Complete this expression using the distributive property
1 answer:
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Answer:
Hazel will have knitted 25 centimeters of the scarf
SOLUTION
Problem Statement
We are told Hazel knits 5 centimeters of scarf every night for 5 nights. We are required to find the length of the scarf Hazel will have knitted after 5 nights.
Solution
We are told Hazel makes 5 centimeters of scarf every night. Thus, for each night up till 5 nights, we just need to add the length of scarf Hazel has made.
Let us count for each night.
Night 1:
Hazel makes 5 centimeters of the scarf.
Night 2:
Hazel makes extra 5 centimeters, which means she has made:
Night 3:
Hazel makes extra 5 centimeters, which means she has made:
NIght 4:
Hazel makes extra 5 centimeters, which means she has made:
NIght 5:
Hazel makes extra 5 centimeters, which means she has made:
Final Answer
Thus, Hazel will have knitted 25 centimeters of the scarf
Recall that a rational function:
has a vertical asymptote at x₀ if and only if:
Also, the roots of the above rational function are the same as P(x).
Since the rational function has a vertical asymptote at x=-1, we get that its denominator must be:
Since the rational function has a double zero at x=2 we get that its numerator must be of the form:
Finally, since the rational function has y-intercept at (0,2) we get that:
Simplifying the above equation we get:
Dividing the above equation by 4 we get:
Therefore, the rational function that satisfies the given conditions is:
Answer:
The numerator is:
The denominator is: