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AB : BC = 3 : 1

No prob.....you did 99% of the work   !!!!

Ah yes, I missed that part.

Note  that we can simplify DewdropDancer's answer just a little  more

(x^(3/2)) ^(1/3)  =  x^[ (3/2) * (1/3) ]  =  x^(1/2)   =  √ x

Actually, when people see titles like @Guests's, they likely won't help because it's something called "cheating" . 

Correct, DewdropDancer   !!!!

Well not everyone can answer your questions, just try them. Its not like you can just ask questions on a test... 

\(\sqrt[3]{x\sqrt{x}} =\sqrt[3]{x^{1+\frac{1}{2}}} =\sqrt[3]{x^{\frac{3}{2}}}\)

I already answered some of these questions, please stop posting these same problems and wait for someone to help you, or you can go ahead and do them yourself.

I think this is right...

By the triangle inequality, (P,Q) = (1/2,3/2).

19) There are 112 three digit numbers divisible by 8. 

12) For \(7^{2010}\) we have to multiply by 7 so this gives 49 for the last two digits. 

14) I memorized this: 3, 4, and 5 are lengths of a right triangle

15) \(\left(2^x\right)^2+2^x=12\)

\(\left(u\right)^2+u=12\)

\(u=3,\:u=-4\)

Thats a lot of questions, so I think you should at least try some of them, they aren't so hard. Just give them a try!

I NEED HELP TOO

1)  There are 60 minutes in an hour, therefore 60 * 24 = minutes in a day and, 60 * 24 * 7 = minutes in a week, so 60 * 24 = 1440. and 60* 24 * 7 → 1440 * 7 = 10080 minutes in a week.

4)  

\(2^{10}\cdot \:4^{20}\cdot \:8^{30}=2^n\)

\(2^{140} = 2^n\)

\(\mathrm{True\:for\:all}\:x;\quad \:2^{140}=2^n\)

6) 

x = 12+1*x-2

x = 12 + x - 2

x = x + 12 -2

x = x+10

x - x = x + 10 - x

     0 = 10

No Solution

Please, I need help with these problems too!!!!!!!!!11  Please, hurry!!!!!!!!!!!!!  I need the answers really soon!!!!!  Like right now!!!!!!!

11. If x + 1/x = 2, then find x^2 + 1/x^2

12. what are the last two digits of 7^2010?

13. What is smallest number of integers needed to be selected from the set {1,2,3,...,2020} to guarantee 2 of selected numbers relatively prime?

14. Three consecutive integers form the sides of a right triangle.  What are the three integers?

15. Solve 4^x + 2^x = 12.

16. How many ordered triples of positive integers (a,b,c) are there such that 1<= a <= b <= c <= 10?

17. How many perfect squares are factors of 79!?

18. What is the sum of all proper fractions with a denominator less than or equal to 10?

19. How many three-digit numbers are divisible by 8?

20. Triangle ABC is an isosceles triangle with AC=BC and angle C =120°. Points D and E are chosen on segment AB so that AD=DE=EB. Find angle CDE

Pleeez, I really need the answers!!!!!!!!!!!!!!!!!!!!!!  Hurrry!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  HURRY!!!!!!!!!!!!!!!!!!!!!

Choose   any 2 of  5 teachers and  any 4  of  10 students

C(5,2)  * C(10,4)    =   2100 committees

Note that NR  =15/2 = 7.5  PN

Draw a perpendicular   MS   to   PR

Then triangle  PMS  is  similar to triangle PQN

Then since MP is 1/2   of PQ  then  PS  =  1/2 of PN =  7.5/2=  15/4  = 3.75    

And triangle PMS  is similar to  triangle PQN

So

PS/ PN  =  MS/QN

3.75/ 7.5  =  MS /QN

1/2 = MS/10

MS = (1/2) 10  = 5

And triangle    RSM  is similar to triangle  RNO

RS =  3.75 + 7.5 = 11.25

So

MS / RS  =  ON / NR

5/11.25 =  ON / 7.5

(7.5)(5) / 11.25 =  ON    =   10/3

Because of the rotation, the number of ways is 8!/6 = 6720.

AC because angle B is largest

Sorry ... I didn't realize.

Close, but not quite.

Let x be the age of the father and let y be the age of the son.

\(x=9y\\ x+3=6(y+3)\\ 9y+3=6y+18\\ 3y=15\\ x=5\)

So the son is actually 5 years old.

By the Conformal Mapping Theorem, f(-i) = 2 + i.

By the quadratic formula, c = 10.