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3 years ago

Represent the following sentence as an algebraic expression, where "a number" is the

Mathematics

1 answer:

Vlad1618 [11]3 years ago

4 0

Answer:
2 (x+3)

twice : multiply by 2
sum of a number and 3 : x+3

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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

Por favor ayúdeme!!

Inessa [10]

Answer:

CHEEEEEEEEESE

Step-by-step explanation:

3 0

4 years ago

PLEASE HELP!!!! Find the value of -7 - 8 - (-8) - 7. 0 14 -14 -30

miskamm [114]

-7 - 8 - (-8) - 7 × 0(14) - 14 - 30

(I think that's what that says)

Do PEMDAS

0(14) = 0

-7 × 0 = 0

You're left with -7 - 8 - (-8) - 14 - 30

Go from left to right

-7 - 8 = -15

-15 - (-8) = -7

-7 - 14 = -21

-21 - 30 = -51

7 0

3 years ago

Read 2 more answers

Please anyone help

serg [7]

5.46 to 3 sig figs means the range is {5.455,5.465} and 17.74 means the range {17.735,17.745}.
p=q²/r has a maximum value when q=5.465 and r=17.735 and a minimum value when 5.455 and r=17.745.
So the range of p is 1.6769 to 1.6840. When we have 2 decimal places we get p=1.68 which accommodates the maximum and minimum values of the range. So 2 decimal places is a suitable degree of accuracy, or we could say 3 significant figures.

7 0

3 years ago

Read 2 more answers

For the circle with equation (x-2)^2+(y+3)^2=9, answer each question. a) whats coords of the center? b) what are the radius and

MrRissso [65]

Answer:

<h2>a) center (2, -3)</h2><h2>b) radius r = 3</h2><h2>c) in the attachment</h2>

Step-by-step explanation:

The standard form of an equation of a circle:

$(x-h)^2+(y-k)^2=r^2$