Alan

I think he just means enter 0.55 and press Enter (not the = sign).

$${\mathtt{0.55}} = {\frac{{\mathtt{11}}}{{\mathtt{20}}}}$$

Questions 9 through 21 are correct.  

Several of the other images are too small for my jaded eyes to make out! 

Well, let's do it in detail:

(x + 10)(x - 10) = x*(x-10) + 10*(x-10) 

                          = x² - 10x  + 10x - 10²

                          = x² - 10²

Does this make it clearer?

If not, show how you got 2x^2.

x + (6/x) = 5

Multiply through by x to get:  x² + 6 = 5x

Subtract 5x from both sides:

x² - 5x + 6 = 0

This factors nicely into:  (x-2)(x-3) = 0

So the two solutions are x = 2 and x = 3

I guess it's the binomial expansion that is giving you problems rosala.

Another way of approaching this is to use the following, iterative formula for square roots (I'll just present it without deriving it):

If we have x² = N then

x_n+1 = (1/2)(x_n + N/x_n)

where n is iteration number.

So, if N = 47 and we start with, say, x₀ = 6

then x₁ = (1/2)(6 +47/6) = 6.917  which is a first approximation

       x₂ = (1/2)(6.917 + 47/6.917) = 6.856 which is a better approximation.

If we start with x₀ = 7

then x₁ = (1/2)(7 + 47/7) = 6.857 which is a better first approximation.

Of course, this depends on your belief in the iterative formula x_n+1 = (1/2)(x_n + N/x_n).  I have just stated it rather than deriving it because the derivation involves calculus, which you probably haven't done yet (actually, there might be a non-calculus derivation, but I can't think of it off-hand!).

I don't know if this helps any! 

Also, the level of precision of the result is not specified in the question, so it could be that just 7 is an acceptable approximation!

This can be written as the difference of two squares:  x² - 10² or x² - 100.

If the question is "what is angle TUV?", then because it is bisected it is just twice TUW, or 106 degrees.  

If this isn't the question, you need to state what it is, or, as rosala noted, supply a picture.

Amount of acid in the 40% solution is 40% of 3 gallons = 1.2 gallons.

Amount of non-acid in the 40% solution is 60% of 3 gallons = 1.8 gallons.

Let x be the total amount of acid in a 90% acid solution.  Then we must have 0.9 = x/(x+1.8)

0.9*x + 0.9*1.8 = x

0.1x = 1.62

x = 16.2 gallons

This is the total amount, so the amount that must be added is this minus the original 1.2 gallons, or 15 gallons.

Depends what x is!