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Alona [7]
3 years ago
5

lng rordoin a party contextat the Vine House HotelYour House Hotelparty $20 $750 Chargesfor Sarah per 30 ow thperson pluspeoplet

hat there for the will be each personcost will 60 extra be people at the party.

Mathematics
1 answer:
S_A_V [24]3 years ago
3 0

So in this problem we can see that there will be 60 people at the party. Following the conditions for this event that state the following: $750 for up to 30 people and every extra person pays $20. To show that the cost will be $1350 in total we simply do this:



For 30 people we have $750 dollars. Now every other person after pays only $20. That means that another the other 30 people will pay in total only $600.



If we add them we get: $750 + $600 = 1350. This shows that the cost will be $1350.

<span>
I hope it helps, Regards.</span>

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How many solutions does the system of equations shown below have?
rjkz [21]

Answer:

one solution with a y value of 5

Step-by-step explanation:

/| x+y-4 = 0| x-y-6 = 0

We try to solve the equation: x+y-4 = 0

x+y-4 = 0 // - x-4

y = -(x-4)

y = 4-x

We insert the solution into one of the initial equations of our system of equations

We get a system of equations:

/| x+x-6-4 = 0| y = 4-x

2*x-10 = 0 // + 10

2*x = 10 // : 2

x = 10/2

x = 5

We insert the solution into one of the initial equations of our system of equations

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y = 4-5

y = -1

We get a system of equations:

/| y = -1| x = 5

4 0
3 years ago
4x + 3y = 6<br> 3x + 5y = -1<br> Solve the simultaneous equations.<br><br> y= <br> z=
Kisachek [45]

Answer:

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12x+20y= -4

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3 years ago
Can someone please help me with this problem?
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5 0
3 years ago
Read 2 more answers
Guys help me this is hard​
Leokris [45]

Answer:

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Step-by-step explanation:

5 0
3 years ago
What is all of the surface area and volume of this Castle? Find the surface area and volume of all the figures below, then out o
motikmotik

Answer:

Step-by-step explanation:

There are a few formulas that are useful for this:

  • lateral area of a pyramid or cone: LA = 1/2·Ph, where P is the perimeter and h is the slant height
  • lateral area of a cylinder: LA = π·dh, where d is the diameter and h is the height
  • area of a rectangle: A = lw, where l is the length and w is the width
  • volume of a cone or pyramid: V = 1/3·Bh, where B is the area of the base and h is the height
  • volume of a cylinder or prism: V = Bh, where B is the area of the base and h is the height

You will notice that for lateral area purposes, a pyramid or cone is equivalent to a prism or cylinder of height equal to half the slant height. And for volume purposes, the volume of a pyramid or cone is equal to the volume of a prism or cylinder with the same base area and 1/3 the height.

Since the measurements are given in cm, we will use cm for linear dimensions, cm^2 for area, and cm^3 for volume.

___

The heights of the cones at the top of the towers can be found from the Pythagorean theorem.

  (slant height)^2 = (height)^2 + (radius)^2

  height = √((slant height)^2 - (radius)^2) = √(10^2 -5^2) = √75 = 5√3

The heights of the pyramids can be found the same way.

  height = √(13^2 -2^2) = √165

___

<u>Area</u>

The total area of the castle will be ...

  total castle area = castle lateral area + castle base area

These pieces of the total area are made up of sums of their own:

  castle lateral area = cone lateral area + pyramid lateral area + cylinder lateral area + cutout prism lateral area

and ...

  castle base area = cylinder base area + cutout prism base area

So, the pieces of area we need to find are ...

  • cone lateral area (2 identical cones)
  • pyramid lateral area (2 identical pyramids)
  • cylinder lateral area (3 cylinders, of which 2 are the same)
  • cutout prism lateral area
  • cylinder base area (3 cylinders of which 2 are the same)
  • cutout prism base area

Here we go ...

Based on the above discussion, we can add 1/2 the slant height of the cone to the height of the cylinder and figure the lateral area of both at once:

  area of one cone and cylinder = π·10·(18 +10/2) = 230π

  area of cylinder with no cone = top area + lateral area = π·1^2 +π·2·16 = 33π

  area of one pyramid = 4·4·(13/2) = 52

The cutout prism outside face area is equivalent to the product of its base perimeter and its height, less the area of the rectangular cutouts at the top of the front and back, plus the area of the inside faces (both vertical and horizontal).

  outside face area = 2((23+4)·11 -3·(23-8)) = 2(297 -45) = 504

  inside face area = (3 +(23-8) +3)·4 = 84

So the lateral area of the castle is ...

  castle lateral area = 2(230π + 52) +33π + 504 + 84 = 493π +692

  ≈ 2240.805 . . . . cm^2

The castle base area is the area of the 23×4 rectangle plus the areas of the three cylinder bases:

  cylinder base area = 2(π·5^2) + π·1^2 = 51π

  prism base area = 23·4 = 92

  castle base area = 51π + 92 ≈ 252.221 . . . . cm^2

Total castle area = (2240.805 +252.221) cm^2 ≈ 2493.0 cm^2

___

<u>Volume</u>

The total castle volume will be ...

  total castle volume = castle cylinder volume + castle cone volume + castle pyramid volume + cutout prism volume

As we discussed above, we can combine the cone and cylinder volumes by using 1/3 the height of the cone.

  volume of one castle cylinder and cone = π(5^2)(18 + (5√3)/3)

  = 450π +125π/√3 ≈ 1640.442 . . . . cm^3

 volume of flat-top cylinder = π·1^2·16 = 16π ≈ 50.265 . . . . cm^3

The volume of one pyramid is ...

  (1/2)4^2·√165 = 8√165 ≈ 102.762 . . . . cm^3

The volume of the entire (non-cut-out) castle prism is the product of its base area and height:

  non-cutout prism volume = (23·4)·11 = 1012 . . . . cm^3

The volume of the cutout is similarly the product of its dimensions:

  cutout volume = (23 -8)·4·3 = 180 . . . . cm^3

so, the volume of the cutout prism is ...

  cutout prism volume = non-cutout prism volume - cutout volume

  = 1012 -180 = 832 . . . .  cm^3

Then the total castle volume is ...

  total castle volume = 2·(volume of one cylinder and cone) + (volume of flat-top cylinder) +2·(volume of one pyramid) +(cutout prism volume)

  = 2(1640.442) + 50.265 +2(102.762) +832 ≈ 4368.7 . . . . cm^3

4 0
3 years ago
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