Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. the four quantum numbers, the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms) have strict rules which govern the possible values. identify allowable combinations of quantum numbers for an electron. select all that apply.
a) n= 3 l= -2 ml=-1 ms= +1/2
b) n=3 l= 2 ml= -1 ms= -1/2
c) n= 4 l=4 ml=-1 ms= +1/2
d) n=2 l=1 ml=-1 ms=1
e) n=4 l=1 ml=2 ms=-1/2
f) n=5 l=4 ml=4 ms=+1/2

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

the cost function, c(x), is the total cost of manufacturing x units of the product. how many units must the company produce and sell if they wish to make a b. if the company produces and sells 2000 units, would they obtain a profit or loss?