Step 1 :Given vectors m and n as m = 2i - 5j and n = -7i + 17j respectively.
Step 2 :The sum of vectors m and n can be calculated by adding the corresponding components of the vectors. So, m + n = (2 - 7)i + (-5 + 17)j = -5i + 12j.
Step 3 :The magnitude of a vector is calculated using the Pythagorean theorem, which states that the magnitude of a vector is the square root of the sum of the squares of its components.
Step 4 :Applying the Pythagorean theorem to the sum of vectors m and n, we get |m + n| = \(\sqrt{(-5)^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169}\)
Step 5 :Calculating the square root of 169 gives us 13.0.
Step 6 :\(\boxed{13.0}\) is the magnitude of the sum of vectors m and n.