Alan

The first set has no solutions (Multiply the second equation by -5 and you get 2x -5y = -3/2 which cannot hold at the same time as 2x - 5y = 3)

I entered the wrong data in the matrix approach!  But since that approach isn't one you understand, here's how to do it by a process of elimination:

17) is c.

I think all the others have been answered.

3c^2 = 5c   Rewrite as  3c^2 - 5c = 0  The left-hand side factors as  c*(3c - 5)

10x^2 + 9x + 2 = 0   The LHS factors as (2x + 1)*(5x + 2)

9y^2 + 16 = -24y  Rewrite as 9y^2 + 24y + 16 = 0  The LHS factors as (3y + 4)^2

4m^2 = 25  Rewrite as 4m^2 - 25 = 0   The LHS is the difference between two squares, so: (2m + 5)*(2m - 5)

The term "googol" was coined in 1938 by 9-year-old Milton Sirotta, nephew of Edward Kasner - see the book Mathematics and the Imagination by Kasner and Newman.  (It's a good book - published in 1940, it's still worth reading today.)

sin(pi/12 + pi/2) = sin(pi/12 + 6pi/12) = sin(7pi/12) = 0.9659258262890682867497431997289

 (numerical result copied from the Microsoft Windows calculator!)

Take logs of both sides

log(3^x) = log(49)

x*log(3) = log(49)

x = log(49)/log(3)

$${\mathtt{x}} = {\frac{{log}_{10}\left({\mathtt{49}}\right)}{{log}_{10}\left({\mathtt{3}}\right)}} \Rightarrow {\mathtt{x}} = {\mathtt{3.542\: \!487\: \!498\: \!322\: \!844\: \!4}}$$

For question 5) the average velocity is (x(4secs) - x(2secs))/(4secs - 2secs)

This is (5 - 10)/(4 - 2) = -5/2 = -2.5 m/s

So b is the correct answer.

A googol is 10^100

A googolplex is 10^googol

I've never heard of a googolplexian!

If you meant this to be (45/x) - 14 = 22, then

Add 14 to both sides

45/x = 36

Mulitply both sides by x

45 = 36x

Divide both sides by 36

x = 45/36 = 5/4 = 1.25

tan(angle) = opposite/adjacent

Here:  opposite = height; adjacent = 8ft;  angle = 64°,

So: tan(64°)=height/8  or height = 8*tan(64°) ft

$${\mathtt{height}} = {\mathtt{8}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{64}}^\circ\right)} \Rightarrow {\mathtt{height}} = {\mathtt{16.402\: \!430\: \!732\: \!632}}$$

height ≈ 16.4 ft