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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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Write equations for the vertical and horizontal lines passing through the point (0, -3).
Natasha2012 [34]

Answer:

Vertical line will be x=0, and horizontal line will be y=-3

Step-by-step explanation:

Draw a vertical line through point (0,-3). You will see it's on the y-axis. The equation of the line on y-axis is always x=0, because no matter what point you choose on the line, the x coordinate will be 0. (0,-3), (0, -2), etc.

Next draw a horizontal line through (0,-3). It's parallel to the x axis, and no matter what point on the line you choose, the y coordinate will be -3. (0,-3), (1, -3), etc

8 0
3 years ago
Anton defines an acute angle as an angle that is not obtuse. Is Anton's definition valid ?
kobusy [5.1K]

Answer:

Anton's definition is not valid.

Step-by-step explanation:

We have been given that Anton defines an acute angle as an angle that is not obtuse. We are asked to find whether Anton's definition is valid or not.

We know that an angle is known as acute angle whose measure is greater than 0 and less than 90 degrees.

We also know that an angle is known as obtuse angle whose measure is greater than 90 degrees and less than 180 degrees.

We know that a right triangle is neither acute nor obtuse. Since Anton hasn't mentioned a right triangle to his definition, therefore, his definition is not valid.

4 0
3 years ago
Find the equation of the line through point (8, -9) and perpendicular to 3x +8y =4
deff fn [24]

Answer:

y = 8/3x - 91/3

*view attached graph*

Step-by-step explanation:

3x +8y =4

-3x    -3x

8y = -3x + 4

/8      /8

y = -3/8x + 1/2

Perpendicular lines have reciprocal slopes. So, the slope of -3/8 will now be 8/3

y = mx + b

y = 8/3x + b

-9 = 8/3(8) + b

-9 = 64/3 + b

3(-9 = 64/3 + b)

-27 = 64 + 3b

-64 -64

-91 = 3b

/3    /3

-91/3 = b

y = 8/3x - 91/3

Check your answer using (8, -9):

y = 8/3x - 91/3

-9 = 8/3(8) - 91/3

-9 = 64/3 - 91/3

-9 = -27/3

-9 = -9

This statement is true.

Hope this helps!

4 0
3 years ago
You pay $2 to play a game in which you roll one fair die. If you roll a 5 on the first roll, you win $5. If you roll a 1 or a 2,
Kazeer [188]

Answer:

The answer is 4

Step-by-step explanation:

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6 0
3 years ago
Read 2 more answers
Help pls ..........................
VARVARA [1.3K]
I believe the answer is
A: 40°
B: 36°
7 0
3 years ago
Read 2 more answers
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