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We have 60 decades from 1 to 600 ( 1st decade is 1,2,3,4,5,6,7,8,9,10) every one of this include 1 time the number 5 but from 500 to 599 include 100 times and for every decade with 5x exp. 150-159 include 10 times so from 1-100 include (5,15,25,35,45,65,75,85,95) 9+10 times so 19 times total,the same and from 100 to 499 so (19*5)+100= 195 total times include the number 5 from 1-600!

I hope I helped you!

sorry, i meant 3ax^2+2bx+c

do you mean f(x) = 3a² + 2bx + x

or do you mean f(x) = 3a² + 2bx + x² ?

Don't blame me, blame the game.

And for CPhill, when I put this:

"and how many friends must they BOTH have to achieve this?"

I figured people would assume it to mean "each", like I did.

Well...the question is a little unclear....I took "both" to mean the sum...but maybe the question  should be "each".....

No matter....each will have 91  and  both will have 182 total

3 days to get TOTAL 91 each but i dont understand why you think 182 its false answer?

I'm not sure why you guys kept doubling the number of friends you guys originally found, I just tried 91 friends each and it was correct.

Answer: 3 days to get 91 friends each.

Thank you for the help!

You answer faster than me :p :(

I think its easy to think about it the correct answer is 3 because 1st day A(ni) will have 71 2nd day 81 and 3rd day 91 and M(agali) 1st day will have 85 2nd day 88 and 3rd 91 but in matg we write this:

a(x)= 10x + 61 

m(x)= 3x + 82

10,3 is friend per day and 61,82 friend now 

We wont a(x) = m(x) so

10x +61 = 3x + 82 <=>

7x= 21 so x=3 so 3 days 

And the friends both is 91+91= 182 friends both!

I hope I helped you!

The days were correct, but the number of friends was incorrect.

This is for a sort of math game, Prodigy, not sure if you've ever heard of it.

The game gives pretty cryprtic hints. This is the hint for this paticular problem:

"We need to come up with 2 linear equations based off the question.

Allow y to equal the friends, and x to equal the number of days

\(y=10x+61\) is one of the equations.

Determine the other equation, then solve for x and y using substitution"

The substitution part is what's throwing me off here, I've never been able to do this properly.

Still, thanks anyway. As I said, the # of days was correct, but the friends are incorrect.

We want to solve this

61 + 10D  = 82 + 3D     where D is the number of days we are looking for

subtract 3D, 61 from  both sides

7D  = 21    divide both sides  by 7

D  = 3  =   number of days it will take to have the same number of friends

And the number of friends both them will have  is just twice the number of friends that either will have  =  2 [  82 + 3*3]   =  2 [ 82 + 9 ]  =   2 [ 91  ] =    182

Very nice, hectictar.....!!!

I can't find how to add a file that's an image, soorry about that 

You're welcome!

Thanks for the quick response! I didn't mention that I was asking for x as a decimal, but the fraction was easy enough to convert.

\(x=2.13\)

Again, thanks!

Its -5(3x) -(-5)4=-29 +8x <=> -15x +20 = -29 + 8x <=> 20 + 29 = 8x + 15x <=> 49 = 23x <=> x=49/23

So x=49/23  is the answer!

I hope I helped you! 

Its sure 243 i don't find answer but look at this maybe help you:

for example 6138 = abcd a=6,b=1,c=3,d=8 if we dont know the numbers so:

we have x it's the  originally enter 

x -> x^2 -> abcd (the result) -> press a -> bcd ->(bcd)^2 -> efghij -> press e ->fghij BUT fghij=243 SO fghij-> fgh with f=2,g=4,h=3 and e=1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9.The biggest is e=9 so efgh=9243 But sqrt(9243)=96.1 so (bcd)^2 its bc NOT 3 numbers and a=1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 the biggest is 9 But sqrt(999)=32 SO

x<32

and we have finally:

x -> x^2 -> abc -> press a -> bc -> (bc)^2 -> efgh -> press e -> fgh but no one for numbers 1423,2243,3243,4243,5243,6243,7243,8243,9243 dont have integer result for this reason i ask you if its 243 for sure!

I hope I helped you! 

Thanks :)

Exactly 

Hmmmm....ohh...I think you are right 

This is a true statement:

For  ∠A to be the largest angle, it must be that  0 < x < 100

So there is more than one possible value of  n - m .

(  And it is also true that if  2.9999 < x < 3 ,  then ∠A  is the largest angle,

   But it is not true that it  must  be that  2.9999 < x < 3  for  ∠A  to be the largest angle.  )

(25 + ki)(3 + 2i)  =  75 + 50i + 3ki + 2ki²   =   75 + 50i + 3ki - 2k

Let's find what value of  k  makes  50i + 3ki  =  0

50i + 3ki  =  0

i(50 + 3k)  =  0

50 + 3k  =  0

3k  =  -50

k  =  -\(\frac{50}{3}\)

When  k  =  -\(\frac{50}{3}\)  ,    (25 + ki)(3 + 2i)   is a real number.

Let the radius of the smaller circle  =  s

Let the radius of the bigger circle  =  b

And let's label the point of tangency " P ".

Side  s  is drawn from the center of the circle to  P ,  so side  s  meets  AB  at a right angle.

And by the hypotenuse-leg theorem, the two triangles are congruent.  And  AB =  80  So...

AP + PB  =  80

                               And we know  AP  =  PB

PB + PB  =  80

2 * PB  =  80

PB  =  40

By the Pythagorean theorem....

40²  +  s²  =  b²

1600 + s²  =  b²

1600  =  b² - s²

area of shaded region  =  area of bigger circle - area of smaller circle

area of shaded region  =   π b²   -   π s²

area of shaded region  =  π( b² - s² )

area of shaded region  =  1600π     (sq units)  

Ok for some reason I can't edit my answer

EDIT: testing

"In the triangle shown, for A to be the largest angle it must be that m

You found the "optimal" values for m and n- the largest value for m that satisfies the statement and the smallest value for n that satisfies the statement. It is also correct to say that x must be between 0 and 100, which is why the guest asked for the "least possible value of n-m". In other words, we are asked to find the difference between the least upper bound and the largest lower bound of the values of x that satisfy the statement. You found the least upper bound (9/2) and the largest lower bound (5/3) so by finding the difference between them you found the answer.

"In the triangle shown, for A to be the largest angle it must be that m

You found the "optimal" values for m and n- the largest value for m that satisfies the statement and the smallest value for n that satisfies the statement. It is also correct to say that x must be between 0 and 100 (0

Thank you again, Chris