Kirstin knows that the initial fee for adopting a dog from the animal shelter is $75. This fee needs to be considered when calcu
1 answer:
Answer:
The function is represented by .
Step-by-step explanation:
In this case, we must observe that total cost of the dog () is the sum of two components: i) <em>Fixed cost</em> (
) - Adoption fee, ii) <em>Variable cost</em> (
) - Daily cost of feeding the dog, both measured in US dollars.
In addition, we suppose that variable cost is directly proportional to the number of days that Kirstin owns her dog. That is:
Where:
- Number of days that Kirstin owns her dog, measured in days.
- Daily feeding costs, measured in US dollars per day.
If , then:
The function is represented by .
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To answer this question, we have to do the long division process for polynomials. We can do the operation as follows:
To do this division process, we have:
1. Divide the first term of the dividend by the first element of the divisor. They are:
2. Now, we have to multiply this result by the divisor, and the result will change its sign since we have to subtract that result from the dividend as follows:
And since we to subtract this result from the dividend, we end up with:
3. Then we have the following algebraic addition:
4. Again, we need to divide the first term of the dividend by the first term of the divisor as follows:
5. And we have to multiply 5 by the divisor, and the result will be subtracted from the dividend:
Since we have to subtract this from the dividend, we have:
6. And we have to add this algebraically to the dividend we got in the previous step:
And this is the remainder of the division, x + 5.
As we can see from the division process, we got as:
1. The quotient: -x + 5
2. The remainder: x + 5.
Since we have that the dividend = divisor * quotient + remainder.
Therefore, the result for this division is:
The domain of the function C(m) = 0.05m + 20 is (0, ∞) and the range of the function C(m) = 0.05m + 20 is (20, ∞).
<h3>What is the linear system?</h3>A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
Haley pays a monthly fee of $20 for her cell phone and then pays 5 cents per minute used. The total cost of Haley’s monthly cell phone bill can be expressed by the function
The domain of the function is from zero to infinity because time can never be negative.
Then the range of the function will be
At m = 0, the value of C(m) will be
C(m) = 0.05(0) + 20
C(m) = 20
At m = ∞, the value of C(m) will be
C(m) = 0.05(∞) + 20
C(m) = ∞
Thus, the domain of the function is (0, ∞) and the range of the function is (20, ∞).
More about the linear system link is given below.