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4 years ago

Find the greates common factor of the following monomials:2r^4s^2 and 36r^4s^3

Mathematics

1 answer:

ki77a [65]4 years ago

6 0

The greatest common factor is 2 $r^{4} s^{2}$

This is because we start by taking the largest factor that goes into both coefficients. Since the first coefficient is 2, we have to try 2 and 1. Since 2 is larger and goes into 36 evenly, we use that.

Then we use the smallest number of each variable. There are 4 r's in both equations. So, that is the number that we take. There are 2 s's in the first term, so we take that number.

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(help)Name the intersection of the two planes in the image below.

serg [7]

Answer:

Step-by-step explanation:

The intersection of the 2 planes is along the line XZ

3 0

3 years ago

The sum of a rational number and an even integer is rational. A) Always True B) Sometimes True C) Usually True D) Never True

SOVA2 [1]

I think that the sum will always be a rational number
let's prove that

any rational number can be represented as a/b where a and b are integers and b≠0

and an integer is the counting numbers plus their negatives and 0
so like -4,-3,-2,-1,0,1,2,3,4....

so, 2 rational numbers can be represented as

a/b and c/d (where a,b,c,d are all integers and b≠0 and d≠0)

their sum is
a/b+c/d=
ad/bd+bc/bd=
(ad+bc)/bd

1. the numerator and denominator will be integers
2. that the denominator does not equal 0

alright
1.
we started with that they are all integers
ab+bc=?
if we multiply any 2 integers, we get an integer
like 3*4=12 or -3*4=-12 or -3*-4=12, etc.
even 0*4=0, that's an integer
the sum of any 2 integers is an integer
like 4+3=7, 3+(-4)=-1, 3+0=3, etc.
so we have established that the numerator is an integer

now the denominator
that is just a product of 2 integers so it is an integer

2. we originally defined that b≠0 and d≠0 so we're good

therefore, the sum of any 2 rational numbers will always be a rational number is the correct answer.

6 0

3 years ago

Math help @LIEMONDER

klio [65]

First picture)
I: 5x+2y=-4
II: -3x+2y=12

add I+(-1*II):
5x+2y-(-3x+2y)=-4-12
8x=-16
x=-2

insert x=-2 into I:
5*(-2)+2y=-4
-10+2y=-4
2y=6
y=3

(-2,3)

question 6)
I: totalcost=115=3*childs+5*adults
II: 33=adults+childs
33-adults=childs

insert childs into I:
115=3*(33-adults)+5*adults
115=99-3*adults+5*adults
16=2*adults
8=adults

insert adults into II:
33-8=childs
25=childs

so it's the last option

question 7)
a) y<6 and y>2 can also be written as 2<y<6, so solution 3 exist for example
b) y>6 and y>2 can also be written as 2<6<y, so solution 7 exist for example
c) y<6 and y<2 inverse of b: y<2<6, so for example 1
d) y>6 and y<2: y<2<6<y, this is impossible as y can be only either bigger or smaller than 2 or 6

so it's the last option

question 8)
I: x+y=12
II: x-y=6

subtract: I-II:
x+y-(x-y)=12-6
2y=6
y=3

insert y into I:
x+3=12
x=9

(9,3)

question 9)
I: x+y=6
II: x=y+5

if you take the x=y+5 definition of II and substitute it into I:
(y+5)+y=6

which is the second option :)

5 0

3 years ago

Ok just answer this and im gonna mark as brainliest

suter [353]

Paperbacks and notebooks

3 0

3 years ago

(07.03 MC)

Umnica [9.8K]

The probability of pulling a blue marble and the coin landing tails up is 360/2500

<h3>How to determine the probability?</h3>

The tables of values are given as:

Color Times

Blue 18

Green 20

Yellow 12

Heads Tails

20 30

The probability of obtaining a blue marble is:

P(Blue) = 18/50

The probability of landing tails up is:

P(Tail) = 20/50

The required probability is:

P = P(Blue) * P(Tail)

This gives

P = 18/50 * 20/50

Evaluate the product

P = 360/2500

Hence, the probability of pulling a blue marble and the coin landing tails up is 360/2500