Divide the given equation by 3
x^2 - (4/3)x + 5 = 0
This has the same roots
(b, c) = ( -4/3 , 5)
x^2 + 10x + y^2 - 8y = 59 complete the square on x, y
x^2 + 10x + 25 + y^2 - 8y + 16 = 59 + 25 + 16
(x + 5)^2 + ( y - 4)^2 = 100
r^2 = 100
2x^2 - 3x - 35 = -43 + jx
2x^2 - ( 3 + j)x + 8 = 0
To only have one solution, the discriminant = 0
(3 + j)^2 - 4 * 2 * 8 = 0
(3 + j*2 - 64 = 0
(3 + j)^2 = 64 take both roots
3 + j = 8 3 + j = -8
j = 5 j = -11
No real numbers make this true
See WolframAlpha's solution here : https://www.wolframalpha.com/input?i=x+%2B+y++%3D+10+%2C+x%5E3+%2B+y%5E3++%3D+x%5E2+%2B+y%5E2+%2B+162
Laverne says 1 , 6 , 11, 16, 21
Progressive sums = 1 , 7 , 18 , 34 , 55
21
(a + 2) /(a + 1) = b / 8
8(a + 2) / (a + 1) = b
a b
0 16
1 12
3 10
7 9
-2 0
-3 4
-5 6
-9 7
Note that every second, the adults close the gap by ( 4 - 3) = 1 yd per second
So.....to close the gap of 18 yds it must have taken 18 seconds
The adults traveled = Time * Rate per second = 18 * 4 = 72 yds
6i * sqrt 3 + 6i * i =
6sqrt (3) i + 6i^2 {i^2 = -1}
6sqrt (3) i - 6
-6 + 6sqrt (3) i
First term = 1 = a
Second term = 14
15th term = 1 + 14 * 13 = 183
S15 = [ first term + last term ] (no.of terms / 2) =
]1 + 183 ] / (15/2) =
1380 = S15
Here's a similar problem
https://web2.0calc.com/questions/help-with-geometry_22606
