Melody

Hi Alan,

It would still be congrent though.

You could translate it too then it would be in a different position so it would not be the same triangle. :)

sqrt of what?

This is the equation of a line so it has an infinite number of points. :)

y-2x=-6

y=2x-6

Do you want to wait longer for Heureka to answer you?

I am reasonabley sure he will answer if you wait long enough.  :)

Find the number of distinct triangles with the measurements a=5, b=2, and A=51

There appears to only be one.

note that      $$a\ne0\;\;\;x\ne0\;\;\;a+x\ne0$$

The lowest common denominator is ax(a+x) so I am going to multiply both sides by this

$$\\(a+x)^2=x(a+x)+a^2x\\\\
a^2+x^2+2ax=x^2+ax+a^2x\\\\
a^2+ax=a^2x\\\\
a^2+ax-a^2x=0\\\\
a(a+x-ax)=0\\\\
a\ne0\;\;so\\\\
a+x-ax=0\\\\
x(1-a)=-a\\\\
x=\frac{-a}{1-a}\\\\
x=\frac{a}{a-1}\\\\$$

I saw the pop up!  You beat me Heureka  :))

Add cold air and the room gets colder.

+ - = -

-15-14= -29

4 1/2 ÷ 100 = 9/200

$${\mathtt{22}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{55}}^\circ\right)} = {\mathtt{18.021\: \!344\: \!974\: \!358}}$$

$${\frac{{\mathtt{14}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}{\mathtt{52\,000\,000}} = {\mathtt{7\,280\,000}}$$