CPhill

Correct.....!!!

Look at Melody's graph here, Mathtoo : https://www.desmos.com/calculator/fpruev1hep

Note that that all the coordinates  (a, b)  on the graph have a corresponding point (b, a) on the  graph

For instance....note that the point  (0,6)  is on the graph....and note also that  the point  (6, 0)  is also on the graph

[ The inverse  of a function just reverses the coordinates produced by that function ]

Does that make sense  ???

Here's a geometric proof of the Pythagorean Theorem using similar triangles :

Let  ABC  be a righ triangle with a right angle at C

And CD is an altitude  with right angles ADC  and BDC

We want to prove that  AC^2  + BC^2 =  AB^2

So...looking at triangles ABC  and ADC

Angle A  = angle A

Angle ACB  = angle CDA

So...by AA  congruency.....Δ ACB ~Δ ADC  →  AC /AB  = AD/ AC  →  AC^2  = AB * AD

Similary  Δ ACB ~ ΔCDB → AB / BC = BC / DB  →  BC^2  = AB * DB

So

AC^2  + BC^2  = AB* AD   + AB * DB

AC^2 + BC^2  = AB ( AD + DB)

AC^2 + BC^2  = AB (AB)

AC^2 + BC^2  = AB^2

a · b = 20

b · c = 12

a + b + c =12 

a=? b=? c=?

a =  20/b

c  = 12/ b

So

a +  b +  c  = 12    substitute for a, c

20/b + b + 12/b  =  12      multiply through by b

20 + b^2 + 12  = 12b     rearrange and simplify

b^2 - 12b + 32   =  0       factor

(b - 4) ( b - 8)  = 0

Set each factor to 0   and solve for  b  and we have that

b  = 4   or  b  = 8

If we want  a and c to  be integers, then b = 4  is the only solution

And  a  = 20 / b = 20 / 4  = 5

And c  = 12/b  = 12/4   = 3

So

a * b  = 5 * 4  = 20

b * c =  4 * 3   = 12

And

a + b + c  = 5 + 4 + 3   = 12

So  (a, b, c)  = ( 5 , 4, 3)

Thanks, Daisy....here's another way to do this  :

We  have 4 choices for the leading digit...and for the second digit, we have 10 choices....the last digit is the same as the  leading digit....

So....4  * 10  = 40 palindromes  between 100 and 500

Eh...no big deal, Hectictar...now we know the area and  perimeter.......LOL!!!

Hectictar has given the perimeter of the third one....to find the area

If we moved the triangle above the red line down and joined it to the bottom  of the figure....we would have a square that is  23 ft on each side....so..the area  is   side^2 =  23^2  = 529 ft^2

C  is true

f(t)   = beginning population * ( 1 + growth rate)^t

f(t)  =    4800  ( 1 +  .02)^t

First of all...there are about   1.09 yds  in one meter

So  

3.7 m  x   1.09 yds / 1 m   =   [cancel the  m  ] and we have    3.7 x 1.09  ≈  4.033  yds

I'm unsure about the  "c"   in part (f)  ...is this supposed  to  be  centiliters  ???

17.5  kg  =   17500 g

The volume of the solid is

300 * 100 * .25  = 7500 cm^3

So...the density  is     17500 g  / 7500 cm^3   ≈  2.33 g / cm^3