What coordinate plane shows the graph of 3x+y>9 ?
1 answer:
Answer:
(d) see attached
Step-by-step explanation:
All of the answer choices show shading above a dashed line, so we need to look a little closer at the equation of the boundary line. Written as an equation, it is ...
3x +y = 9
When you set each variable to zero and solve for the other, you find the intercepts to be ...
y = 0, x-intercept: 3x = 9 ⇒ x = 3
x = 0, y-intercept: y = 9
The only graph that has x- and y-intercepts matching these values is the one attached.
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Answer:
Step-by-step explanation:
As the statement is ‘‘if and only if’’ we need to prove two implications
is surjective implies there exists a function
such that
.
- If there exists a function
Let us start by the first implication.
Our hypothesis is that the function is surjective. From this we know that for every
there exist, at least, one
such that
.
Now, define the sets . Notice that the set
is the pre-image of the element
. Also, from the fact that
is a function we deduce that
, and because
the sets
are no empty.
From each set choose only one element
, and notice that
.
So, we can define the function as
. It is no difficult to conclude that
. With this we have that
, and the prove is complete.
Now, let us prove the second implication.
We have that there exists a function such that
.
Take an element , then
. Now, write
and notice that
. Also, with this we have that
.
So, for every element we have found that an element
(recall that
) such that
, which is equivalent to the fact that
is surjective. Therefore, the prove is complete.