The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. if the veterinarian gives a 30-pound dog 3/5 milligram of the medicine, which equation relates the weight, w, and the dosage, d?

a. d=1/50w
b. d=3/5w
c. d=18w
d. d=50w

Option A is correct

Step-by-step explanation:

Direct variation says that:

then;

the equation is in the form of

, where k is the constant of variation

As per the statement:

The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog.

Here, w represents the weight and d represents the dosage

then ,by definition of direct variation we have;

        .....[1]

It is also given that if the veterinarian gives a 30-pound dog 3/5 milligram of the medicine

⇒w = 30 pound and d = 3/5 milligram

Substitute in [1] we have;

Multiply both sides by 5 we have;

Divide both sides by 150 we have;

Simplify:

⇒

therefore, equation relates the weight, w, and the dosage, d is:

simple answer a

Step-by-step explanation:

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis