The hood above the stove in a restaurant kitchen is filled with fans and other ventilation parts.

A triangular prism. The triangular sides have a base of 3 feet and height of 2 feet. The prism has a height of 4 feet.

How much space is there inside the empty hood?

8 feet cubed

12 feet cubed

36 feet cubed

38 feet cubed

The space inside the empty hood is option 2. 12 feet cubed.

Step-by-step explanation:

Step 1:

To determine the space inside the hood, we need to determine the volume of the triangular prism.

To determine the volume of the prism, we multiply the height of the prism with the area of the base.

The base of the prism is a triangle and the area of a triangle is half the product of its base length and its height.

The area of a triangle

Step 2:

The triangle has a base length of 3 feet and a height of 2 feet.

So the area of a triangle square feet.

The volume of the prism = (The area of the base)(height).

The height of the prism is 4 feet and the area of the base is 3 square feet.

The volume of the prism cubic feet = 12 ft³.

The volume of the prism is 12 feet cubed which is option 2.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct

c = 0.429t

step-by-step explanation:

the constant rate at which carlos harvests cassava is 35 minutes per 15 cassavas 15/35 = 0.429 cassava per minute

therefore, an equation that models the number of cassava (c) that harvest carlos in a time (t) is the following:

where t is the time in minutes.

this means that when 35 minutes have elapsed 15 cassava have been harvested, at 70 minutes 30 cassava have been harvested and so on.