PLEASE HELP QUICK! The following polygons are given. All of the polygons are regular polygons.
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Answer:
1. Convex 15-gon, Convex 18-gon, Convex 45-gon
2. Increases
3. Decreases
4. Increases
5. Stays the same
Step-by-step explanation:
The formula for finding the measure of an interior angle, θ, of a polygon with 'n' sides is given as follows;
[tex]\theta = \dfrac{(n - 2) \times 180}{n}[/tex]
1. Polygons that have interior angles with whole numbers are factors of 180
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180
Therefore, from the options, the polygon that have whole number interior angles are;
15, 18, and 45
Which gives;
Convex 15-gon
θ₁₅ = (15 - 2) × 180°/15 = 156°
Convex 18-gon
θ₁₈ = (18 - 2) × 180°/18 = 160°
Convex 45-gon
θ₄₅ = (45 - 2) × 180°/45 = 172°
2. From the equation of the interior angles of a polygon, [tex]\theta = \dfrac{(n - 2) \times 180}{n}[/tex], we have;
As n increases, (n - 2)/n increases towards 1
Therefore, as the number of sides 'n' of a polygon increases, the interior angle of the polygon increases
3. Given that the sum of the interior and exterior angles of a polygon is 180°, as the interior angles increases as the number of sides increases, the exterior angle decreases
4. The total sum of the angles increases as the number of sides of the polygon increases and decreases as the number of sides of the polygon decreases
5. The sum of the exterior angles of a polygon is given as follows
[tex]n \times (180^{\circ} - \theta) = n \times \left(180^{\circ} - \dfrac{(n - 2) \times 180^{\circ}}{n} \right) = n\cdot 180^{\circ} - n\cdot 180^{\circ} + 360^{\circ}[/tex]
[tex]n \times (180^{\circ} - \theta) = 360^{\circ}[/tex]
Therefore, total sum of the exterior angles of a regular polygon is always (remains the same) 360°.
Related Questions
what is. perfect square
Answers
Answer:
a four sided parallelogram where all angles are the same and all sides are the same length
christian has a collection of 18 shark teeth he has 6 tiger shark what precentage is tiger
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Answer:
33.3% I think lpl
Step-by-step explanation:
Darryl was shopping for a new camera. He found one with an original price of $125.00 and is marked 45% off. Sales tax for the item is 5.2%. What is the final price of the camera, including tax?
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Answer:
$75.25
Step-by-step explanation:
Given data
Original price =$125
Discount =45%
Tax=5.2%
Let us find the discount
45/100*125
0.45*125
56.25
Let us find the tax
5.2/100*125
0.052*125
6.5
Hence the amount is
125-56.25+6.5
=$75.25
The equation SA = 6s can be used to calculate the surface area, SA, of a cube with side length S. What is the
surface area, in square meters, of a cube with a side length of 0.5 meter?
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=6 • 6 = 36
36 sq ft.
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
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help please fast 10min left :(
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Answer:
The angle corresponding to angle 4 is angle 8
How do you know you're good at sleeping I need help
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Answer:
You can do it with your eyes closed
Step-by-step explanation:
Which line is the correct graph for y = -3/4x
A/ blue line
B/ purple line
C/ green line
D/ red line
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Answer:D
Step-by-step explanation:
^^the question above in the photo
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Answer:
11
Step-by-step explanation:
1. The function h defined by h(t)=(49 + 4.9t)(10 - t) models the height, in meters, of an object t seconds after it is dropped from a helicopter. Find or approximate the time when the object hits the ground. Explain your method.
2.The function h defined by h(t)=(49 + 4.9t)(10 - t) models the height, in meters, of an object t seconds after it is dropped from a helicopter.
From what height is the object dropped? Explain how you know.
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Answer:
Step-by-step explanation:
Let's FOIL this out and get it into standard form. That gives us:
[tex]h(t)=-4.9t^2+490[/tex] For #1, then:
The height of something when it is on the ground is 0; that means that the h(t) is 0. This allows us to factor the quadratic and solve for t:
[tex]-4.9t^2=-490[/tex] and divide both sides by 4.9 to get
[tex]t^2=100[/tex] so
t = 10. Notice that one of the factors for that quadratic is 10 - t. That factor represents the time it takes to hit the ground. So you might ask why, then, we FOILed this out in the first place if the answer was ight in front of our noses. The reason is becase of #2 that is asking us what the initial height of the object was. That is found in the standard form...in the constant in particular. The initial height is 490 m. That's how you know (because the constant represents the height from which an object is dropped in either free fall, which this is, or in parabolic motion).
Can someone help me which expression is equal to 16
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Answer:
D.(4^1/2)^4
hope this helps
have a good day :)
Step-by-step explanation:
after reading the directions to paint,on the paint drum, the information indicated two coats of paints is required when using the 5 liter paint and one coat with the 20 liter drum. With both paints 1 litre of paint covers 9 meter squared.
There are 28 rooms to be painted.Show with calculations which will be cheaper paint to buy
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A rectangle has vertices E(4,8), F(2,8), G(2,-2) and H(-4,-2). The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,5). Which algebraic reprensentation represents this dilation
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Note: The image of G after the dilation must be G'(5,-5) instead of G'(5,5).
Given:
The vertices of a rectangle are E(4,8), F(2,8), G(2,-2) and H(-4,-2).
The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,-5).
To find:
The algebraic representation that represents this dilation.
Solution:
If a figure is dilated by factor k with origin as the center of dilation, then the dilation is defined as:
[tex](x,y)\to (kx,ky)[/tex] ...(i)
Let the given rectangle is dilated by factor k with origin as the center of dilation. Then,
[tex]G(2,-2)\to G'(k(2),k(-2))[/tex]
[tex]G(2,-2)\to G'(2k,-2k)[/tex]
The image of G after dilation is G'(5,-5). So,
[tex](2k,-2k)=(5,-5)[/tex]
On comparing both sides, we get
[tex]2k=5[/tex]
[tex]k=\dfrac{5}{2}[/tex]
So, the scale factor is [tex]k=\dfrac{5}{2}[/tex].
Substituting [tex]k=\dfrac{5}{2}[/tex] in (i), we get
[tex](x,y)\to \left(\dfrac{5}{2}x,\dfrac{5}{2}y\right)[/tex]
Therefore, the required algebraic representation to represents this dilation is [tex](x,y)\to \left(\dfrac{5}{2}x,\dfrac{5}{2}y\right)[/tex].
find the number between 1 over 10 and 3 over 5
Answers
Answer:
7/20
Step-by-step explanation:
1 over 10 is .1
3 over 5 is .6
write them out
.1 .2 .3 .4 .5 .6
number between is .35
.35 = 35/100 = 7/20
7/20
Why are (1, 2) and (2, 1) sot equal ordered pairs
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Answer:
Step-by-step explanation:
(1,2) and (2,1) are not equal ordered pairs becasue their corresponding elements are not equal.
Two Ordered Pairs are said to be equal if the corresponding first components are equal alongside the corresponding second components are equal.
for example:
(3,1) and (3,1)
here corresponding element of 3 is 3 and of 1 is 1 .so they are called equal ordered pairs.
The vertices of quadrilateral DEFG are D(-2, 6), E(-4, 6), F(-6, 9), and G(-1, 9). Find the coordinates of the image of quadrilateral DEFG after a translation using the rule (x, y) → (x + 1, y - 6), a reflection over the x-axis, and a reflection over the y-axis
Answers
Answer:
the coordinates from all of the transformations are (1,0) (3,0) (5,-3) (0,-3)
Step-by-step explanation:
after using the first rule the coordinates were (-1,0)(-3,0)(-5,3)(0,3)
after reflectiong it over the x-axis (-1,0)(-3,0)(-5,-3)(0,-3)
after reflecting it over the y-axis it gave the final answer of (1,0) (3,0) (5,-3) (0,-3)
Brainliest goes to whoever answers correctly
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Answer:
The answer is C.
What is the point used to write the equation y-2=4(x+5) in point slope form?
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Answer: y−26=4(x−1)
Step-by-step explanation:
Compré un TV que costó 35.000 pesos. Si en la aduana debo pagar 10 % por impuesto de nacionalización y 12 % sobre el precio nacionalizado de IVA. ¿Cuánto dinero pagué en total solo en impuestos?
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Answer:
7700 in taxes
27300 pesos remaining
7700 en impuestos
Quedan 27300 pesos
Step-by-step explanation:
I bought a TV that cost 35,000 pesos. If at customs I must pay 10% for nationalization tax and 12% on the nationalized VAT price. How much money did I pay in total just in taxes?
Find the value of x.
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Answer:
Step-by-step explanation:
The equation for this is
12(x + 1) = 10(10 - x) and
12x + 12 = 100 - 10x and
22x = 88 so
x = 44
if CH CD and DG CD, then CH ? DG.
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Answer:
The answer is A
Step-by-step explanation:
If two lines are perpendicular to that same line, then they are parallell.
Pls help I have to find the area
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Answer:
28 square units
Step-by-step explanation:
The area of a rectangle is A = l x w.
The length of this rectangle is 7 square units.
The width is 4 square units.
7 x 4 = 28 square units
Find the lateral area of a cone with a diameter of 10 centimeters and a slant height of 9 centimeters round to the nearest tenth
Answers
Answer:
The lateral area of a cone is 141.4 square centimeters
Step-by-step explanation:
Mathematically, we have the formula for the lateral area of a cone as;
A = pi * r * l
where r is the radius of the cone and l
is the slant height of the cone
Mathematically, the radius is simply half the measure of the diameter
we have that as 10/2 = 5 cm
So substituting these values;
A = 22/7 * 9 * 5
A = 141.4 square centimeters
Which scenario could be represented by the algebraic expression n minus 13?
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write an equation to represent the function.
input (x)
0
3
9
output
(y)
0
1
3
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Answer:
Step-by-step explain
the answer is c
determine whether the given lines are parallel or not right with the reason
Answers
Answer:
[tex]AB[/tex] is parallel to [tex]CD[/tex] ([tex]AB ||CD[/tex])
Step-by-step explanation:
In a set of parallel lines cut by the traversal, [tex]\angle AHG[/tex] and [tex]\angle DGH[/tex] are alternate interior angles. In a set of parallel lines cut by a traversal, alternate interior angles are always equal. Therefore, since [tex]\angle AHG=\angle DGH=115^{\circ}[/tex] (they are equal), the lines AB and CD must be parallel.
*A set of parallel lines proves that alternate interior angles are always equal, but the converse is also true in that equal alternate interior angles proves a set of parallel lines. This is because if you changed the angle measure of either of the angles, the relative slope of the lines must change and they would no longer be parallel.
Help plzzzz !!!!!!!!!
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= 3^2*pi*150/360
=11.8 m^2 to nearest tenth
Warm-Up
Construct a perpendicular bisector to PQ
by following these steps.
1. Move the compass center to P and
draw a long arc that intersects PQ.
Then move the compass to Q and
draw an arc that intersects the first
arc in two places.
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Note that the perpendicular bisector to line PQ is constructed and attached accordingly. Here is how to do it.
How do you construct a perpendicular bisector to PQ?
Note that the first stage is to draw a line PQ. But this has already been done.
Next is to place the compass on P as shown in the image above. If you allow you compass (locked at the same degree) to rotate about point P, you will get a circle. However, that is not the objective.
If you also place your compass on point Q, locked to the same degree as when it was on P, and take a rotation around point Q, you will also get a circle.
At some point, you will notice that both circles intersect at two point, which we can call AB₁ and AB₂.
Now you are done with the compass. Take up your ruler, and place it such that it meet both AB₁ and AB₂ but allowing you space to mark a line connecting both points.
Next, using your live or online pencil tool, draw the line from AB₁ to AB₂. Now you have the Perpendicular bisector which you can call AB₁₂.
Note that a perpendicular bisector is a line or plane that intersects a line segment at its midpoint, forming a right angle and dividing the segment into two equal parts.
Learn more about Perpendicular Bisector on:
https://brainly.com/question/24753075
#SPJ1
The cost of 5 kg of mangoes is rupees 147. At what rate per kg are the mangoes
being sold.
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Step-by-step explanation:
the cost of 1 kg mangoes = 147/ 5
= Rs. 29.40
mark me as brainliest
Answer:
cost of 1 kg mango = rupees 29.4
Step-by-step explanation:
cost of 5 kg mangoes =rupees 147
cost of 1 kg mango =?
Now, lets find cost of 1 kg mangoes
CP od 1 kg mangoes = cost of 5 kg mangoes/5 kg
=rupees 147/5
=rupees 29.4
can someone please help me with this?? please please please help me
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Step-by-step explanation:
base is 12, hypotenuse is 20
so X² is h²-b²
so X=16
