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3 years ago

Write the equation of the line that passes through the point (2, 4) and has a slope of 3

Mathematics

2 answers:

Dmitry_Shevchenko [17]3 years ago

4 0

Answer:

Step-by-step explanation:

y - 4 = 3(x - 2)

y - 4 = 3x - 6

y = 3x - 2

standard form

-3x + y = -2

lidiya [134]3 years ago

3 0

Answer:

this will be step by step so bear with me

Step-by-step explanation:

first you must plug it into the point slope form

y-y1=m(x-x1)

plug in

y-y1=3(x-2)

distribute the three into the ()

y-4=3x-6

now add 4 to both sides

y=3x-2

now standard form

Ax+By=C

y=3x-2

add 2 to both sides

y+2=3x

subtract y from both sides

2=3x-y

flip around the equation

3x-y=2

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Please help me<br> 2/3÷(−5/6)

agasfer [191]

I hope this helps you

2/3÷(-5/6)

2/3× -6/5

2×-6/3×5

-12/15

-4/5

3 0

3 years ago

Read 2 more answers

8 2– 2 5 ) ÷ (24 ÷ 6) + 3 2

Ray Of Light [21]

Answer:

46.25

Step-by-step explanation:

82-25=57

24/6=4

57/4=14.25

14.25+32=46.25

7 0

3 years ago

There are 42 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time

harkovskaia [24]

Answer:

A) 0.99413

B) 0.00022

Step-by-step explanation:

A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:

Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes

Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:

μ = n*μ_s ample = 42 × 5 = 210 minutes

While the standard deviation for the population would be:

σ = √nσ_sample = √(42 × 6) = 15.8745 minutes

To find the z-score, we will use the formula;

z = (x - μ)/σ

Thus;

z = (250 - 210)/15.8745

z = 2.52

From the z-distribution table attached, we have;

P(Z < 2.52) ≈ 0.99413

B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.

Thus, total time is now 250 + 10 = 260 minutes

Similar to the z-formula in A above, we have;

z = (260 - 210)/15.8745

z = 3.15

P(Z > 3.15) = 0.00022

5 0

2 years ago

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

2 years ago

Jameson has 4300 in credit card debt with 14% interest that he wants to pay off in 24 months. He will need to make monthly payme

lakkis [162]

Answer:

Total cost of repayment $= 4955.04$

Net interest paid $= 655.04$

Step-by-step explanation:

Given

Amount taken on loan $= 4300$

Repayment plan

Monthly installment $=$ $206.46$

Yearly installment $= 206.46 * 12 = 2477.52$

Rate of interest per year $= 14$ %

Time Period for repaying the loan $= 2$ years

The total amount repaid by Jameson at the rate of $206.46$ per month for next $24$ months

$= 206.46 *24\\= 4955.04$

Net interest paid

$= 4955.04 - 4300\\= 655.04$

Total cost of repayment $= 4955.04$

Net interest paid $= 655.04$

8 0

2 years ago