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Iteru [2.4K]
3 years ago
8

What is the corollary to the polygon angle sum theorem?

Mathematics
1 answer:
Lina20 [59]3 years ago
5 0
Theorem<span> 6.2 </span>POLYGON<span> EXTERIOR </span>ANGLES THEOREM<span> - The </span>sum<span> of the measures of the exterior </span>angles<span>, one from each vertex, of a CONVEX </span>polygon<span> is 360 degrees. The </span>Corollary<span> to </span>Theorem<span> 6.2 - the measure of each exterior </span>angle<span> of a regular n-gon</span>
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given examples of relations that have the following properties 1) relexive in some set A and symmetric but not transitive 2) equ
rodikova [14]

Answer: 1) R = {(a, a), (а,b), (b, a), (b, b), (с, с), (b, с), (с, b)}.

It is clearly not transitive since (a, b) ∈ R and (b, c) ∈ R whilst (a, c) ¢ R. On the other hand, it is reflexive since (x, x) ∈ R for all cases of x: x = a, x = b, and x = c. Likewise, it is symmetric since (а, b) ∈ R and (b, а) ∈ R and (b, с) ∈ R and (c, b) ∈ R.

2) Let S=Z and define R = {(x,y) |x and y have the same parity}

i.e., x and y are either both even or both odd.

The parity relation is an equivalence relation.

a. For any x ∈ Z, x has the same parity as itself, so (x,x) ∈ R.

b. If (x,y) ∈ R, x and y have the same parity, so (y,x) ∈ R.

c. If (x.y) ∈ R, and (y,z) ∈ R, then x and z have the same parity as y, so they have the same parity as each other (if y is odd, both x and z are odd; if y is even, both x and z are even), thus (x,z)∈ R.

3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial but not transitive, so the relation provided in (1) satisfies this condition.

Step-by-step explanation:

1) By definition,

a) R, a relation in a set X, is reflexive if and only if ∀x∈X, xRx ---> xRx.

That is, x works at the same place of x.

b) R is symmetric if and only if ∀x,y ∈ X, xRy ---> yRx

That is if x works at the same place y, then y works at the same place for x.

c) R is transitive if and only if ∀x,y,z ∈ X, xRy∧yRz ---> xRz

That is, if x works at the same place for y and y works at the same place for z, then x works at the same place for z.

2) An equivalence relation on a set S, is a relation on S which is reflexive, symmetric and transitive.

3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial and not transitive.

QED!

6 0
3 years ago
Which ordered pairs cause this relation not to be a function? why? {(0, 0.5), (0.5, 1), (3, 1), (1, 6), (3, 2)}?
frosja888 [35]

Answer:

  (3, 1), (3, 2)

Step-by-step explanation:

Pairs that have the same x-value are not allowed in a relation that is a function.

3 0
3 years ago
A quality control inspector tested 235 CDs and found 8 defective
antiseptic1488 [7]

Answer:

235 C D s =

8 =

Step-by-step explanation:

7 0
3 years ago
)A bicyclist rides 14 miles in 112 minutes. If she continues at this speed, how long will it take her to travel 35 miles?
gogolik [260]
280 minutes cause you have to elim
4 0
3 years ago
Help me please i’ll give brainliest the
Vladimir [108]

Answer:

y=-1/2x+-1

Step-by-step explanation:

try desmos with this equation.

y=mx+b

m=the slope which is -1/2. It goes down 1 it is negative because it is going down, and to the right 2.

b=y-intercept meaning the point which the line crosses the line y .-1

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