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anygoal [31]
3 years ago
13

a rectangle on a coordinate plane is translated 5 units up and 3 units to the left. which rule describes the translation?

Mathematics
2 answers:
andre [41]3 years ago
9 0
The correct answer is (x, y) → (x – 3, y + 5) 
Ymorist [56]3 years ago
5 0

The correct answer is c

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For x, y ∈ R we write x ∼ y if x − y is an integer. a) Show that ∼ is an equivalence relation on R. b) Show that the set [0, 1)
vodomira [7]

Answer:

A. It is an equivalence relation on R

B. In fact, the set [0,1) is a set of representatives

Step-by-step explanation:

A. The definition of an equivalence relation demands 3 things:

  • The relation being reflexive (∀a∈R, a∼a)
  • The relation being symmetric (∀a,b∈R, a∼b⇒b∼a)
  • The relation being transitive (∀a,b,c∈R, a∼b^b∼c⇒a∼c)

And the relation ∼ fills every condition.

∼ is Reflexive:

Let a ∈ R

it´s known that a-a=0 and because 0 is an integer

a∼a, ∀a ∈ R.

∼ is Reflexive by definition

∼ is Symmetric:

Let a,b ∈ R and suppose a∼b

a∼b ⇒ a-b=k, k ∈ Z

b-a=-k, -k ∈ Z

b∼a, ∀a,b ∈ R

∼ is Symmetric by definition

∼ is Transitive:

Let a,b,c ∈ R and suppose a∼b and b∼c

a-b=k and b-c=l, with k,l ∈ Z

(a-b)+(b-c)=k+l

a-c=k+l with k+l ∈ Z

a∼c, ∀a,b,c ∈ R

∼ is Transitive by definition

We´ve shown that ∼ is an equivalence relation on R.

B. Now we have to show that there´s a bijection from [0,1) to the set of all equivalence classes (C) in the relation ∼.

Let F: [0,1) ⇒ C a function that goes as follows: F(x)=[x] where [x] is the class of x.

Now we have to prove that this function F is injective (∀x,y∈[0,1), F(x)=F(y) ⇒ x=y) and surjective (∀b∈C, Exist x such that F(x)=b):

F is injective:

let x,y ∈ [0,1) and suppose F(x)=F(y)

[x]=[y]

x ∈ [y]

x-y=k, k ∈ Z

x=k+y

because x,y ∈ [0,1), then k must be 0. If it isn´t, then x ∉ [0,1) and then we would have a contradiction

x=y, ∀x,y ∈ [0,1)

F is injective by definition

F is surjective:

Let b ∈ R, let´s find x such as x ∈ [0,1) and F(x)=[b]

Let c=║b║, in other words the whole part of b (c ∈ Z)

Set r as b-c (let r be the decimal part of b)

r=b-c and r ∈ [0,1)

Let´s show that r∼b

r=b-c ⇒ c=b-r and because c ∈ Z

r∼b

[r]=[b]

F(r)=[b]

∼ is surjective

Then F maps [0,1) into C, i.e [0,1) is a set of representatives for the set of the equivalence classes.

4 0
3 years ago
The mean length of 7 childrens' index finger is 9.4cm. The mean length of 5 adults' index finger is 10.2cm. What is the mean len
Deffense [45]

Answer:

9.73  cm to 2 DP

Step-by-step explanation:

Total of the  lengths involved = 7*9.4 +  5*10.2

= 116.8 cm

So the mean of the 12 fingers

= 116.8/12

= 9.73  cm to 2 DP.

3 0
2 years ago
Read 2 more answers
Which set of lengths are not the side lengths of a right triangle? (A-28, 45, 53) (B-13, 84, 85) (C-36, 77, 85) (D-16, 61, 65) [
nikklg [1K]
Side lengths 16, 61, and 65 are not part of a right triangle.

A right triangle's sides should follow this formula, C being the largest number:

a^{2} + b ^{2} = c^{2}

16^{2} = 256

61^{2} = 3721

65^{2} = 4225

256 + 3721 = 3977

3977  \neq 4225
6 0
2 years ago
10. For a popular Broadway musical, the theater box office sold 356 tickets at $80 apiece, 275 tickets at $60 apiece, and 369 ti
V125BC [204]
I thank it is B you have to add all the tickets and times that by the the amount of money  
6 0
3 years ago
Two companies, A and B, package snack-size bags of cashews. Let X represent the weight of the packages from company A, and let Y
Vitek1552 [10]

The answer choice that correctly calculates and interprets the standard deviation of the sum, S = X + Y is D. Sigma Subscript s = 0.8; companies A and B can expect the total weight of packages to vary by approximately 0.8 ounces from the mean.

<h3>What does the standard deviation means?</h3>

A standard deviation means the all measure of how dispersed the data is in relation to the mean. It should be noted that low standard deviation means that the data are clustered around the mean, and the high standard deviation means that the data are more spread out.

In this case, the answer choice that correctly calculates and interprets the standard deviation of the sum, S = X + Y is the sigma Subscript s = 0.8; companies A and B can expect the total weight of packages to vary by approximately 0.8 ounces from the mean.

In conclusion, the correct option is D.

Learn more about standard deviation on:

brainly.com/question/12402189

#SPJ2

8 0
1 year ago
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