1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tiny-mole [99]
2 years ago
11

Last Question of the day!

Mathematics
1 answer:
Thepotemich [5.8K]2 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 \: \: :)
You might be interested in
Find the distance between the points (0, 10) and (–9, 1).
Assoli18 [71]
D=sqrt[(x1-x2)^2+(y2-y1)^2]
(0,10) x1=0 y1=10 and (-9,1) x2=-9 y2=1
now d=sqrt[(-9-0)^2+(1-10)^2]=12.72792206 units
6 0
3 years ago
A right triangle has a hypotenuse of 15 cm. What are possible lengths for the two legs of the
saw5 [17]

Answer:5 and 3

Step-by-step explanation:

you can multiply 5x3 to get 15

3 0
2 years ago
Which is the graph of f(x) = (x + 3)(x - 2​
yanalaym [24]

Answer:

Step-by-step explanation:

f(x) = (x + 3)(x - 2​) has two zeros:  One stems from (x + 3) = 0 and is (-3, 0); the other stems from (x - 2) = 0 and is (2, 0).  

The axis of symmetry is a vertical line located halfway between -3 and 2:  

x =  -1/2.

The graph opens up because the given (x + 3)(x - 2) has a positive leading coefficient (+1).

With this information we can eliminate the last two possible answers.  Note that the x-intercepts of the first graph are -3 and 2,  Thus, the first graph is the correct one.

5 0
2 years ago
Given the function f(x) = 3|x – 2| + 6, for what values of x is f(x) = 18?
Nikolay [14]

Answer:

x = -2, x = 6

Step-by-step explanation:

18 = 3|x - 2| + 6

12 = 3|x - 2|

4 = |x - 2|

4 = x - 2    and    -4 = x - 2

x = 6    and    x = -2

4 0
2 years ago
Read 2 more answers
Help asap need answers need help
Lesechka [4]

Answer: hope you get some help

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • 25x2-8x=12x-4 <br> Can someone please help me on this ?????
    9·2 answers
  • Which algebraic expression is a difference with two terms
    12·1 answer
  • Question is in the picture, please help me
    10·1 answer
  • Find the x-coordinate of the vertex, y-coordinate of the vertex, and the x-intercepts.
    15·1 answer
  • If F(x)=9x which of the following is the inverse of F(x)
    15·2 answers
  • Sheila bought burgers and fries for her children and some friends. the burgers cost $2.05 each and the fries are $.85 each. she
    7·1 answer
  • Select the correct text in the passage.
    10·1 answer
  • Can someone help me with this problem? Please!?
    10·1 answer
  • Consider this linear system:
    9·2 answers
  • Please someone help with that
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!