The greatest common factor (GCF) of 15ab and 5b2 is 5b.
5a2 - 20ab - 25b2 = 5(a2 - 4ab - 5b2) = 5(a2 - 4ba - 5b2) since -5b*b = -5b2 and -5b + b = -4b, then = 5(a - 5b)(a + b)
12ab + 13b + 4 (assuming there's addition in the spaces)
Well, assuming that x ∈ R and assuming that by "sum" you mean the sum of the area under curve and above the line y=0, and that the term you are giving is a function where f(x) = 10x - 62, then.. f(x) = 10x - 36 ∴∫f(x)dx = 5x2 - 36x + C Now, if you know the range in which you want this area, you can say: a ∫f(x)dx = 5a2 - 36a - 5b2 + 36b b But I'm guessing that this isn't a calculus question at all, and that you should probably go do your own homework.
The GCF of 15ab and 5b squared is 5b.
The greatest common factor (GCF) of 15ab and 5b2 is 5b.
4a2 - 20ab2 + 25b4 (2a - 5b2)(2a - 5b2) (2a - 5b2)2
b3 - 5b2 + 12 = (b - 2)(b2 - 3b - 6)Check:(b - 2)(b2 - 3b - 6)= b(b2 - 3b - 6) - 2(b2 - 3b - 6)= b3 - 3b2 - 6b - 2b2 + 6b + 12= b3 - 5b2 + 12
It is: (-5b+2)(b-1) with the help of the quadratic equation formula
5a2 - 20ab - 25b2 = 5(a2 - 4ab - 5b2) = 5(a2 - 4ba - 5b2) since -5b*b = -5b2 and -5b + b = -4b, then = 5(a - 5b)(a + b)
12ab + 13b + 4 (assuming there's addition in the spaces)
5b2 = 8b therefore 5b =8 therefore b = 1.6
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Suppose we start with the opposite view. That is, the square root of 5 is rational. This means that it can be expressed as a ratio of two integers. Let the square root of 5 in its simplest terms be a/b so that a and b are integers with no common factors and b > 0.sqrt(5) = a/b so 5 = a2/b2that is, 5b2= a25 is a factor of the left hand side (LHS) so 5 must be a factor of the right hand side (RHS).Since 5 is a prime and a is an integer, 5 must be a factor of a. That is, a = 5c for some integer c and since a and b are coprime b and c must also be coprime.But now,5 = (5c)2/b2so that 5 = 25c2/b2and so b2= 5c2. As before, this implies that 5 must be a factor of b. But that contradicts the supposition that a and b are coprime.The contradiction implies that the original assumption was incorrect. That is, sqrt(5) cannot be rational.
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