In a triangle the sum of two sides is always greater than the third side.
9-9 < x < 9+9
0 < x < 18 ← answer
Answer:
The equation of the circle is ![(x+2)^2+(y-1)^2=25](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%2B%28y-1%29%5E2%3D25)
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
where
(h,k) is the center
r is the radius
step 1
Find the radius of the circle
The radius of the circle is equal to the distance from the center to any point on the circle
we have
(–5, –3) and (–2, 1)
Find the distance
the formula to calculate the distance between two points is equal to
substitute
step 2
Find the equation of the circle
we have
![(h,k)=(-2,1)](https://tex.z-dn.net/?f=%28h%2Ck%29%3D%28-2%2C1%29)
substitute
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
![(x+2)^2+(y-1)^2=5^2](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%2B%28y-1%29%5E2%3D5%5E2)
![(x+2)^2+(y-1)^2=25](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%2B%28y-1%29%5E2%3D25)
therefore
The equation of the circle is ![(x+2)^2+(y-1)^2=25](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%2B%28y-1%29%5E2%3D25)
1) EF = 2 and DF = 4
2) KL = 4√3 and JL = 8
3) ST = 6 and RS = 6√3
4) PQ = 4.5√3 and RQ = 4.5
<u>Step-by-step explanation</u>:
<u>Rules for special triangles 30°,60°,90°</u> :
- The length of the side opposite to 30° is a.
- The length of the side opposite to 60° is a√3.
- The length of the side opposite to 90° is 2a.
1) DE = 2√3 is opposite to 60°
⇒ 2√3 = a√3
⇒ a = 2
EF = a which is opposite to 30°.
⇒ EF = 2
DF = 2a which is opposite to 90°.
⇒ DF = 4
2) KJ = 4 is opposite to 30°
⇒ a = 4
KL = a√3 which is opposite to 60°.
⇒ KL = 4√3
JL = 2a which is opposite to 90°.
⇒ JL = 8
3) RT = 12 is opposite to 90°
⇒ 2a = 12
⇒ a = 6
ST = a which is opposite to 30°.
⇒ ST = 6
RS = a√3 which is opposite to 60°.
⇒ RS = 6√3
4) PR = 9 is opposite to 90°
⇒ 2a = 9
⇒ a = 4.5
PQ = a√3 which is opposite to 60°.
⇒ PQ = 4.5√3
RQ = a which is opposite to 30°.
⇒ RQ = 4.5
Answer:
Step-by-step explanation:
![Mean = \frac{Sum \ of \ all \ the \ data}{number \ of \ data}\\\\= \frac{3.8+5.1+4.1+3.8+3.3+3.6}{6}\\\\=\frac{23.7}{6}\\\\= 3.95](https://tex.z-dn.net/?f=Mean%20%3D%20%5Cfrac%7BSum%20%5C%20of%20%5C%20all%20%5C%20the%20%5C%20%20data%7D%7Bnumber%20%5C%20of%20%5C%20data%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B3.8%2B5.1%2B4.1%2B3.8%2B3.3%2B3.6%7D%7B6%7D%5C%5C%5C%5C%3D%5Cfrac%7B23.7%7D%7B6%7D%5C%5C%5C%5C%3D%203.95)
Mean = 3.95
B) To find the median, arrange the data in ascending order
3.3 ; 3.6 , 3.8 ; 3.8 ; 4.1 ; 5.1
As number of data is even, median = Average of (n/2)th term and (n/2)th term +1
= Average of 3 and 4th term
![= \frac{3.8+3.8}{2}\\\\= 3.8\\](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B3.8%2B3.8%7D%7B2%7D%5C%5C%5C%5C%3D%203.8%5C%5C)
Median = 3.8
C) 3.8 occurs two times.
So, Mode = 3.8
d) 14.6 is above the mean. So, if we add a data above the mean, then the mean will increase
e) If April (3.8) is deleted from chart, Mean will increase. If we remove a data below the mean, then mean will increase
If April is deleted from chart, there will be no change in median.
Still median will be 3.8 only
Answer:
wow
Step-by-step explanation:
.-.
what an amazing qUeStIoN