Mathematics, 30.06.2019 21:20 silsnod3119

The sum of 4 consecutive integers is -18. what is the greatest of these integers?

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Answer from: shanua

Okay. What I know so far is that the integers will all be negative. We don't have to count too high to do this. So for this, it's like pick any four numbers. Or you could divide 18 by half and find the addition problems that you know would equal 9. What I see is that -3 + -4 + -5 + -6 = -18. There are all four consecutive integers. The trend is that you can draw a line tracing to the number of the opposite side of the question and you can see they each equal nine. Most people would be tricked and say 6, because they ignore the negative symbol, but here's the catch. The lower the number in front of the negative sign, the greater it is. So in this case, the lowest number in front of the negative symbol is 3, which would also mean that -3 is the highest when it comes to all of these numbers. So -3 is the greatest out of the four consecutive integers.

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

a and c

step-by-step explanation:

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