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:
no f-ing clue
Step-by-step explanation:
Answer:
Because 4 is a perfect square
Step-by-step explanation:
When simplifying a radical, you have to look for perfect squares. 4 is a perfect square but x is not. Variables are only perfect squares if they have even numbered exponents so the x has to stay in the radical.
Answer:
Step-by-step explanation:
the formula for density is:
where d is density, m is mass, and V is volume.
solving for m in the last equation:
so if we find the volume and multiply it by the density 
we will get the mass of the object.
The volume of a rectangular prism is given by:
where 
is length, 
is width and 
is height:
we substitute to find the volume:
since the density has units of 
we need the volume also in units of , so we make the conversion using:
multiplying by 30:
and now we find the mass with the equation:
substituting d and V:
the nearest gram is:
Answer:
9x+7
Step-by-step explanation:
This is because you combine like terms:
5x and 4x contain the same variable and amount of variables so you can combine them making 9x. You are then left with two numbers 5, and 2 they aren't attached to any variables and are in common in that way so you combine them too! This makes them 7, lastly you make it into an expression so you can't combine 9x and 7 so you leave it as 9x+7!!!
