Final answer:
The quotient of 12 and the product of 5 and t is 12 / (5t). To solve the quadratic equation t² + 10t - 2000 = 0, one can use the quadratic formula after rearranging it to equal zero.
Step-by-step explanation:
To find the quotient of 12 and the product of 5 and t, you must first express the product. The product of 5 and t is written as 5t. The quotient of 12 and 5t is then expressed as 12 / (5t).
When solving a quadratic equation such as t² + 10t - 2000 = 0, you would typically use the quadratic formula. The quadratic formula is written as t = ∛(-b ± √(b² - 4ac)) / (2a) where a, b, and c are the coefficients of the terms t², t, and the constant, respectively. In the equation t² + 10t - 2000, a is 1, b is 10, and c is -2000.
It's important to first rearrange the equation so that it equals zero before applying the quadratic formula. Once in the correct form, you can substitute the values of a, b, and c into the formula to solve for t.