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.
 
        
             
        
        
        
Answer:
The principal must be = $8991.88
Step-by-step explanation:
Formula for compound interest is:

Where A is the amount after 't' years.
P is the principal amount
n is the number of times interest is compounded each year.
r is the rate of interest.
Here, we are given that:
Amount, A = $15000
Rate of interest = 13 % compounded quarterly i.e. 4 times every year
Number of times, interest is compounded each year, n = 4
Time, t = 4 years.
To find, Principal P = ?
Putting all the given values in the formula to find P.

So, <em>the principal must be = $8991.88</em>
 
        
             
        
        
        
Answer:
8,000 in the 8% account
20,000 in the 9% account.
Step-by-step explanation:
x + y = 28000
0.08 x + 0.09 y = 2440
0.08 x + 0.09 (28000 − x) = 2440
0.08 x + 2520 − 0.09 x = 2440
80 = 0.01 x
x = 8000
y = 20000
 
        
             
        
        
        
(-8, -11) because the points are just the opposite sign when reflecting over the x-axis