Answer:

Step-by-step explanation:
Given


Required

Initial expression of f(x) is 
From the question; we understand that f(x) was shifted down by 3 units;
This implies that

Also from the question; we understand that this new f(x) is equivalent to g(x);
In other words;

Substitute
and 
This gives

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Subtract 0.5x to both sides

Rearrange


Multiply both sides by -1



The volume of the original prism is calculated by multiplying the area of the base by the height,
volume = (8 cm²)(6 cm) = 48 cm³
By the word dilated we mean to say that the dimensions of the new prism is 5/4 times that of the original solid. If we let x be the volume of the new solid,
x / 48 cm³ = (5/4)³
The value of x from the equation above is equal to 93.75 cm³.
Answer:
The lateral surface is 120
, which agrees with the third answer option of the list.
Step-by-step explanation:
Notice that the prism has 5 equal lateral faces, which are all rectangles of eight 6". The width of the prisms can be obtained by using the fact that the perimeter of the pentagon is 20", which gives a side length of 20/5 = 4 " which is the same as the with of the lateral rectangles.
Then the lateral area of the prism is:
Lateral area= 5 (6" x 4") = 5 (24) = 120 
3km means 3000m so 3000m less than 5000m