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4 years ago

Which figure has an order 3 rotational symmetry? right triangle equilateral triangle regular hexagon right trapezoid

Mathematics

2 answers:

ella [17]4 years ago

7 0

Equilateral triangle.

<h3>Further explanation</h3>

We at present know an equilateral triangle occupies three sides and angles that are congruent with three interior angles of each 60°.

Next, we discuss the order of rotational symmetry on an equilateral triangle.

A figure possesses rotational symmetry if it can be rotated at an angle between 0° and 360° around a center point so that the figure coincides with the initial position again. It means the shape does not appear to change.
The center of rotation is the point at which we rotate the figure, or, the center of the shape.
The rotation angle is the angle we need to rotate, or in other words, the smallest angle at which shape can be rotated to coincide with itself.
The order of rotational symmetry represents the number of times a shape fits on top of itself in one rotation.

See the attached picture.

An equilateral triangle possesses rotational symmetry of order 3.
The rotation angle of 120° is calculated from $\boxed{ \ \frac{360^0}{3} = 120^0 \ }.$
It can be rotated through 120° as much as 3 times still be the same original shape.

When we rotate this shape, we discover three different positions, each of which looks the same.

<h3>Learn more</h3>

The order of rotational symmetry of rhombus brainly.com/question/4228574
A triangle is rotated 90° about the origin brainly.com/question/2992432
Determine the coordinates of the image of a point after the triangle is rotated 270° about the origin brainly.com/question/7437053

Keywords: the equilateral triangle, rotational symmetry, order 3, three sides and angles, congruent, interior angles, the center of rotation, shape

kvv77 [185]4 years ago

5 0

Answer:- Equilateral triangle has an order 3 rotational symmetry.

Explanation:-

In geometry, a figure has rotational symmetry if it moves onto itself under rotation about an angle at center of rotation.

The order of rotational symmetry is the number of times the shape moves onto itself throughout a rotation of 360°.

An equilateral triangle has all its sides equal with equal interior angle of 60°.

It moves onto itself three times throughout a rotation of 360°.

⇒Equilateral triangle has an order 3 rotational symmetry.

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maw [93]

Answer:

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Step-by-step explanation:

All of the possible answers are correct except for E. Answer E is 0.001 less than -4 which would not make the equation true. Hope this helps!!

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3 years ago

A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable).

Juli2301 [7.4K]

Answer:

a) 240 ways

b) 12 ways

c) 108 ways

d) 132 ways

e) i) 0.55

ii) 0.4125

Step-by-step explanation:

Given the components:

Receiver, compound disk player, speakers, turntable.

Then a purcahser is offered a choice of manufacturer for each component:

Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood => 5 offers

Compact disc player: Onkyo, Pioneer, Sony, Technics => 4 offers

Speakers: Boston, Infinity, Polk => 3 offers

Turntable: Onkyo, Sony, Teac, Technics => 4 offers

a) The number of ways one component of each type can be selected =

$\left(\begin{array}{ccc}5\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right)$

$= 5 * 4 * 3 * 4 = 240 ways$

b) If both the receiver and compact disk are to be sony.

In the receiver, the purchaser was offered 1 Sony, also in the CD(compact disk) player the purchaser was offered 1 Sony.

Thus, the number of ways components can be selected if both receiver and player are to be Sony is:

$\left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right)$

$= 1 * 1 * 3 * 4 = 12 ways$

c) If none is to be Sony.

Let's exclude Sony from each component.

Receiver has 1 sony = 5 - 1 = 4

CD player has 1 Sony = 4 - 1 = 3

Speakers had 0 sony = 3 - 0 = 3

Turntable has 1 sony = 4 - 1 = 3

Therefore, the number of ways can be selected if none is to be sony:

$\left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right)$

$= 4 * 3 * 3 * 3 = 108 ways$

d) If at least one sony is to be included.

Number of ways can a selection be made if at least one Sony component is to be included =

Total possible selections - possible selections without Sony

= 240 - 108

= 132 ways

e) If someone flips switches on the selection in a completely random fashion.

i) Probability of selecting at least one Sony component=

Possible selections with at least one sony / Total number of possible selections

$\frac{132}{240} = 0.55$

ii) Probability of selecting exactly one sony component =

Possible selections with exactly one sony / Total number of possible selections.

$\frac{\left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right)}{240}$

$= \frac{(1*3*3*3)+(4*1*3*3)+(4*3*3*1)}{240}$

$\frac{27 + 36 + 36}{240} = \frac{99}{240} = 0.4125$

5 0

3 years ago

Which dimensions can create more than one triangle? A. Three angles measuring 75°,45°, and 60°. B. 3 sides measuring 7, 10, 12?

NeTakaya

This is vague. Any dimensions that make a triangle can make more than one, just draw another right next to it. What's really being asked is which dimensions can make more than one non-congruent triangle.

<span>A. Three angles measuring 75°,45°, and 60°.

That's three angles, and 75+45+60 = 180, so it's a legit triangle. The angles don't determine the sides, so we have whole family of similar triangles with these dimensions. TRUE

<span>B. 3 sides measuring 7, 10, 12?

</span>Three sides determine the triangles size and shape uniquely; FALSE

<em>C. Three angles measuring 40</em></span><span><em>°</em></span><em>, 50°</em><span><em>, and 60°? </em>

40+50+60=150, no such triangle exists. FALSE

<em>D. 3 sides measuring 3,4,and 5</em>

Again, three sides uniquely determine a triangle's size and shape; FALSE

</span>

7 0

3 years ago

Read 2 more answers

The expression 2(128 + 5) + V7 can be used to find the perimeter of the triangle. What does

Mama L [17]

You do the things in the parentheses first then multiply them by 2

5 0

3 years ago

20 Point!

ludmilkaskok [199]

determinant: $\sqrt{b^2-4ac}$