hectictar

If g( f(x) ) = g( 7 ) , then that means f(x) must equal 7.

f(x) = 7

2x + 5 = 7

2x = 7 - 5

2x = 2

x = 1

f(x) = 2x + 5

and

g(x) = x² - 25

So to find g( f(x) ), replace every x in g(x) with f(x) .

g( f(x) ) = (2x + 5)² - 25

g( f(x) ) = (2x + 5)² - 25

g( f(x) ) = (2x + 5)(2x + 5) - 25

g( f(x) ) = 4x² + 10x + 10x + 25 - 25

g( f(x) ) = 4x² + 20x

f² - 79 = -15

Add 15 to both sides.

f² - 64 = 0

This is now a "perfect square binomial," and you can write it like this:

(f - 8)(f + 8) = 0         :)

First, I suggest drawing a picture of what the problem says so you can see what I'm talking about.

I would upload one, but I can't right now on this computer.

tan = opposite / adjacent

Plug in the numbers you know.

tan 43º = AC / 9.3

Multiply both sides by 9.3 .

9.3tan43º = AC

Put this into a calculator to get that

AC ≈ 8.672

You had it right!! 

arc length = radius * angle measured in radians

Convert 80º to radians.

80º * (π / 180º) rad. = 4π / 9 rad.

24π = radius * 4π / 9

54 = radius

What are you trying to do?

\(\sqrt{128}\\=\sqrt{2*2*2*2*2*2*2}\\=\sqrt{2*2}*\sqrt{2*2}*\sqrt{2*2}*\sqrt{2}\\=2*2*2*\sqrt2\\=8\sqrt{2}\)

Well....I like math okay...  

Your settings are fine..but the tangent values repeat every time you add 180º

So the inverse tangent of 8/13 ≈ 31.607º and  31.607º + 180º = 211.607º

And you can keep adding 180º as many times as you want and the tangent of that angle will still be 8/13 . 

Hmm... I interpreted it as

\(\sqrt{-64^3}\)

In which case the answer is

\(\sqrt{-262,144}=512i\)     :)