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.
Greta is painting two different rectangular prisms. The prisms have the following dimensions.
Prism A:
Length: 1 foot
Width: 4 inches
Height: 8 inches
Prism B:
Length: 10 inches
Width: 2 inches
Height: 1.5 feet
Which prism has a greater surface area, and what is its surface area in square inches?
Answer:
prism B is greater
Step-by-step explanation:
prism A
lenght: 1×4=4
width: 4×8=32
height: 8×1=8
add them all up and multiply it by 2 = 4+32+8×2=52
prism B
lenght: 10×2=20
width: 2×1.5=3
height:1.5×10=15
add them all up and multiply it by 2= 20+3+15×2=76
Find the vertex. f(x)=2^2 - 8
Answer:
(0, -√2)
Step-by-step explanation:
Given :
f(x) = x² - 8Finding vertex :
Given by (h, k)h = -b/2a = 0k = -D/4aD = √0 - 4(1)(-8) = √32 = 4√2k = -4√2/4 = -√2Vertex is (0, -√2)Use the diagrams to determine which statements are true. Select all statements that are true.
Answer:
I don't see your questions.
Egypt. Africa. America
PLEASE HELP! URGENT! ASAP! WILL GIVE BRAINLEST!
Answer:
0.25π
Step-by-step explanation:
→ Expand the bracket
4 × cos²Ф = 2
→ Divide both sides by 2
cos²Ф = 0.5
→ Square root both sides
cos Ф = [tex]\frac{\sqrt{2} }{2}[/tex]
→ Inverse cosine [tex]\frac{\sqrt{2} }{2}[/tex]
cos⁻¹ ( [tex]\frac{\sqrt{2} }{2}[/tex] ) = 0.25π
Answer:
Answer:
0.25π
Step-by-step explanation:
→ Expand the bracket
4 × cos²Ф = 2
→ Divide both sides by 2
cos²Ф = 0.5
→ Square root both sides
cos Ф =
→ Inverse cosine
cos⁻¹ ( ) = 0.25π
Step-by-step explanation:
What is the perimeter of the triangle below?
48.0 units
14.7 units
16.7 units
24.0 units
HELP!!!!!!
This is the only thing i dont understand in my math class
Answer:
{1, 2, 3, 4}
Step-by-step explanation:
Concepts
The domain of a function is all the possible x-values for that function. In other words, it's all the x-coordinates listed in the graph.
Application
In this case, we have to list the domain of the given function. To do this, we have to first label the points, and then list their x-coordinates in increasing order.
Solution
Points:
(1, 4)(2, 3)(3, 2)(4, 1)X-Coordinates:
1, 2, 3, 4Domain:
{1, 2, 3, 4}I NEED HELP IN THIS PLSSS
Answer:
1. A
2. i think c not sure
Step-by-step explanation:
Determine each segment length in right triangle ABC
The length of BC= 7√2 and BD = 7.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given:
AD= 7, AC= 14
In Δ BDC
cos 45 = B/ H
1/√2 = 7/ BC
BC= 7√2
In Δ BDC
sin 45 = P/H
1/√2= BD / 7√2
BD = 7
Learn more about trigonometry here:
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Question 3
ceiling fan the blades of a ceiling fan have a length of 26 inches. the tips of the blades follow a circular path. how far does the tip of a
blade travel in 1/5 of a rotation? round to the nearest hundredth of an inch,
________inches
The distance the blades travel in 1/5 of a rotation is 32.67 in
Since the distance the blades of the ceiling fan rotate is the length of an arc, we find this length
What is the length of an arc?The length of an arc is given by
L = Ф/360° × 2πr where
Ф = angle of rotation and r = length of blades of fanSince
Ф = 1/5 of a rotation = 1/5 × 360° = 72° and r = 26 inThe distance the blades travelSo, substituting the values of the variables into the equation, we have
L = Ф/360° × 2πr
L = 72°/360° × 2π × 26 in
L = 1/5 × 52π in
L = 10.4π in
L = 32.67 in
So, the distance the blades travel in 1/5 of a rotation is 32.67 in
Learn more about length of an arc here:
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Is anyone free to help?
Answer:
-4 C (Negative 4 C)
Step-by-step explanation:
If its 20 C less in Moscow, then it must be 16-20 = - 4 C in Moscow.
Look up rules on subtracting large numbers from small numbers to understand how I got - 4.
please help me I will give brainliest
Answer:
D
Step-by-step explanation:
um well just based on what its asking for it wants a sentence that uses both.
A straight line whose equation is 3y-2x=-2 meets the x-axis at R determine the coordinates of R
Answer:
3y-2x=-2
The straight line meets the X-axis when y = 0
Hence, 3(0) - 2(x) = -2
2x = 2
x = 1
Therefore, the coordinates of R is (1,0)
Yolanda says she can use a sphere to model the surface area of the boulders on this beach. explain whether yolanda is correct. yolanda is . since the boulders have , the best shape to model the surface area is a .
Yolanda is correct since the boulders have a circular shape, the best shape to model the surface area of a sphere.
What is a sphere?
A sphere is a three dimensional object that has all the set of all points equidistant from a single point in space. An example of a sphere is a ball. The boulder in this question has a spherical shape.
Surface area of a sphere = 4πr²
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Answer:
Step-by-step explanation:
Yolanda is correct since the boulders have a circular shape, the best shape to model the surface area of a sphere.
What is a sphere?
A sphere is a three dimensional object that has all the set of all points equidistant from a single point in space. An example of a sphere is a ball. The boulder in this question has a spherical shape.
Surface area of a sphere = 4πr²
To learn more about the surface area of a sphere, please check: brainly.com/question/27267844
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Please help me! Im so confused. If you could explain, too that would be great!!! <3
Answer:
the base length is 8 units
Step-by-step explanation:
You can use pythagorean theorem to solve this
The perimeter of a rectangle is 22,411 inches. The width of the
rectangle is 260 inches. What is the length, in inches, of the rectangle?
Answer:
Step-by-step explanation:
P = perimeter of the rectangle; and w = width of the rectangle.Use the formula:
Length(L) = P/2 - wPlug In:
22,411 ÷ 2 - 260
Solve:
22,411 ÷ 2 = 11205.510945.5Answer is L = 10,945.5 inches
explain: perimeter is all 4 sides added together
We know one side is 260
we know the perimeter is 22,411
260 + 260 + L + L = 22,411
combine like terms
520 + 2L = 22,411
subtract 520 from both sides to isolate 2L
2L = 21,891
divide both sides by 2 to isolate L
L = 10,945.5 inches
A box with square base and a height of 8cm has a volume of 1 332 cm3. find the length of the side base
Answer:
12.9 cm
Explanation:
Volume of rectangular box = Length × Width × Height
Given following:
Height = 8 cmConsider one of the base side as xSolve for volume:
L × W × H = Vx × x × 8 = 1332x² = 1332/8x = √166.5 ≈ 12.9 cmPLEASE HELP!
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Answer:
For the circle with the diameter of 7cm, the area is about 38.48cm and the circumference is about 22cm
For the circle with the diameter of 5cm, the area is about 19.63cm and the circumference is about 15.7cm
Step-by-step explanation:
The formula to find the area of a circle is pi*r^2
The formula to find the circumference is 2*pi*r
r = radius, which can be determined simply by taking the diameter, and dividing it by 2.
Answer:
See below ~
Step-by-step explanation:
Circle 1 :
Area = πr² = 22/7 x (7/2)² = 11 x 7/2 = 77/2 = 37.5 cm²Circumference = 2πr = 2 x 22/7 x 7/2 = 2 x 11 = 22 cmCircle 2 :
Area = πr² = 22/7 x (5/2)² = 22/7 x 25/4 = 550/28 = 19.64 cm²Circumference = 2πr = 2 x 22/7 x 5/2 = 220/14 = 15.71 cmA loaf of bread and 4 scones cost £3.30. If the loaf costs 90 pence how much would one scone cost ? .
Answer:
Step-by-step explanation:
Givens
4 scones
1 loaf of bread
Total cost = 3.30
Equation
Let the loaf of bread = b
Let the scones = s
Cost = b + 4s
Solution
Substitute the givens into the equation
b + 4s = Cost
90 + 4s = 3.30 Subtract 90 from both sides
90-90 + 4s = 3.30-90 Combine
4s = 2.40 Divide by 4
4s/4 = 2.40/4
s = 0.6 of a pound
Answer: 1 scone = 60 pence.
what is the diffrence between -25 and -12
The volume of this rectangular prism is 51,615 cubic yards. What is the value of v? (will mark brainliest)
Answer:
v = 37 yards
Step-by-step explanation:
Volume of a rectangular prism = width × length × height
Given:
volume = 51,615 yd³width = vlength = 93 ydheight = 15 ydSubstituting the given values into the formula and solving for v:
⇒ 51615 = v × 93 × 15
⇒ 51615 = 1395 v
⇒ v = 51615 ÷ 1395
⇒ v = 37
Answer:
v = 37 yds
Step-by-step explanation:
Volume of a rectangular prism: length × width × height
V = L×W×H
v = 51,615 yd³l = 93 ydsw = v ydsh = 15 ydsSubstitute the values above and solve for v:
51,615 = 93 × v × 15
51,615 = 1395v
51,615/1395 = 1395v/1395
37 = v
Final answer: 37 yds
Hope this helps!
solve 3y= x+1 and 2y= x
Answer:
(2, 1 )
Step-by-step explanation:
3y = x + 1 → (1)
2y = x → (2)
substitute 2y = x into (1)
3y = 2y + 1 ( subtract 2y from both sides )
y = 1
substitute y = 1 into either of the 2 equations and solve for x
substituting into (2)
2(1) = x
2 = x
solution is (2, 1 )
Answer:
{y,x} = {-1,-2}
Step-by-step explanation:
2y = - 2
[2] y = - 1
// Plug this in for variable y in equation [1]
[1] 3•(-1) - x = -1
[1] - x = 2
// Solve equation [1] for the variable x
[1] x = - 2
// By now we know this much :
y = -1
x = -2
{y,x} = {-1,-2}
hope this helps
pls mark brainliest
I will mark brainliest!!!
What is the slope?
A. 3/2
B. 1/2
C. 3/4
D. 2/3
x² + y² = 34
=
y = x+2
Show your working.
Answer:
[tex]\left \{ {{y=5} \atop {x=3}} \right.[/tex] or [tex]\left \{ {{y=-3} \atop {x=-5}} \right.[/tex]
Step-by-step explanation:
Answer:
(- 5, - 3 ) , (3, 5 )
Step-by-step explanation:
x² + y² = 34 → (1)
y = x + 2 → (2)
substitute y = x + 2 into (1)
x² + (x + 2)² = 34
x² + x² + 4x + 4 = 34
2x² + 4x + 4 = 34 ( subtract 34 from both sides )
2x² + 4x - 30 = 0 ( divide through by 2 )
x² + 2x - 15 = 0 ← in standard form
(x + 5)(x - 3) = 0 ← in factored form
equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 3 = 0 ⇒ x = 3
substitute these values into (2) for corresponding values of y
x = - 5 : y = - 5 + 2 = - 3 ⇒ (- 5, - 3 )
x = 3 : y = 3 + 2 = 5 ⇒ (3, 5 )
What is the circumference of the following circle? Diameter=3 Radius=1.5
Answer: 3π in terms of pi or 9.42 if in π or pi= 3.14
Step-by-step explanation:
Please help!!!!!!!! Thank you sooo much!
Answer:
see explanation
Step-by-step explanation:
(a)
∠ XBC = 55° because it corresponds to ∠ AXY
(b)
since XB = XC then Δ XBC is isosceles with base angles congruent, that is
∠ XBC = ∠ XCB = 55°
the sum of the 3 angles in Δ XBC = 180° , then
∠ BXC + 55° + 55° = 180°
∠ XBC + 110° =180° ( subtract 110° from both sides )
∠ XBC = 70°
James is given the diagram below and asked to prove that ZD ZF. What
would be the missing step of the proof?
Given: DE = FE, and Eo forms the angle bisector of ZDEF.
Prove: ZD ZF
E
D
o
Reasons
Given
Statements
1. DEFE, EO forms the angle
bisctor of ZDEF
2.
3. EO EO
4. ADEO AFEO
5. ZD ZF
Definition of an angle bisector
Reflexive Property of Equality
SAS Congruency Theorem
Corresponding parts of congruent
triangles are congruent
O A. ZEDO ZEDO
O B. ZEDO: ZEFO
O C. ZDEO = ZFEO
O D. ZEOF ZEOD
Answer:
C, ∠DEO ≅ ∠FEO
Step-by-step explanation:
The bisector EO bisects the angle ∠DEF, an interior angle of ΔDEF.
This means the angle is divided into 2 equal angles.
⇒ ∠DEO ≅ ∠FEO
Help Find the unit rate.
4,928 rooms on 112 floors =
rooms per floor
4928 rooms / 112 floors
2464 rooms / 56 floors
---Really, all we are doing here is simplifying a fraction until we have a 1 in the denominator
44 rooms / 1 floor
Hope this helps!
Help please right now you will get thanks and brainlest and 25 points it's due at 9
Answer:
B.
Step-by-step explanation:
Answer:
See below ~
Step-by-step explanation:
Question 4
P(6) = Number of 6 rolled / Total rollsP(6) = 10/50P(6) = 1/5 = 0.2 = 20% [A, B, and E]Question 11
Part A
The complement of the event is all of the unlikely possibilitiesBasically everything other than rolling a 4[A, B, C, E, and F]Part B
P' (4) = 1 - P (4)P' (4) = 1 - 1/6P' (4) = 5/6
This is the question picture
Answer:
A = X
B=Z
C=Y
Step-by-step explanation:
As they are congruent, their corresponding angles are also congruent
Answer:
a)
angle a is congruent to angle x
angle b is congruent to angle z
angle c is congruent to angle y
b)
line ab is congruent to line xz
line ac is congruent to line xy
line bc is congruent to line zy
c)
triangle bca is congruent to triangle zyx
Find the surface area of the prism. Enter your answer in the box.
Answer:
Area of the prism = 2(lw + lh + wh)
l = length = 6 m
w = width = 3 m
h = height = 12 m
—
Area of the prism = 2(6*3 + 6*12 + 3*12) = 2(18 + 72 + 36) = 2(126) = 252 m²
—
Have a nice day!!