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tiny-mole [99]
3 years ago
11

Last Question of the day!

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
7 0
GEOMETRIC \: \: PROGRESSIONS \\ \\ \\\\Taking \: \: L.H.S. \: \\ \\ 0.999... \: = \: 0 \: + \: \frac{9}{10} \: + \: \frac{9}{100} \: + \: \frac{9}{1000} + \: ... \: \: \infty \\ \\ \\ 0.999... \: = \: \frac{9}{10} \: ( \: 1 \: + \frac{1}{10} \: + \: \frac{1}{100} \: + \: \frac{1}{1000} + \: ... \: \: \infty \: \: ) \\ \\ \\ 0.999... \: = \: \frac{9}{10} \: ( \: 1 + \: \: \frac{1}{ {10}^{1} } \: + \: \frac{1}{ {10}^{2} } \:+ \: \frac{1}{ {10}^{3} } \: + \: ... \: \: \infty \: ) \\ \\ \\ As \: we \: can \: see \: \: , \: \\ \\ Above \: expression \: in \: bracket \: forms \: a \: \\ Infinite \: Geometric \: Progression \\ \\ Where \: \: ,\: \: \: \: \\ a = 1 \: \: \: \: \: and \: \: \: \: \: r = \frac{1}{10} \\ \\ Sum \: of \: Infinite \: Geometric \: \\ Progression \: \: = \: \: \frac{a}{1 - r} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{1 - \frac{1}{10} } \: \: = \: \: \frac{1}{ \frac{9}{10} } \: \: = \: \: \frac{10}{9} \\ \\ \\ Putting \: in \: above \: , \: we \: get \: - \: \\ \\ 0.999... \: \: = \: \: \frac{9}{10} \times \frac{10}{9} \: \: \\ \\ \\ 0.999... \: \: = \: \: 1 \: \: = \: R.H.S. \\ \\ Hence , \: above \: expression \: is \: TRUE \: \: :)
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One side of a triangle is 2 times the second side. The third side is 15 feet longer than the second side. The perimeter of a
ch4aika [34]

Answer:

16, 8, 23

Step-by-step explanation:

2x+x+x+15=47

4x+15=47

4x=32

x=8

2x=16

x+15=23

7 0
3 years ago
Solve the following equation for g: 2(g - h) = b + 4
DaniilM [7]

Answer:

g = \frac{b+4+2h}{2}

Step-by-step explanation:

Given

2(g - h) = b + 4 ← distribute parenthesis on left side

2g - 2h = b + 4 ( add 2h to both sides )

2g = b + 4 + 2h ( divide both sides by 2 )

g = \frac{b+4+2h}{2}

6 0
3 years ago
Consider A is a set and B is another set, if Au B=A n B, then
Y_Kistochka [10]

Answer:

A = B

Step-by-step explanation:

The correct option is;

A = B

Check:

A = {2,3,4}

B = {2,3,4}

Au B = A n B = {2,3,4}

A or B cannot be null.

check

A = {2,3,4}

B = {}

Au B = {2,3,4}

A n B = {}

7 0
3 years ago
1. The ratio of boys to girls in Mr. Okafor's after-school club is the same as the ratio of boys to girls in Ms. Williams' after
Serjik [45]
27 is correct I hope you pass !
8 0
3 years ago
Multiply (2n + 2)(2n – 2) A. 4n 2 – 4 B. 4n 2 – 4n – 4 C. 4n 2 + 2n – 4 D. 4n 2 + 4n – 4
sattari [20]
This system can be a bit tricky unless you write it out:
(2n + 2)(2n - 2) ~ First you have to take one variable and multiply it to each of the other two variables, like:
2n * 2n ~ And:
2n * -2 ~ This gives you:
4n^2 - 4n
Now we do this with the other:
2 * 2n
2 * -2
4n - 4
Now we combine them both while adding like terms:
4n^2 - 4
Therefore your answer is: A. 4n^2 - 4
(This is due to how when having the positive 4n subtracted by the negative it cancels it out. Leaving us with the remaining two terms left.)

I hope this helps, have a great rest of your day! ^ ^
~Ghostgate
7 0
3 years ago
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