X and y are the numbers
x>y
diffference is 42
x-y=42
larger is 3 less than 6 times smaller
x=-3+6y
subsitute -3+6y for x
x-y=42
-3+6y-y=42
-3+5y=42
add3 to both sides
5y=45
divide both sides by 5
y=9
sub back
x=-3+6y
x=-3+6(9)
x=-3+54
x=51
the numbers are 51 and 9
Answer:
B. 
Step-by-step explanation:
The given quadratic trinomial is;

Comparing this to
, we have a=5,b=17,c=6.

Two factors of 30 that add up to 17 is 15 and 2.
We split the middle term to obtain;

We factor by grouping;

Factor further

The correct answer is B.
Usually I would use my head, but you can use whatever you want.
a.
has an average value on [5, 11] of

b. The mean value theorem guarantees the existence of
such that
. This happens for

Answer:
is in proportion.
is not in proportion.
is in proportion.
is in proportion.
Step-by-step explanation:
The first example is
and it is in proportion.
This is because, you will get the same simplest fraction (
) from the fraction
by dividing its numerator and denominator by 5.
The second example is
and it is not in proportion.
This is because, you can not get the simplest fraction (
) from the fraction
after simplification.
The third example is
and it is in proportion.
This is because, you will get the same simplest fraction (
) from the fraction
by dividing its numerator and denominator by 2 and from the fraction
by dividing its numerator and denominator by 3.
The fourth example is
and it is in proportion.
This is because, you will get the same simplest fraction (
) from the fraction
by dividing its numerator and denominator by 5. (Answer)