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sergejj [24]
3 years ago
13

What is the value of x? Enter your answer as a decimal.

Mathematics
2 answers:
V125BC [204]3 years ago
8 0
<h3>Answer: 42.9</h3>

There are two triangles: triangle MAB and triangle MNP

The slanted sides on the right side of the triangles are MB and MP. They correspond to one another. So they form a ratio MB/MP. I have the smaller piece up top. So we'll have the smaller piece of MAB's other known side which is MA = 35.2 (subtract 67.22 and 32) and we'll divide MA over MN = 67.2 making the ratio MA/MN

Solve the proportion for x

MB/MP = MA/MN

x/81.9 = 35.2/67.2

67.2*x = 81.9*35.2 <<--- cross multiply

67.2*x = 2882.88

x = 2882.88/67.2 <<--- divide both sides by 67.2

x = 42.9

Pavlova-9 [17]3 years ago
4 0

Answer:

42.9

Step-by-step explanation:

Remark

When lines are parallel and they are cut by a transversal, their corresponding angles are equal.

  • <MAB = <MNP        Corresponding Angles are equal
  • <MBA = <MPN         Corresponding Angles are equal
  • <M = <M                   Reflexive Property: an angle equals itself
  • These Triangles are similar by AAA

Therefore Corresponding Sides of Similar Triangles are in a ratio

Equation

MA / MN = MB/MP

Givens

  • MA = 67.2 - 32 = 35.2
  • MN = 67.2        
  • MB = x
  • MP - 81.9

Solution

35.2/67.2 = x / 81.9        Cross Multiply

35.2 * 81.9 = 67.2 * x      Combine the left

2883 = 67.2 * x               Divide by 67.2

2883/67.2 = x

x = 42.9                           Answer

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b): R = {(0,0),(1,1),(2,0),(2,2),(2,3),(3,3)}

R is antisymmetric, because if the (a,b)∈R and if the (b, a) ∈ R, than a=b (since (2,0) ∈ R and (0,2) ∉ R; and (2,3) ∈ R and (3,2) ∉ R )

R is reflexive, because (a,a) ∈ R of every element a ∈ A.

R is transitive , because if the (a,b)∈R and if the ( b , c )∈R . then a = b or b = c ( since there are only two element not of the form ( a , a ) and that pair does not satisfy ( a,b ) ∈ R and ( b , a ) ∈ R ), which implies ( a , c ) = ( b , c ) ∈ R or ( a , c ) = ( a , b ) ∈ R.

R is a partial ordering, because R is reflexive, antisymmetric and transitive.

c): R =  {(0,0),(1,1),(1,2),(2,2),(3,1),(3,3)}

R is reflexive, because (a,a)∈R of every element a ∈ A.

R is antisymmetric, because if the ( a , b )∈R and if the ( b , a )∈R . then a = b ( since ( 1 , 2 )∈R and ( 2 , 1 ) ∉ R; ( 3 , 1 ) ∈ R and ( 1 , 3 ) ∉ R ).  

R is not transitive , because ( 3 , 1 ) ∈ R and ( 1 , 2 )∈R, while ( 3 , 2 ) ∈ R.

R is not a partial ordering. because R is not transitive .

d): R =  {(0,0),(1,1),(1,2),(1,3),(2,0),(2,2),(2,3), (3,0),(3,3)}

R is the reflexive, because ( a , a )∈R of every elements∈A.

R is the antisymmetric, because if the ( a , b )∈R and if the ( b , a )∈R, then a = b ( since ( 1 . 2 )∈R and ( 2 . 1 )∉R; similarly, all other elements not of the form (a,a) ).

R is not transitive, because ( 1 , 2 )∈R and ( 2 , 0 )∈R, while ( 1 . 0 )∉R.

R is not a partial ordering, because R is not transitive,

e):  R = { ( 0 , 0 ) , ( 0, 1 ) , ( 0 , 2 ) , ( 0 , 3 ) , ( 1 , 0 ) , ( 1 , 1 ) , ( 1 , 2 ) , ( 1 , 3 ) , ( 2 , 0 ) , ( 2 , 2 ) , ( 3 , 3 ) }

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R is not antisymmetric, because ( 1 , 0 )∈R and ( 0 , 1 )∈R while 0 is not equal to 1.

R is not transitive, because ( 2 , 0 )∈Rand ( 0 , 3 )∈R, while ( 2 , 3 )∉R .

R is not a partial ordering, because R is not the antisymmetric and not the transitive.

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