For there to be 2 rational roots, the derivative has to be a positive square.
(17^2 + 4c) is a positive square like (1, 4, 9, 16...)
Take it from here. :))
=^._.^=
6, 6, 6, 6, 6, 6, 6, 6
196^213 last digit is 6
3, 9, 7, 1, 3, 9, 7, 1
213^196 last digit is 1
6*1 = 6
Using similar triangles.
8/15x+x = 8
(23/15)x = 8
15/8x+x = 15
(23/8)x = 15
Solve either of those equations.
[0, 81]
x^2 can't be negative, so the lowest value is 0, 0^2.
The highest x^2 can be is 81, 9^2.
If the diameter is 99, the radius is 99/2.
The volume of a sphere is 4/3*pi*r^3
Don't forget to divide by 2 since you're looking for half of it.
z + 1/z = -1
(z + 1/z)^3 = -1
z^3 + 3z + 3/z + 1/z^3 = -1
z^3 + 3(z + 1/z) + 1/z^3 = -1
z^3 + 3(-1) + 1/z^3 = -1
z^3 + 1/z^3 = 2
can you take it from here?
|x|+x+y=14
x+|y|-y=12
Both x and y are positive.
2x + y = 14
x = 12
y = -10
WRONG (since -10 isn't positive)
x is positive and y is negative
x - 2y = 12
4x + 2y = 28
5x = 40
x = 8, y = -2
CORRECT
Since angle AEB = DEC (vertical angles), ABE = CDE by SAS.
Can you take it from here?
Thank you. :))
Shorts cost 12 dollars.
T shirts cost 15 dollars. (12+3)
x = number of t shirts
3/4x = number of shorts
15x + (12)(3/4x) = 384
24x = 384
x = 16
He bought 16 t shirts, 15 dollars each, for a total of 240 dollars.
For it to be divisable by 66, it has to be divisable by 2, 3, 11.
2 just means the end is even.
18 + a + b = divisable by 3.
16 = a + b + 2
Solve for a and b. :))