Convert 11.42424242 … to a rational expression in the form of a over b, where b ≠ 0.

Mathematics

1 answer:

babymother [125]3 years ago

3 0

$x = 11\frac{42}{99}$

Step-by-step explanation:

$11.42424242.... = 11. \overline{42} \\ let \: x = 11. \overline{42} .....(1)\\ 100x = 1142.\overline{42}....(2) \\ subtracting \: (1) \: from \: (2) \: \\ 100x - x = 1142.\overline{42} - 11. \overline{42} \\ 99x = 1131 \\ x = \frac{1131}{99} \\x = 11\frac{42}{99} \\$

You might be interested in

Ok so I need help thank you

Liula [17]

Answer:

2.56

Step-by-step explanation:

I'm pretty sure, I'm sorry if its wrong

5 0

2 years ago

What number is in the middle of 25 and 50?

Firdavs [7]

(50-25)/2
25/2
12.5
25+12.5=37.5

6 0

2 years ago

Read 2 more answers

Let f and g be the functions defined by f(x) = 10^ (x+2 / 3) and g(x) = log (x3 / 100) for all positive real numbers,

Vaselesa [24]

Answer:

F(x) and g(x) are not inverse functions.

Step-by-step explanation:

In order to calculate the inverse function of a function, we have to isolate X and after that, we change the variables.

As our function f(x) is a exponentian function, we can apply logarithm with base 10 (log) in both sides in order to isolate X. Remember that log10=1.

$[tex]y=10^{(x+\frac{2}{3}) }\\\\log y=log 10^{(x+\frac{2}{3}) }\\log y = (x+\frac{2}{3}) . log10\\\frac{log Y}{log10} = (x+\frac{2}{3})\\\frac{log Y}{1} = (x+\frac{2}{3})\\log Y-\frac{2}{3}=x$ [/tex]