A four-character password to log onto a computer is drawn from the digits 0-9 and a subset of 23 letters of the alphabet (repetition is permitted). Determine the number of passwords possible if
a) the letters used are not case sensitive (that is, a lowercase letter is treated the same as an uppercase letter).
b) the letters used are case sensitive (that is, an uppercase letter is considered different than the same lowercase letter).

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: