If we're only counting 5 vowels (A, E, I, O, U) and 20 consonants (everything else, minus T), then there are

ways of picking the vowels, and

ways of picking the consonants.
We want the word to start with T, and we'll allow any arrangement of the other 4 letters, so that the total number of words is

Keep in mind that this means words like TRIES and TIRES are treated as different.
The slope of first line is m 1= ( 1 - 0 ) / ( - 2 - ( - 6 ) );
m = 1 / 4 ;
Because the second line is perpendicular to the first line, m2 * m1 = - 1 ;
m2 * ( 1 / 4 ) = -1;
m2 = - 4 ;
The equation of the second line is : y - 3 = ( - 4 )( x - 2 );
y - 3 = -4x + 8 ;
y = -4x + 11.
Since you have y alone on one side of the equation......
Use substitution and plug in 1/2x-4 for y in the other equation.

Distribute

Combine like terms

Add 8 to both sides

Divide by 4
and 
Plug this value in for x

Simplify

Multiply everything by 8 and simplify

Divide.....

Your answers are:

Answer:
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Step-by-step explanation:
Hope it helps
For a function to have a derivative in a point has to be continuous at the point, that is, it has to be defined at that point, other wise the derivative would be meaningless.