Melody

(1/6)x-(1/12)y= -(1/2) <--Fractions  (1)

Mult both sides of (1) by 12 to get rid of the fractions

2x-1y=-6    (2)

2x-y=-6

Now these equations are identical so there is an infinite number of solutions.

If you graph them, they are the exact same line.    

Yes you are right mathematician  

Darla and Bill play a game where they pick 2 different numbers from the set {1, 2, 3, 4}. If the sum is larger than the product Darla wins. Otherwise Bill wins. What is the probability that Darla wins?

1,2      s=3    P=2      D

1,3      S=4    p=3     D

1,4      S=5    P=4      D

2,3       S=5   p=6       B

2,4       S=6   P=8         B

3,4       S=7    P=12      B

THE PROBABILTY THAT DARLA WILL WIN IS   1/2     OR     0.5     OR     50%

I've never heard the term alternate exterior angles

Alternate angles on parallel lines make a z shape and they are congruent (equal) to each other.

No other regular answerers are on a present.  I might be quicker to google your question.  

FV = 7300(1+0.035)^6

Interest = FV- 7300

3x^2 +2x-1=0

I am looking for 2 numbers that mult to 3*-1=-3   and add to +2

I see that the numbers are  -3 and +1

so now I will split 2x into  -3x+1x

$$\\3x^2 +2x-1=0\\
3x^2-3x +1x-1=0\\
3x(x-1) +1(x-1)\\
(3x+1)(x-1)=0$$

3x+1=0   or    x-1=0

3x=-1      or     x=1

x= -1/3    or     x=1

Sorry, not the stuff you have been presenting.

I can tackle some Australian business maths but I think you are using terms that are country based.

Anyway i am not familiar with the terms.

I'll  message you:)

how about 1 and 25

You don't know if b is the hypotenuse or the other short side so you can't definitively find it.

By definition a is the side opposite angle A

If b was the other short side then it would be the adjacent side 

and    tan15=347/b

etc

this has to be the third or the forth quad because sin is neg

In a first quad 'equivalent' triangle  opp=2, hyp=3  so adj = sqrt(9-4)=sqrt5

From here you should be able to name the other trig ratios. :)

The 1.1526 is correct to  4 decimal places.

So the phase of this complex number is the angle       $$tan^{-1}\left(\frac{9}{4}\right)\;\approx\; 1.1526$$

My knowledge of complex numbers is very rusty but I think all of this is correct.