To the nearest tenth, what is the value of (t^3 - 35t^2)/(-4t - 8) when t = 12?

Rationale

To the nearest tenth, the value of (t^3 - 35t^2)/(-4t - 8) when t = 12 is 59.1.

To find the value of the expression when t = 12, we substitute 12 into the equation and simplify, resulting in 59.1. This value is derived from performing the necessary calculations accurately.

A (14.4) YOUR ANSWER

This choice results from an incorrect calculation of the expression. The value of (12^3 - 35(12^2))/(-4(12) - 8) does not yield 14.4, indicating a significant miscalculation in either the cubing of t or the simplification of the denominator.

B (59.1) CORRECT

This choice reflects the correct computation of the expression. Substituting t = 12 into (t^3 - 35t^2)/(-4t - 8) gives the correct value of 59.1, as all calculations align correctly with the order of operations.

C (23) YOUR ANSWER

This option arises from errors in simplifying either the numerator or the denominator. Specifically, miscalculating the cubic and quadratic terms in the numerator leads to an incorrect result, as the actual calculations yield a significantly different value.

D (87.4) YOUR ANSWER

This choice suggests an overestimation of the result, likely due to miscalculating the negative denominator or failing to apply the correct arithmetic operations. The calculations do not support this outcome, reinforcing that the correct result is indeed lower than 87.4.

Conclusion

The accurate determination of the expression (t^3 - 35t^2)/(-4t - 8) when t = 12 yields a value of 59.1. All other options stem from various computational errors, whether in the arithmetic process or the application of algebraic principles. Understanding the correct order of operations and careful substitution are essential for achieving the right answer in such expressions.

To the nearest tenth, what is the value of (t^3 - 35t^2)/(-4t - 8) when t = 12?

To the nearest tenth, the value of (t^3 - 35t^2)/(-4t - 8) when t = 12 is 59.1.

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