Answer:
Okay, there are many ways to find if a triangle is congruent.
Let's start with some different terminology.
For the sake of simplicity let us say that S stands for when a side is congruent for both triangles and A stands for when an angle (<) is congruent between both the triangles as well.
So, you need to memorize some rules. If you find that 2 triangles are congruent in the sense of; SSS, SAS, AAS, SAA, and ASA. One thing to remember is that Angle Side Side isn't congruent and is called <em>Donkey Theorem</em>. This theorem only works for right triangles.
One way to know if your triangle isn't congruent is if you can find a part of the triangle that is different.
I know that wasn't the best explanation but I hope it helped anyhow. :)
Perpendicular slopes have a product of -1, thus
solve for "d"
The notation in its current form isn't entirely clear.
Did you mean to write 
? The 4 isn't in the square root.
If so, then the expression is in simplest form because we cannot simplify 
any further (note how 10 doesn't have any perfect square factors other than 1).
Also, the 3/4 portion is fully reduced already.
------------------------
Or,
Did you mean to write 
? This time the 4 is inside the square root.
If so, then we can simplify like this
This means that 
Answer: Hello mate!
we know that p(x,y) means "Student x has taken class y"
and the used symbols are:
∃: this means "existence", you use this symbol to say that there exists at least one object that makes true the sentence.
∀: this means "for all", you use this symbol to say that the sentence is true for all the elements, then:
a) ∃x∃yP (x, y)
"exist at least one student x, that took at least one class y"
b) ∃x∀yP (x, y)
"exist at least one student x, that took all the classes y"
c) ∀x∃yP (x, y)
"every student x, took at least one class y"
d) ∃y∀xP (x, y)
"exist at least one class y, that has been taken by all the students x"
e) ∀y∃xP (x, y)
"for every class y, there is at least one student x that took the class"
f) ∀x∀yP (x, y)
"all the students x took all the classes y"
D. divide 1000
hope this helped
