Sample space: H1, H2, H3, H4, T1, T2, T3, T4
All outcomes if the card is three: H3, T3
I was unclear about the last two parts of the question.
There is no way to factor this so i would assume the answer is no solution.
Answer:
![b = \frac{y-12x}{12}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7By-12x%7D%7B12%7D)
Step-by-step explanation:
subtract 12x from both sides, then divide by twelve.
In every triangle, the largest side, is opposite the largest angle.
Also, the smallest side, is opposite the smallest angle.
a.
![70^o\ \textgreater \ 60^o\ \textgreater \ 50^o](https://tex.z-dn.net/?f=70%5Eo%5C%20%5Ctextgreater%20%5C%2060%5Eo%5C%20%5Ctextgreater%20%5C%2050%5Eo)
so
![|RQ|\ \textgreater \ |PR|\ \textgreater \ |PQ|](https://tex.z-dn.net/?f=%7CRQ%7C%5C%20%5Ctextgreater%20%5C%20%7CPR%7C%5C%20%5Ctextgreater%20%5C%20%7CPQ%7C)
,
because RQ is opposite angle P, the largest,
PR is opposite angle Q , the middle
and PQ is opposite angle R, the smallest.
Greatest side: RQ
b. The sum of the measures of the interior angles of any triangle is 180°,
so
![m(A)+m(B)+m(C)=180^o\\\\50^o+45^o+x=180^o\\\\x=180^o-50^o-45^o=85^o](https://tex.z-dn.net/?f=m%28A%29%2Bm%28B%29%2Bm%28C%29%3D180%5Eo%5C%5C%5C%5C50%5Eo%2B45%5Eo%2Bx%3D180%5Eo%5C%5C%5C%5Cx%3D180%5Eo-50%5Eo-45%5Eo%3D85%5Eo)
thus, m(C) is the largest angle. This means the largest side is the side AB.
Answers:
a) RQ
b)AB
X=1
because you would add two to the other side and have 2x=2 divide by 2 and you would be left with x=1