How many lateral faces does a pentagonal prism have? Explain its actually 8 for anyone who needs this in the future
Answers
Explanation:
You can see the attached figure for better understanding.
A pentagonal prism has 2 bases (the bottom and top faces), each pentagonal, and 5 lateral faces.
The pentagon is a figure with 5 sides. Hence, from each side, the prism will have one lateral face that goes from one base to the other.
The figure attached shows a pentagonal prism where you can see what I explained.
A pentagonal prism has five lateral faces.
A pentagonal prism is a three-dimensional geometric figure with two parallel pentagonal bases and rectangular lateral faces. To determine the number of lateral faces:
(1) Visualize the pentagonal bases; a pentagon has five sides.
(2) Each side of the pentagon is perpendicular to a corresponding rectangle, forming a lateral face.
So, a pentagonal prism has five lateral faces, matching the number of sides of its base pentagon.
An octahedron, a completely different shape, has eight triangular faces, not to be confused with the prism.
Related Questions
Assume that the weights of all packages of a certain brand of cookies are normally distributed with a mean of 32 ounces and a standard deviation of 0.3 ounce. find the probability that the mean weight, x¯, of a random sample of 20 packages of this brand of cookies will be between 31.8 and 31.9 ounces.
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When searching for a lost animal, the search party often creates a circular area with a search radius. Two points of interest in the search are the last known locations the animal was sighted. The two points of interest in this case are the pet’s home, which is located at (-4,5), and the neighbor’s yard, located at (-9,10). If the pet’s home is the center of the circle and the neighbor's yard is on the circle, find the radius of the circle.
Answers
C----------> the center of a circle
C (-4,5)
A-----------> a point on the circle
A (-9,10)
we know that
the distance between point A and point C is the radius of the circle
A (-9,10) C (-4,5)
d=√[(y2-y1)²+(x2-x1)²]--------> √[(5-10)²+(-4+9)²]
=√[(-5)²+(5)²]------> √[(25)+(25)]---------> √50
d=7.07 units
r=d--------> r=7.07 units
the equation of a circle is
(x+4)²+(y-5)²=50
see the attached figure
the answer is
the radius of a circle is 7.07 units
10 + 1 = a. dieciuno c. veintiuno b. once d. nueve
Answers
5 plus 500% of 10 is the same as 110% of what number?
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55÷110%=50
so 5 plus 500% of 10 is the same as 110% of 50
What is the equation for 5n+7=21
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5n = 14
14 / 5 = 2.8
N = 2.8
Hope I helped!
Let me know if you need anything else!
~ Zoe (Rank:'Genius')
To start, you must first isolate the 5n term so that you can solve for the variable of n.
To do this, subtract 7 from both sides:
5n+7=21
-7 -7
5n=14
Now, divide both sides by 5 to isolate the n term:
5n/5=14/5
You should get a result of n=14/5
Therefore, your final answer should be n=14/5.
To check if the answer is correct, simply plug 14/5 for the variable n in the original equation. If you get a correct mathematical statement when you simplify, the value is correct:
n=14/5
5(14/5)+7=21
14+7=21
21=21
Therefore, n=14/5 is correct.
Hope this helps and have a marvelous day! :)
Find the values of a b and c for which the quadratic equation ax^2+bx+c=0 has the solutions -3 and 1
Answers
.. a(x +3)(x -1) = 0
.. a(x^2 +2x -3) = 0
The quadratic
.. ax^2 +bx +c = 0 will have solutions -3 and 1 for ...
.. a ≠ 0
.. b = 2a
.. c = -3a
if tyrone works 40 hours per week and has no other sources of income what is his total monthly cash inflow
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[tex]18 \times 40 = 720[/tex]
[tex]720 \times 4 = 2880[/tex]
[tex]2880 - 1800 = 1080[/tex]
~~
Answer : B
~~
I hope that helps you out!!
Any more questions, please feel free to ask me and I will gladly help you out!!
~Zoey
a sperical water tank holds 12,500 ft^3 of water what is the diameter of the tank
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if a spherical water tank holds 12,500 ft³of water then the diameter of the tank is 29 ft.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that the spherical water tank holds 12,500 ft³of water
We need to find the volume of the spherical water tank.
We know that volume of sphere=4/3πr³
Volume of sphere is 12,500 ft³
12500=4/3×3.14r³
12500=4.186r³
Divide both sides by 4.186
12500/4.186=r³
2986.144=r³
Take cube root on both sides
∛2986.144=r
14.40=r
We know diameter=2r
Diameter=2×14.4
=28.8=29
Hence, if a spherical water tank holds 12,500 ft³of water then the diameter of the tank is 29 ft.
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how do you write 6 less than the product of 3 and a number X?
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How many times bigger is 7 billion than 700 million
Answers
7,000,000,000/700,000,000=10
martin paid $120 towards his $2400 credit card bill. what percentage did he pay
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120/2400*100/1 =120/24 =5%
What is the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5?
y = x – 8
y = x + 1
y = x + 1
y = x + 10
Answers
then there is slope coefficijent
S1= - 1/ S2
In our case we must first transform given line from standard form to slope form
2x+3y= -5 => 3y = - 2x-5 => y = (-2/3)x -5
The slope coefficijent od the given line is S= - 2/3
Then the slope coefficijent of the requested line is
S1= - 1/(-2/3) => I suppose that you know to solve double fraction
S1=3/2
The equation for the line which passes through one point is
y-y1 = S1 (x-x1) => y-1 = 3/2 (x-(-6)) => y-1 =3/2 (x+6)
We will multiply both sides of the equation with number 2 and get
2y-2=3x+18 => 2y=3x+18+2 => 2y = 3x+20
When we divide the both sides with number 2 we finally get
y= (3/2)x+10.
Good luck!!!!
Answer:
[tex]y=\frac{3}{2}x+10[/tex]
Step-by-step explanation:
Given equation of line : [tex]2x + 3y = -5[/tex]
Standard form of equation of line = [tex]y=mx+c[/tex] ---A
Where m is the slope
Convert the given equation in standard form
[tex]2x + 3y = -5[/tex]
[tex] 3y = -5-2x[/tex]
[tex] y =\frac{-5}{3}-\frac{2}{3}x[/tex]
So, slope =[tex]m = -\frac{2}{3}[/tex]
If the two lines are perpendicular then the product of their slopes is -1
Let n be the slope of required equation of line
So, [tex]m \times n = -1[/tex]
[tex]-\frac{2}{3}\times n = -1[/tex]
[tex]n=\frac{3}{2}[/tex]
Substitute this value in A
[tex]y=\frac{3}{2}x+c[/tex] --B
Now we are given that the required perpendicular line passes through the point (–6, 1)
So, substitute (–6, 1) in B
[tex]1=\frac{3}{2}(-6)+c[/tex]
[tex]1-(\frac{3}{2}(-6))=c[/tex]
[tex]10=c[/tex]
Substitute the value of c in B
[tex]y=\frac{3}{2}x+10[/tex]
Hence the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5? is [tex]y=\frac{3}{2}x+10[/tex]
If the two equal sides of an isosceles triangle are 2 cm long, find the length of the third side thatmaximizes the area of the triangle.
Answers
Area = (1/2)(2 cm)²×sin(β)
This will be a maximum for β = 90°. The corresponding length of the third side is
2√2 cm
≈ 2.2828 cm
Push technology is also known as _____.
simulcast
Webcasting
connectivity
data-driven decision-making
Answers
WEBCASTING
According to wikipedia ,
push technology is is a style of Internet-based communication where the request for a given transaction is initiated by the publisher or central server.
A webcast is a media presentation distributed over the Internet using streaming media technology to distribute a single content source to many simultaneous listeners/viewers.
Leo multiplied all numbers from 1 to 11 and wrote the answer on the board. During the break three digits were erased 39,9...6,8... ... . What are the erased digits?
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The erased digits are 1, 0, 0.
Charlie reads quickly. He reads 1 and 3 seventh pages every 2 third minutes. Charlie reads at a constant rate. How many pages does charlie read per minute?
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Charlies reads 15/7, or 2 1/7, page per minute.
Hope this helps a bit.
If the sum of four consecutive odd integers is 208, what is the smallest of the four integers?
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Peyton has two pizzas each Pizza is cut into 10 equal slices she and her friends eat 14 slices what part of the pizzas did they eat write your answer as a decimal please help
Answers
14/20 <---Fraction eaten over total
7/10 <---Fraction reduced to tenths
0.7 <---is a decimal equal to 7/10
solve x=4+(4x-4)^(1/2)
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First, we rewrite the expression:
x = 4 + (4x-4) ^ (1/2)
x = 2 (2+ (x-1) ^ (1/2))
x = 4 + 2 (x-1) ^ (1/2)
From here we get a solution for x = 10
To check it we substitute x = 10 in the expression:
10 = 4 + 2 (10-1) ^ (1/2)
10 = 4 + 2 (9) ^ (1/2)
10 = 4 + 2 (3)
10 = 4 + 6
10 = 10
Answer:
The solution is:
x = 10
Answer: Option B
x = 10
Step-by-step explanation:
just did it on edge
Answer and how you get then answer
Answers
= (480/540 -1)*100%
≈ -11.11%
The number of calories in a child's meal was reduced about 11%.
is possible to have a shape with different dimensions while having the same volume?
Answers
yes,
a cuboid with dimensions 2, 4, 8 has volume = 64 unit^3
a cube with side 4 has volume = 64 unit^3
so, they have different shapes but same volume
guy finds how car his house is several locations and makes the table shown how much farther away from guy's house is the library than the cafe?
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A cylinder has a radius of 4x+2 and a height of 5x+4. Which polynomial in standard form best describes the total volume of the cylinder. Use the formula V=pir^2h for the volume of a cylinder.
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Searches related to Elon sat on the dock with his fishing rod, when suddenly he felt the rod being pulled down! He reeled in his catch, causing it to ascend at a constant rate of 0.10, point, 1 meters per second. When it reached the water's surface after 35 seconds, Elon found it was only an old shoe. Graph the shoe's altitude (in meters relative to the water's surface) as a function of time (in seconds).
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We first graph the point where his catch reached the surface, (35, 0). Since it travels upward at a constant rate, the graph will be linear. We also need to know where it starts (what depth it is at when he begins reeling it in). We can use the formula d=rt as a template for our function. d would be distance (in our case, depth), r is the rate (speed) and t is the amount of time.
To find how far the catch had to travel to reach the surface, we set up our equation as:
d = 0.1(35)
This will tell us how much distance it traveled in 35 seconds. 0.1(35)=3.5, so the catch started 3.5m under water. It then travels up at 0.1 m per second.
The sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?
Answers
one number = x
the other number = 3x
Given that the sum of these two number is 44.
x + 3x = 44
4x = 44
x = 44 ÷ 4
x = 11
x = 11
3x = 11 x 3 = 33
The two numbers are 11 and 33
x = larger number
y = smaller number
Set up equations:
[tex]x + y = 44[/tex]
[tex]3y = x[/tex]
Solve by substituting. I will use the x already given to us (in second equation) to substitute in 1st equation (x = 3y):
[tex]3y + y = 44[/tex]
[tex]4y = 44[/tex]
[tex]y = 11[/tex]
Plug it back into 2nd equation to solve for x:
[tex]3y = x[/tex]
[tex]3(11) = x = 33[/tex]
So, our two values are: x = 33 and y = 11.
We can check, x + y = 33 + 11 does equal 44 and 33 times is 3 times larger than 11. So, the initial criteria work out and we are right.
what term has to be added to x^2-3x to be a trinomial 3/2 9/4 6 9
Answers
The given expression is:
[tex] x^{2} -3x[/tex]
The formula of [tex] (a-b)^{2} [/tex] is [tex] a^{2} -2ab+ b^{2} [/tex]
Re-writing the given expression:
[tex] x^{2} - 2(x)( \frac{3}{2}) [/tex]
So, we have the square of first term and twice the product of first and second term. What is missing is the square of second term.
So, the complete expression for perfect square will be:
[tex] x^{2} -2(x)( \frac{3}{2})+ ( \frac{3}{2} )^{2} \\ \\ x^{2} -2(x)( \frac{3}{2})+ \frac{9}{4} [/tex]
Therefore, 9/4 should be added to the given expression to make it a perfect square.
Answer: The correct option is (B) [tex]\dfrac{9}{4}.[/tex]
Step-by-step explanation: We are given to find the term that has to be added to [tex]x^2-3x[/tex] to be a perfect trinomial.
Let, c denote the term to be added.
Then,
[tex]x^2-3x+c\\\\=x^2-2\times x\times \dfrac{3}{2}+c\\\\\\=x^2-2\times x\times \dfrac{3}{2}+\dfrac{9}{4}+c-\dfrac{9}{4}\\\\\\=\left(x-\dfrac{3}{2}\right)+c-\dfrac{9}{4}.[/tex]
Therefore, the given expression will be a perfect trinomial if
[tex]c-\dfrac{9}{4}=0\\\\\\\Rightarrow c=\dfrac{9}{4}.[/tex]
Thus, the required term to be added is [tex]\dfrac{9}{4}.[/tex]
Option (B) is CORRECT,
Use the following diagram to complete the required information. m∠ROS = 20 deg 15' 40", m∠SOT = 10 ° 12' 30" m∠ROT = 30 ° 27' 10" 31 ° 28' 10" 30 ° 28' 10"
Answers
Answer:
Third option 30° 28' 10"
Brainlist?
Step-by-step explanation:
m∠ROT, formed by adjacent angles m∠ROS (20° 15' 40") and m∠SOT (10° 12' 30"), measures 30° 28' 10" according to the Angle Addition Postulate.
Attached diagram.
To find the measure of angle ROT (m∠ROT), you can use the Angle Addition Postulate.
The Angle Addition Postulate states that the measure of an angle formed by two adjacent angles is equal to the sum of the measures of those two angles.
Here m∠ROS and m∠SOT as adjacent angles forming m∠ROT.
m∠ROS = 20 degrees 15 minutes 40 seconds
m∠SOT = 10 degrees 12 minutes 30 seconds
To find m∠ROT, add the measures of m∠ROS and m∠SOT:
m∠ROT = m∠ROS + m∠SOT
First, add the degrees, then the minutes, and finally the seconds separately:
Degrees: 20 degrees + 10 degrees = 30 degrees
Minutes: 15 minutes + 12 minutes = 27 minutes
Seconds: 40 seconds + 30 seconds = 70 seconds
Now, simplify the seconds by converting any excess seconds into minutes:
70 seconds = 1 minute and 10 seconds
Now, add the minutes to the total:
27 minutes + 1 minute = 28 minutes
So, m∠ROT is:
30 degrees 28 minutes 10 seconds
Therefore, the measure of the angle m∠ROT = 30 degrees 28 minutes 10 seconds.
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The above question is incomplete, the complete question is:
Use the following diagram to complete the required information. m∠ROS = 20 deg 15' 40", m∠SOT = 10 ° 12' 30"
m∠ROT =
30 ° 27' 10"
31 ° 28' 10"
30 ° 28' 10"
Attached diagram.
Find the percentages. 15m is what percent of 60m; 3m; 30m; 1.5 km?
Answers
25% of 60m
500% of 3m
50% of 30m
1000% of 1.5m
Here are the calculations to find the percentages:
1. [tex]15\text{m}$ is what percent of $60\text{m}?[/tex]
[tex]\frac{15\text{m}}{60\text{m}} \times 100\% = \frac{1}{4} \times 100\% = 25\%[/tex]
2. [tex]15\text{m}$ is what percent of $3\text{m}?[/tex]
[tex]\frac{15\text{m}}{3\text{m}} \times 100\% = 5 \times 100\% = 500\%[/tex]
3. [tex]15\text{m}$ is what percent of $30\text{m}?[/tex]
[tex]\frac{15\text{m}}{30\text{m}} \times 100\% = \frac{1}{2} \times 100\% = 50\%[/tex]
4. [tex]15\text{m}$ is what percent of $1.5\text{km}?[/tex]
[tex]1.5\text{km} = 1500\text{m}[/tex]
[tex]\frac{15\text{m}}{1500\text{m}} \times 100\% = \frac{1}{100} \times 100\% = 1\%[/tex]
Therefore, the percentages are:
1. [tex]15\text{m}$ is $25\%$ of $60\text{m}[/tex]
2.[tex]15\text{m}$ is $500\%$ of $3\text{m}[/tex]
3. [tex]15\text{m}$ is $50\%$ of $30\text{m}[/tex]
4. [tex]15\text{m}$ is $1\%$ of $1.5\text{km}[/tex]
which quadrant is (8, -1) in (A) | (B) || (C) ||| (D) ||||
Answers
this would be the 4th quadrant.
the answer is D
see picture:
2x+5y=-6 , wht is the x intercept, what is the y intercept
Answers
The x-intercept is (-3,0) and the y-intercept is (0,-6/5).
Explanation:The x-intercept is the point where the line crosses the x-axis. To find the x-intercept, we set y=0 and solve for x. In the equation 2x+5y=-6, we substitute 0 for y and solve for x:
2x + 5(0) = -6
2x = -6
x = -3
So, the x-intercept is the point (-3,0).
The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we set x=0 and solve for y. In the equation 2x+5y=-6, we substitute 0 for x and solve for y:
2(0) + 5y = -6
5y = -6
y = -6/5
So, the y-intercept is the point (0,-6/5).