Answers:
faces = n+2edges = 3nvertices = 2n===========================================================
Explanation:
Think of a hexagonal room with n = 6 walls, i.e. the floor is a hexagon with n = 6 sides. The floor and ceiling are parallel to each other, and congruent hexagons. That's 2 faces so far. Then we have another 6 faces to account for the walls. This gives 2+6 = 8 faces of a hexagonal prism.
In more general terms, a prism with a base of n sides will have 2 parallel and congruent base faces, and n walls or lateral faces. This gives n+2 total faces.
------------------------
Let's go back to the hexagonal prism. The floor has 6 sides to it, and so does the ceiling. We have 6+6 = 12 edges so far. Then we have another 6 edges where each of the rectangular walls meet up. That gives 12+6 = 18 edges total of this hexagonal prism room.
For any more general case, each base has n sides. That gives 2n sides so far for just the bases. Then add on another n for the lateral edges and we get 3n total edges.
--------------------------
Once again lets revisit the room with the hexagonal floor and ceiling. The floor has 6 vertices and the ceiling has the same vertex count. Therefore, this prism has 6+6 = 12 vertices.
For the general case, each base has n vertices. There are 2 such identical bases giving 2n vertices total.
---------------------------
One way to check the answer:
We could use Euler's Polyhedron Formula which is
F+V-E = 2
where,
F = number of facesV = number of verticesE = number of edgesFor the hexagonal prism we found
F = 8V = 12E = 18Then notice how
F+V-E = 2
8+12-18 = 2
20-18 = 2
2 = 2
This confirms the formula works for a hexagonal prism.
Now let's check it for the more general case
We found earlier that,
F = n+2V = 2nE = 3nSo,
F+V-E = 2
n+2+2n-3n = 2
3n-3n+2 = 2
0n+2 = 2
0+2 = 2
2 = 2
This helps confirm the answer for any prism with the base of n sides.
write y=x^2-6x+17 in vertex form. step by step
Step-by-step explanation:
the general vertex form is
y = a(x - h)² + k
with (h, k) being the vertex.
after doing all the multiplications we get
y = a(x² - 2hx + h²) + k = ax² - 2ahx + ah² + k
our original equation is
y = x² - 6x + 17
and now we simply compare the cording parts :
ax² = x²
a = 1
-2ahx = -2hx = -6x
-2h = -6
h = -6/-2 = 3
ah² + k = 17
3² + k = 17
9 + k = 17
k = 8
so the vertex form is
y = (x - 3)² + 8
Avery just got hired for a new job and will make $55,000 in her first year. avery was
told that she can expect to get raises of $1,500 every year going forward. how much
money in salary would avery make in her 18th year working at this job?
Avery's salary after 18 years will be equal to $82000.
What is the salary?The amount of money paid by any company to their employees on monthly basis is called salary.
Given that:-
Avery just got hired for a new job and will make $55,000 in her first yearAvery was told that she can expect to get raises of $1,500 every year going forward.The amount of salary taken by Avery in her 18th year will be:-
Per year incrememnt = $1500
So total increment in 18 years will be = 1500 x 18 = $27000
Total salary in 18th year will be = 55000 + 27000 = $82000
Therefore Avery's salary after 18 years will be equal to $82000.
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Here are some of the numbers that were picked out of the bag at bingo evening:
20 32 95 16 18 31 24 17
36. Which of these numbers is a square number?
37-38. Which of these numbers are prime numbers?
A random sample of students at North High School were polled on whether they prefer a 15-minute break between classes in the morning or in the afternoon. The results are shown in the frequency table.
A 4-column table with 4 rows. The first column has no label with entries 10th, 11th, 12th, total. The second column is labeled morning with entries 21, 16, 19, 56. The third column is labeled afternoon with entries 17, 25, 20, 62. The fourth column is labeled total with entries 38, 41, 39, 118.
What is the joint relative frequency for 11th graders who want the break in the afternoon? Round to the nearest percent.
21%
25%
40%
61%
Answer:
21
Step-by-step explanation:
Answer: A. 21%
No equation
Dan had $34 to spend at the fair if the admission to the fair is $10 and the rides cost $1.50 each, what is the greatest number of rides dan can go on. write an inequality that represents dan's situation
Answer:
Equation: 1.50x + 10 [tex]\leq[/tex] 34
Amount of rides Dan can go on: 16 rides
Step-by-step explanation:
We can represent this situation using this equation:
1.50x + 10 [tex]\leq[/tex] 34
The $10 Dan has to pay as admission is the fixed number because it doesn't vary and always remains the same, so no x goes next to 10.
Each ride costs $1.50 so this is the variable number as it changes with how many rides Dan goes on, therefore an x will go next to 1.50 to represent the amount of rides Dan goes on.
Lastly, Dan has $34 to spare, so the amount spent has to be less than or equal 34.
Solve the equation for x to find the greatest amount of rides Dan can go on:
1.50x + 10 [tex]\leq[/tex] 34 Subtract 10 from 34
1.50x [tex]\leq[/tex] 24 Divide 24 by 1.50
x [tex]\leq[/tex] 16
So, Dan has enough money to go on 16 rides or less.
Let's check this answer:
1.50(16) + 10 [tex]\leq[/tex] 34 Multiply 1.50 by 16
24 + 10 [tex]\leq[/tex] 34 Add 24 and 10
34 [tex]\leq[/tex] 34
Hope this helps! Good luck and if you have any questions let me know in the comments!
There are 34 students and five teachers going on a trip if each ticket costs $9.50 how much money do they need to raise
Which inequality is equivalent to −x<12?
Answer:
bottom left
Step-by-step explanation:
when divideing/mult by neg number, sign flips.
The sun came out and the temperature quickly rose 18 degrees. the a thunderstorm hits and the temperature drops 6 degrees. the sun comes back out the temperature raises 12 degrees. the temperature is now 94 degrees. what was the starting temperature?
By solving a linear equation we will see that the initial temperature was 66 degrees.
What was the initial temperature?
Let's define T as the initial temperature.
First, it increases by 18 F, then it decreases 6 F, and finally, it increases another 12 F, such that the end temperature is 94F.
Then we can write:
T + 18F - 6F + 12F = 94F
Now we can solve that linear equation to find T.
T = 94F - 18F + 6F - 12 F = 66 F
In this way, we conclude that the initial temperature was 66 degrees.
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Find the equation of a line that passes through point (2,4) and has a gradient of 3
Answer:
y=3x-2
Step-by-step explanation:
y-y0=m(x-x0)
y-4=3x-6
y=3x-2
[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Find the equation of a line that passes through (2,4) and has a gradient of 3.
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
First, let's take a look at our provided information.
| Provided information:-
Point (2,4)Gradient 3What we need to find:-the line's equationHow to find it using our provided information (gradient & point)? write the equation of the line in point-slope form
point-slope form:-[tex]\sf{y-y_1=m(x-x_1)}[/tex]how to solve:-Replace y₁ with 4Replace m with 3 (m is the gradient)Replace x₁ with 2therefore,[tex]\sf{y-4=3(x-2)}[/tex]
[tex]\bigstar[/tex] On simplification,
[tex]\sf{y-4=3x-6}[/tex][tex]\bigstar[/tex] On further simplification,
[tex]\sf{y=3x-6+4}[/tex]Which results in:-
[tex]\sf{y=3x-2}[/tex]Good luck with your studies.[tex]\rule{300}{1}[/tex]
Question 6
Points 1
Anne measured the volume of an object and recorded it as 46 cubic cm which
was 15% high from the actual volume. Find the actual volume.
Answer:
Actual volume = 40 cm^3.
Step-by-step explanation:
15% = 0.15 as a decimal fraction.
Let the actual volume be x cm^3, then we have the equation:
x + 0.15x = 46
1.15x = 46
x = 46 / 1.15
= 40 cm^3.
A pyramid has a height of 8 inches and a volume of 120 cubic inches. Determine 2
possibie shapes, with dimensions, for the base.
Answer:
1. 9 * 5 in.
2. 3 * 15 in.
Step-by-step explanation:
Volume = 1/3 * area of the base * height
120 = 1/3 * A * 8
So A = 120 / (8/3)
= 120 * 3/8
= 45 in^2.
So the dimensions of the base could be 9 * 5 in
or 3 * 15 in.
The possible shapes of the base are a square and a rectangular base.
What is a pyramid?The volume of a pyramid depends upon the type of pyramid’s base, whether it is a triangle, square or rectangle. A pyramid is a polyhedron figure which has only one base. The base of the pyramid is a poly sided figure.
Given here: A pyramid has a height of 8 inches and a volume of 120 cubic inches. Then we have volume of the pyramid as
120=l×b×8
l×b = 15
Therefore possible dimensions can be 7.5 &7.5 (Square base ) and 5×3 (rectangular base)
Hence, The possible shapes of the base are a square and a rectangular base.
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Compute a value for x that satisfies the equation below.
-x + 5 = 1
A. x=4
B. x=-1
C. x = 0
D. X= 4
Step-by-step explanation:
-4+5
=1
therefore the answer is A.
Answer:
D) x=4
Step-by-step explanation:
-x+5=1
-x=1-5
-x=-4
x=4
Grade 8 Mathematics level 3
The value of x in the given equation [ √( 1 + (25/144) ) = 1 + (x/12) ] is 5.
What is an Equation?
An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.
Given that;
√( 1 + (25/144) ) = 1 + (x/12)Find the value of x.First, we square both sides
√( 1 + (25/144) ) = 1 + (x/12)
(√( 1 + (25/144) ))² = (1 + (x/12))²
1 + (25/144) = 1 + ( x²/144)
Collect like terms
1 - 1 + (25/144) = ( x²/144)
25/144 = x²/144
We cross multiply
25 × 144 = x² × 144
Multiply each sides by 1/144
x² = 25
x = √25
x = 5
Therefore, the value of x in the given equation [ √( 1 + (25/144) ) = 1 + (x/12) ] is 5.
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Solve for x, y and z. Round your answers to the nearest tenth.
Answer:
Step-by-step explanation:
A linear function is shown below. Choose the two points that are on the graph of the inverse of this function.
A- (-1, 4)
B (2 , -6)
C ( 2, -2)
D ( 1, 0)
E ( 0 , -1 )
F ( -4 , 3)
The points (2, -2) and (0, -1) lies on the inverse of the function y = (-x -2)/2 if the function is y = -2x - 2 option (C) and (E) are correct.
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 every value in the domain is related to exactly one value in the range.
In the graph, a linear equation is represented.
We can find the function of linear equation from the two points:
(-1, 0) and (0, -2)
x/-1 + y/-2 = 1
2x + y = -2
y = -2x - 2 ..(1)
From the equation, first take subject as x and find the value of x
2x = -y -2
x = (-y -2)/2
Replacing x→y and y →x
y = (-x -2)/2
The inverse of a function:
y = (-x -2)/2
Points (2, -2) and (0, -1) lies on the inverse of the function(refer to attached picture)
Thus, the points (2, -2) and (0, -1) lies on the inverse of the function y = (-x -2)/2 if the function is y = -2x - 2 option (C) and (E) are correct.
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In the diagram, the radius is 7 and tangent AB has length of 24. Determine the length of OA rounded to the nearest whole number
Given the radius r and the tangent line AB, the length of the line OA is 24 units
How to determine the length OA?The radius r and the tangent line AB meet at a right angle.
By Pythagoras theorem, we have:
AB² = OA² + r²
So, we have:
24² = OA² + 7²
Rewrite as:
OA² = 24² - 7²
Evaluate
OA² = 527
Take the square root of both sides
OA = 23
Hence, the length of OA is 24 units
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This is part of Ivan's homework. A line segment, AB, goes from the point A(4, 7) to the point B(9, 3). AB is translated 3 squares left and 2 squares down. The image of AB is AB. Work out the coordinates of A' and B. Solution A' is at (7, 5). B' is at (12, 1). Ivan has worked out the coordinates of A' and B' incorrectly.
Explain the mistake that he has made.
Ivan mixed up left and right.
He mistakenly added 3 to the x coordinate to shift the points 3 units right, when instead he should have subtracted 3 from the x coordinate to go 3 units left.
Luckily, Ivan correctly shifted the points 2 units down.
The coordinates of A' and B' should be (1,5) and (6,1) respectively.
Refer to the diagram below.
What is the value of x when [tex](f°g)(x)=-8[/tex]
According to the table,
f(x) = -8 ⇒ x = -4
and according to the definition of g(x),
g(x) = -4 ⇒ x = 3
Then
(f o g)(x) = f(g(x)) = -8 ⇒ g(x) = -4 ⇒ x = 3
The expression below represents the perimeter, in feet, of Manual’s garden. 15 + 2x + 7 + 15 + 2x + 7 Use exactly two terms to write an equivalent expression to represent the perimeter, in feet, of Manual’s garden. The area, measured in square feet, of Manual’s garden is found by calculating 15(2x + 7). Manual incorrectly says the area can also be found using the expression 30x + 7. Describe the error in Manual’s expression. Also, find the difference, in square feet, between the actual area of Manual’s garden and the area found using his expression as a part of your explanation. Manual’s friend Sasha designs a square garden. Each side measures 3x + 5 in length. The perimeter of Sasha’s garden is how much larger than the perimeter of Manual’s garden?
Step-by-step explanation:
just keep on adding all of those up
are the breadth of your books perpendicular to their lengths
The breadth of your books are perpendicular to the length because they meet at right angles.
How to know perpendicular lines?
The shape of a book is a rectangle. A rectangle has four enclosure. This means they are formed by 4 lines.
The opposite sides are equal in length.
The sides of the book has a pair of breadth and a pair of length.
The breadth and length are straight lines.
When this straight line meets, it forms a right angle(90 degrees). This means the breadth and the length are perpendicular to each other.
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Ruth’s credit card has an apr of 10.91%, and it computes finance charges using the previous balance method on a 30-day billing cycle. during the april billing cycle, she made a $45.17 payment on april 10th and a $88.34 purchase on april 17th. her total at the start of may was $847.64. what was her balance at the beginning of april? a. $890.91 b. $797.22 c. $796.87 d. $804.47
Based on the balance at the start of May and the purchases and payments made by Ruth, the balance at the beginning of April was b. $797.22.
What was the beginning balance in April?First find the monthly rate:
= 10.91% / 12
= 0.909%
The beginning balance is x:
May balance = (Beginning balance x (1 + monthy rate) + Purchases - Payments
847.64 = x × 1.00909 + 88.34 - 45.17
1.00909x = 847.64 - 88.34 + 45.17
x = $797.22
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Answer:
B on edge
Step-by-step explanation:
The area of a rectangle is 6x^2+8x+2. The length of the rectangle is 3x+1. What is the width?
Answer:
A=L*W
Step-by-step explanation:
6x²+8x+2=LX(3x+1)
2x+2
Two quantities are proportional if their ___ are equal.
A) numerator
B) denominators
C) cross products
Answer:
C) cross products
Step-by-step explanation:
Let's say you were solving [tex]\frac{1}{2}=\frac{x}{4}[/tex] for example. You would need to use cross products to simplify the problem. Here, the left side would be 1*4, and the right side would be 2*x, giving you [tex]4=2x[/tex], thus, leading to the solution [tex]x=2[/tex]. We can see clearly that the cross products would thus need to be equal to each other.
Help?????????????????
Answer:
please make the image less blurry
Step-by-step explanation:
can someone help me figure out how to solve this without a protractor or anything if possible? I have issues with focusing and i cant figure out the easiest way without a protractor; if it's even possible.
Answer:
C. Equilateral
Step-by-step explanation:
Every pair has equal angle
Answer:
A
Step-by-step explanation:
BECAUSE IT IS KIND OF ANGEL
Write the equation of a line perpendicular to y=-12x+2 going through (0,-1)
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]
Write the equation of a line perpendicular to y=-12x+2 going
through (0, -1)
[tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]
First, let's take a look at our provided information:-
A line [tex]\text{y=-12x+2}[/tex]A point (0, -1)The line [tex]\text{y=-12x+2}[/tex] is perpendicular to the line that goes through (0, -1)If two lines are perpendicular to each other, their slopes are opposite reciprocals of each other.
So we take the slope of the given line, which is -12, change its sign from minus to plus:-
[tex]\Large\textit{12}[/tex]
And now, We flip the number over:-
[tex]\Large\text{$\displaystyle\frac{1}{12}$}[/tex]
Now that we've found the slope of the line, let's find its equation.
The first step is to write it in point-slope form as follows:-
[tex]\longmapsto\sf{y-y_1=m(x-x_1)}[/tex]
Replace letters with numbers,
[tex]\longmapsto\sf{y-(-1)=\displaystyle\frac{1}{12}(x-0)}[/tex]
On simplification,
[tex]\longmapsto\sf{y+1=\displaystyle\frac{1}{12} (x-0)}[/tex]
On further simplification,
[tex]\longmapsto\sf{y+1=\displaystyle\frac{1}{12} x}[/tex]
Subtracting 1 on both sides,
[tex]\longmapsto\sf{y=\displaystyle\frac{1}{12} x-1}[/tex]
[tex]\Uparrow\texttt{Our equation in slope-intercept form}[/tex]
Good luck with your studies.#TogetherWeGoFar
[tex]\rule{300}{1}[/tex]
Evaluate 2(5a – 2) a=3
Please solve
Answer:
26
Step-by-step explanation:
a=3
2(5x3-2)
5x3=15
15-2=13
2x13=26
What is a name for the marked angle?
Answer: [tex]\angle BAD[/tex]
Reason:
The arc goes from ray AB to ray AD. The two rays join at angle A which is the vertex point. When naming an angle, always use the vertex point in the middle. The order of the other two letters does not matter.
We could name this angle as [tex]\angle BAD[/tex] or [tex]\angle DAB[/tex] to mean the same exact thing. All that matters is that "A" is in the middle.
Ignore point C, and ignore ray AC entirely.
Answer:
(b) ∠BAD
Step-by-step explanation:
An angle can be named by the names of three points. The first point is on one of the rays that form the angle; the second point is the vertex; the third point is on the other ray.
Apparently the "marked" angle is identified by the arc extending from ray AB to ray AD. Point A is the vertex of the angle, so one possible name for it is ...
∠BAD
It can also be called
∠DAB
cuanto es: −2(−5n+6)+5(2−7n)
Answer:
here is the required answer hope it help u
Step-by-step explanation:
−2(−5n+6)+5(2−7n)
10n-12+10-35n
-25n-2
MATHHH HELPPPPP I NEED TO FINISH THIS BUT IM STUCK
Answer:
10 I think but not sure. but It has to be an Evan number
