Answer:
Option C is correct.
The equation 
represents the function.
Step-by-step explanation:
Using slope intercept form to find the equation of line :
For any two points 
and 
the equation of line is given by:
......[1] ;where m is the slope given by:
Consider any two points from table :
let (4, 2) and (0, 4) be any two points.
calculate slope:
Now, substitute in equation [1] we have:
Distributive property i.e, 
Add both sides 2 we get;
Simplify:
Since, y= f(x)
therefore, the equation represents the function.
Part A: slope is 40
And i don’t know the rest I’m sorry
Let with X is denoted the length of the third side.
For a triangle the following statements must be true:
The sum<span> of the </span>lengths<span> of any two sides of a </span>triangle<span> is greater than the </span>length<span> of the third side.
This means that this inequality can be written: X<10+18 ,X<28
</span>
Answer:
V(max) = 8712.07 in³
Dimensions:
x (side of the square base) = 16.33 in
girth = 65.32 in
height = 32.67 in
Step-by-step explanation:
Let
x = side of the square base
h = the height of the postal
Then according to problem statement we have:
girth = 4*x (perimeter of the base)
and
4* x + h = 98 (at the most) so h = 98 - 4x (1)
Then
V = x²*h
V = x²* ( 98 - 4x)
V(x) = 98*x² - 4x³
Taking dervatives (both menbers of the equation we have:
V´(x) = 196 x - 12 x² ⇒ V´(x) = 0
196x - 12x² = 0 first root of the equation x = 0
Then 196 -12x = 0 12x = 196 x = 196/12
x = 16,33 in ⇒ girth = 4 * (16.33) ⇒ girth = 65.32 in
and from equation (1)
y = 98 - 4x ⇒ y = 98 -4 (16,33)
y = 32.67 in
and maximun volume of a carton V is
V(max) = (16,33)²* 32,67
V(max) = 8712.07 in³
