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Longer leg = x 

Hypotenuse = x + 1

x + (x + 1) = 121

x = 60     

Shorter leg = sqrt[(x + 1)² - x²] = 11

perimeter = 11 + 60 + 61

Ask again if you still are confused

Also to solve it just remeber the pythagorean theorem, a^2+b^2=c^2 to solve this. FYI c is the hypotenuse

Wait isnt the longer leg the hypotenuse?

[BXY]/[ABC] = 25/98

DE = 93 / tan(25º) = 199.4

Big circle radius => R

Small circle radius => r

Distance between the centers => m

? = n

n = R - r - m 

Thanks! I knew it would be something simple like that but I just couldn't figure it out lol

Note that if the circles had the same center (concentric) , the value would be R1- R2

    But R2 is moved a distance  equal to  the distance between  C2 and C1   this reduces R1-R2   by this amount

So the line will be      (R1-R2) -  distance betweenC2 and C1    (sorry...that black R1 should be labelled R2)

The black line represents x =2         f(2) is the y value of where the black line crosses the graph....

Thanks for confirmation

Yes, that is it !

Well the first year it would be 1500 penguins but since they lost 20% you multiply 1500 by 0.2 to get 300. 1500-300 = 1200. Then if you repeat the steps you should be able to get the final answer. P.S. dont half 1000 half the number of penguins that you got previously.

agreed

Here is a Venn diagram of this situation:

asada d gg

Hey Guest! So an easy way to simplify this question is: how many ways can you split 5 in two? Please tell me if this is incorrect but my thinking is that you can put 4 balls in one box and 1 in the other. In a similar way you can put 2 in one box and 3 in the other. When done in this way you should get 2. But you can also swap them since they are distinguishable so when you reverse then previous pairs you also get 2. So 2+2=4 . I believe the answer is 4 but I could be wrong. 

You are welcome !    ~EP

See diagram below....drop a vertical from the apex

a) sin gih = opp/hyp = 7/25

b) sin ghi =   can you figure this one out?

Thanks for the help

Here is one way....use law of sines

93 is to sin 25    as   DE is to sin 65

93 / sin25   =   DE/sin 65

sin 65^o  *  93  / sin 25^o   = DE        Use your calculator to finish !  

https://web2.0calc.com/questions/a-researcher-observes-and-records-the-height-of-a_2

A/(x - 1) + B/(x + 1) = (8x + 3)/(x^2 - 1)      Multiply both sides of the equation by (x^2-1)

A (x+1)   + B (x-1)  = 8x+3

Ax + A    +  Bx -B = 8x+3                equat the 'x' parts   and the constant parts

A+B = 8       and     A-B = 3     <======= two equations two unknowns.....solve for A and B

Add the two equations   2A = 11      so     A = 5.5   then B = 2.5

The blue graph is just the red graph shifted two units to the right

blue is then   y = f(x-2)

https://web2.0calc.com/questions/i-don-t-get-it_6