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Darya [45]
3 years ago
11

Prove algebraically that 0.5 recurring = 5/9

Mathematics
1 answer:
ad-work [718]3 years ago
3 0

Answer and Step-by-step explanation:

We want to prove that 0.5555... = 5/9.

First, let's set 0.555... equal to x:

x = 0.555...

Now multiply this by 10:

10x = 5.555...

Now subtract the original from this new one:

   10x = 5.555...

-       x = 0.555...

______________

     9x = 5

Note that we could cancel all the recurring terms because they were the same for both 5.555... and 0.555... since the 5's go up to infinity.

We now have 9x = 5, so divide both sides by 9:

x = 5/9, as desired

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What is the slope of the line whose equation is y−4=5/2(x−2)?
postnew [5]

Answer:

m=\dfrac{5}{2}

Step-by-step explanation:

If the equation of the line is

y=mx+b,

then m represents the slope of the line and b represents the y-intercept of the line. This equation is called the equation of the line in the slope form.

Rewrite the equation of the line in the slope form

y-4=\dfrac{5}{2}(x-2)\\ \\y-4=\dfrac{5}{2}x-\dfrac{5}{2}\cdot 2\\ \\y-4=\dfrac{5}{2}x-5\\ \\y=\dfrac{5}{2}x-1

Thus, the slope of the line is

m=\dfrac{5}{2}

7 0
3 years ago
Read 2 more answers
a cylinder and a cone have the same radius and height. The volume of the cylinder is 534ft3 . what volume of the cone?
DochEvi [55]

Answer: 178 ft^3

Step-by-step explanation:

A cylinder has the formula V=pi radius ^2 height

A cone has the formula V= 1/3 pi radius ^2 height

So 1/3 of the volume of the cylinder is the volume of a cone

1/3 of 534 = 178 ft^3

5 0
2 years ago
Pls help meh<br><br> 6th grade math
defon

Answer:

100%

Step-by-step explanation:

It says 38 out of 38 votes were for hunger relief. If it were like that, it would be 100%. Same as if it were 22 out of 22 votes. Like, think about if you were taking a test with 20 questions, and you got 20 questions right. You'd get a hundred percent, right? Same thing here, just a different equation.

Hope this helps

6 0
3 years ago
Read 2 more answers
URGENT
Ivan

This is a question of proportions:

First we can work out how many feet it goes up for each feet he steps back:

5.5/6 ft per each feet he steps back.

Now we can multiply this by the amount of ft back the cliff is:

(5.5/6)*30 = 27.5 ft

Thus the cliff is 27.5 ft tall,

Hope this helps :)

3 0
3 years ago
Customers arrat a service window according to a poisson process with an average of 0.2 per minute.
suter [353]

Answer:

Step-by-step explanation:

Given that customers arrat a service window according to a poisson process with an average of 0.2 per minute

=  12 per hour.

a)  the probability that the time between two successive arrivals is less than 6 minutes

= For one hour more than 60/6 =10 customers arrive.

P(X>10) = 0.6528

b) Prob that there will be exactly three arrivals during a given 10-minute period

P(x=3) for average 2

= 0.1804

3 0
3 years ago
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