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never [62]
11 months ago
11

Hazel knits 5 centimeters of scarf eachnight. After 5 nights of knitting, how manycentimeters of scarf will Hazel have knit into

tal?centimeters
Mathematics
1 answer:
natta225 [31]11 months ago
5 0

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:

\begin{gathered} (5+5)\text{centimeters} \\ =10\text{ centimeters} \end{gathered}

Night 3:

Hazel makes extra 5 centimeters, which means she has made:

\begin{gathered} (10+5)\text{centimeters} \\ =15\text{ centimeters} \end{gathered}

NIght 4:

Hazel makes extra 5 centimeters, which means she has made:

\begin{gathered} (15+5)\text{centimeters} \\ =20\text{ centimeters} \end{gathered}

NIght 5:

Hazel makes extra 5 centimeters, which means she has made:

\begin{gathered} (20+5)\text{centimeters} \\ =25\text{ centimeters} \end{gathered}

Final Answer

Thus, Hazel will have knitted 25 centimeters of the scarf

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Given f(x) = x^2 + 1 and g(x) = x-2

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===================

problem a.

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(f-g)(x) = f(x) - g(x)

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(f-g)(-2) = f(-2) - g(-2)

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f(x) = x^2 + 1

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problem b.

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g(x) = x-2

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answer for b is:

f(g(5)) = 10

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in general, you substitute whatever value is replacing x in the equation to get your answers.

looking at problem b in this way, we would get a general solution as follows:

f(x) = x^2 + 1

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substitute g(x) for x:

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substitute the equation for g(x) on the right hand side.

f(g(x)) = (x-2)^2 + 1

remove parentheses:

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