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Lubov Fominskaja [6]
3 years ago
7

Find the y-intercept of the line:

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
6 0
(0,-6)
I'm not 100% sure!
Hope I could help!
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<img src="https://tex.z-dn.net/?f=The%20%5C%3A%20%20value%20%20%5C%3A%20of%20%20%5C%3A%20%20%5Csqrt%7B6%20%2B%20%20%5Csqrt%7B6%2
saul85 [17]

\large\underline{\sf{Solution-}}

<u>Let us assume that:</u>

\sf \longmapsto x =  \sqrt{6 +  \sqrt{6 +  \sqrt{6 + ... \infty } } }

We can also write it as:

\sf \longmapsto x =  \sqrt{6 +  x }

Squaring both sides, we get:

\sf \longmapsto  {x}^{2}  =6 +  x

\sf \longmapsto  {x}^{2} - x - 6  =0

By splitting the middle term:

\sf \longmapsto  {x}^{2} - 3x + 2x - 6  =0

\sf \longmapsto x(x - 3) + 2(x - 3 ) =0

\sf \longmapsto (x+ 2)(x - 3 ) =0

<u>Therefore:</u>

\longmapsto\begin{cases} \sf (x+ 2) =0 \\ \sf (x - 3) = 0 \end{cases}

\sf \longmapsto x =  - 2,3

<u>But x cannot be negative. </u>

\sf \longmapsto x = 3

Therefore, the value of the expression is 3.

\large\underline{\sf{Verification-}}

Given:

\sf\longmapsto x=3

We can also write it as:

\sf\longmapsto x = \sqrt{9}

\sf\longmapsto x = \sqrt{6+3}

\sf\longmapsto x = \sqrt{6 + \sqrt{9}}

\sf\longmapsto x = \sqrt{6 + \sqrt{6+3}}

\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{9}}}

\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+3}}}

This pattern will continue.

\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+...\infty}}}

7 0
3 years ago
What is 38.86 rounded to one decimal place
emmasim [6.3K]
38.9 
..........
Bcz 6 >5
:)
3 0
4 years ago
Read 2 more answers
Susan has 50% more books than Michael. Michael has 40 books. If Michael buys 8 more books, will Susan have more or less books th
ololo11 [35]

Answer:

Susan has more books than Michael.

Step-by-step explanation:

If Susan has 50% more books and Michael has 40 books, that means Susan has 1.5 times 40 = 60

40 + 8 = 48

60 is more than 48, so Susan has more books than Michael

7 0
3 years ago
The equation x2+y2=14 represents a
Ann [662]

Answer:

r = √14

Step-by-step explanation:

Is this what you meant?  If so heres' the answer

Equation of circle

Center the origin

r = √14

5 0
3 years ago
Read 2 more answers
100 POINTS!!! Please solve this question step by step and explain each step for 100 points.
djverab [1.8K]

2\dfrac 29 = -\dfrac 45  m \\\\\implies 2+ \dfrac 29 =- \dfrac 45 m \\\\\implies \dfrac{20}9 = -\dfrac 45 m \\\\\implies 5(20) = (-4m)9\\\\\implies 100 = -36m\\\\\implies m = -\dfrac{100}{36} \\\\\implies m =  -\dfrac{25}9\\\\\implies m=-2\dfrac 79

3 0
2 years ago
Read 2 more answers
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