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charle [14.2K]
3 years ago
11

Find all numbers whose absolute value is 6.

Mathematics
1 answer:
Nana76 [90]3 years ago
5 0

Answer:

6 and -6

|6|=6

|-6|=6

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ME AYUDAN PORAVOR 1. Relaciona cada ecuación con su solución.
barxatty [35]

Answer:

a. 5 + x = -5 (Subtraction) 0.

b. -17 + x = 0 (Addition) 17.

c. 30 + x = 0 (Subtraction) -30.

d. x + (-27) = 0 (Addition) 27.

e. x + (-30) = 0 (Addition) 30.

Step-by-step explanation:

In this exercise, students are required to match each equation with its solution. (The corresponding operations must be presented at the end of this point

a. 5 + x = -5 (Subtraction) 0.

x = -5 - 5

x = 0

b. -17 + x = 0 (Addition) 17.

x = 0 + 17

x = 17

c. 30 + x = 0 (Subtraction) -30.

x = 0 - 30

x = -30

d. x + (-27) = 0 (Addition) 27.

x - 27 = 0

x = 0 + 27

x = 27

e. x + (-30) = 0 (Addition) 30.

x - 30 = 0

x = 0 + 30

x = 30

7 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
Kevin Durant is trying to break the single
finlep [7]

Answer: 41 more games.

Step-by-step explanation:

4030-2595 to find out how many points he needs to score.

1435

If he averages 35 per game lets divide 1435 by 35 to get the answer of 41.

6 0
2 years ago
Read 2 more answers
The diagram shows a triangle ABC where AB=AC , BC=AC, and ⦟BAC = 20 degree, find ⦟ADB​
Mariulka [41]

Answer:

hello something is wrong with the question. if ab= AC, and AC = BC, AB=BC, it'd make this an equilateral triangle and the degree wouldn't be 20 degrees

6 0
3 years ago
Please help!!! i'm having some trouble with this question
QveST [7]
STEP 1
Bandages: multiply number of total kits by number of bandages per kit

9 * 24= 216 bandages total


STEP 2
Antiseptic Wipes: multiply number of total kits by number of antiseptic wipes per kit

9 * 16= 144 antiseptic wipes total


STEP 3
find difference between steps 1 & 2
= 216 bandages - 144 antiseptic wipes
= 72 more bandages


ANSWER: She packed 72 more bandages than antiseptic wipes.

Hope this helps! :)
4 0
3 years ago
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