 169 " ;   ↔  B = 169 − 6x = 91 ; 

When "x  = 13 " ; does: " B = 91 " ? 

→ Plug in our "solved value" of " 13 " for "x" ;

      → to see if:  "B = 91" ; (when "x = 13") ;

→  B = 169 − 6x ; 

         = 169 − 6(13) ; 

         = 169 − (78)______________________________________________________
→ B = " 91 " . 
______________________________________________________
6 0
3 years ago
What is the simplest form of 3/27a2b7?
krok68 [10]

Answer:

the solution is A

Step-by-step explanation:

\sqrt[3]{27a^{3}b^{7}  } \\

\sqrt[3]{(3)^3(a^3)(b^6)b}\\\\3ab^2\sqrt[3]{b}

4 0
2 years ago
Read 2 more answers
Segment AB has point A located at (4, 2). If the distance from A to B is 3 units, which of the following is the coordinate for p
olganol [36]
The distance between two points is given by:
d² = (x₂-x₁)² + (y₂ - y₁)²
9 = (x₂ - 4)² + (y₂ - 2)²
Now, we can check different ordered pairs in this equation to see which satisfies it:
The one that satisfies this equation is (4 , -1).
3 0
2 years ago
Read 2 more answers
Priya noticed in the last activity that between the 2 triangles, you only need to know 4 angles to show that they are similar. S
ValentinkaMS [17]

Answer:

Please find attached a drawing of the triangles ΔRST and EFG showing the angles

The angle on ΔEFG that would prove the triangles are similar is ∠F = 25°

Step-by-step explanation:

In order to prove that two triangles are similar, two known angles of each the triangles need to be shown to be equal

Given that triangle ∠R and ∠S of triangle ΔRST are 95° and 25°, respectively, and that ∠E of ΔEFG is given as 90°, then the corresponding angle on ΔEFG to angle ∠S = 25° which is ∠F should also be 25°

Therefore, the angle on ΔEFG that would prove the triangles are similar is ∠F = 25°.

3 0
3 years ago
Solve:7 +42-32-32 = 14.3-2a +7<br> A = -3<br> A= 0<br> A= 3<br> no solution
madreJ [45]

Answer:

a = 18.15

Step-by-step explanation:

7+42-32-32=14.3-2a+7

Combine like terms on the left side of the equation first. Add 7 and 42, then subtract 32 from the answer you get, then subtract 32 from that answer. This is going by order of PEMDAS.

Remember PEMDAS: (numbers 3 & 4 and numbers 5 & 6 are solved from left to right)

  1. Parentheses
  2. Exponents
  3. Multiplication
  4. Division
  5. Addition
  6. Subtraction

-15=14.3-2a+7

After combining like terms on the left side, you get -15. Now combine like terms on the right side of the equation by adding 14.3 and 7.

-15=21.3-2a

Get -2a alone by subtracting 21.3 from both sides.

-36.3=-2a

Divide both sides by -2.

a=18.15

In this equation, a should equal \boxed{18.15}.

5 0
3 years ago
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