What is 5.57575757... as a fraction ?

Assuming you can't use a calculator:

5.575757... = 5 + 0.575757...

let 0.575757... = x

1) Substitute x for 0.575757...

5.575757... = 5 + x

2) Multiply both sides by 100

100(5.575757...) = 100(5+x)            

557.575757... = 500 + 100x    

3) Subtract 500 from both sides

57.575757... = 100x          

4) 57.575757... can be written as 57 + 0.575757...              

57 + 0.575757... = 100x

5) Substitute x for 0.575757...

57 + x = 100x

6) Subtract x from both sides

57 = 99x

7) divide both sides by 99

x = 57/99

8) plug in 57/99 for x in our original equation

5.575757... = 5 + (57/99)

9) simplify

5.575757... = ((5*99)/99) + (57/99)

5.575757... = (495/99) +(57/99)

5.575757... = (495+57)/99

5.575757... = 552/99

5.575757... as a fraction is 552/99

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

idk

step-by-step explanation: