Answer and Step-by-step explanation:
Suppose x = 0.2355555... .
Multiply x by 100 and 1000:
100x = 23.5555....
1000x = 235.5555....
Let's subtract the first equation from the second:
1000x - 100x = 235.5555.... - 23.555.....
Because the decimal part for each goes on forever, we can simply cancel them out in our subtraction statement:
900x = 235 - 23 = 212
Divide both sides by 900:
x = 212/900 = 53/225
Thus, since x = 0.235555..., we know that:
0.23555.... = 53/225
Since p = 53 and q = 225 are integers, we have proven that this repeating decimal can be written as a fraction.
<em>~ an aesthetics lover</em>
Answer:
y = -6
Step-by-step explanation:
To simplify this equation as much as possible, we have to get the variable y by itself.
To do this, we would do the inverse operation of subtraction and add 7 to the left and right side of the equation.
-7 + 7 + 5y = -37 + 7
The 7s cancel out on the left side because -7+7 = 0 and so we are left with,
5y = -30
Then we would do the inverse operation of multiplication and divide by 5 on the left and right side of the equation.
5y/5 = -30/5
y = -6
Answer:
21.204
Step-by-step explanation:
