The length of a pole is to be 6.5ft. The actual length of the pole may vary by as much as 0.02ft. Write an absolute value inequa
1 answer:
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4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.
Start with
Taken mod 4, the last two terms vanish and we're left with
We have , so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.
Taken mod 7, the first and last terms vanish and we're left with
which is what we want, so no adjustments needed here.
Taken mod 9, the first two terms vanish and we're left with
so we don't need to make any adjustments here, and we end up with .
By the Chinese remainder theorem, we find that any such that
is a solution to this system, i.e. for any integer
, the smallest and positive of which is 149.
Answer:
roses and
sunflowers
Step-by-step explanation:
Since the ratio of roses to sunflowers is , we can represent how many there are of each as
and
, respectively. We know that there are
more sunflowers than roses, so we can set up the following equation to solve for
:
Solving for , we get:
(Subtract
from both sides of the equation to isolate
)
(Simplify)
(Symmetric Property of Equality)
(Divide both sides of the equation by
to get rid of
's coefficient)
(Simplify)
Therefore, since , we know that there are
roses and
sunflowers. Hope this helps!