Question

The area of the triangle when x = 2 is 14. Which equation can be used to represent the area of the triangle, A(x)? A(x) = 2(f ∙ g)(x) A(x) = 0.5(f ∙ g)(x) A(x) = 2(g + f)(x) A(x) = 0.5(g + f)(x)

Answer 1

The equation that can be used to represent the area of the triangle is A(x) = 0.5(f ∙ g)(x) ⇒ 2nd answer

Step-by-step explanation:

The formula of the area of a triangle is A = $\frac{1}{2}$ b h, where

• b is the length of the base of the triangle
• h is the length of the height of the triangle

∵ The area of the triangle when x = 2 is 14

∴ The base and the height of the triangle are functions of x

Assume that the length of the base of the triangle is represented by f(x) and the length of the height of the triangle is represented by g(x)

∵ A = = $\frac{1}{2}$ b h

∵ b = f(x)

∵ h = g(x)

- Substitute b by f(x) and h by g(x) in the rule and replace A by

   A(x) because the area of the triangle is a function of x

∴ A(x) = $\frac{1}{2}$ f(x) . g(x)

∵ f(x) . g(x) can be written as (f . g)(x)

∴ A = $\frac{1}{2}$ (f . g)(x)

∵  $\frac{1}{2}$  = 0.5

∴ A = 0.5(f . g)(x)

The equation that can be used to represent the area of the triangle is A(x) = 0.5(f ∙ g)(x)

Learn more:

You can learn more about the functions in brainly.com/question/2645523

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