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I'm so sorry, CPhill. I meant to type the second one not as 1 but 2.

Nice, Chris!!!

Yes, they will!

Also, posting these questions on the college math forum will help a lot!!!

Yes, it is! Nice, CU!

I'll do the 14th percentile as an example:

Using a standard normal table, the z value that corresponds to an are of 0.14 is -1.08 or z = -1.08

The corresponding x value is

x = z*σ + µ = -1.08*5 + 41 = -5.4 + 41 = 35.6

Now use this to find the 5th percentile. Hope this helped!

See answer #7 here:  https://web2.0calc.com/questions/help_85792

thanks !! :))

\(f(x)=g(x)\)

The problem already gives us the respective expressions for these 2 functions. We can rewrite this as:

-2x = x²-3

Adding 2x on both sides, get :

0 = x²+2x-3

we can factor this into:

(x+3) * (x-1) = 0

Our roots for this quadratic are then:

x = -3

x = 1

Thank you for your answer. My Approach initially was that I saw f(x) = inverse is the same as f(f(x)) = x, so I tried plugging it in, but that was more complex (though I think I may have gotten the correct answer that way too). I think that if I tried this method and thought about it in a more logical perspective, it would have been much better. Thank you!

It was nice reading old posts. TitaniumRome you sure gave this forum a spirit! :)

Do you see triangle BFD?
 

All angles in a triangle add up to 180.

That means angle B + angle D + angle BFD = 180

You know angle BFD = 100

So substitute that in.

Angle B + angle D + 100 = 180.

Now with simple algebra, you can find angle B + angle D, which is your answer.

AFD is a straight angle, which is 180 degrees.

If you know AFG, can you find BFD?

You don't need to find B and D.

Remember: All angles in a triangle add up to 180.

AGF is an isosceles triangle. Can you find AFG? Then I can walk you thru once you find AFG

I'm not very educated in college mathz as I'm still in primary school.

These forums may help:

oh im dumb.

I got (2x +a)/(bx-2) = (2x + a)/bx - 2) and I thought I did something wrong. I never learned inverse I only know how to switch out x and y after look up some google images XD

This is actually really fast if you notice it.

See triangle BFD. All angles in a triangle add to 180 degrees.

If you want to find angle B + angle D then all you need to do is find angle BFD and do simple algebra.

Can you find angle BFD?

9 and 41 what is a third number to form a right triangle

1)     sqrt ( 9² + 41² ) = 41.97618372     ( This is the number too ) 

2)     sqrt ( 41² - 9² ) = 40       

I don't have too much experience with doing graphing letters specifically, but I'd imagine using parametric equations would make the job substantially easier. Maybe complex too?

If  f(x)  =  (2x + a) / (bx - 2)  we can find f^-1(x) by following these steps:

1)  replace  f(x)  by  y:           y  =  (2x + a) / (bx - 2)

2)  interchange  x  and  y:     x  =  (2y + a) / (by - 2)

3)  solve for y:            x(by - 2)  =  2y + a

                                   bxy - 2x  =  2y + a

                                   bxy - 2y  =  2x + a

                                  y(bx - 2)  =  2x + a

                                             y  =  (2x + a) / (bx - 2)

Very interesting -- the function is its own inverse!

So, when does  (2x + a) / (bx - 2)  =  (2x + a) / (bx - 2)  for all values of x?

Well,  a  can be any number; but, it's different for  b  because the denominator can't be zero.

When the denominator equals zero,  bx  equals  2.

To prevent the denominator from ever equaling zero, get rid of the  bx  term  by making  b = 0.

[If  b  is any other number, there is a value of  x  that will make  bx  equal to  2.]