All categories

3 years ago

How many lines of symmetry does a regular polygon with x sides have

Mathematics

2 answers:

anastassius [24]3 years ago

6 0

There are actually 2 variations in this case.

> First case: the number of sides is an odd number

The number of lines of symmetry is simply equal to number of sides

> Second case: the number of sides is an even number

The number of lines of symmetry is equal to twice the number of sides

BaLLatris [955]3 years ago

6 0

X sides because every regular polygon has the same amount of lines of symmetry as the amount of sides.

You might be interested in

Why is -16 the leading coefficient in quadratic applications

Lady bird [3.3K]

Answer:

Step-by-step explanation:e equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. ... Another method for solving quadratics is the square root property. The variable is squared.

3 0

2 years ago

Read 2 more answers

POSSIBLE POINTS: 15

almond37 [142]

There’s 355 milliliters of soda in one can

7 0

2 years ago

A polygon that has all sides the same measure and all angles the same measure is called what? A. Convex polygon B. Co

Schach [20]

D. Regular polygon.

A polygon that has all sides the same measure and all angles the same measure is called Regular polygon.

Hoped I helped!

8 0

3 years ago

Eddi Din [679]

Answer:

a) $y=\dfrac{5}{2}x$

b) yes the two lines are perpendicular

c) $y=\dfrac{5}{4}x+6$

Step-by-step explanation:

a) All this is asking if to find a line that is perpendicular to 2x + 5y = 7 AND passes through the origin.

so first we'll find the gradient(or slope) of 2x + 5y = 7, this can be done by simply rearranging this equation to the form $y = mx + c$

$5y = 7 - 2x$

$y = \dfrac{7 - 2x}{5}$

$y = \dfrac{7}{5} - \dfrac{2}{5}x$

$y = -\dfrac{2}{5}x+\dfrac{7}{5}$

this is changed into the $y = mx + c$ , and we easily see that -2/5 is in the place of m, hence $m = \frac{-2}{5}$ is the slope of the line 2x + 5y = 7.

Now, we need to find the slope of its perpendicular. We'll use:

$m_1m_2=-1$ .

here both slopes $m_1$ and $m_2$ are slopes that are perpendicular to each other, so by plugging the value -2/5 we'll find its perpendicular!

$\dfrac{-2}{5}m_2=-1$ .

$m_2=\dfrac{5}{2}$ .

Finally, we can find the equation of the line of the perpendicular using:

$(y-y_1)=m(x-x_1)$

we know that the line passes through origin(0,0) and its slope is 5/2

$(y-0)=\dfrac{5}{2}(x-0)$

$y=\dfrac{5}{2}x$ is the equation of the the line!

b) For this we need to find the slopes of both lines and see whether their product equals -1?

mathematically, we need to see whether $m_1m_2=-1$ ?

the slopes can be easily found through rearranging both equations to $y=mx+c$

Line:1

$2x + 3y =6$

$y =\dfrac{-2x+6}{3}$

$y =\dfrac{-2}{3}x+2$

Line:2

$y = \dfrac{3}{2}x + 4$

this equation is already in the form we need.

the slopes of both equations are

$m_1 = \dfrac{-2}{3}$ and $m_2 = \dfrac{3}{2}$

using

$m_1m_2=-1$

$\dfrac{-2}{3} \times \dfrac{3}{2}=-1$

$-1=-1$

since the product does equal -1, the two lines are indeed perpendicular!

c)if two perpendicular lines have the same intercept, that also means that the two lines meet at that intercept.

we can easily find the slope of the given line, y = − 4 / 5 x + 6 to be $m=\dfrac{-4}{5}$ and the y-intercept is $c=6$ the coordinate at the y-intercept will be (0,6) since this point only lies in the y-axis.