Problem page it takes the hot water faucet twice as long to fill a bathtub as it does the cold water faucet. left on together, the cold and hot water faucets take 5 minutes to fill the tub. how long will it take the cold water faucet to fill the tub by itself?

  7.5 minutes

Step-by-step explanation:

If we let x represent the number of minutes it takes for the cold faucet to fill the tub, then it takes 2x minutes for the hot faucet. The total rate of filling in tubs per minute is ...

  1/x + 1/(2x) = 1/5

Multiplying by 10x, we have ...

  10 + 5 = 2x

  x = 15/2 = 7.5

It takes the cold faucet 7.5 minutes to fill the tub.

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)