It’s 2/3.
Dividing 10 and 15 by 5 gives you 2 and 3, so the simplified answer is 2/3
Answer:
8th term is 179.15904
Step-by-step explanation:
The sequence is geometric with a common ration = 6/5
r = 60/50 = 72/60 = 6/5
Use the formula
![a_{n} = ar^{n - 1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20ar%5E%7Bn%20-%201%7D)
In your case a = 50, r = 6/5 and n = 8
![a_{8} = 50(6/5)^{8 - 1} \\ = 50(6/5)^{7} \\ = 50(279936/78125)\\ = 179.15904](https://tex.z-dn.net/?f=a_%7B8%7D%20%3D%2050%286%2F5%29%5E%7B8%20-%201%7D%20%5C%5C%20%20%20%20%20%20%20%20%20%20%3D%2050%286%2F5%29%5E%7B7%7D%20%5C%5C%20%20%20%20%20%20%20%20%20%20%3D%20%2050%28279936%2F78125%29%5C%5C%20%20%20%20%20%20%20%20%20%20%3D%20%20%20179.15904)
Out of the choices given, B and E will be opposite of each other when the folding occurs. You have to imagine what it would look like, once folded.
Answer:
The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.
Step-by-step explanation:
The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.
We have to find the roots of this given equation.
If a quadratic equation is of the form ![ax^{2}+bx +c=0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%2Bbx%20%2Bc%3D0)
Its roots are
and ![\frac{-b-\sqrt{b^{2}-4ac } }{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b-%5Csqrt%7Bb%5E%7B2%7D-4ac%20%7D%20%7D%7B2a%7D)
Here the given equation is
= 0
a = 2
b = -4
c = -1
If the roots are
, then
= ![\frac{-2+\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}](https://tex.z-dn.net/?f=%5Cfrac%7B-2%2B%5Csqrt%7B%28-4%29%5E%7B2%7D-4%5Ctimes%202%5Ctimes%20%28-1%29%7D%7D%7B2%5Ctimes%202%7D)
= ![\frac{4 +\sqrt{24}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4%20%2B%5Csqrt%7B24%7D%7D%7B4%7D)
= ![\frac{2+\sqrt{6} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%2B%5Csqrt%7B6%7D%20%7D%7B2%7D)
= ![\frac{-2-\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}](https://tex.z-dn.net/?f=%5Cfrac%7B-2-%5Csqrt%7B%28-4%29%5E%7B2%7D-4%5Ctimes%202%5Ctimes%20%28-1%29%7D%7D%7B2%5Ctimes%202%7D)
= ![\frac{4 +\sqrt{8}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4%20%2B%5Csqrt%7B8%7D%7D%7B4%7D)
= ![\frac{2-\sqrt{6} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2-%5Csqrt%7B6%7D%20%7D%7B2%7D)
These are the two roots of the equation.