Step-by-step explanation:
The equation of a circle can be the expanded form of
\large \text{$(x-a)^2+(y-b)^2=r^2$}(x−a) 
2
 +(y−b) 
2
 =r 
2
 
where rr is the radius of the circle, (a,\ b)(a, b) is the center of the circle, and (x,\ y)(x, y) is a point on the circle.
Here, the equation of the circle is,
\begin{gathered}\begin{aligned}&x^2+y^2+10x-4y-20&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4-49&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &x^2+10x+25+y^2-4y+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &(x+5)^2+(y-2)^2&=&\ \ 7^2\end{aligned}\end{gathered} 
⟹ 
⟹ 
⟹ 
⟹ 
 
x 
2
 +y 
2
 +10x−4y−20
x 
2
 +y 
2
 +10x−4y+25+4−49
x 
2
 +y 
2
 +10x−4y+25+4
x 
2
 +10x+25+y 
2
 −4y+4
(x+5) 
2
 +(y−2) 
2
 
 
=
=
=
=
=
 
 0
 0
 49
 49
 7 
2
 
 
 
From this, we get two things:
\begin{gathered}\begin{aligned}1.&\ \ \textsf{Center of the circle is $(-5,\ 2)$.}\\ \\ 2.&\ \ \textsf{Radius of the circle is $\bold{7}$ units. }\end{aligned}\end{gathered} 
1.
2.
 
 Center of the circle is (−5, 2).
 Radius of the circle is 7 units. 
 
 
Hence the radius is 7 units.
 
        
             
        
        
        
The x represents the ticket prices and the y represents the popcorn price. If we distribute the expression, we get 4x +2x + 2y. This shows us that all 6 people bought a ticket, and two bought popcorn. Now plug in the given values and solve. 
6*7.25 + 2*3.25 = $50
        
             
        
        
        
Answer:
Hope that the payment picture will help you.Please mark me brilliant
 
        
             
        
        
        
Step-by-step explanation:
Equation of line is y-y1 = m(x-x1), where m is the slope and (x1,y1) is the given point.
y-2 = 1/4*(x-(-4))
y-2 = 1/4 * (x+4)
4*(y-2) = x+4
Equation of the line is,
x-4y = -12
 
        
             
        
        
        
It’s 5 and 4
Have fun on that test