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it is not very easy to see me on the leaderboard

Work from the inside out:  first find the inverse of 3 and then find the inverse of that answer.

Since  f(4) = 3,  f^-1(3) = 4

Since f(7) = 4,  f^-1(4) = 7.

I dont have very many :(

But congrats on 320!!

I mean 900 points

Um about 900 I guess and I am in the leaderboard

and answers

Largest value will be  y= 1    when x = 0

   as x goes to infinity this tends toward zero....    take it from here   

get lots of hearts

Am I right?

I'm really sure this is right

C(6,3)=20

answer=20

Find y-axis intercept (when x = 0)     y = 6

find x-axis intercepr Iwhen y= 0)       x = 6

Noy you have a right triangle with leg1 = 6    and leg2 = 6        area = 1/2 leg1 x leg2  units²

Andy      =   12 pieces

Bert        =    4 pieces

Charles  =    4 pieces

Nuts         =    4 pieces

Plain        =    8 pieces

Caramel  =    8 pieces

Give Bert the 4 with nuts.

Give Charles 4 with caramel.

Give Andy the 8 plain and 4 with caramel.

https://web2.0calc.com/questions/find-the-number-of-ordered-pairs-a-b-of-real-numbers

I already found the answer, thanks!

thank you so much that is correct! :))

huh, this actually was wrong.

is there another way to do this or was there maybe some double counting

Wait i think i know what went wrong,

we WANT the sequence to begin with L so idn't think we should have subtracted it from 840.

is that correct?

Start off by subtracting 2 from 10, which is 8.

Subtract 6 from 24 as two books are taken off each of the 3 shelves. 

This leaves us with 8/18, which simplifies to 4/9.

Please correct me if I'm wrong .

I found the maximum using a parabola but dont know how to find the minimum.

"And finally, find  OR = 5*sqrt(2)"         5*sqrt(2) = 7.07106781   INCORRECT !!!

The correct answer is:        OR = 7 / cos(29.7448813º) = sqrt(65) 

Ohh so I just needed to apply this theorem?

The total ways to make sequences of 4 letters using the letters P, R, O, B, L, E, M, using each letter only once, without restrictions, is 7 * 6 * 5 * 4 = 840.

Let's use complementary counting for this problem (So, we find the situations we DON'T want and subtract them from the total)! :D

Ways that a sequence begins with L = 1 * 6 * 5 * 4 = 120

Ways that a sequence ends with P = 6 * 5 * 4 * 1 = 120

Ways that a sequence begins with L and ends with a P = 1 * 5 * 4 * 1 = 20

120 + 120 - 20 = 220

There are 220 ways which we DON'T want!

So, since the total is 840, we subtract 840 from 220 to get \(\fbox{620}\) :D

EDIT: Sorry I misread the problem! This answer is false.

Thank you!

To be in Q I   it will need to be ABOVE the line drawn..... the x - point it will be midway between the two points

   x = 4

coordinate will be    4, y        and the distance from either of the given points will be 8

  use distance formula from  0,5  (easiest)   and    4,y    to find the distance 8

8^2 = (4-0)^2 + (y-5)^2        solve for y

Solving using b

So we know that all angles in a triangle add up to 180°.

The equation we get is 50°+a+b=180°

Because there are two variables, we need to equations, and the other is already given. Which is a-b=40

We can use substitution and get 50°+(b+40°)+b=180°.

Just add and subtract a few things to get 2b=90°, and b=45°

We can take b back into the equation and get a=85°.

Solving using a

If we want to solve using a, we can substitute b=a-40 into the first equation.

We get 50°+2a-40°=180°. 2a=170° and a=85°.