4x+10 + 3x+5 +y =180
solve for y y=third angle
combine like terms
7x+15+y =180
subtract 7x+15 from each side
y = 180 -(7x+15)
y = 180 -7x-15
y = 165 -7x
The third angle equals 165-7x
The Mean Value Theorem:
If a function is continuous on [ a, b ] and differentiable on ( a , b ) than there is a point c in ( a, b ) such that:
f ` ( c )= ( f ( b ) - f ( a ) ) / ( b - a )
f ` ( c ) = ( f ( 2 ) - f ( 0 ) ) / ( 2 - 0 )
f `( x ) = 10 x - 3
f ` ( c ) = 10 c - 3
2 f ` ( c ) = 16 - 2
f ` ( c ) = 7
7 = 10 c - 3
c = 1
Answer:
Yes, the function is continuous on [ 0, 2 ] and differentiable on ( 0, 2 ).
Long way: try to divide. But we are lazy, so it's no go. Option number one: all rational numbers that could give you a division can be taken from "THE List": you build it by taking the constant term, that is 6, and all its divisors (1,2,3,6), the highest term coefficent, 3 in this case, its divisors (1,3) , and you divide every one in the first list by the second, and adding a in front of them. Our list is: .
Since -3 is part of THE List, it might be a divisor - that system would garantee you that, for example, x-4 would NOT be a factor.
Cheap way. if (x+3) is a factor of g(x), then g(-3) = 0. Let's replace.
Since we didn't get zero, is not a factor of g(x)