Lim x→25 x−25 /√x−5
1 answer:
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Answer:
Construct MO, where O is the midpoint of CG. (As shown in the attached figure)
(1) LM = MG //given, CM is the median to the hypotenuse
(2) CO = OG // construction
(3) MO is a mid-segment //(1), (2) , Definition of a mid-segment
(4) MO // LC //triangle mid-segment theorem
(5) ∠MOG ≅ ∠LCO // corresponding angles in two parallel lines intersected by a transversal line (CG)
(6) m∠LCO=90° //given, ΔLCG is a right triangle
(7) m∠MOG=90° //(5), (6), definition of congruent angles
(8) m∠MOC=180° – 90° = 90° // linear pair
(9) ∠MOG ≅ ∠MOC //(7),(8), definition of congruent angles
(10) MO=MO //common side, reflexive property of equality
(11) ΔMCO ≅ ΔMGO //(2), (9), (10) Side-Angle-Side postulate
(12) MC = MG // Corresponding sides in congruent triangles (CPCTC)
(13) MG= ½LG // Given, CM is the median to the hypotenuse
(15) MC = ½LG //(12) , (13), substitution
Subtraction Property of Inequality is used to solve the given inequality
<em><u>Solution:</u></em>
Given inequality is:
To solve the inequality, subtract 8 on both sides,
We know that,
Adding or subtracting the same quantity from both sides of an inequality leaves the inequality symbol unchanged
Also, by Subtraction Property of Inequality,
If you minus a number from one side of an inequality, you have to minus that same number from the other side of the inequality as well
Thus, Subtraction Property of Inequality is used
5/6 is your answer, explanation is in the image, hope this helps! :D
