Ageometry student says; "i got lost in that lesson - i wrote down that ad/ab = ac/ab but i have no idea
where it comes from."
which of the following should have been the proportion that the student wrote?
answer choices:
a) ad/ab=ab/ac
b) ad/ac=ab/ab
c) ab/ad=ab/ac
d) ab/ac=ab/ad

Therefore the choice is

a) AD/AB=AB/AC

Step-by-step explanation:

In  Δ ADB and Δ ABC  

∠A ≅ ∠A    …………..{Reflexive Property}

∠ ADB ≅ ∠ ABC      ..............{ measure of each angle is 90° given }

Δ ADB ~ Δ ABC ….{Angle-Angle  Similarity test}

If two triangles are similar then their sides are in proportion.

Therefore the choice is

a) AD/AB=AB/AC

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.