Let a > 0, b > 0, and 2a > 3b. If (2a + 3b) : (2a - 3b) = 7 : 5, then which of the following is equivalent to (4a² + 9b²) : (4a² - 9b²)?

Rationale

(4a² + 9b²):(4a² - 9b²) = 49:25:00.

This ratio can be derived from the given conditions and the relationship established between 2a and 3b. By manipulating the ratio (2a + 3b):(2a - 3b) = 7:5, we can determine the corresponding ratio for (4a² + 9b²):(4a² - 9b²).

A (3:5) YOUR ANSWER

This choice does not accurately reflect the calculated ratio. Since the problem involves manipulating proportions based on the relationship derived from (2a + 3b):(2a - 3b) = 7:5, the resulting values do not simplify to 3:05.

B (55:53:00) YOUR ANSWER

This option incorrectly represents the ratio derived from (4a² + 9b²):(4a² - 9b²). The values need to be consistent with the mathematical derivation based on the given ratio, and 55:53:00 does not correlate with any steps from the calculations.

C (37:35:00) YOUR ANSWER

This choice also fails to match the required ratio. The ratios derived from the original conditions do not lead to these specific numbers, indicating a miscalculation or misunderstanding of the relationship between the variables.

D (5:3) YOUR ANSWER

This ratio does not represent the equivalent values derived from (4a² + 9b²):(4a² - 9b²). The manipulation of the original ratio results in a much different outcome, thus making this option incorrect.

E (49:25:00) CORRECT

This choice accurately reflects the derived ratio from (4a² + 9b²):(4a² - 9b²). By applying the proper algebraic manipulations based on the initial condition, we find this ratio to be the correct solution.

Conclusion

The problem involves finding an equivalent ratio based on the initial condition relating 2a and 3b. By solving for (4a² + 9b²):(4a² - 9b²) through the established proportions, we correctly conclude that the ratio is 49:25:00, highlighting the importance of accurate algebraic manipulation in deriving the correct answer.

Let a > 0, b > 0, and 2a > 3b. If (2a + 3b) : (2a - 3b) = 7 : 5, then which of the following is equivalent to (4a² + 9b²) : (4a² - 9b²)?

(4a² + 9b²):(4a² - 9b²) = 49:25:00.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test