One-third of the rancher’s cattle Are calves. If he puts 2 calves in each of his 20 stalls, how many head of cattle does the rancher have?

The total heads of cattle = 120 heads

Step-by-step explanation:

Let the total heads of cattle = x

One-third of the rancher’s cattle Are calves

The total heads of calves =  ⇒ (1)

But, the rancher puts 2 calves in each of his 20 stalls

∴ The total heads of calves = 2 * 20 = 40  ⇒(2)

From (1) and (2)

= 40  ⇒ multiply both side by 3

∴ x = 3 * 40 = 120

∴The total heads of cattle = 120 heads

37

step-by-step explanation:

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)