the lenght of the longer leg of a right triangle is 9 ft longer than the lenght of the shorter leg x. The hypotenuse is 9 ft shorter than twice the lenght of the shorter leg.

see below

Step-by-step explanation:  5 23  8 03

the lenght of the longer leg of a right triangle is 9 ft longer than the lenght of the shorter leg x. The hypotenuse is 9 ft shorter than twice the lenght of the shorter leg.

shorter leg    = x

longer leg     = x + 9

hypotenuse  =  2x - 9

Pythagorean theorem  =    a² + b²  = c²

             shorter-leg² + longer-leg² = hypotenuse²

                         x²  +  (x+9)²  = (2x - 9)²                  solve for x

                  x² +  (x+9) (x+9)  =  (2x - 9)(2x - 9)

                 x² +  (x²+18x+81)  =  (4x² - 36x + 81)

                       (2x²+18x+81)  =  (4x² - 36x + 81)

                                          0 =   2x² -54x

                                          0 =  x(2x - 54)  

                           0 = x      and         0 = 2x -54  

                                                       54 = 2x

                                                      27 =  x

shorter leg    = 27        

longer leg     = 36

hypotenuse  =  45

divided all the values by 9 and you get a 3, 4, 5  right triangle, so the answer checks correct  

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.