Mathematics, 13.07.2019 14:20 tra80

Can someone ? you. show all work.

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Question 1. 1) <2 and <5 = Given 2) <3 is congruent to <2 = Vertical angles 3) <3 and <5 are supplementary = same side interior angles 4) L is parallel to M = if two lines are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the two lines are parallel.

question 2. B is incorrect because subraction should have been done instead of addition.

question 3. Line 1 is a horizontal line so the equation of the line for line 1 is Y = 8 Line 2, first solve the slope of the line using points ( -4 , -5) and ( 0, -2) M = (y1 – y2) / (x1 – x2) M = ( -5 – ( -2)) / ( -4 – 0) M = ¾ Since its y intercept is at ( 0,-2) B = -2 Y = ¾ x -2 For c and d you should give a point at which the line is perpendicular or parallel

Answer from: Quest

536

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.

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