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3 years ago

Which of the following equations is an example of inverse variation between

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

6 0

Answer:

The correct answer is option D

Step-by-step explanation:option A : y = x/12 ⇒ x = 12y (wrong option)

option B : y = 12/x ⇒ y * x = 12 (wrong option) and c will be equal 12

option C : y = x + 12 ⇒ not similar to the general form (wrong option)

option D : y = 12/x (corect option)( I meant to switch it around)

The general form of inverse variation between the variables x and y is as following:

where c is constant

So, the correct option is D

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Hannah notices that segment HI and segment KL are congruent in the image below: Two triangles are shown, GHI and JKL. G is at ne

BlackZzzverrR [31]

Answer:

segment IG ≅ segment LJ

Step-by-step explanation:

Please refer to the attached image as per the triangles as given in the question statement.

$\triangle HGI, \triangle JKL$

$G\left(-3,1\right),\ H\left(-1,1\right),\ I\left(-2,3\right)$

$J\left(3,3\right),K\left(1,3\right),L\left(2,1\right)$

Given that:

$HI\cong KL$ and

$\angle I \cong \angle L$

<em>SAS congruence </em>between two triangles states that two triangles are congruent if two corresponding sides and the angle between the two sides are congruent.

We are given that one angle and one sides are congruent in the given triangles.

We need to prove that other sides that makes this angle are also congruent.

To show the triangles are congruent i.e. $\triangle GHI \cong \triangle JKL$ by SAS congruence we need to prove that

segment IG ≅ segment LJ

Let us use Distance formula to find IG and LJ:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$IG =\sqrt{(-2+3)^2+(3-1)^2} =\sqrt5\ units$

$LJ =\sqrt{(2-3)^2+(1-3)^2} =\sqrt5\ units$

Hence, segment IG ≅ segment LJ

$\therefore$ ΔGHI ≅ ΔJKL by SAS

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Step-by-step explanation:

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