Answer:
The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even
Step-by-step explanation:
![4^1 = 4\\4^2 = 16\\4^3 = 64\\4^4 = 256 \\4^5 = 1024\\4^6 = 4096\\4^7 = 16384\\4^8 = 65536](https://tex.z-dn.net/?f=4%5E1%20%3D%204%5C%5C4%5E2%20%3D%2016%5C%5C4%5E3%20%3D%2064%5C%5C4%5E4%20%3D%20256%20%5C%5C4%5E5%20%3D%201024%5C%5C4%5E6%20%3D%204096%5C%5C4%5E7%20%3D%2016384%5C%5C4%5E8%20%3D%2065536)
The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even
To prove this conjecture
unit digit = 6
hence the property is true for ; n = 1 and n = 2 and also for every odd and even number ( i.e. from 1 to 8 )
Answer:
![\frac{15y-10}{15y-3}](https://tex.z-dn.net/?f=%5Cfrac%7B15y-10%7D%7B15y-3%7D)
Step-by-step explanation:
First at all, we need to use
to convert this expression into a fraction, like:
to convert into
.
Expand the fraction to get the least common denominator, like
![\frac{3y}{3*1}-\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3y%7D%7B3%2A1%7D-%5Cfrac%7B2%7D%7B3%7D)
Write all numerators above the common denominator, like this:
![\frac{3y-2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3y-2%7D%7B3%7D)
The bottom one used the same way to became simplest form, like this:
![y+\frac{1}{5}](https://tex.z-dn.net/?f=y%2B%5Cfrac%7B1%7D%7B5%7D)
![\frac{y}{1} +\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B1%7D%20%2B%5Cfrac%7B1%7D%7B5%7D)
![\frac{5y}{5*1}+\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B5y%7D%7B5%2A1%7D%2B%5Cfrac%7B1%7D%7B5%7D)
![\frac{5y+1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B5y%2B1%7D%7B5%7D)
And it became like this:
![\frac{3y-2}{3}/\frac{5y+1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B3y-2%7D%7B3%7D%2F%5Cfrac%7B5y%2B1%7D%7B5%7D)
Now, we are going to simplify this complex fraction. We can use cross- multiply method to simplify this fraction.
![\frac{3y-2}{3}*\frac{5y+1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B3y-2%7D%7B3%7D%2A%5Cfrac%7B5y%2B1%7D%7B5%7D)
3y-2(5) and 5y-1(3)
and it will becomes like this in function form:
![\frac{3y-2(5)}{5y+1(3)}](https://tex.z-dn.net/?f=%5Cfrac%7B3y-2%285%29%7D%7B5y%2B1%283%29%7D)
Then, we should distribute 5 through the parenthesis
![\frac{15y-10}{5y+1(3)}](https://tex.z-dn.net/?f=%5Cfrac%7B15y-10%7D%7B5y%2B1%283%29%7D)
![\frac{15y-10}{15y+3}](https://tex.z-dn.net/?f=%5Cfrac%7B15y-10%7D%7B15y%2B3%7D)
And.... Here we go. That is the answer.
Answer:
= 5u
Step-by-step explanation:
You combine like terms
( 2u+ 8u = 10u )
( -5u + 10 u =5u)
0.15(34) = x......with x representing what they will save