Which expression is equivalent to 6X equals 10 X +20

Amanda uses the equation y = kx to determine how much money (y) she earns after working any number of hours (x). Amanda earned $

kondaur [170]

Given the equation y = kx
Also given that she:
earned $350 after working 40 hours
y = how much earned
x = number of hours
Plug it in
y = kx
350 = k(40)
divide both sides by 40 to find out how much k is
8.75 = k

k = 8.75 so your answer is A.) 8.75

Hope this helps :)

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3 years ago

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Suppose that, in addition to edge capacities, a flow network has vertex capacities. That is each vertex has a limit l./ on how m

storchak [24]

Answer:

See explanation and answer below.

Step-by-step explanation:

The tranformation

For this case we need to construct G' dividing making a division for each vertex v of G into 3 edges that on this case are $v_1, v_2 and l(v)$ .

We assume that the edges from the begin are the incoming edges of $v_1$ and all the outgoing edges from v are outgoing edges from $v_2$

We need to construct $G' = (V', E')$ with capacity function a' and we need to satisfy the follwoing:

For every $v \in V$ we create 2 vertices $v_1, v_2 \in V'$

Now we can add a new edge asscoiated to $v_1, v_2 \in E'$ with the condition $a' (v_1,v_2) = l(v)$

Now for each edges $(u,v)\in E$ we can create the following edge $( u_r, v_1) \in E'$ and the capacity is given by: $a' (u_r, v_1) = a (u,v)$

And for this case we can see this:

$|V'| = 2|V|, |E'|= |E| +|V|$

Now we assume that x is the flow who belongs to G respect vertex capabilities. We can create a flow function x' who belongs to G' with the following steps:

For every edge $(u,v) \in G$ we can assume that $x' (u_r ,v_1) = x(u,v)$

Then for each vertex $u \in V -t$ and we can define $x\(u_1,u_r) = \sum_{v \in V} x(u,v)$ and $x' (t_1,t_2) = \sum_{v \in V} x(v,t)$

And after see that the capacity constraint on this case would be satisfied since for every edge in G' on the form $(u_r, u_1)$ we have a corresponding edge in G because: