A model of a tractor-trailer is shaped like a rectangular prism and has a width of 2 in., a length of 11 in., and a height of 4 in.. The scale of the model is 1 font size decreased by 10 : font size decreased by 10 34. How many times the volume of the model is the volume of the actual tractor-trailer?

The volume of the actual tractor-trailer is 2992 in³

Step-by-step explanation:

To determine how many times the volume of the model is the volume of the actual tractor-trailer,

First, we will determine the volume of the model tractor-trailer.

Since, the model tractor trailer is shaped like a rectangular prism, the volume of the model tractor-trailer can be calculated using the formula for volume of a rectangular prism.

Volume of rectangular prism = length × width × height

From the question,

length = 11 in

width = 2 in

and height = 4 in

∴ Volume of model tractor-trailer = 11 in × 2 in × 4 in

Volume of model tractor-trailer = 88 in³  

From the question,

The scale of the model is 1 font size decreased by 10 : 34 font size decreased by 10.

That is 1 : 34

Then, if the the volume of the actual tractor-trailer is y, we can write that

Then,

y = 88 × 34

y = 2992 in³

Hence, the volume of the actual tractor-trailer is 2992 in³.

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2