Answer:
First term a = 41
Step-by-step explanation:
Arithmetic Progression:
Common differences d = -2
![S_{n}=\frac{n}{2}(2a+[n-1]d)\\\\S_{20}=\frac{20}{2}(2a+19*[-2])\\\\](https://tex.z-dn.net/?f=S_%7Bn%7D%3D%5Cfrac%7Bn%7D%7B2%7D%282a%2B%5Bn-1%5Dd%29%5C%5C%5C%5CS_%7B20%7D%3D%5Cfrac%7B20%7D%7B2%7D%282a%2B19%2A%5B-2%5D%29%5C%5C%5C%5C)
= 10*(2a - 38)
= 10*2a - 10*38
=20a - 380
![S_{22}=\frac{22}{2}(2a+21*[-2])\\\\](https://tex.z-dn.net/?f=S_%7B22%7D%3D%5Cfrac%7B22%7D%7B2%7D%282a%2B21%2A%5B-2%5D%29%5C%5C%5C%5C)
= 11 (2a -42)
=11*2a - 11*42
= 22a - 462
22a - 462 = 20a - 380
22a = 20a - 380 + 462
22a = 20a + 82
22a - 20a = 82
2a = 82
a = 82/2
a = 41
First term a = 41
The midpoint of the diameter endpoints is the center of the circle...
((2+9)/2, (4+4)/2)
(5.5, 4) is the center of the circle...
The distance between the two endpoints is the diameter of the circle...
d^2=(4-4)^2+(9-2)^2
d^2=0+49
d^2=49
d=7
So the radius is d/2 which is 3.5
Now the equation of a circle is:
(x-h)^2+(y-k)^2=r^2 where (h,k) is the coordinates of the center and r is the radius.
Earlier we found (h,k) to be (5.5, 4) and r=3.5 so our equation is:
(x-5.5)^2+(y-4)^2=3.5^2
(x-5.5)^2+(y-4)^2=12.25
Answer:
13.5
Step-by-step explanation:
Mark me brainliest!
Or 13 with a remainder of 5
13R5
or
13 5/8
Answer:
5+15w
Step-by-step explanation:
:)
(a) 8(4x+3) > -1 + 7x
32x + 24 > -1 + 7x
32x - 7x > -1 -25
25x >-26
x > -26/25
(b) 167 < 6 + 7(2 - 7r)
167 < 6 + 14 - 49r
49r < 6 + 14 - 167
49r < - 147
r < - 3
(c) 8x + 40 > -8 ( 1 - 7x)
8x + 40 > -8 + 56x
56x - 8x < 48
48x < 48
x < 1
(d)5( 6 + 3r) + 7 > 127
30 + 15r + 7 > 127
15r > 127 - 37
15r > 90
r > 6
