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emmasim [6.3K]
3 years ago
14

The triangles below are similar. By what ratio was triangle XYZ enlarged by to create triangle LMN? Use this information to calc

ulate the length of the missing side. Show your work.

Mathematics
1 answer:
aliina [53]3 years ago
4 0

Answer:

Ratio: 3:2

LN = 18

Step-by-step explanation:

"similar" means that all the angles are the same and the sides were all increased by the same proportion.

Thus, we know that MN/YZ = LM/XY = NL/ZX

First, we need to find the ratio. To do this, we write MN/YZ as a fraction, and simplify.

MN/YZ = 15/10 = 3/2

(If you want, you can double check this using LM nd XY. 8 * 3/2 = 12, so this is correct)

To find the missing side, we simply multiply XZ by 3/2.

12 * 3/2 = 18, so LN = 18.

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The formula for the nth term of the arithmetic sequence first term is 9 common difference is -2
Yanka [14]

Answer:

a_n = 9 - 2(n-1)

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and is called common difference.

The nth term is given by the following equation:

a_n = a_1 + (n-1)d

In which a_1 is the first term and d is the common difference.

First term is 9 common difference is -2

This means that a_1 = 9, d = -2

So, the nth term is given by:

a_n = a_1 + (n-1)d

a_n = 9 + (n-1)(-2)

a_n = 9 - 2(n-1)

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