Mathematics, 05.03.2020 13:17 OhDee8269

Triangle ADE is similar to triangle ABC. Which statement is TRUE concerning the slope of the line formed by the hypotenuse of each triangle? A) EA DE = CB AC B) DE EA = CB AC C) DE EA = AC CB D) EA DE = AC CB

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Answer from: mucciak2854

$B) \frac{DE }{EA} =\frac{CB}{AC}$

Step-by-step explanation:

If ant two given triangles are SIMILAR, then they have equal corresponding angles and their corresponding sides are PROPORTIONAL.

For example: if Δ ABC ≈ Δ PQR, then

∠A = ∠P , ∠B = ∠Q and ∠C = ∠R

and $\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}$

Now, here given: Δ ADE ≈ Δ ABC

Then by the SIMILAR postulate their corresponding angles are equal and their corresponding sides are Proportional.

$\implies \frac{AD}{AB} = \frac{DE}{BC} = \frac{AE}{AC}$ ............. (1)

Consider from above:

$\frac{DE}{BC} = \frac{AE}{AC}\\\implies \frac{DE}{AE} = \frac{BC}{AC}$ ............. (2)

Here, the given options are:

$A) \frac{EA }{DE} =\frac{CB}{AC}$ FALSE

$B) \frac{DE }{EA} =\frac{CB}{AC}$ TRUE (from 2)

$C) \frac{DE }{EA} =\frac{AC}{CB}$ FALSE

$C) \frac{EA}{DE} =\frac{AC}{CB}$ FALSE

Answer from: Quest

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.

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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