Step-by-step explanation:
![area = \frac{1}{2} a.b \sin(C) \\ from \:cosine \: rule \\ {c}^{2} = {a}^{2} + {b}^{2} - 2a.b \cos(C) \\ 36 = 144 + 81 - (2 \times 12 \times 9) \cos(C) \\ 189 = 216 \cos(C) \\ \cos(C) = 0.875 \\ C = \cos {}^{ - 1} (0.875) \\ C = 28.96 \degree \\ area = \frac{1}{2} \times 144 \times 9 \times \sin(28.96 \degree) \\ area = 313.8 \: sq \: units](https://tex.z-dn.net/?f=area%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20a.b%20%5Csin%28C%29%20%20%5C%5C%20from%20%5C%3Acosine%20%5C%3A%20rule%20%5C%5C%20%20%7Bc%7D%5E%7B2%7D%20%20%3D%20%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20-%202a.b%20%5Ccos%28C%29%20%20%5C%5C%2036%20%3D%20144%20%2B%2081%20-%20%282%20%5Ctimes%2012%20%5Ctimes%209%29%20%5Ccos%28C%29%20%20%5C%5C%20189%20%3D%20216%20%5Ccos%28C%29%20%20%5C%5C%20%20%5Ccos%28C%29%20%20%3D%200.875%20%5C%5C%20C%20%3D%20%20%5Ccos%20%7B%7D%5E%7B%20-%201%7D%20%280.875%29%20%5C%5C%20C%20%3D%2028.96%20%5Cdegree%20%5C%5C%20area%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%20144%20%5Ctimes%209%20%5Ctimes%20%20%5Csin%2828.96%20%5Cdegree%29%20%20%5C%5C%20area%20%3D%20313.8%20%5C%3A%20sq%20%5C%3A%20units)
No, because any real valued term with degree 0 would be a constant. All constants in an expression can be combined into single term. Therefore if the expression were of degree 0, all the terms would be constants and could be combined into a single term making the expression a monomial.
Answer:
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Answer:
The value of y is 3.
Step-by-step explanation:
Given points: P(12,-2), Q(5,-10), R(-4,10) and S(4,y).
We need to find the value of y so that line PQ is perpendicular to line RS.
Slope formula:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Slope of PQ is
![m_{PQ}=\dfrac{-10-(-2)}{5-12}=\dfrac{-8}{-7}=\dfrac{8}{7}](https://tex.z-dn.net/?f=m_%7BPQ%7D%3D%5Cdfrac%7B-10-%28-2%29%7D%7B5-12%7D%3D%5Cdfrac%7B-8%7D%7B-7%7D%3D%5Cdfrac%7B8%7D%7B7%7D)
Slope of RS is
![m_{RS}=\dfrac{y-10}{4-(-4)}=\dfrac{y-10}{8}](https://tex.z-dn.net/?f=m_%7BRS%7D%3D%5Cdfrac%7By-10%7D%7B4-%28-4%29%7D%3D%5Cdfrac%7By-10%7D%7B8%7D)
The product of slopes of two perpendicular lines is -1.
![m_{PQ}\times m_{RS}=-1](https://tex.z-dn.net/?f=m_%7BPQ%7D%5Ctimes%20m_%7BRS%7D%3D-1)
![\dfrac{8}{7}\times \dfrac{y-10}{8}=-1](https://tex.z-dn.net/?f=%5Cdfrac%7B8%7D%7B7%7D%5Ctimes%20%5Cdfrac%7By-10%7D%7B8%7D%3D-1)
![\dfrac{y-10}{7}=-1](https://tex.z-dn.net/?f=%5Cdfrac%7By-10%7D%7B7%7D%3D-1)
![y-10=-7](https://tex.z-dn.net/?f=y-10%3D-7)
Add 10 on both sides.
![y=-7+10](https://tex.z-dn.net/?f=y%3D-7%2B10)
![y=3](https://tex.z-dn.net/?f=y%3D3)
Therefore, the value of y is 3.
Total of all angles should equal 360 degrees. So 360-132-68-66=94, angle F is 94 degrees.