Mathematics, 18.12.2020 01:10 ramirezzairap2u4lh

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Answer from: deeknuk

z ≥−4

Step-by-step explanation:

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

answer-

the equation that models this pattern is $y=32000(0.5)^x$

solution-

a researcher placed a petri dish with 32,000 bacterial cells. one hour after being placed in the vacuum chamber, the number of cells in the petri dish had halved. another hour later, the number of cells had again halved.

this can be represented as exponential decreasing function,

$y=a(1 - r)^x$

where,

a = starting amount = 32000r = rate = 50% = 0.5 as the sample becomes halved in each hour x = hours

putting the values,

$\rightarrow y=32000(1 - 0.5)^x$

$\rightarrow y=32000(0.5)^x$

y-intercept means, where x=0, so

$\rightarrow y=32000(0.5)^0\\\\\rightarrow y=32000\times 1=32000$

the coordinate of this poin will be (0, 32000)

this means when x=0 or at the starting of the research, the number of bacteria cells was 32000.

after 3 hours, number of bacteria cells will be,

$\rightarrow y=32000(0.5)^3$

$\rightarrow y=32000\times 0.125$

$\rightarrow y=4000$

the coordinate of this point will be (3, 4000)

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