Answer:
24 unit
Step-by-step explanation:
Given,
The vertices of the triangle ABC are,
A (1,1), B (7,1), and C (1,9),
By the distance formula,
![AB=\sqrt{(7-1)^2+(1-1)^2}=\sqrt{6^2}=6\text{ unit}](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%287-1%29%5E2%2B%281-1%29%5E2%7D%3D%5Csqrt%7B6%5E2%7D%3D6%5Ctext%7B%20unit%7D)
![BC=\sqrt{(1-7)^2+(9-1)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10\text{ unit}](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B%281-7%29%5E2%2B%289-1%29%5E2%7D%3D%5Csqrt%7B6%5E2%2B8%5E2%7D%3D%5Csqrt%7B36%2B64%7D%3D%5Csqrt%7B100%7D%3D10%5Ctext%7B%20unit%7D)
![CA=\sqrt{(1-1)^2+(1-9)^2}=\sqrt{8^2}=8\text{ unit}](https://tex.z-dn.net/?f=CA%3D%5Csqrt%7B%281-1%29%5E2%2B%281-9%29%5E2%7D%3D%5Csqrt%7B8%5E2%7D%3D8%5Ctext%7B%20unit%7D)
Thus, the perimeter of the triangle ABC = AB + BC + CA = 6 + 10 + 8 = 24 unit
4(m + 2) expanded is 4 x m and 4 x 2
simplified: 4m + 8
2 is the base and (
![\sqrt[4][a^5 b^3]](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%5Ba%5E5%20b%5E3%5D)
) is the exponent.
the 4 is called an index and it means to fi d the fourth root of the expression under the (
![\sqrt[][text]) symbol.\\a fourth root is a factor that was multiplied four times. ex: 2*2*2*2=16. the fourth root of 16 is two. \\when you do square roots, you take the number representing the factor out of the radical. anything else that is not a square root stays under. ex: \\([tex]\sqrt[9][text])\\([tex]\sqrt[3*3*3][text]) there is one set of two 3's so\\([tex]3\sqrt[3][text])\\with a fourth root, you look for groups of four. the symbol of that group is placed outside the radical. anything else stays in.\\ ([tex]\sqrt[4][a^5 b^3]](https://tex.z-dn.net/?f=%5Csqrt%5B%5D%5Btext%5D%29%20symbol.%5C%5Ca%20fourth%20root%20is%20a%20factor%20that%20was%20multiplied%20four%20times.%20ex%3A%202%2A2%2A2%2A2%3D16.%20the%20fourth%20root%20of%2016%20is%20two.%20%5C%5Cwhen%20you%20do%20square%20roots%2C%20you%20take%20the%20number%20representing%20the%20factor%20out%20of%20the%20radical.%20anything%20else%20that%20is%20not%20a%20square%20root%20stays%20under.%20ex%3A%20%5C%5C%28%5Btex%5D%5Csqrt%5B9%5D%5Btext%5D%29%5C%5C%28%5Btex%5D%5Csqrt%5B3%2A3%2A3%5D%5Btext%5D%29%20there%20is%20one%20set%20of%20two%203%27s%20so%5C%5C%28%5Btex%5D3%5Csqrt%5B3%5D%5Btext%5D%29%5C%5Cwith%20a%20fourth%20root%2C%20you%20look%20for%20groups%20of%20four.%20the%20symbol%20of%20that%20group%20is%20placed%20outside%20the%20radical.%20anything%20else%20stays%20in.%5C%5C%20%28%5Btex%5D%5Csqrt%5B4%5D%5Ba%5E5%20b%5E3%5D)
)
(
![\sqrt[4][a*a*a*a*a*b*b*b]](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%5Ba%2Aa%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab%5D)
) there is one group of 4 a's so
(
![a\sqrt[4][a* b^3]](https://tex.z-dn.net/?f=a%5Csqrt%5B4%5D%5Ba%2A%20b%5E3%5D)
)
there really isn't anything else to do to simplify the expression
-2 because you have to reduce