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den301095 [7]
2 years ago
9

What are the coordinates of point G?

Mathematics
1 answer:
SSSSS [86.1K]2 years ago
5 0

Answer:

D. (4,9)

Step-by-step explanation:

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26. Define a relation ∼ ∼ on R 2 R2 by stating that ( a , b ) ∼ ( c , d ) (a,b)∼(c,d) if and only if a 2 + b 2 ≤ c 2 + d 2 . a2+
Tresset [83]

Answer:

~ is reflexive.

~ is asymmetric.

~ is transitive.

Step-by-step explanation:

~ is reflexive:

i.e., to prove $ \forall (a, b) \in \mathbb{R}^2 $, $ (a, b) R(a, b) $.

That is, every element in the domain is related to itself.

The given relation is $\sim: (a,b) \sim (c, d) \iff a^2 + b^2 \leq c^2 + d^2$

Reflexive:

$ (a, b) \sim (a, b) $ since $ a^2 + b^2 = a^2 + b^2 $

This is true for any pair of numbers in $ \mathbb{R}^2 $. So, $ \sim $ is reflexive.

Symmetry:

$ \sim $ is symmetry iff whenever $ (a, b) \sim (c, d) $ then $  (c, d) \sim (a, b) $.

Consider the following counter - example.

Let (a, b) = (2, 3) and (c, d) = (6, 3)

$ a^2 + b^2 = 2^2 + 3^2 = 4 + 9 = 13 $

$ c^2 + d^2 = 6^2 + 3^2 = 36 + 9 = 42 $

Hence, $ (a, b) \sim (c, d) $ since $ a^2 + b^2 \leq c^2 + d^2 $

Note that $ c^2 + d^2 \nleq a^2 + b^2 $

Hence, the given relation is not symmetric.

Transitive:

$ \sim $ is transitive iff whenever $ (a, b) \sim (c, d) \hspace{2mm} \& \hspace{2mm} (c, d) \sim (e, f) $ then $ (a, b) \sim (e, f) $

To prove transitivity let us assume $ (a, b) \sim (c, d) $ and $ (c, d) \sim (e, f) $.

We have to show $ (a, b) \sim (e, f) $

Since $ (a, b) \sim (c, d) $ we have: $ a^2 + b^2 \leq c^2 + d^2 $

Since $ (c, d) \sim (e, f) $ we have: $ c^2 + d^2 \leq e^2 + f^2 $

Combining both the inequalities we get:

$ a^2 + b^2 \leq c^2 + d^2 \leq e^2 + f^2 $

Therefore, we get:  $ a^2 + b^2 \leq e^2 + f^2 $

Therefore, $ \sim $ is transitive.

Hence, proved.

3 0
3 years ago
Solve for p. will give brainiest
erik [133]
2(p+1)=16
2p+2=16
2p= 16-2
2p= 14
p= 14 ÷2
p= 7
7 0
3 years ago
Read 2 more answers
Snowflake the snowman wants to buy new scarves if each scarf cost $4.27 how much did snowflake spend if he buys 5
Korvikt [17]

Answer:

21.35

Step-by-step explanation:

4.27 * 5 i hope this is one of your answers

4 0
3 years ago
Write two expressions where the solution is 19
marysya [2.9K]
1) 
12+ (26-?) = 19 Find The Missing Value.

2)
x - 5 = 14 What Is The Value Of x ?

Hope This Helps xox
7 0
3 years ago
Read 2 more answers
In parallelogram MNPQ, side MN is seven inches longer than twice the length of side NP. If the perimeter of MNPQ is 68 inches, t
Svetlanka [38]

Answer: NP = 9 inches

Step-by-step explanation:

In a parallelogram, the opposite sides are equal.

If the length of the longer side is MN, it means that the length of the two opposite longer sides is 2MN.

If the length of the shorter side is NP, it means that the length of the two opposite shorter sides is 2NP.

The perimeter is 2MN + 2NP

If the perimeter of MNPQ is 68 inches, it means that

2MN + 2NP = 68- - - - - - - - - - - -1

In parallelogram MNPQ, side MN is seven inches longer than twice the length of side NP. It means that

MN = 2NP + 7- - - - - - - - - - -2

Substituting equation 2 into equation 1, it becomes

2(2NP + 7) + 2NP = 68

4NP + 14 + 2NP = 68

4NP + 2NP = 68 - 14

6NP = 54

NP = 54/6

NP = 9 inches

6 0
3 years ago
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