Anju plots points showing equivalent ratios on the coordinate plane below
2 answers:
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! is factorial
it means multipliy all numbers from 1 to that number together
example
1!=1
2!=2*1
3!=3*2*1
etc
some things to note
7!*8=8!
4!*5*6=6!
so we can rewrite it as
=
=
it means multipliy all numbers from 1 to that number together
example
1!=1
2!=2*1
3!=3*2*1
etc
some things to note
7!*8=8!
4!*5*6=6!
so we can rewrite it as
The volume of a cube with side length equal to x, is 
,
thus, the volume of a cube shaped box, whose side length is (5a+4b) is :
,
The volume is already expressed in terms of a and b, but we can expand the expression
, as follows:
![(5a+4b)^{3} =(5a+4b)(5a+4b)^{2}= (5a+4b)[ (5a)^{2}+2(5a)(4b)+ (4b)^{2}]](https://tex.z-dn.net/?f=%285a%2B4b%29%5E%7B3%7D%20%3D%285a%2B4b%29%285a%2B4b%29%5E%7B2%7D%3D%20%285a%2B4b%29%5B%20%285a%29%5E%7B2%7D%2B2%285a%29%284b%29%2B%20%284b%29%5E%7B2%7D%5D)
![=(5a+4b)[ 25a^{2}+40ab+ 16b^{2}]](https://tex.z-dn.net/?f=%3D%285a%2B4b%29%5B%2025a%5E%7B2%7D%2B40ab%2B%2016b%5E%7B2%7D%5D)
![=(5a)[ 25a^{2}+40ab+ 16b^{2}]+(4b)[ 25a^{2}+40ab+ 16b^{2}]](https://tex.z-dn.net/?f=%3D%285a%29%5B%2025a%5E%7B2%7D%2B40ab%2B%2016b%5E%7B2%7D%5D%2B%284b%29%5B%2025a%5E%7B2%7D%2B40ab%2B%2016b%5E%7B2%7D%5D)
Answer:
,
or
thus, the volume of a cube shaped box, whose side length is (5a+4b) is :
The volume is already expressed in terms of a and b, but we can expand the expression
Answer:
or
Answer:
Now, add these two equations.
You get,
Given,
You can test this to the other equation as well.
Hence, the two numbers are 14 and 10.