Alan

One way to do it is just to add the degrees to 1/60 times the minutes plus 1/3600 times the seconds. For example:

$${\mathtt{91}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{35}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{54}}}{{\mathtt{3\,600}}}} = {\mathtt{91.598\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

To partition a positive integer you write it as a sum of other positive integers, all possible ways.

Since there are nearly 200 million ways of partitioning 100, I don't fancy trying to partition 1331 ( = 11³)!

For the second one, -2x² +7x + 15 =0, you could either use the quadratic formula, or do the following:

Divide through by -2

x² - (7/2)*x + (15/2) = 0

This factors as:

(x + 3/2)*(x - 10/2) = 0  or  (x + 3/2)*(x - 5) = 0

This gives the two values for x as x = -3/2 and x = 5

I'll do the first one for you:

-3 = 1 + x/2  

Subtract 1 from both sides

-4 = x/2

Multiply both sides by 2

-8 = x

(or x = -8)

See if you can do the others.  First get the term that doesn't multiply or divide x on the other side of the equation, then multiply or divide both sides of the equation by the term that divides or multiplies the x. 

$$\frac{1}{3}\times x = 5\\\\ x = 3 \times 5\\\\ x = 15$$

-12x + 7 = 4x - 9

Add 12x to both sides

7 = 16x - 9

Add 9 to both sides

16 = 16x

Divide both sides by 16

x = 1

Let length be L and W be width.  Then we have two equations:

L = W + 8   and

2*L + 2*W = 52

Replace L in the second equation using the first equation:

2*(W + 8) + 2*W = 52

So

4*W + 16 = 52

4*W = 36

W = 9

So L = 9 + 8

L = 17 inches

Hmm.  Just downloaded Firefox (which I'm using now).  I don't even get the icons!  It must be me!!

What browser are you using Chris?  I just get icons in Google Chrome and in IE.

I can right-click and select Open image in new tab to see them, but I also have to put up with a lot of extraneous material, like adverts, this way.

5% commission on $46,350 is:

$${\frac{{\mathtt{5}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}{\mathtt{46\,350}} = {\frac{{\mathtt{4\,635}}}{{\mathtt{2}}}} = {\mathtt{2\,317.5}}$$

Add this to $24000

$${\mathtt{24\,000}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2\,317.5}} = {\mathtt{26\,317.5}}$$

$26,317.5 is less than $28,560, so the salary without commission option is better here.