a. What is the hypothesis of the statement below?
   "If 2 triangles are isosceles right triangles, then they are similar".
b. The endpoints of PQ are P(-7,12) and Q(3,-2). What are the coordinates of  
   the midpoint?
c. Solve the system of equations:
   3x + 2y = 17
   2x - y = 9
d. Find the measure of the hypotenuse of a 30-60-90 triangle whose longer leg 
   has a measure of 6 meters. Give the answer in simplified radical form.
e. Write an equation of the line that passes through the point at (4,4) and is
   perpendicular to the line whose equation is 2x+y= 7

Hi again teatea!
These are the answers to your questions.

a. "In conditional statements the part follows the 'if' is the
hypothesis. The part follows the 'then' is the conclusion"

Logical Reasoning
http://www.efn.org/~kinne/geogirls/info/logic.html

Therefore, in this case the statement

"2 triangles are isosceles"

is the hypothesis, and

"they are similar"

is the conclusion.


b. The formula to find the coordinates of the midpoint of segment PQ
is the following:

( (-7+3)/2 , (12-2)/2 )
(    2     ,    5     )

Thus (2,5) is the midpoint of segment PQ where P is in (-7,12) and Q
is in (3,-2). You can see the explanation at the following link:

Midpoint formula
http://regentsprep.org/Regents/math/midpoint/Lmidpoint.htm


c. The solution to this system of equations can be found by isolating
one of the variables in one of the equations and then substituting it
in the other equation. For example, let's take:

2x - y = 9

Isolating y, we get:

y = 2x - 9

Now we substitute this in the other equation (3x + 2y = 17)

3x + 2(2x-9) = 17
3x + 4x - 18 = 17
          7x = 35
           x = 35/7
           x = 5

Finally, in order to find y, we substitute this value in any of the equations:

y = 2x - 9
y = 2*5 - 9
y = 10 - 9
y = 1


d. "In a 30°-60°-90° triangle the sides are in the ratio 1:2:sqrt(3)"

Topics in trigonometry
http://www.themathpage.com/aTrig/30-60-90-triangle.htm

The 'sqrt(3)' stands for "square root of 3". As you can see in the
link, the sqrt(3) corresponds to the longer leg and the 2 corresponds
to the hypothenuse. The equation we must solve in order to find the
length of the hypothenuse when the longer leg's measure is 6 is the
following:

   2        x
------- = ------
sqrt(3)     6

The reason for this equation is the the ratio between the hypothenuse
and the longer leg must be [2/sqrt(3)]. We also know that the longer
leg's measure is 6. So we must find a measure for the hypothenuse such
that the ratio is [2/sqrt(3)]. Isolating 'x' from that equation we
find:

       12
  x = -----
      sqrt(3)

So the measure of the hypothenuse is 12/sqrt(3).


e. You can find the definition of "perpendicular" in the following link:

Perpendicular
http://mathworld.wolfram.com/Perpendicular.html

You can also see in this page that a line with slope m1 is
perpendicular to a line with slope -1/m1.

First let's rewrite the equation for the line we know in
Slope-Intercept form. We have 2x+y=7. We can rewrite it as:

y = -2x + 7

So we know that the slope of this line is -2. Therefore, the slope of
a line that is perpendicular to this line must be -1/(-2), which is
equal to 1/2. So now we know that the equation of the unknown line is:

y = (1/2)x + b

So we just need to find 'b' in order to have the full equation for
this line. Since we know that the line passes through (4,4) and we
know its slope, it's easy to find 'b'. That the line passes through
(4,4) means that:

4 = (1/2)*4 + b

Simplifying, we get:

b = 2

So the equation of this line is:

y = (1/2)x + 2


Google search strategy
30-60-90 triangle
hypothesis conclusion logic
midpoint segment


I hope this helps! If you have any doubts regarding my answer, please
don't hesitate to request a clarification before rating it. Otherwise
I await your rating and final comments.

Best wishes!
elmarto