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nydimaria [60]
3 years ago
13

Write without absolute value: y=|x−3|+|x+2|−|x−5|, if x>5

Mathematics
1 answer:
Serga [27]3 years ago
5 0
If x > 5, all the quantities inside absolute value signs are positive, so
|x - 3| = x - 3
|x + 2| = x + 2
|x - 5| = x - 5

The expression becomes x - 3 + x + 2 - (x - 5) which simplifies to x + 4.
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The next two terms are 67.5 and 101.25 in that order.

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

Explanation:

Divide the second term over the first to get 30/20 = 1.5

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The common ratio is 1.5, which means we multiply 1.5 by each term to get the next term

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fourth term = 1.5*(third term) = 1.5*45 = 67.5

fifth term = 1.5*(fourth term) = 1.5*67.5 = 101.25

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As a shortcut you can plug n = 4 and n = 5 into the function t(n) = 20*(1.5)^(n-1) to get the fourth and fifth terms respectively.

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