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Answer:
Option D.
LA Theorem or Postulates
Explanation:
LA theorem or postulates is leg-acute states that if the leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.
In and
[Given]
[Acute angle] [Given]
[Given]
By LA theorems or postulates,
Therefore, LA theorems or postulates support the conclusion that the triangles are congruent.
A second degree polynomial function has the general form:
, where 
.
The leading coefficient is a, so we have a=-1.
5 is a double root means that :
i) f(5)=0,
ii) the discriminant D is 0, where
.
Substituting x=5, we have
f(5)=a(5)^2+b(5)+c,
and since f(5)=0, and a is -1 we have:
0=-25+5b+c
thus c=25-5b.
By ii)
.
Substituting a with -1 and c with 25-5b we have:
Finally we find c: c=25-5b=25-50=-25
Thus the function is
Remark: It is also possible to solve the problem by considering the form
directly.
In general, if a quadratic function has leading coefficient a, and has a root r of multiplicity 2, then its form is
The leading coefficient is a, so we have a=-1.
5 is a double root means that :
i) f(5)=0,
ii) the discriminant D is 0, where
Substituting x=5, we have
f(5)=a(5)^2+b(5)+c,
and since f(5)=0, and a is -1 we have:
0=-25+5b+c
thus c=25-5b.
By ii)
Substituting a with -1 and c with 25-5b we have:
Finally we find c: c=25-5b=25-50=-25
Thus the function is
Remark: It is also possible to solve the problem by considering the form
In general, if a quadratic function has leading coefficient a, and has a root r of multiplicity 2, then its form is