Which linear inequality is represented by the graph?
y < 2/3x + 3
y > 3/2 x + 3
y > 2/3 x + 3
y < 3/2x + 3

y < 2/3x + 3

Explanation:

In the graph, the grey region corresponds to the region non-allowed by the inequality.

We see that for x=0, y is allowed to be only less than 3: this means that the correct inequality must be in the form y<mx+3, so only the 1st option or the 4th option.

In order to choose the correct option, we should find the value of m, the slope of the line in the graph. This slope can be found by calculating the variation of y divided by the variation of x:

Choosing for example the points x=0 (which corresponds to y=3) and x=3 (which corresponds to y=5), we find

So, the equation of the line is

and so the correct inequality is

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)