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A construction company is analyzing which of its older projects need renovation. Building B was built two years before building C. Building C was built two years before building D. The product of building B's age and building D's age is at least 195. If x represents the age of building C, which inequality represents this situation?

A. 12 + 80 + 16 > 195
B. x² + 4 > 195
C. a² + 6x + 8 < 195
D. 2 + 4x + 4 > 195

User Mises
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1 Answer

2 votes

Final answer:

The correct inequality to represent the situation is (x - 2)(x + 2) ≥ 195, which simplifies to x^2 ≥ 199. However, none of the provided options in the question match this inequality, so there might be a typo in the student's options or an error in the question itself.

Step-by-step explanation:

The student is asking how to represent a mathematical situation involving the ages of buildings with an inequality. If we let x be the age of Building C, then Building B was built two years before, so it is x - 2 years old. Building D was built two years after Building C, so it is x + 2 years old. The question states that the product of Building B's age and Building D's age is at least 195, which translates to the inequality (x - 2)(x + 2) ≥ 195.

Expanding this out, we get x2 - 4 ≥ 195. When we move -4 to the other side of the inequality, we have x2 ≥ 199, which is not one of the provided options. Hence, the correct inequality must be the one that's algebraically equivalent once simplified properly. Option B, x2 + 4 > 195, when simplified, gives us x2 > 191, which is not equivalent to our inequality. However, none of the provided options match exactly, which indicates there may be a typo or mistake in the options provided by the student or the question itself.

User Beikeni
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