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Klio2033 [76]
3 years ago
10

Pls help I will give BRAINLIEST ​

Mathematics
2 answers:
Elena L [17]3 years ago
8 0

Answer: M<2=38 m<3=142 m<4=38

Step-by-step explanation:

142+142+38+38=360-Both side

142+38=180- one side

180-142=38

Veseljchak [2.6K]3 years ago
5 0

Answers:

  • angle 2 = 38 degrees
  • angle 3 = 142 degrees
  • angle 4 = 38 degrees

========================================================

Explanation:

Angle 1 is given to be 142 degrees. Angle 3 is equal to this measure since vertical angles are congruent. Vertical angles are angles that form when you have an X shape like this. They are opposite angles.

Angles 2 and 4 are the other pair of congruent vertical angles. This means angle 2 = angle 4.

Note how angle 1 and angle 2 form a straight line. These two angles add to 180.

(angle1) + (angle2) = 180

(142) + (angle2) = 180

angle2 = 180-142

angle2 = 38 degrees

angle 4 is also 38 degrees since angles 2 and 4 are a congruent vertical angle pairing.

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What is Permutations and Combinations?
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Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

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2 years ago
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