1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Svetllana [295]
3 years ago
11

Find the length of the missing side, given the information below. PLEASE HELP I NEED THIS

Mathematics
1 answer:
Advocard [28]3 years ago
3 0

Answer:

x = 2

UV = 9 ft

VW = 6 ft

WU = 5 ft

Step-by-step explanation:

The perimeter of a figure can be represented as the sum of lengths of all of its sides. In this case we can write:

P = UV + VW + WU

Now, we can substitute the values which we have:

20 = 4x + 1 + 8 - x + 2x + 1

We can combine like terms...

20 = 5x + 10

5x = 10

x = 2

Since UV is represented by 4x + 1, we can substitute in x to find its length.

UV = 4x + 1

UV = 4(2) + 1

UV = 6 + 1

UV = 9

We can do the same for the other two sides:

VW = 8 - x

VW = 8 - 2

VW = 6

WU = 2x + 1

WU = 2(2) + 1

WU = 4 + 1

WU = 5

You might be interested in
Which of the following equations uses the commutative property of addition to rewrite 1/3 + 2/5?
luda_lava [24]

The commutative property states that you can invert the order of the terms of a sum:

a+b=b+a

So, if you start with

\dfrac{1}{3}+\dfrac{2}{5}

Applying the commutative property you'll get

\dfrac{2}{5}+\dfrac{1}{3}

3 0
3 years ago
the kline family went on vacation last year and paid $199 a night for the hotel room. This year, the price has increased by 5% .
dangina [55]

Answer: $208.95

Step-by-step explanation: $199 x .05= 9.95 + $199= $208.95

8 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
Simplify 4+(9×2)÷(4-2)+1
kogti [31]

First we have to work out everything inside the parentheses (according to PEMDAS):

9 × 2 = 18

4 - 2 = 2

Now, we can rewrite the expression:

4 + 18 ÷ 2 + 1

According to PEMDAS, we should complete the division in the middle first:

18 ÷ 2 = 9

Now we can rewrite the expression again:

4 + 9 + 1

And now it's as simple as just adding the three numbers together:

4 + 9 + 1 = 14


Your final answer is 14. :)

3 0
3 years ago
Read 2 more answers
Which of these is NOT an Element of Art?
lesantik [10]

Answer:

i think line?

Step-by-step explanation:

im not sure but thatts my best geuss!

6 0
3 years ago
Other questions:
  • Critical thinking. Make a conjecture about the relationship between three consecutive whole numbers based on this relationship i
    13·1 answer
  • If the measure of Angle AXC=8x-7 and Angle AXB = 3x+10 find the measure of ANGLE AXC
    10·2 answers
  • -3(-x+4)=5+3(x+1) please help​
    7·2 answers
  • A line passes through the point and has a slope of -4/3 and (6, -6).
    5·1 answer
  • What is the area of the triangle below?
    5·2 answers
  • If I have a circle that is 12 in in diameter and it's cold and a half and then folded in half again what is the area of the resu
    7·1 answer
  • 3. In the equation below, k is a constant. If x = 9, what is the value of k?<br> Vk + 2 - x = 0
    10·1 answer
  • What is the answer to this math question!?
    9·2 answers
  • Function f is defined by the equation f(x) = x2 1. What is f(2) ?​
    10·2 answers
  • Pls help!!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!