Answer:
The smallest positive integer solution to the given system of congruences is 30.
Step-by-step explanation:
The given system of congruences is


where, m and n are positive integers.
It means, if the number divided by 5, then remainder is 0 and if the same number is divided by 11, then the remainder is 8. It can be defined as



Now, we can say that m>n because m and n are positive integers.
For n=1,


19 is not divisible by 5 so m is not an integer for n=1.
For n=2,



The value of m is 6 and the value of n is 2. So the smallest positive integer solution to the given system of congruences is

Therefore the smallest positive integer solution to the given system of congruences is 30.
Answer:
D. 140
Step-by-step explanation:
volume equals length times width times height 7 times 4 times 5 equals 140 good luck
Answer:
The vertex of this parabola,
, can be found by completing the square.
Step-by-step explanation:
The goal is to express this parabola in its vertex form:
,
where
,
, and
are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at
.
The vertex form can be expanded to obtain:
.
Compare that expression with the given equation of this parabola. The constant term, the coefficient for
, and the coefficient for
should all match accordingly. That is:
.
The first equation implies that
is equal to
. Hence, replace the "
" in the second equation with
to eliminate
:
.
.
Similarly, replace the "
" and the "
" in the third equation with
and
, respectively:
.
.
Therefore,
would be equivalent to
. The vertex of this parabola would thus be:
.
Answer:
D. 1/2
Step-by-step explanation:
Because if you choose A , you get +4
if you choose B ,you get -12
Choose C , you get +20
D is the correct answer.