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Bad White [126]
2 years ago
12

Solve for x. See picture for full problem. Please and thank you!

Mathematics
1 answer:
Nadya [2.5K]2 years ago
8 0

Answer:

x = 16

Step-by-step explanation:

All 3 right triangles are similar, so the lengths of corresponding sides are in proportion.

8√3 / 12 = x / 8√3

12x = (8√3)²

12x = 64 × 3

4x = 64

x = 16

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Answer:

-1,4,-7,10,...  neither

192,24,3,\frac{3}{8},...  geometric progression

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Step-by-step explanation:

Given:

sequences: -1,4,-7,10,...

192,24,3,\frac{3}{8},...

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To find: which of the given sequence forms arithmetic progression, geometric progression or neither of them

Solution:

A sequence forms an arithmetic progression if difference between terms remain same.

A sequence forms a geometric progression if ratio of the consecutive terms is same.

For -1,4,-7,10,...:

4-(-1)=5\\-7-4=-11\\10-(-7)=17\\So,\,\,4-(-1)\neq -7-4\neq 10-(-7)

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\frac{4}{-1}=-4\\\frac{-7}{4}=\frac{-7}{4}\\\frac{10}{-7}=\frac{-10}{7}\\So,\,\,\frac{4}{-1}\neq \frac{-7}{4}\neq \frac{10}{-7}

Hence,the given sequence does not form a geometric progression.

So, -1,4,-7,10,... is neither an arithmetic progression nor a geometric progression.

For  192,24,3,\frac{3}{8},... :

\frac{24}{192}=\frac{1}{8}\\\frac{3}{24}=\frac{1}{8}\\\frac{\frac{3}{8}}{3}=\frac{1}{8}\\So,\,\,\frac{24}{192}=\frac{3}{24}=\frac{\frac{3}{8}}{3}

As ratio of the consecutive terms is same, the sequence forms a geometric progression.

For -25,-18,-11,-4,... :

-18-(-25)=-18+25=7\\-11-(-18)=-11+18=7\\-4-(-11)=-4+11=7\\So,\,\,-18-(-25)=-11-(-18)=-4-(-11)

As the difference between the consecutive terms is the same, the sequence forms an arithmetic progression.

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Answer:

These should be right hopefully! Hope it helps!

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