Omg

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Explanation:

There's a lot to get lost in here, so I can see why it's intimidating. For me, it helps to focus on a few things at a time and try to build from there.

We only need 4 pieces of info to help find x. I'll circle what we need in the diagram below (see attached image). Note the color coding to see how the terms match up.

Since we have similar figures, the corresponding sides form proportional ratios. This means DE/ST is the exact same as EA/TP. I've indicated this in the diagram as well.

So that's why 2/x = 4/(4.8)

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Let's solve for x in the equation below.

2/x = 4/(4.8)

2*4.8 = x*4 ... cross multiply

9.6 = 4x

4x = 9.6

x = (9.6)/4 .... divide both sides by 4

x = 2.4

Therefore, segment ST is 2.4 units long.

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Side note: The decimal 2.4 converts to the improper fraction 12/5, which is equivalent to the mixed number 2 & 2/5.

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.