(3x+2)-5y
The Distributive property tells us that we can do this.
Answer:
A. 6
Step-by-step explanation:
Let n represent number of tables.
We have been given that to furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. There are 5 chairs in the warehouse and if 150 different combinations are possible.
Since 2 chairs are being selected from 5 chairs, so we can choose 2 chairs in
ways.
There are n tables and we can choose 2 tables from n table in
ways.
We can represent our given information in an equation as:
![5C2\times nC2=150](https://tex.z-dn.net/?f=5C2%5Ctimes%20nC2%3D150)
![\frac{5!}{2!(5-2)!}\times \frac{n!}{2!(n-2)!}=150](https://tex.z-dn.net/?f=%5Cfrac%7B5%21%7D%7B2%21%285-2%29%21%7D%5Ctimes%20%5Cfrac%7Bn%21%7D%7B2%21%28n-2%29%21%7D%3D150)
![\frac{5*4*3!}{2*1*3!}\times \frac{n!}{2!(n-2)!}=150](https://tex.z-dn.net/?f=%5Cfrac%7B5%2A4%2A3%21%7D%7B2%2A1%2A3%21%7D%5Ctimes%20%5Cfrac%7Bn%21%7D%7B2%21%28n-2%29%21%7D%3D150)
![10\times \frac{n!}{2!(n-2)!}=150](https://tex.z-dn.net/?f=10%5Ctimes%20%5Cfrac%7Bn%21%7D%7B2%21%28n-2%29%21%7D%3D150)
![\frac{n!}{2!(n-2)!}=15](https://tex.z-dn.net/?f=%5Cfrac%7Bn%21%7D%7B2%21%28n-2%29%21%7D%3D15)
![\frac{n!}{2*1*(n-2)!}=15](https://tex.z-dn.net/?f=%5Cfrac%7Bn%21%7D%7B2%2A1%2A%28n-2%29%21%7D%3D15)
![\frac{n*(n-1)*(n-2)!}{2*(n-2)!}=15](https://tex.z-dn.net/?f=%5Cfrac%7Bn%2A%28n-1%29%2A%28n-2%29%21%7D%7B2%2A%28n-2%29%21%7D%3D15)
![\frac{n(n-1)}{2}=15](https://tex.z-dn.net/?f=%5Cfrac%7Bn%28n-1%29%7D%7B2%7D%3D15)
![n(n-1)=30](https://tex.z-dn.net/?f=n%28n-1%29%3D30)
![n^2-n=30](https://tex.z-dn.net/?f=n%5E2-n%3D30)
![n^2-n-30=0](https://tex.z-dn.net/?f=n%5E2-n-30%3D0)
![n^2-6n+5n-30=0](https://tex.z-dn.net/?f=n%5E2-6n%2B5n-30%3D0)
![n(n-6)+5(n-6)=0](https://tex.z-dn.net/?f=n%28n-6%29%2B5%28n-6%29%3D0)
![(n-6)(n+5)=0](https://tex.z-dn.net/?f=%28n-6%29%28n%2B5%29%3D0)
![(n-6)=0\text{ (or) }(n+5)=0](https://tex.z-dn.net/?f=%28n-6%29%3D0%5Ctext%7B%20%28or%29%20%7D%28n%2B5%29%3D0)
![n=6\text{ (or) }n=-5](https://tex.z-dn.net/?f=n%3D6%5Ctext%7B%20%28or%29%20%7Dn%3D-5)
Since tables cannot be negative quantity, therefore, 6 tables are in the warehouse.