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3 years ago

The lines of symmetry in a regular polygon are equal to the number of sides minus 2. True or False

Mathematics

1 answer:

galina1969 [7]3 years ago

6 0

Answer:

False

Step-by-step explanation:

A regular polygon may be defined as the polygon that have sides of equal length known as equilateral and angles made up of equal angles, known as equiangular.

The $\text{number of lines}$ of symmetry in a regular polygon is always equal to the number of sides of the polygon. For example, a regular pentagon have 5 sides, so the lines of symmetry of the regular pentagon is also 5, a square having 4 sides also has 4 lines of symmetry.

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

5 0

3 years ago

Find the number of terms in the sequence and find the sum of the sequence: <br><br> 5+9+13+...+145

SashulF [63]

145-13-9-5 that what your looking for

8 0

1 year ago

The area of a rectangle is 44 square feet. The base of the rectangle is 11. Find the height, then find the perimeter

Alecsey [184]

Answer:

Step-by-step explanation:

Since the area of a rectangle = Length times Breath

We are just going to divide your are by breadth which is

Let your length become y

= y × 11 = 44

to get your answer you move× 11 over the equal to sign which becomes ÷11 because any sign that cross the equal to sign changes which is equal to

y = 44÷11

y = 4

what i did was that i divided 44 by 11 which is equal to 4

3 0

3 years ago

A parallelogram in a circumscribed circle must be a

Aleonysh [2.5K]

Hi!

//gm circumscribed by a circle must be a cyclic quadrilateral.

6 0

3 years ago

Jamey says she only has 30% of her book to go before she finishes it. she has read 147 pages so far

Lubov Fominskaja [6]

Let's just change your problem to 147 of 30%

"Of" is always equaling to multiplication (×)

Now, it would be easier to simplify

30% (147)
30% ÷ 100 = 0.3
0.3(147)
Now, we get to your answer which might be 44.1

4 0

3 years ago