Simplify:
1) -sqrt(-9y^2) if y < 0
2) 3sqrt(c^2) if c is greater then or equal to 0
3) -5sqrt(4x^2) if x is greater than or equal to 0
4) -5sqrt(y^2) if y > 0
5) 0.5sqrt(16a^2) if a < 0

5

Step-by-step explanation:

1. -√(- 9y²) < 0

2. 3√(c²) ≤ 0

3. - 5√(4x²) ≤ 0

4. - 5√(y²) > 0

5. 0.5√(16a²) < 0

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)