Final answer:
The question deals with mathematical computations involving significant figures and quadratic formula operations. The principles of significant figures dictate a specific methodology for rounding in addition, subtraction, multiplication, and division. Correctly applying the quadratic formula requires careful computation of discriminant and following standardized steps for solving.
Step-by-step explanation:
The provided student's question contains several mathematical operations that require clarification to address properly. However, the central theme of these operations involves significant figures and the quadratic formula. Using the given examples:
- When adding or subtracting, the result should have as many decimal places as the number with the least number of decimal places in the problem (e.g., 45.99 - 32.8 = 13.2).
- For multiplication and division, the result should be reported with the same number of significant figures as the number with the fewest significant figures in the problem (e.g., 56.7 x 66.99 = 3798 when rounded to four significant figures).
- The correct application of the quadratic formula involves computing the discriminant (√(b² - 4ac)) and then solving for the variable by subtraction or addition and division (e.g., -13 ± √(13² - 4 × 3 × (−10)) / (2 × 3) results in two possible solutions).
These principles help ensure that the computations are precise and conform to the rules of significant figures. For the quadratic formula, it's essential to follow each step carefully to obtain the correct results.