30. To the nearest tenth, what is the value of (t^3 - 35t^2)/(-4t - 8) when t = 12?
Answer: B
The value of (t^3 - 35t^2)/(-4t - 8) when t = 12 is 59.1.
To determine the value of the expression when t = 12, we substitute 12 into the equation, resulting in (12^3 - 35*12^2)/(-4*12 - 8). Upon calculation, this yields approximately 59.1.
A) 14.4
This option is incorrect because substituting t = 12 into the expression does not yield a value close to 14.4. The calculations show that the numerator and denominator do not simplify to this result, indicating a misunderstanding of the operation involved.
B) 59.1
This option is correct as it accurately represents the result obtained from the calculations. When substituting t = 12, the expression evaluates to 59.1, aligning perfectly with the operations performed.
C) 23
This choice is incorrect since substituting t = 12 does not simplify the expression to 23. The calculated value is significantly higher, thus this option does not reflect the correct outcome of the expression.
D) 87.4
This option is also incorrect. The calculations show that when t = 12, the result does not approach 87.4. The operations reveal a much lower value, indicating that this option fails to represent the outcome of the expression.
Conclusion
The correct answer is 59.1, derived from precise calculations of the given expression at t = 12. Other options fail to match the computed value, demonstrating that they do not accurately reflect the result of the mathematical operation involved.