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The answer to your question is the third choice.

Step-by-step explanation:

Equation

From the equation we know that this is a horizontal hyperbola so the transverse axis is horizontal.

The center is (-5, 2)

a = 4

b = 3

              c² = 4² + 3²

              c² = 16 + 9

              c² = 25

              c = 5

The vertices are       V1 = (-9 , 2)  and V2 = (-1, 2)

The foci are               F1 = (0, 2) and F2 = (-10, 2)

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

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