Answer:
1/2
Step-by-step explanation:
Both fractions can be expressed using a denominator of 10. The sum can be reduced by removing a common factor of 5 from numerator and denominator.
![\dfrac{3}{10}+\dfrac{1}{5}=\dfrac{3}{10}+\dfrac{2}{10}\\\\=\dfrac{3+2}{10}=\dfrac{5\cdot 1}{5\cdot 2}=\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B10%7D%2B%5Cdfrac%7B1%7D%7B5%7D%3D%5Cdfrac%7B3%7D%7B10%7D%2B%5Cdfrac%7B2%7D%7B10%7D%5C%5C%5C%5C%3D%5Cdfrac%7B3%2B2%7D%7B10%7D%3D%5Cdfrac%7B5%5Ccdot%201%7D%7B5%5Ccdot%202%7D%3D%5Cdfrac%7B1%7D%7B2%7D)
Answer:
V=lwh=5 x 9 x 3=135cm3
Step-by-step explanation:
Answer:
46
Step-by-step explanation:
Let
represent a number with
in the ten's position and
is the one's position.
This means
actually has value of
.
We are given the sum of those digits of
is 10; this means
.
It says if 18 is added to the number
, then the result is
.
So
has value
and
has value
.
We are given then:
![(ab)+18=(ba)](https://tex.z-dn.net/?f=%28ab%29%2B18%3D%28ba%29)
![10a+b+18=10b+a](https://tex.z-dn.net/?f=10a%2Bb%2B18%3D10b%2Ba)
Subtract
on both sides:
![b+18=10b+a-10a](https://tex.z-dn.net/?f=b%2B18%3D10b%2Ba-10a)
Simplify:
![b+18=10b-9a](https://tex.z-dn.net/?f=b%2B18%3D10b-9a)
Subtract
on both sides:
![18=10b-b-9a](https://tex.z-dn.net/?f=18%3D10b-b-9a)
![18=9b-9a](https://tex.z-dn.net/?f=18%3D9b-9a)
Divide both sides by 9:
![2=b-a](https://tex.z-dn.net/?f=2%3Db-a)
Rearrange by commutative property:
![2=-a+b](https://tex.z-dn.net/?f=2%3D-a%2Bb)
So the system of equations we want to solve is:
![a+b=10](https://tex.z-dn.net/?f=a%2Bb%3D10)
![-a+b=2](https://tex.z-dn.net/?f=-a%2Bb%3D2)
-------------------------Add equations together (this will eliminate the variable
and allow you to go ahead and solve for
:
![0+2b=12](https://tex.z-dn.net/?f=0%2B2b%3D12)
![2b=12](https://tex.z-dn.net/?f=2b%3D12)
Divide both sides by 2:
![b=\frac{12}{2}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B12%7D%7B2%7D)
Simplify:
![b=6](https://tex.z-dn.net/?f=b%3D6)
If
and
, then
.
since 4+6=10.
So the original number is (46).
18 more than 46 is 18+46=(64) which is what we wanted.
We also have the sum of 4 and 6 is 10 as well.
It would seem that the 25% down and 25% increase would cancel each other out and the shoes would remain $60
Answer:
The steps have been shown in the solution below
Step-by-step explanation:
![(3x+1)^{2} - 2(3x+1)=(3x+1)(3x-1)](https://tex.z-dn.net/?f=%283x%2B1%29%5E%7B2%7D%20-%202%283x%2B1%29%3D%283x%2B1%29%283x-1%29)
![9x^{2} +6x+1 -6x-2= (3x+1) (3x-1)\\\\9x^{2} -1=(3x+1)(3x-1)\\\\(3x+1)(3x-1)=(3x+1)(3x-1)\\](https://tex.z-dn.net/?f=9x%5E%7B2%7D%20%2B6x%2B1%20-6x-2%3D%20%283x%2B1%29%20%283x-1%29%5C%5C%5C%5C9x%5E%7B2%7D%20-1%3D%283x%2B1%29%283x-1%29%5C%5C%5C%5C%283x%2B1%29%283x-1%29%3D%283x%2B1%29%283x-1%29%5C%5C)
LHS=RHS Hence, proved.