1) Graph x+y<1 If you take x from both sides you get: y < 1 - x The next step is to graph y = 1 - x. To do this you need to points: if x=0 then y = 1 - 0 = 1. So the first point is (0,1) if y=0 then you have 0 = 1 - x then x = 1. Thus the second pont is (1,0). Next you draw a dotted straight line that passes through both points. The area that is below the line is the graph you are looking for. If select any point (x,y) in that area you can verify that if you add its coordinates up them up, the answer will be smaller than 1. For example: (x,y) = (0, 0). x + y = 0 + 0 = 0 < 1 (x,y) = (-1, -2). x + y = (-1) + (-2) = -3 < 1 (x,y) = (1/2, 1/3). x+ y = 5/6 < 1 The straight line is dotted because none of the points in it verify x + y < 1. 2) Simplifiy. Express in simplest radical form. (√2-3)(√2+3) = (√2)(√2) + (√2)3 + (-3)(√2) + (-3)3 = = 2 + 3√2 - 3√2 - 9 = 2 - 9 = -7 This is know as the difference of squares. Any multiplication that looks like (a - b)(a + b) can expressed as (a.a - b.b) -> that is a squared minus b squared (and viceversa, of course). This happens because when you solve (a – b)(a +b), you always get that ab and (-b)a cancel each other out.

In this case you had (√2-3)(√2+3) and the answer is:

√2√2 – 3.3 = 2 – 9 = -7, like we stated before. This way is easier and faster.

so according to indices laws, (a+b)(a-b)=(a)² – (b)²

so…

(√2-3)(√2+3)=(√2)² – (3)²

= 2-9…according to indices laws again, (√a)² = a

= -7

i figured 2 out though

http://img.photobucket.com/albums/v63/xunfazedx/DSC00794.jpg to see my workings.