Please help. Marika is training for a race.

Mathematics

1 answer:

Anika [276]3 years ago

3 0

Let's call n the number of days Marika's been training for the race, and $a_n$ the distance she runs on the nth day in meters. After the first day, when n = 1, she runs 100 meters, so

$a_1=100$

On the second day, she runs an additional 4 meters, on the third day, another 4, and so on. Here's what that looks like mathematically:

$a_2=100 + 4\\a_3=100 + 4 + 4\\a_4=100+4+4+4$

It would be easier to write this continued addition as multiplication, in which case those same equations would look like

$a_2 = 100 + 4(1)\\a_3 = 100 + 4(2)\\a_4=100+4(3)$

Notice that, in every case, the number 4 is being multiplied by is 1 less than n. We could even write for our first term that $a_1=100+4(0)$ . In general, we can say that

$a_n=100+4(n-1)$

Which is expressed by option B.

(Bonus: What piece of information from this question did we not need to use here?)

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note: the term "translating" is another way of saying "shifting" or "sliding".

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h(x) = f(x)-7 means translating f(x) 7 units down to get h(x). We use the same reasoning as in problem 1. The general form is h(x) = f(x)+k, and in this case, k = -7. The negative k value tells us to shift down.

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h(x) = f(x-14) tells us to shift f(x) 14 units to the right. Same idea as problem 3, but now h = 14.

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