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Ostrovityanka [42]

3 years ago

5

Latisha earns $5 dollars an hour painting her neighbors fence create two variables PART:A determine which is dependent and which

is independent
PART:B list three ordered pairs to show the values of the two variables
PART:C write an equation to represent the relationship between the two variables

2 answers:

Natali [406]3 years ago

4 0

D=dollars earned

T=time spent painting the fence.

(1,5) (2,10) (3,15)

D=5T

ratelena [41]3 years ago

4 0

D=5t d would equal 5t

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Read 2 more answers

<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.

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

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