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:
hli
Step-by-step explanation:
how r u dear hope u r fine
The number 12 is missing in the data set.
<u>Step-by-step explanation</u>:
- The numbers are 9,12,16,18,23.
- The missing number is assumed to be 'x'
Mean = Sum of the integers / Total number of integers.
15 = (9+12+16+18+23+x) / 6
15 = (78+x) / 6
90 = 78+x
x = 90-78
x = 12
24 daises is the answer because if there is 8 roses and the ratio is 1:3 then you would multiply 8 by 3 to solve.
Answer:
The frequency table is attached below.
Step-by-step explanation:
Given the total number of candies in the box = 18
Frequency table is used to list the occurence of a thing or product and it helps to calculate and sort down easily.
<u>Contains caramel</u> <u>Do not contain caramel</u> Total
<u>Contains chocolate</u> 10 2 12
<u>Do not contain </u> 3 3 6
<u>chocolate</u>
Total number of candies as per the frequency tablr = 12 + 6 = 18 which tallies with the given data.
