A Professor at a University sent his phone number in a disorderly manner to his students. The disordered phone number was 64001128454. To know his real phone number, he gave the student the following conditions:

1. Eight (8) must come between two zeros (0's).

2.The first number after the first condition is met must not be an odd number and it must be greater than 5.

3. The seventh number must be 1.

4. The fifth and sixth numbers must be two numbers whose difference is 1 and the bigger number must come first.

5. The fifth and sixth numbers are greater than 2.

6. The ninth and tenth numbers are the same.

7. The eighth number is greater than the last number.

8. The phone number must be 11 digits.

What was the Professor's real phone number?

I found 608054144112

If the number isn't found by the given condition, write a variable to advance. but it is comfortable to solve if you follow them one by one

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4