Final answer:
The value for b in the perfect square trinomial 16x² + bx + 49 should be 56, as it comes from the expansion of (4x + 7)². However, this value is not listed among the answer choices provided.
Step-by-step explanation:
In mathematics, a perfect square trinomial is an expression that can be written as the square of a binomial. To determine the value of b in the trinomial 16x² + bx + 49, we would expect it to take the form (ax + c)² where a and c are the square roots of the first and last terms, respectively. In this case, a perfect square trinomial would be (4x + 7)² because √16x² = 4x and √49 = 7. Expanding (4x + 7)² we get 16x² + 56x + 49. The middle term here is 56x, which means b should be 56. However, since 56 is not an option, the correct answer appears to be missing from the given choices.
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