Answer:
Lets say you have a scale of 2 actual feet is equal to 1 graph inch. And lets say you have a perimeter of 24 inches. You know that for every inch I have graphed, it's an actual 2 feet. So if you multiply those 24 inches by 2, then you will get 48. And you need to change the units to match the description, so I will need to change inches to feet. This will get me 48 feet of perimeter in real life.
Answer to 3 is 441
answer to 4 is 12.4 (using pythagorem theorem which is A squared plus B squared equals C squared)
Answer:
A. Yes, the triangles are congruent by SAS.
Step-by-step explanation:
EF = FG and DF = FH-> Given
angle EFD = angle HFG -> Vertical angles are congruent
DE F = HGF -> SAS Triangle Congruence Theorem
Answer:
x= -3
Step-by-step explanation:
6x+5=8x+11
-2x = 6
x= -3
Answer:
![\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}](https://tex.z-dn.net/?f=%5Cbold%7Bcos%5Cdfrac%7BA%7D%7B2%7D%20%3D%20-%5Cdfrac%7B1%7D%7B%5Csqrt3%7D%7D)
Step-by-step explanation:
Given that:
![cosA=-\dfrac{1}3](https://tex.z-dn.net/?f=cosA%3D-%5Cdfrac%7B1%7D3)
and
![tanA > 0](https://tex.z-dn.net/?f=tanA%20%3E%200)
To find:
![cos\dfrac{A}{2} = ?](https://tex.z-dn.net/?f=cos%5Cdfrac%7BA%7D%7B2%7D%20%3D%20%3F)
Solution:
First of all,we have cos value as negative and tan value as positive.
It is possible in the 3rd quadrant only.
will lie in the 2nd quadrant so
will be negative again.
Because Cosine is positive in 1st and 4th quadrant.
Formula:
![cos2\theta =2cos^2(\theta) - 1](https://tex.z-dn.net/?f=cos2%5Ctheta%20%3D2cos%5E2%28%5Ctheta%29%20-%201)
Here ![\theta = \frac{A}{2}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Cfrac%7BA%7D%7B2%7D)
![cosA =2cos^2(\dfrac{A}{2}) - 1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =cosA+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =-\dfrac{1}3+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =\dfrac{2}3\\\Rightarrow cos(\dfrac{A}{2}) = \pm \dfrac{1}{\sqrt3}](https://tex.z-dn.net/?f=cosA%20%3D2cos%5E2%28%5Cdfrac%7BA%7D%7B2%7D%29%20-%201%5C%5C%5CRightarrow%202cos%5E2%28%5Cdfrac%7BA%7D%7B2%7D%29%20%3DcosA%2B1%5C%5C%5CRightarrow%202cos%5E2%28%5Cdfrac%7BA%7D%7B2%7D%29%20%3D-%5Cdfrac%7B1%7D3%2B1%5C%5C%5CRightarrow%202cos%5E2%28%5Cdfrac%7BA%7D%7B2%7D%29%20%3D%5Cdfrac%7B2%7D3%5C%5C%5CRightarrow%20cos%28%5Cdfrac%7BA%7D%7B2%7D%29%20%3D%20%5Cpm%20%5Cdfrac%7B1%7D%7B%5Csqrt3%7D)
But as we have discussed,
will be negative.
So, answer is:
![\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}](https://tex.z-dn.net/?f=%5Cbold%7Bcos%5Cdfrac%7BA%7D%7B2%7D%20%3D%20-%5Cdfrac%7B1%7D%7B%5Csqrt3%7D%7D)