Answer:
3
Step-by-step explanation:
If y varies directly with x, we have:

When y=12, x=4
Substituting these values into the equation
12=4k
k=12/4
k=3
The constant of proportionality is 3.
Answer:
The expression is given as:
.
Step-by-step explanation:
Sophia expects the number of cows, C, on her farm t years from now to be modeled by the function:

Additionally, she expects the supply of hay, F, in tons, that her crops can provide for each cow t years from now to be modeled by the function

Let H be the total yearly amount of hay produced in Sophia's farm (in tons) t years from now.
Total amount of Hay produced in sophia's farm= Number of cows in farm×Amount of hay required for each cow.
i.e. H(t)=C(t)×F(t)

and we know that 
Hence,
.
Hence, the hay produced on Sophia's farm is used exclusively to feed her cows i.e. we need to write the formula of H ( t ) in terms of C(t) and F (t) is:
.
This is an example
Opposite angles formed by two intersecting lines are equal, so angle 1 is the same as angle 4. That means angle 1 = angle 5 as well.
When a line intersects two parallel lines, the corresponding angles are equal. That is, if r and s are parallel, then the angles formed when l intersects r are the same s the angles formed when l intersects s. Angle 1 = Angle 5, Angle 2 = Angle 6, and so forth. Since we know angle 1 = angle 5, so from that you can see that r and s are parallel