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I'm on the same thing i'm unsure too

Length of DE= 15 cm
Length of AB = 6 cm
Two triangles are similar if they have the same ratio of corresponding sides (among another rule which is not needed here). This means that the length of corresponding sides are proportional. We can see in triangle CDE that side CE is 24 cm. This corresponds to side AC in triangle ABC which is 8 cm. Using these two measurements we can see that the larger triangle is 3 times the size of the smaller triangle. Using equal proportions we can say that line segment BC which is 5 cm corresponds to line segment DE. Line segment DE is 3 times larger, so length of DE is 5x3=15 cm. In triangle CDE line segment CD is given a length of 18 cm. Using the proportion that we now know, we can say that in triangle ABC that line segment AB is 3 times smaller than line segment CD. 18/3= 6 cm. Line segment AB is 6 cm.

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 =.

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

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

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

.

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

slope of the solid line would be =.

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 .

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