The square root of 20 is an irrational number because you cannot turn it into a fraction.
The number on the screenshot is the square root of 20. Because this number doesn't end or repeat, you can't make it a fraction, and therefore it's irrational.
Answer:
-4m/s²
Step-by-step explanation:
(4m/s - 16m/s) / 3s = -12m/s / 3s = -4m/s²
Answer:
1.04P
P+0.04P
Step-by-step explanation:
To add tax, you add 4% or 0.04 of the total paid.
This can represented in many ways including 1.04P or 100% of teh price plus 4% of the price. This is 104% or 1.04 times the price P
You can also add to the price P + 0.4P the percent of the price.
Answer:
x = -1.6
Step-by-step explanation:
To find the value of x
4x - 5 = -6x - 21
Transpose
4x + 6x = -21 + 5
10x = -16
x = -16/10
x = -1.6
Answer:
The statement is true is for any
.
Step-by-step explanation:
First, we check the identity for
:
![(2\cdot 1 - 1)^{2} = \frac{2\cdot (2\cdot 1 - 1)\cdot (2\cdot 1 + 1)}{3}](https://tex.z-dn.net/?f=%282%5Ccdot%201%20-%201%29%5E%7B2%7D%20%3D%20%5Cfrac%7B2%5Ccdot%20%282%5Ccdot%201%20-%201%29%5Ccdot%20%282%5Ccdot%201%20%2B%201%29%7D%7B3%7D)
![1 = \frac{1\cdot 1\cdot 3}{3}](https://tex.z-dn.net/?f=1%20%3D%20%5Cfrac%7B1%5Ccdot%201%5Ccdot%203%7D%7B3%7D)
![1 = 1](https://tex.z-dn.net/?f=1%20%3D%201)
The statement is true for
.
Then, we have to check that identity is true for
, under the assumption that
is true:
![(1^{2}+2^{2}+3^{2}+...+k^{2}) + [2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}](https://tex.z-dn.net/?f=%281%5E%7B2%7D%2B2%5E%7B2%7D%2B3%5E%7B2%7D%2B...%2Bk%5E%7B2%7D%29%20%2B%20%5B2%5Ccdot%20%28k%2B1%29-1%5D%5E%7B2%7D%20%3D%20%5Cfrac%7B%28k%2B1%29%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29-1%5D%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29%2B1%5D%7D%7B3%7D)
![\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)}{3} +[2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bk%5Ccdot%20%282%5Ccdot%20k%20-1%29%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%7D%7B3%7D%20%2B%5B2%5Ccdot%20%28k%2B1%29-1%5D%5E%7B2%7D%20%3D%20%5Cfrac%7B%28k%2B1%29%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29-1%5D%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29%2B1%5D%7D%7B3%7D)
![\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot [2\cdot (k+1)-1]^{2}}{3} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bk%5Ccdot%20%282%5Ccdot%20k%20-1%29%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%2B3%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29-1%5D%5E%7B2%7D%7D%7B3%7D%20%3D%20%5Cfrac%7B%28k%2B1%29%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29-1%5D%5Ccdot%20%5B2%5Ccdot%20%28k%2B1%29%2B1%5D%7D%7B3%7D)
![k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot (2\cdot k +1)^{2} = (k+1)\cdot (2\cdot k +1)\cdot (2\cdot k +3)](https://tex.z-dn.net/?f=k%5Ccdot%20%282%5Ccdot%20k%20-1%29%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%2B3%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%5E%7B2%7D%20%3D%20%28k%2B1%29%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%5Ccdot%20%282%5Ccdot%20k%20%2B3%29)
![(2\cdot k +1)\cdot [k\cdot (2\cdot k -1)+3\cdot (2\cdot k +1)] = (k+1) \cdot (2\cdot k +1)\cdot (2\cdot k +3)](https://tex.z-dn.net/?f=%282%5Ccdot%20k%20%2B1%29%5Ccdot%20%5Bk%5Ccdot%20%282%5Ccdot%20k%20-1%29%2B3%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%5D%20%3D%20%28k%2B1%29%20%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%5Ccdot%20%282%5Ccdot%20k%20%2B3%29)
![k\cdot (2\cdot k - 1)+3\cdot (2\cdot k +1) = (k + 1)\cdot (2\cdot k +3)](https://tex.z-dn.net/?f=k%5Ccdot%20%282%5Ccdot%20k%20-%201%29%2B3%5Ccdot%20%282%5Ccdot%20k%20%2B1%29%20%3D%20%28k%20%2B%201%29%5Ccdot%20%282%5Ccdot%20k%20%2B3%29)
![2\cdot k^{2}+5\cdot k +3 = (k+1)\cdot (2\cdot k + 3)](https://tex.z-dn.net/?f=2%5Ccdot%20k%5E%7B2%7D%2B5%5Ccdot%20k%20%2B3%20%3D%20%28k%2B1%29%5Ccdot%20%282%5Ccdot%20k%20%2B%203%29)
![(k+1)\cdot (2\cdot k + 3) = (k+1)\cdot (2\cdot k + 3)](https://tex.z-dn.net/?f=%28k%2B1%29%5Ccdot%20%282%5Ccdot%20k%20%2B%203%29%20%3D%20%28k%2B1%29%5Ccdot%20%282%5Ccdot%20k%20%2B%203%29)
Therefore, the statement is true for any
.