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3 years ago

What is the greatest common factor of 4k, 18k^4, and 12

Mathematics

1 answer:

Olin [163]3 years ago

7 0

The greatest common factor is 4 because it cannot be factored more than 4

hope this helps! :) -from peachimin

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How can a line plot help you find an average with data given in fractions?

JulsSmile [24]

Because it shows you were everything is placed and you can see were the average is

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4 years ago

Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Ar

Veseljchak [2.6K]

Answer:

The given relation R is equivalence relation.

Step-by-step explanation:

Given that:

$((a, b), (c, d))\in R$

Where $R$ is the relation on the set of ordered pairs of positive integers.

To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.

1. First of all, let us check reflexive property:

Reflexive property means:

$\forall a \in A \Rightarrow (a,a) \in R$

Here we need to prove:

$\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R$

As per the given relation:

$((a,b), (a,b) ) \Rightarrow ab =ab$ which is true.

$\therefore$ R is reflexive.

2. Now, let us check symmetric property:

Symmetric property means:

$\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R$

Here we need to prove:

$\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R$

As per the given relation:

$((a,b),(c,d)) \in R$ means $ad = bc$

$((c,d),(a,b)) \in R$ means $cb = da\ or\ ad =bc$

Hence true.

$\therefore$ R is symmetric.

3. R to be transitive, we need to prove:

$if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R$

$((a,b),(c,d)) \in R$ means $ad = cb$ .... (1)

$((c,d), (e,f)) \in R$ means $fc = ed$ ...... (2)

To prove:

To be $((a,b), (e,f)) \in R$ we need to prove: $fa = be$

Multiply (1) with (2):

$adcf = bcde\\\Rightarrow fa = be$

So, R is transitive as well.

Hence proved that R is an equivalence relation.

8 0

3 years ago

A population numbers 508 organisms initially and increases by 6.2% each year.

IceJOKER [234]

To find the population after t number of years, multiply the starting population by 1 plus the percent increase raised to the number of years.

The equation would be: P = 508(1.062)^t

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3 years ago

Mark sold 2 7/8 gallons of lemonade. Regan sold 2/3 as much as Mark. How much did Regan sold in gallons?

marusya05 [52]

Answer: 1.9166667

Step-by-step explanation:

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3 years ago

Read 2 more answers

What is the slope of y= 5+3x

Alina [70]

The slope for y=5+3x is 3

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3 years ago