Answers
Answer:
n = 18
Step-by-step explanation:
The sides in a regular polygon are equal in length.
⇒ BC = CD
If BC = CD then ΔDCB is an isosceles triangle.
As the base angles of an isosceles triangles are equal:
⇒ ∠DBC = ∠BDC = 10°
Interior angles in a triangle sum to 180°.
⇒ ∠DBC +∠BDC + ∠DCB = 180°
⇒ 10° + 10° + ∠DCB = 180°
⇒ 20° + ∠DCB = 180°
⇒ ∠DCB = 180° - 20°
⇒ ∠DCB = 160°
Therefore, the interior angle of the regular polygon is 160°.
The interior angles of a regular polygon are equal in size.
[tex]\boxed{\begin{minipage}{5.2 cm}\underline{Interior angle of a polygon}\\\\$\dfrac{(n-2) \times 180^{\circ}}{n}$\\\\where $n$ is the number of sides.\\ \end{minipage}}[/tex]
To find the number of sides, equate the formula to the found value of the interior angle and solve for n:
[tex]\begin{aligned}\implies\dfrac{(n-2) \times 180^{\circ}}{n} & =160^{\circ}\\(n-2) \times 180^{\circ} & =n \times 160^{\circ}\\ 180(n-2) & = 160n\\180n-360 & = 160n\\180n & = 160n+360\\180n-160n & = 360\\20n & = 360\\n &= \dfrac{360}{20}\\n & =18\\\end{aligned}[/tex]
Therefore, the regular polygon has 18 sides.
Related Questions
Please answer & explain how the answer was found
Answers
Answer: GEF = 30 DEF = 40
Step-by-step explanation: By angle summation we know the entire angle
GED = 70, so the smaller angles that make up GED (GEF and DEF) will have to sum up to equal GED. Using this we get:
2x + 10 + 5x - 10 = 70
From here we can combine like terms:
7x = 70
and solve for x
x = 10
Then we can plug the value of x back into the equations given to solve for GEF and DEF
GEF:
2x+10 == 2(10)+10 = 30
DEF:
5x-10 == 5(10)-10 = 40
Prism L has length 8 cm.
Prism M has length 20 cm.
Prism M has a volume of 1875 cm3
Work out the volume of prism L.
Answers
The volume of prism L is 750 cm³
What is a prism?A prism is a three-dimensional solid, that has two identical bases, rectangular or parallelogram-shaped faces, and the same cross-section.
The formula for the volume of a prism is V=Bh,
where B = base area and h = height.
We have,
Two similar prism
Prism L:
Length = 8 cm
Prism M:
Length = 20 cm
Volume = 1875 cm³
Applying the volume formula:
V = Bh
Base area = Length x width
1875 = Length x width x height
1875 = 20 x width x height
Width x height = 1875 / 20 = 93.75 _______(1)
Since prisms are similar we can use (1) in finding the Volume of prism L.
The volume of prism L:
= Length x width x height
= 8 x 93.75
= 750
Thus the volume of prism L is 750 cm³
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The complete question is:
L and M are two mathematically similar prisms.
Prism L has a length 8 cm.
Prism M has a length 20 cm.
Prism M has a volume of 1875 cm3
Work out the volume of prism L.
On a highway a wreck occurred and caused a 8 mile
traffic jam on one side of the road. The average car is
13.5 feet in length and the average truck is 20 feet in
length. 75% of the traffic jam consists of cars and 25% of
trucks. If the average distance between vehicles is 3 feet,
how many vehicles are stuck in the traffic jam?
Answers
Answer:
1647
Step-by-step explanation:
Given the following information:
Length of traffic = 8 miles
Average Length of vehicles on the road :
Cars = 14.5 feets
Trucks = 21 feets
18 Wheeler tractor = 73 Feets
% distribution of the different vehicles :
Cars = 70% = 0.7
Trucks = 20% = 0.2
18 wheeler tractor = 10% = 0.1
Distance between vehicles = 4feets
Number of vehicles stuck in the traffic :
Let number of vehicles = v
Summation of (number of vehicles * length of each vehicle) + distance between each vehicle = Length of traffic
Total distance between each vehicle = 4(v-1)
(0.7v * 14.5) + (0.2v * 21) + (0.1v * 73) + 4(v - 1) = 8 miles
1 mile = 5280
8 miles = (5280 * 8) = 42,240
10.15v + 4.2v + 7.3v + 4v - 4 = 42240
25.65v = 42240 + 4
25.65v = 42244
v =42244 / 25.65
v = 1646.939
v = 1647.
Find missing angles of the following
Answers
Answer:
see below
Step-by-step explanation:
angle e is a vertical angle(each of the pairs of opposite angles made by two intersecting lines.) of 114 so e=114 and angle d is the vertical angle of 22 so d=22. and finally angles d+f+e=180
114+22+?=180
?=180-114-22
?=180-136
?=44
e=144
d=22
f=44
22×2÷3÷4 how much is it?
Answers
i used a calculator
2|x|-9 translate 6 units up
Answers
The translation of the function 2 | x | - 9 when translated 6 units up gives the function as 2 | x | - 3.
We are given a function:
2 | x | - 9.
A function from a set X to a set Y assigns to each element of X exactly one element of Y.
We are asked to translate the function 6 units up.
This means that we have to add 6 units to the function.
A function has been “translated” when it has been moved in a way that does not change its shape or rotate it in any way.
So, we get that:
f(x) = 2 | x | - 9 + 6
f(x) = 2 | x | - 3
Therefore, the translation of the function 2 | x | - 9 when translated 6 units up gives the function as 2 | x | - 3.
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What is the surface area of a igloo with a 20 ft. diameter
Answers
The surface area of a igloo with a 20 ft. diameter is [tex]628ft^{2}[/tex]
According to question statement, we are supposed to find the surface area of an igloo with a 20ft. diameter.
Before solving this question, we should be aware of the fact that an igloo is of a Hemispherical shaped object usually made up of ice.
So for finding out area of igloo we find the surface area of of the hemisphere.
Curved Surface area : [tex]2\pi r^{2}[/tex]
Total Surface area: [tex]3\pi r^{2}[/tex]
where r is the radius of igloo.
Radius is half of the diameter therefore [tex]r=\frac{diameter}{2}[/tex]
[tex]r=\frac{20ft}{2} \\r=10ft[/tex]
Therefore radius is 10 ft.
Curved Surface Area: [tex]2*3.14*10^{2} =628ft^{2}[/tex]
Total Surface Area: [tex]3*3.14*10^{2} =942ft^{2}[/tex]
But as we are supposed to find the surface area therefore the answer is [tex]628ft^{2}[/tex].
Hemisphere: A hemisphere is a 3-Dimensional figure which is obtained by bisecting a sphere into two equal halves through its diameter.If you want to learn more about surface areas, click on the link given below:
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There are 38 pencils in the drawer. Sam took 24
pencils from the drawer. How many pencils are now in the drawer ?
Answers
Answer: 14
Step-by-step explanation:
Explain what is meant by confounding. what is a lurking variable? what is a confounding variable?
Answers
Explain what is meant by confounding. what is a lurking variable? what is a confounding variable?
Answer:
A Confounding is the variable that is considered in a research study, and could overall influence the relations between the variables in the study. For example, students wanting to join AP English next semester were told to write a six page essay. When the students turned in their papers and teachers say the difference and grades they believed that the variable was the time that the students handed in the paper. They thought that if the student handed in their paper later than another student that they would receive a lower score, but this was not the case. When asking the students how they prepared for the paper, students replied with different answers. Those who outlined and used other literature for reference scored much higher than those who only used prior knowledge to write their essays. In this study, the lurking variable would be the presence of an outline.
Lurking variable: A variable that is not considered in a research study that could influence the relations between the variables in the study
Confounding variable: A variable that is considered in a research study that could influence the relations between the variables in the study
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Question 2 2.1 2.2 2.2.1 2.2.2 Determine the general solution for sin(x - 30°) = cos 2x Consider the functions f(x) = sin(x-30°) and g(x) = cos 2x Write down the period of g. State the range of f.
Answers
The general solution for the given equation is 40°+120°n.
The period of g(x) is π.
The range of f(x) is [-1, 1].
sin(x-30°) = cos 2xsin(x-30°) = sin(90°-2x)(x-30°) = (90°-2x) + 360°nx + 2x = 90° + 30° + 360°n3x = 120° + 360°nx = (120° + 360°n)/3The general solution (x) is 40° + 120°n. g(x) = cos 2xThe period of cos x is 2π. If the multiplying factor of x is 'n', then it decreases the period by n times.Here, in g(x), n is 2.The period of g(x) is equal to half the period of cos x. The period of g(x) = 2π/2The period of g(x) is π.f(x) = sin(x-30°)"Sin" is a trigonometric function which has a range from -1 to 1.To learn more about period, visit :
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PLEASE HELP ME!!!
WILL GIVE YOU A FOLLOW
Answers
which is equal to:
4x10^-2
As there are two digits behind the decimal point up to( and including the 4) thus the 10^-2
And as the digit is a 4 you multiply 10^-2 by 4
help with this question please! show word needed!
Answers
Answer: u = 80° v = 25°
Step-by-step explanation:
(a) angles on a straight line = 180° - 130° = 50°
In isosceles triangle, both angles on each side is equal, so
180° - 50° - 50° = 80°
u = 80°
(b) u = (2v + 30°) because opposite angles of a parallelogram are equal.
u = 80°
80° = 2v + 30°
80 - 30 = 50
50° = 2v
25° = v
If the smaller of two numbers is one-half of the larger number and the sum of the two numbers is 75
Answers
Step-by-step explanation:
let the larger number=n
then the smaller number=½n
We conclude from the question that
n+½n=75
3/2n=75
3n=150
n=150/3=50
Therefore the larger number=50 and the smaller number=½×50=25
are 8x and 2x^3 like terms ??
Answers
Answer:
No they are not 'like' terms
Step-by-step explanation:
8x and 2x WOULD be 'like' terms
8x and 2x^2 are not
8x and 2x^3 are not either
HELP PLEASE! Use the diagram below to analyze another student's work.
S
80°
45°
Nathan stated that angle q is 20 degrees because 80 degrees + 20 degrees = 100
degrees. Straight lines are measured as 100 degrees.
Did Nathan correctly calculate the measurement for angle q? Justify your answer
1pt for identifying if Nothan was
correct or not
2pts for justification
Answers
Answer: No, Nathan didn't measure angle correctly
Step-by-step explanation:
The sum of angles that are formed on a straight line is equal to 180°
So the value angle q is 80° because the sum of angle q and 100° is 180°
∠q+100°=180°∠q= 180°-100°
∠q= 80°
No, Nathan didn't measure angle correctly.
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5 6 7 8 9 10
TIME REMAINING
10:31
What is true about the completely simplified sum of the polynomials 3x2y2 − 2xy5 and −3x2y2 + 3x4y?
The sum is a trinomial with a degree of 5.
The sum is a trinomial with a degree of 6.
The sum is a binomial with a degree of 5.
The sum is a binomial with a degree of 6.
Answers
Answer:D) the sum is a binomial with a degree of 6
Step-by-step explanation:
Which one is correct
Answers
All rhombus are parallelograms, parallelogram have exactly two pairs of parallel lines, therefore all rhombus have exactly two pairs of parallel lines, so option A is correct.
What is parallelogram?
A unique kind of quadrilateral created by parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but for it to be a parallelogram, its opposite sides must be parallel.
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. Every rhombus is a parallelogram because its opposite sides are all parallel. But all parallelograms cannot be rhombus as a rhombus have all sides equal.
Both a square and a rhombus have equal numbers of sides. The square's diagonals are also perpendicular to one another and divide the opposing angles. A square is a rhombus as a result.
Thus, all rhombus are parallelograms as they have one pair of parallel sides.
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There are 48 trees at the park. ¼ of the trees are oak trees. How many oak trees are at the park
Answers
Answer:
12 oak trees
Step-by-step explanation:
1/4 of 48 =12
At a rate of 42 miles per hour, it takes Henry 9 minutes to drive from the library to his house. Show how to find the distance that Henry traveled.
Answers
42 mph x .15 hours= 6.3 miles
Thomas records the masses of several rocks as 7.40 g, 7.85 g, 7.60 g, and 7.40 g. what is the mode of thomas’s data set? 0.45 7.40 7.55 7.60
Answers
By observation or by inspection, 7.40 appears the most, thus mode.
What Is the Mode?The value that appears most frequently in a data set is called the mode. One mode, several modes, or none at all may be present in a set of data. The mean, or average of a set, and the median, or middle value in a set, are two more common measurements of central tendency.
Data can be disseminated in statistics in a number of different ways. The traditional normal (bell-curve) distribution is the one that is referenced the most. The midpoint of this distribution, as well as some others, coincides with the peak frequency of observed values and is where the mean (average) value is located.
The mean, median, and mode all have the same values for such a distribution. This indicates that this value—the one that appears the most frequently in the data—is the average value, the middle value, and the mode.
When analyzing categorical data, such as automobile models or soda taste varieties, where a mathematical average median value based on ordering cannot be computed, mode is most helpful as a gauge of central tendency.
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Which is a factor of 6z^2 -3z-2+4z?
A:2z+1
B:3z-2
C:z+2
D:2z-1
Answers
Answer:
D. (2z-1)
Step-by-step explanation:
If you solve 6x^2-3z-2+4z you should get (2z-1)(3z+2). Which automatically gives you a factor of 2z-1.
what do you notice about absolute 6 and -6
Answers
Answer: they have the same absolute value
Step-by-step explanation: -6 and positie 6 are both 6 units from zero
The only measure of center that can be found for both quantitative and qualitative data is the.
Answers
The only measure of center that can be found for both quantitative and qualitative data is the mode.
What is the mode?The measure of mode can be calculated for both quantitative and qualitative data. When it is unique, the mode is the value that appears the most frequently in a data set, and it, like the median and mean, can be used as a measure of central tendency. However, there are times when there is no mode or when there are multiple modes. When all observed values appear the same number of times in a data set, there is no mode. To find the mode, arrange the numbers (this makes counting easier), then count how many of each number there are. A mode is a number that appears frequently.Therefore, the only measure of center that can be found for both quantitative and qualitative data is the mode.
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Which statistics best describe the center and spread of the data in the histogram? which statistics best describe the center and spread of the data in the histogram? median and standard deviation mean and standard deviation median and iqr mean and iqr
Answers
A histogram is a graph that shows the frequency of numerical data using rectangles.
A set of quantitative data with varying values may be shown as a list or a data display.
Center and spread are ways to describe data sets like this.
Center describes a typical value of a data point. Two measures of center are mean and median.
Spread describes the variation of the data. Two measures of spread are range and standard deviation.
The mean is useful for describing the center of data with similar values.
The mean is the average value.
mean = sum of values / number of values
A histogram is a graph that shows the frequency of numerical data using rectangles.
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Evaluate the expression (2+5)4
Answers
Since the 2 + 5 is in parenthesis, we do that first.
7(4) =
7 * 4 = 28
Hey there!
Assuming:
(2 + 5)(4) or (2 + 5)^4
Simplifying:
(2 + 5)(4)
= 7(4)
= 28
Simplifying:
(2 + 5)^4
= (7)^4
= 7^4
= 7 * 7 * 7 * 7
= 49 * 49
= 2,401
We’re going to assuming equation #1 in our assumption as your question.
That being said, your answer is most likely: 28
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Use the given equation to determine if the points in the brackets are on the graph
of the line determine by the equation 4x- 3y=-6
{(0,2),(1,3),(4,7),(6,10)}
Answers
The points in the brackets are on the graph are (0, 2) and (6, 10)
How to determine if the points in the brackets are on the graph?The equation of the line is given as
4x - 3y = -6
The points are given as:
{(0,2),(1,3),(4,7),(6,10)}
Rewrite as
(x, y) = {(0,2),(1,3),(4,7),(6,10)}
Next, we substitute the x and y values in the equation 4x - 3y = -6
So, we have
(0, 2):
4(0) - 3(2) = -6
-6 = -6 ---- true
(1, 3):
4(1) - 3(3) = -6
-5 = -6 ---- false
(4, 7):
4(4) - 3(7) = -6
-5 = -6 ---- false
(6, 10):
4(6) - 3(10) = -6
-6 = -6 ---- true
Hence, the points in the brackets are on the graph are (0, 2) and (6, 10)
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PLEASE HELP! Need help quick!
Joaquin started an online music collection with 105 songs. Each week, Joaquin purchases 4 new songs to add to his collection.
Which inequality can be used to find w, the number of weeks after starting his collection, when Joaquin will have more than 200 songs in his collection?
A- 105w+4<200
B- 105w+4>200
C- 4w+105<200
D- 4w+105>200
Answers
Answer: The answer will be D
Step-by-step explanation: I think the answer will be C because you can multiply this as I did to get the answer so its C
An appliance store is having a liquidation where everything in the store is 70% off the regular price. what is the price of a dishwasher that is regularly $519.89? a. $36.39 b. $70.00 c. $155.97 d. $363.92 please select the best answer from the choices provided a b c d
Answers
With 70% off the regular price, a dishwasher, regularly priced at $519.89, will be $155.97 only. The answer is C.
Discount is the deduction in the price of a good or service. When this reduced price is expressed in percentage then we call it a discount rate.
If the discount is given in percent, then the amount of discount can be found by using the formula:
Amount of Discount = Regular Price × Rate of Discount
If the regular price of a dishwasher is $519.89, and the discount rate is 70%, using the formula, solve for the discount value.
Amount of Discount = $519.89 x 70%
Amount of Discount = $519.89 × 0.70
Amount of Discount = $363.92
To get the final price of the dishwasher, subtract the discount value from the original or regular price.
price = $519.89 - $363.92
price = $155.97
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What is the slope of the line passing through the points (-3, 4) and (2, -1)?
Answers
Answer:
-1
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (-1 - 4)/(2 - (-3)) = -5/(2 + 3) = -5/5 = -1
tom do this one too.
Answers
Answer:
x=36
y=144
Step-by-step explanation:
ABD=2x
z rule
BDE=2X
therefore 2x+3x=180
5x=180
x=36
solving for y
180-y+2x+2x=180
y=4x
y=4(36)
y=144
