3 years ago

Which figures are polygons ? Select each correct answer. Figure A Figure B Figure C Figure D

Mathematics

1 answer:

Korolek [52]3 years ago

6 0

Answer: Figure A, B and C

Step-by-step explanation:

Because C has rounded angles, it is not a polygon.

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In a geometric sequence, a4 = 54 and a7 = 1,458. what is the 12th term? <br><br> answer: B) 354,294

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Option B:

The 12th term is 354294.

Solution:

Given data:

$a_4=54$ and $a_7=1458$

To find $a_{12}:$

The given sequence is a geometric sequence.

The general term of the geometric sequence is $a_n=a_1\ r^{n-1}$ .

If we have 2 terms of a geometric sequence $a_n$ and $a_k$ (n > K),

then we can write the general term as $a_n=a_k\ r^{n-k}$ .

Here we have $a_4=54$ and $a_7=1458$ .

So, n = 7 and k = 4 ( 7 > 4)

$a_7=a_4\ .\ r^{7-4}$

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This can be written as

$$r^3=\frac{1458}{54}$

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$$r^3=3^3$

Taking cube root on both sides of the equation, we get

r = 3

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$=1458\ .\ r^5$

$=1458\ .\ 3^5$

$a_{12}=354294$

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