Answer:
7.7
Step-by-step explanation:
To find the intersection points of the line and the circle we have to set up a system with their equations and solve. The system would look like this:

To solve, substitute 1 for x in the second equation to get:

Solving, we get:

Therefore, the two points of intersection are
and
. The distance between these two points (the length of the chord in the circle) is
which is 7.745966692414... which is 7.7 rounded to the nearest tenth.
Hope this helps :)
Answer:
We verified that ![a^3+b^3+c^3-3abc=\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%2Bc%5E3-3abc%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
Hence proved
Step-by-step explanation:
Given equation is ![a^3+b^3+c^3-3abc=\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%2Bc%5E3-3abc%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
We have to prove that ![a^3+b^3+c^3-3abc=\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%2Bc%5E3-3abc%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
That is to prove that LHS=RHS
Now taking RHS
![\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
(using
)
(adding the like terms)
![=\frac{a+b+c}{2}[2a^2+2b^2+2c^2-2ab-2bc-2ac]](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B2a%5E2%2B2b%5E2%2B2c%5E2-2ab-2bc-2ac%5D)
![=\frac{a+b+c}{2}\times 2[a^2+b^2+c^2-ab-bc-ac]](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5Ctimes%202%5Ba%5E2%2Bb%5E2%2Bc%5E2-ab-bc-ac%5D)
![=a+b+c[a^2+b^2+c^2-ab-bc-ac]](https://tex.z-dn.net/?f=%3Da%2Bb%2Bc%5Ba%5E2%2Bb%5E2%2Bc%5E2-ab-bc-ac%5D)
Now multiply the each term to another each term in the factor
![=a^3+ab^2+ac^2-a^2b-abc-a^2c+ba62+b^3+bc^2-ab^2-b^2c-abc+ca^2+cb^2+c^3-abc-bc^2-ac^2]](https://tex.z-dn.net/?f=%3Da%5E3%2Bab%5E2%2Bac%5E2-a%5E2b-abc-a%5E2c%2Bba62%2Bb%5E3%2Bbc%5E2-ab%5E2-b%5E2c-abc%2Bca%5E2%2Bcb%5E2%2Bc%5E3-abc-bc%5E2-ac%5E2%5D)
(adding the like terms and other terms getting cancelled)
=LHS
Therefore LHS=RHS
Therefore ![a^3+b^3+c^3-3abc=\frac{a+b+c}{2}[(a-b)^2+(b-c)^2+(c-a)^2]](https://tex.z-dn.net/?f=a%5E3%2Bb%5E3%2Bc%5E3-3abc%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5B%28a-b%29%5E2%2B%28b-c%29%5E2%2B%28c-a%29%5E2%5D)
Hence proved.
Answer:
yes
Step-by-step explanation:
Answer:
A = 7
Step-by-step explanation:
Pythagorean triple
Answer:
Expression is:16n+2.50
For buying 4 tickets: 66.50
Step-by-step explanation:
You first have to set up the equation and each ticket cost 16 and you have to buy sixteen that is why it is 16n and then you have to pay 2.50 because you are buying online. Then you put four in for N because you are getting 4 tickets. Finally multiply 16 and 4 then add 2.50.