Mathematics, 27.09.2019 16:00 lymariluna73016

Find the value of x and y that make these triangles congruent by hl.

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Answer from: Snowball080717

the correct option is (A) x = y = 2.

Step-by-step explanation: We are given to find the values of x and y that makes the triangles in the figure congruent by HL.

From the figure, we note that

triangles ABC and AED are right-angled triangles with hypotenuse AC, AD and one congruent side BC, ED.

Also, AC = 2x + 3, AD = 3y+1, BC = x and ED = y.

Since the triangles are congruent by HL postulate, so we must have

$x=y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2x+3=3y+1~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the value of x from equation (i) in equation (ii), we get

$2x+3=3x+1\\\\\Rightarrow 3x-2x=3-1\\\\\Rightarrow x=2.$

So, from equation (i), we arrive at

x = y = 2.

Thus, the correct option is (A).

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

aloha~! my name is zalgo and i am here to you out on this amazing day. to answer your question, yes, nonzero numbers can have a greatest common factor and that would be 1. still don't get it? let me considering every number is divisible by 1 and hence every number has 1 as a factor of theirs. so, if 2 nonzero numbers didn't share any gcf (greatest common factor), they would still have a factor in common and that would be 1.

i hope that this ! : p

"stay and stay proud! " - zalgo

(by the way, do you mind marking me as brainliest? i'd greatly appreciate it! mahalo! x3)

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Find the value of x and y that make these triangles congruent by hl.
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