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3 years ago

8

The angle measures in a triangle are in the ratio 1:3:5. The longest side of the triangle measures 5 inches. What is the approxi

mate perimeter of the triangle? 9.0 in. 9.4 in. 11.1 in. 12.7 in.

1 answer:

yawa3891 [41]3 years ago

8 0

Answer:

Step-by-step explanation:

X + 3x + 5x = 180

9x = 180

x = 20

So the angles are

20

60 and

100

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Write the rule for the nth term of the following sequence.

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Answer:

$2^{n-3}$ is the nth term of the given sequence.

Step-by-step explanation:

The sequence given is

$\frac{1}{4},\frac{1}{2},1,2,4 .....$

We can clearly see that 1st term is $\frac{1}{4}$ and 2nd term is $\frac{1}{2}$

2nd term is obtained by multiplying the 1st term by 2.

2nd term is $\frac{1}{2}$ and 3rd term is 1.

3rd term is obtained by multiplying the 2nd term by 2.

3rd term is 1 and 4th term is 2.

4th term is obtained by multiplying the 3rd term by 2.

Clearly, the given series is a <em>Geometric Progression(GP)</em> with

First term, $a = \frac{1}{4}$

Common Ratio, $r = 2$

We know that $n^{th}$ term for a GP is:

$a_n = ar^{n-1}$

Putting values of <em>a</em> and <em>r</em>

$a_n = \dfrac{1}{4}2^{n-1}\\a_n = \dfrac{1}{2^{2} }2^{n-1}\\a_n = 2^{n-1-2}\\a_n = 2^{n-3}$

Hence, $2^{n-3}$ is the nth term of the given sequence.

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