Which is a better buy in the long run-a 60cents light bulb that lasts for 1000 hours or an 89cents bulb that last for 2000 hours?

Well, the 89c bulb lasts twice as much, but costs less than twice as much. So, it's a better option. Here are two other ways to figure this out:

1) After 2000 hours, you will have used two 60c bulbs (each of them lasted 1000 hours). So, you will have spend 1.2 dollars. On the other hand, in the same 2000 hours, you would have needed only one 89c buls (which would have lasted the whole 2000 hours).

2) You can compute the dollars-per-hour ratio: spending 60c for 1000 hours means that you pay

dollars per hour. Similarly, the other bulb costs

dollars per hour, which is less.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)