Math shortcuts help me plz

Test Preparation
1

<p>Okay here's some questions I want some of you to solve for me if you could do so please</p>

<p>1) If -1 less than or equal to x less than or equal to 3, which of hte following inequalities describes the set of all possible values of x squared?</p>

<p>A) -1 less than or equal to x squared less than or equal to 3
B) 0 less than or equal to x squared less than or equal to 9
C) 1 less than or equal to x squared less than or equal to 3
D) 1 less than or equal to x squared less than or equal to 6
E) 1 less than or equal to x squared less than or equal to 9</p>

<p>2) You have a right triangle looking figure but the angle is not 90 degrees, this angle is greater than 90 degrees. Why is the hypotenuse^2 greater than (leg1)^2 + (leg2)^2?</p>

<p>3) In the xy-coordinate plane, the coordinates of two opposite vertices of a square are (3,4) and (6,7). What is the sum of the x-coordinate and the y-coordinate of another vertex?</p>

<p>4) You have a right angle, which is made up of subangles x and y. therefore x+y=90</p>

<p>if 2y<x<3y, what is one possible value of y and why?</p>

<p>Please help me, as these took me a couple of minutes of backsolving/strategic guessing/etc to do them.</p>

2

<p>nvm about 2 and 3,</p>

<p>but someone clarify on 1 and 4 plz</p>

3

<p>Well, for number 1 I believe the answer is B. Any number squared is positive so A is gone, and x could be a fraction or 0. 0 squared equals 0 and a fraction squared can infinitely approach 0. Therefore B is the only possible choice. For number 4, I'd just do a little plugging in. First I'd recognize that x has to be a good bit bigger then y (you can see this just by looking at the problem). So I immediately plugged in 60 for x and 30 for y (because the sum must equal 90), nice round numbers. I got 60<60<90. Ok, that doesn't quite work so I make x slightly smaller and y slightly bigger by using 59 and 31, giving me 62<59<93. Whallah. I took me 15 seconds or so. I could probably have tried it algebraically, but it would have been a waste of my time.</p>

4

<p>thank you.</p>

5

<p>Unfortunately, I was half asleep when I responded, so the answer to number 4 doesn't quite work. 62<59? What could I have been thinking. Plug in 29 for x and 61 for y and you get 58<61<87. Much better.</p>