# Tutor profile: Armine S.

## Questions

### Subject: Geometry

We are given a right triangle with sides 3 in & 4 in. What is the length of the hypotenuse?

Since the triangle in question is a right triangle, we can use the Pythagorean Theorem: a^2 + b^2 = c^2, in which a and b correspond to the 2 sides, while c is the hypotenuse --> a^2 + b^2 = c^2 Plug in values --> 3^2 + 4^2 = c^2 Square --> 9 + 16 = c^2 Add --> 25 = c^2 Take the square root of both sides --> 5 = c The length of the hypotenuse is 5 in. Alternatively, if we know our Pythagorean triangle ratios (i.e. 3:4:5 , 5:12:13 etc...) then we would instantly know that the hypotenuse length is 5.

### Subject: Biology

What is the balanced formula for photosynthesis?

6CO2 + 6H2O -l-i-g-h-t-> C6H12O6 + 6O2

### Subject: Algebra

Find x: x^2 + x = 30

Bring all terms to one side --> x^2 + x - 30 = 0 Reverse FOIL (first, outer, inner, last) --> in this case, since the x term is positive and the constant (30) is negative, this means that we will have (x - [some number])(x + [some number]) --> we must find the two numbers whose product will give us -30 and when combined together will give +(1)x --> these numbers are -5 and 6 --> (x-5)(x+6) = 0 --> Separate: (x-5) = 0 ; (x+6) = 0 --> x = 5 and -6 --> FOIL to check we are correct --> (x-5)(x+6) = x^2 + 6x - 5x -30 = x^2 + x - 30

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