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Yes I know my answer is the same. I did not discuss it because Sabi specifically requested Heureka to answer him :)

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. :)

Wow, its 2 against one then. 

But nobody can defeat my most powerful weapon yet, the Fire Demon! Its too much for a gun to handle cuz its a meele weapon

and if that somehow doesnt do anything, then ill use my Storm Hammer which has am actual range of area effect, meaning i can attack you with this hammer from a distance apart and i dont have to stand right next to you

oh yea, i also got titanium armor 3.0, this time instead of crystals or rubies, its adamants

and some dark mayter generators and mine launchers and my Mech 3.0 will be enough to stop you heroes from always ruining my plans, especially this operation

cuz this operation, its going well

weve already planted the power plant thatll turn fanta nasty

and weve already convinced china japan and korea to join us

im chilling with mexico and thats a good sign

Rome and greece are already ready

in about 24 hours we shall attack the Arabian Penninsula

oh yea youre right Heather, lets borrow cannons from the ottomans to combat the walls

Depends what is meant by "distinct" I guess.  If you reflect Melody's triangle in any of its sides, you get another one that can't be rotated into the first.

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kes, you have written "Rational number is a number that is expressed in the form pq , where p and q are Integers and q ≠ 0."

This is incorrect.  It should read: "Rational number is a number that is expressed in the form p/q , where p and q are Integers and q ≠ 0."  Note the "p/q" not "pq".

This comment affects some of your other statements as well.  I recommend that you edit your note to correct these.

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Your answer is the same as heureka's, sabi92; it just looks slightly different!  Multiply the top and bottom of your expression by -1 to get it to look like heureka's.

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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.

dont worry, im on and okay!

ok Kid Danger, ready to beat up and defeat the appearently most powerful and most life threatening kid villain on Camelot Kingdom?

Tin Can Of Worms, prepare to serve your sentence in prison for the forums shutdown and for using tanks appearently to harm innocent anons during a war which i cannot say what kind cuz then everyone will panick. its time someone teaches you a few lessons of peasant life, Royal! (dang, i hate fighting royals more than fighting ordinary villains, thats why you never betray the Queen or the To-Be-Queen appearently, and you TR are appearently messing with the To-Be-Queen). Not everything in life will be of Royal life.

Re to TR: Wow, and you're now gonna try to beat up Kid Danger? To be honest Rome it isnt a fair fight. Maybe you should do 1 V 1 for the first time in a long time and not rely on your army. And if youre gonna use your ultimate weapons, you should use them on Capt. Man maybe

Re to KD: Maybe you should bring Capt. Man with you and the odds will slowly turn in your favor.

heuruka if i am writing it this way:

a+x=xa

x-xa=-a

x(1-a)=-a

x=-a/(1-a)

the answer is incomplete then how do i get your answer?i need to divide it or  something?

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  :))

$$\small{\text{$
\begin{array}{rcl}
\dfrac{a+x}{ax} &=& \dfrac{1}{a}+\dfrac{a}{a+x} \\\\
\dfrac{a}{ax}+\dfrac{x}{ax} &=& \dfrac{1}{a}+\dfrac{a}{a+x} \\\\
\dfrac{1}{x}+\dfrac{1}{a} &=& \dfrac{1}{a}+\dfrac{a}{a+x} \\\\
\dfrac{1}{x} &=& \dfrac{a}{a+x} \\\\
a+x &=& xa \\
xa &=& a+x \\
xa-x &=& a\\
x(a-1) &=& a \\\\
\mathbf{x} & \mathbf{=} & \mathbf{\dfrac{a}{a-1}}
\end{array}
$}}$$

I don't think you need scientific notation for this one but it's $${\mathtt{5.601}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{3}}}$$

Add cold air and the room gets colder.

+ - = -

-15-14= -29

4 1/2 ÷ 100 = 9/200

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

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

Thanks Alan :)

Note from the original diagram that there is a right-angle sign between the force arrow and the beam AC, and just to make Melody's reply clearer, here is the diagram with the 'X' that Melody used marked on it.

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If we assume you meant out of 125 beads, 113 were gold and 12 were silver, then (assuming there were only gold and silver beads in the container):

Gold/5000 = 113/125 so Gold = 5000*113/125 = 4520

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please help !!! In an arithmetic sequence, t(8) = 145 and t(50) = 607. Find t(129).

$$\small{\text{$
\begin{array}{lrcl}
& t_8 = a+(8-1)d &=& a+7d \\
& t_{50} =a + (50-1)d &=& a+49 d\\
\\
(1) & \dfrac{ t_{50}+t_8 }{2} &=& a + 28d \\
\\
& t_{50}-t_8 &=& 42d \\
(2) & ( t_{50}-t_8 )\cdot \dfrac{100}{42} &=& 100d\\
\\
& t_{129} &=& a + (129-1)d \\
& t_{129} &=& a + 128d \\
& t_{129} &=& a + 28d + 100d \qquad | \qquad a + 28d = \dfrac{ t_{50}+t_8 }{2} \qquad 100d =( t_{50}-t_8 )\cdot \dfrac{100}{42} \\
& t_{129} &=& \dfrac{ t_{50}+t_8 }{2} + ( t_{50}-t_8 )\cdot \dfrac{100}{42}\\\\
& t_{129} &=& \dfrac{607+145}{2} + (607-145)\dfrac{100}{42}\\\\
& t_{129} &=& 376 + 1100 \\
&\mathbf{ t_{129} }& \mathbf{=} & \mathbf{ 1476 }\\
\end{array}
$}}$$

Its PEMDAS, just like how my great 5th grade teacher taught us students.

PEMDAS=parentheses () exponents x^y multiplication * division / addition + and subtraction -

since addition and subtraction work in a similar way, all you need to do is work out the problem from beginning to end

so like=

-5+8=3

3-7=-4

-4-13=-17

-17+2=15

15+9=-6

and -6 is your answer