A prism is created using 2 regular pentagons as bases. the apothem of each pentagon is 2.8 centimeters. a regular pentagonal prism is shown. the apothem of each pentagon is 2.8 centimeters. the height of the prism is (2 x 1). all sides of the pentagon are congruent. which expression represents the volume of the prism, in cubic centimeters? 9x2 7x 14x2 7x 16x2 14x 28x2 14x
Answers
The expression that represents the volume of the prism, in cubic centimetres is [tex]28.476(2x+1) \: \rm cm^3[/tex] approx
How to find the volume of a prism?If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross section is same as its base, then its volume is:
[tex]V = B \times h[/tex]
where h is the height of that prism and B is the area of the base of that prism.
For this case, we are provided a prism which has pentagon as its cross sections, and its height is [tex]2x + 1[/tex] units.
Let B be the area of those pentagons, then:
Volume of the prism = [tex]B(2x + 1) \: \rm cm^3[/tex]
It is provided that the apothem of the pentagon is 2.8 cm.
An n sided regular polygon has internal angles' sum as 180(n-2)°
Thus, each internal angle would be of 180(n-2)/n°
For n = 5, this comes as 108°
Since the line AO is bisecting the internal angle, the angle OAB is o of 108/2 = 54°
Using the tangent ratio, we get:
[tex]\tan(54^\circ) = \dfrac{|OD|}{|AD|}\\\\|AD| = \dfrac{2.8}{\tan(54^\circ)} \approx 2.034 \: \rm cm[/tex]
Thus, area of the triangle AOD = [tex]\dfrac{1}{2} \times |AD| \times |OD| \approx \dfrac{1}{2} \times 2.034\times 2.8 = 2.8476 \: \rm cm^2[/tex]
There are 10 such triangles, all congruent, thus:
Area of pentagon = [tex]B \approx 10 \times 2.8476= 28.476 \: \rm cm^2[/tex]
Thus, volume of the pentagonal prism is:
[tex]V = B \times h \approx 28.476(2x+1) cm^3[/tex]
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Answer:
14x^2+7x
B
Step-by-step explanation:
I did the test.
Related Questions
I have five apples and ten oranges. If a fruit basket must contain at least one piece of fruit, how many kinds of fruit baskets can I make
Answers
Answer:
answer is 15
please that is what I'm thinking
Please help me with 20 through 22 please I really appreciate it! Thank you very much!
Answers
Answer:
20. 2x+y
21. 4
22. x+y
Step-by-step explanation:
20. 9x+2y - x-2y find your LCM
4 4
=(9x+2y)-(x-2y) clear bracket
4
=9x+2y-x+2y collect terms
4
=9x-x+2y+2y
4
=8x+4y factorize
4
=4(2x+y)
4
=2x+y
with this, you will understand the following
21. 4x + 8y
x+2y x+2y
=4x+8y
x+2y
=4(x+2y)
x+2y
=4
22. 2x-y + 2x+5y
4 4
=2x-y+2x+5y
4
=4x+4y
4
=4(x+y)
4
=x+y
7^-6/7^-2 rewrite it using a singular positive exponent
Answers
Answer:
1/7^4
Step-by-step explanation:
negative exponents flip to opposite side of the fraction and add to like-base terms.
What are all that apply?
Answers
height or altitude for a parallelogram means the perpendicular distance from one parallel side to the other. Check the picture below.
Suppose that spain has a workforce of 22.85 million people, and that the average salary for each person is €24,200 annually. spain has imports of €290.85 billion and exports of €200.13 billion. if the spanish government levies a 7% tariff on exports, an 18% tariff on imports, and a 21% income tax, how will the revenue gained from tariffs and the revenue gained from income tax compare? a. the government will earn €80.7214 billion more from tariffs than from income tax. b. the government will earn €29.5030 billion more from tariffs than from income tax. c. the government will earn €63.7707 billion more from income tax than from tariffs. d. the government will earn €49.7616 billion more from income tax than from tariffs.
Answers
The revenue that the Spain government gained from tariffs and the revenue gained from income tax compare as given by: Option d. the government will earn €49.7616 billion more from income tax than from tariffs.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
For this case, we have these information:
Import amount = €290.85 billionTariff on import = 18% on import amountExport amount = €200.13 billionTariff on export = 7% on export amountTotal people in Spain = 22.85 millionEach person's average salary = €24,200 annuallyTax on income = 21%Calculating the earnings from tariffs and income tax:
Tax generated from income = 21% of €552970 =
[tex]\dfrac{552.97 \times 10^9}{100}\times 21 = 116.1237 \: \rm billion \: euros[/tex]
Earning from tariffs = 52.353 billion + 14.0091 billion = 66.3621 billion
Difference in earning from income tax and tariffs is:
116.1237 billion - 66.3621 billion = 49.7616 billion euros.
Thus, the revenue that the Spain government gained from tariffs and the revenue gained from income tax compare as given by: Option d. the government will earn €49.7616 billion more from income tax than from tariffs.
Learn more about percent here:
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Question
Find the slope of the line.
Answers
Answer:
undefined
Step-by-step explanation:
The slope of a line is the ratio of the vertical change between two points to the horizontal change between those same two points. When the line is vertical, the horizontal change is zero. That means the slope is some (non-zero) value divided by zero. Division by 0 gives a result that is "undefined."
The slope of a vertical line is "undefined."
How is the graph of the parent function, y = StartRoot x EndRoot transformed to produce the graph of y = StartRoot negative 2 x EndRoot? It is translated horizontally by 2 units and reflected over the x-axis. It is translated horizontally by 2 units and reflected over the y-axis. It is horizontally compressed by a factor of 2 and reflected over the x-axis. It is horizontally compressed by a factor of 2 and reflected over the y-axis.
Answers
Answer:
The answer is D
Step-by-step explanation:
The parent function will be reflected over the x-axis, compressed by a factor of 0.4, and translated into 2 units right.
It is given that the two functions one is the parent function [tex]\rm y = \sqrt[3]{-x}[/tex] and the transformed function [tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex].
It is required to find the transformation rules.
What is a function?It is defined as a special type of relationship and they have a predefined domain and range according to the function.
We have parent function:
[tex]\rm y = \sqrt[3]{-x}[/tex]
and transformed function:
[tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex]
If we multiply the parent function with a negative value it will f(x) over the x axis.
By the transformation rules of the function y = -f(x) reflects f(x) over x-axis.
After applying the transformation to the parent function:
[tex]\rm y = -\sqrt[3]{-x}[/tex]
By the transformation rules of the function if multiply the function with less than the unit value it will be compressed by the multiplied factor ie.
y = k f(x) and k<1, the function will be compressed by the k factor hence:
[tex]\rm y = -0.4\sqrt[3]{-x}[/tex] (after applying the second transformation)
As we can see the transformed function is subtracted by -2
By rules of transformation, for y=f(x-A) it would be a horizontal translation of 'A' unit to the right.
After applying this transformation we get:
[tex]\rm y = -0.4 \sqrt[3]{-x-2}[/tex] which is a transformed function derived after applying the transformation to the parent function.
Thus, the parent function will be reflected over the x-axis, compressed by a factor of 0.4, and translated into 2 units right.
Learn more about the function here:
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Line segment AB has endpoints A(−1,6) and B(5,−6).
What are the coordinates of the point that partitions AB according to the part-to-part ratio 1:5?
(0,4)
(−4,4)
(4,0)
(4,−4)
Answers
Answer:
(0,4)
it was correct
Tiles with numbers 1 through 9 are placed in a bag. What is the probability of choosing an even number that is greater than or equal to 4? 1/9, 2/9, 3/9 or 4/9
Answers
Answer:
3/9
Step-by-step explanation:
Okay, first let's list all the numbers between 1 and 9
1, 2, 3, 4, 5, 6, 7, 8, 9
Now let's list all of the even numbers from the previous list
2, 4, 6, 8
Now let's list all of the numbers from the previous list that are equal to, or greater than, 4
4, 6, 8
That's only three potential numbers, out of a total of nine numbers
So it's a 3/9 chance
I’ll give you brainiest to who ever gets it right
Answers
Answer:
Line a is the best fit.
Step-by-step explanation:
The dots are more evenly spread across line a while with line b the dots at the bottom are far away from it. Line a passes through the center of the spread of the dots
6. Complete a glide translation (x-2, y) and then reflect over x axis. What would be the new ordered pairs for P'and S'?
Answers
The glide translation and the reflection over x-axis are illustrations of transformation
The new ordered pairs for P'and S'are (x - 2, -y)
How to determine the new ordered pairs?The given parameters are:
Glide translation (x-2, y)
Reflection over x axis
Assume the coordinates of point P and S are (x,y)
When translated, the new points would be:
(x-2, y)
The rule of reflection over the x-axis is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex](x - 2,y) \to (x - 2,-y)[/tex]
Hence, the new ordered pairs for P'and S'are (x - 2, -y)
Read more about transformation at:
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What is the area of this triangle?
y
5
D
4
F
Enter your answer in the box.
3
2
1
E
units2
Answers
Answer: 6 units squared.
Step-by-step explanation: The equation for area of a triangle is 1/2 * length of base * the length of the height.
The length of the base is D to E, which is 3 units.
The length of the height is from F to the base of the triangle, which is 4 units.
Therefore, the area of the triangle would be 1/2 * 3 * 4 = 6 units squared.
PLEASE HELP!!! I am stuck!!
How do I get question c)?
Answers
-15/-21 -14/x
-15x = -21 * -14
x = -19.6
answer -14c = -19.6 or about -20
answer 3c = .6 or about 1
formula would be
y= 1.2x -3
partial variation means the line doesn't go through (0,0)
A survey asked 100 seventh graders if they have either a cell phone or a tablet. Of the 32 students that have a cell phone, 19 do not have a tablet. Of the 70 students that have a tablet, 57 do not have a cell phone. A total of 11 students stated they do not have a cell phone or a tablet. Some of this information is included in the frequency table.
help please
Answers
Answer:
I don't know sir actually I didn't understand your question no need to reply to my answer bye
Answer:
13
Step-by-step explanation:
if you read through the paragraph and pot your data on the table, the answer will show and is 13
The density of apple juice is 1. 04 grams per cm^3
Answers
Answer:
1,040kg/m³
Step-by-step explanation:
1g/cm³ =1,000kg/m³
1.04g/cm³=?
= 1.04×1000
Density =1,040kg/m³
What is the pattern: April 3, March 31, March 28, March 25?
A) 30 days earlier
B) 1 week earlier
C) 3 days earlier
D) 3 days later
Answers
pls help me to answer this
Answers
Answer:
so i just went on spreadsheets and created this and screenshotted it i hope this helps
Step-by-step explanation:
Is the following function even, odd, or neither f(x)=x^3/x+1
Answers
Answer: Odd
Step-by-step explanation:
Odd functions are functions where the exponent of the leading term is odd. In this case, the exponent of 3 is odd, so the function is odd.
The table shows the number of points Malik and Alexia scored while playing a video game together.
The table is titled Video Game Scores. The table has two columns and three rows. The first column is labeled Malik's Score represented by m, the second column is labeled Alexia's Score represented by a. Malik scored sixty, Alexia scored ninety. Malik scored seventy, Alexia scored one hundred. Malik scored eighty, Alexia scored one hundred ten.
Which equation relates Alexia’s score, a, to Malik’s score, m
Answers
Answer:
a = m+30
Step-by-step explanation:
malik is always 30 points under alexia so in order for malik to be equal to alexia he would have to add an additional 30. i hope this helps :)
Area of square= 625 m sq Perimeter =??
Answers
Answer:
100 m
Step-by-step explanation:
Given :
Area of square = 625 m²#1) Finding the side length
Area = (side length)²⇒ side length = √Area⇒ side length = √625⇒ side length = 25 m#2) Calculating perimeter
Perimeter = Total length of the sides of the shapePerimeter = 4 x side length [a square has 4 equal sides]⇒ Perimeter = 4 x 25⇒ Perimeter = 100 mAnswer:
100 m.
Step-by-step explanation:
So the area of a square (or any rectangle) is length (l) x width (w). Additionally, all sides of a square are the same length. So if your area is 625 m sq, then one side length would be the square root of 625, which is 25.
So, as we know that one side length is 25 m, and that the perimeter is all side lengths added together, and that a square has four equal sides,
we can add the four lengths of 25 together: (4)(25) [25+25+25+25].
(4)(25) = 100.
The perimeter of the square is 100 m.
In the 2004 Summer Olympics, the U.S. won 11 more medals than Russia. Together they won 195 medals. How many medals did the U.S. win?
Answers
Answer:
The U.S. won 101 medals.
Step-by-step explanation:
101
Hope it helped and have a great day!
"the square of y decreased by
quotient of 36 and 6"?
Answers
Here's your answer, folks! ↓
[tex]y^2 - (36 * 6)[/tex]
A candy bar box is in the shape of a triangular prism. The volume of the box is 2,400 cubic centimeters.
A triangular prism is shown with base of triangle labeled 16 cm, sides of triangles labeled 17 cm, and length of the box equal to 20 cm.
Part A: What is the height of the base? Show your work. (5 points)
Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)
Answers
Answer: the answer is 1000cm2.
The volume of a triangular prism shaped box is 2,400 cubic centimeters.
Base of the triangle = 16cm
Sides of the triangle = 17cm
Length of the box = 20cm
Triangular prismA triangular prism is a three-sided prism made of a triangular base and a corresponding side.
A. To find the height of the base = 3 x the volume divided by the base area = 15cm. B. The approximate amount of card board used to make the candy box:Using the lateral prism as the sides will be:Lateral area = Perimeter of triangle X height of the prism
Lateral area = (16 + 17 + 17) X 20
Lateral area = 50 X 20
Lateral area = 1,000 cm2
Therefore, the answer is 1000cm2.
Two six-sided dice are rolled and their product is taken. How many elements are in the subset of even numbers?
Answers
12 in all:
{2, 4, 36, 6, 8, 10, 12, 16, 18, 20, 24, 30}
Answer:
Step-by-step explanation:
Kim says that 1/4 x 12 is the same as dividing 12 by 4 do you agree with Kim? explain your answer.
Answers
Answer:
yes i do
Step-by-step explanation:
1/4 x 12= 3
12 divided by 4 = 3
PLEASE HURRY NEEDED ASAP
Answers
Answer:
1: Is a function
2: Isnt a function
3: Is a function
4: Isnt a function
Reminder: Functions CAN"T have the same x values but different y values!!!!
Have a great day!!
Please rate and mark brainliest!!
Answer:
Sorry, all I know is the first one is a function.
Step-by-step explanation:
It's linear, and passing the vertical line test because it only has a point on each part of the x-axis, if you were to graph it.
I AM GIVING AWAY 30 POINTS TO WHOEVER ANSWERS ME
Answers
Answer:
Answer B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The venn diagram of the option B is correctIt is a fact that all whole numbers are real numbersBut, all real numbers, such as 3/4, are not always whole numbersfind the x-intercept of the following linear equation -2x + 3y = 12
Answers
Answer:
X = 6
Step-by-step explanation:
Hope this helped!!
maybe mark brainiest
Combine like terms:
-4k+15k-30=-78
(must be a decimal)
Answers
Answer:
I don't know sorry, I wish I could help you
Let's combine like terms:-
[tex]\bigstar{\sf{-4k+15k-30=-78}[/tex]
Add the k's:-
[tex]\bigstar{\sf{11k-30=-78}[/tex]
Add 30 to both sides:-
[tex]\bigstar{\sf{11k=-78+30}[/tex]
[tex]\bigstar{\sf{11k=-48}[/tex]
Divide both sides by 11:-
[tex]\bigstar{\boxed{\sf{k=4.36}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
Can you help me solve for #1 please?
Answers
Answer:
x = 15
It is a Pythagorean triple.
Step-by-step explanation:
1.
a² + b² = c²
9² + 12² = x²
81 + 144 = x²
x² = 225
x = 15
The three numbers, 9, 12, 15 do form a Pythagorean triple since they are integers.