Since BC=DC, you know the two missing angle measurements in triangle BCD are the same. Since you also know that the total degrees of a triangle must add up to 180 degrees, you can simply do (180-82)/2
=98/2
=49
The degree of y should equal 49
The vertex form of
![f(x)=ax^2+bx+c](https://tex.z-dn.net/?f=f%28x%29%3Dax%5E2%2Bbx%2Bc)
![f(x)=a(x-h)^2+k](https://tex.z-dn.net/?f=f%28x%29%3Da%28x-h%29%5E2%2Bk)
where:
![h=\dfrac{-b}{2a};\ k=f(h)](https://tex.z-dn.net/?f=h%3D%5Cdfrac%7B-b%7D%7B2a%7D%3B%5C%20k%3Df%28h%29)
We have:
![f(x)=x^2-6x+13\to a=1;\ b=-6;\ c=13](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2-6x%2B13%5Cto%20a%3D1%3B%5C%20b%3D-6%3B%5C%20c%3D13)
substitute:
![h=\dfrac{-(-6)}{2\cdot1}=\dfrac{6}{2}=3\\\\k=f(3)=3^2-6\cdot3+13=9-18+13=4](https://tex.z-dn.net/?f=h%3D%5Cdfrac%7B-%28-6%29%7D%7B2%5Ccdot1%7D%3D%5Cdfrac%7B6%7D%7B2%7D%3D3%5C%5C%5C%5Ck%3Df%283%29%3D3%5E2-6%5Ccdot3%2B13%3D9-18%2B13%3D4)
The vertex form of f(x):
![f(x)=(x-3)^2+4](https://tex.z-dn.net/?f=f%28x%29%3D%28x-3%29%5E2%2B4)
The value of minimum is equal k.
Therefore:
Answer: (x + 7)(x - 7)
Explanation: If a variable is taken to an even power, that variable is a perfect square. In this case, x² would therefore be a perfect square.
Since 49 is also a perfect square, what we have here is the difference of two squares. That can be factored as the product of two binomials one with a plus in the middle and one with a minus in the middle.
In the first position will be the factors of x² that are the same.
So we have <em>x</em> and <em>x</em>.
In the second position we will have the
factors of 49 that are the same, 7 and 7.
(x + 7)(x - 7) is your answer which is a factored version of x² - 49.
Answer:
90
Step-by-step explanation:
120 - (120/4)
120 - 30 = 90