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3 years ago

Solve for x: two thirds(x − 2) = 4x.

Mathematics

1 answer:

Sveta_85 [38]3 years ago

5 0

Answer:

$x = - 0.4$

Step-by-step explanation:

$\frac{2}{3} (x - 2) = 4x$

Expand with the distributive rule:

$\frac{2}{3} x - \frac{2}{3} \times 2 = 4x$

$\frac{2}{3} x - \frac{4}{3} = 4x$

Add 4/3 to both sides:

$\frac{2}{3} x = 4x + \frac{4}{3}$

Subtract 4x from both sides

$- \frac{10}{3} x = \frac{4}{3}$

$- 10x = 4$

$x = - 0.4$

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3 years ago

Read 2 more answers

A small town has 2000 inhabitants. At 8 AM, 160 people have heard a rumor. By noon half the town has heard it. At what time will

QveST [7]

Answer:

3:36 PM

Step-by-step explanation:

Let fraction (y) of the people that heard the rumor , the differential equation that is satisfied by the by y is,

$\frac{dy}{dt} = ky(1-y)$

Solving the differential equation,

$y(t) = \frac{y_{o}}{[y_{o} + (1 + y_{o})e^{-kt}]}$

The total number of inhabitants of the town = 2000

The number of people that heard the rumor = 160

At 8 AM, let t = 0,

$y(0) = \frac{160}{2000}$

= 0.08

By noon, half of the town as heard the rumor.

Then,

$y(4) = \frac{1}{2}$

Therefore,

$\frac{1}{2} = \frac{0.08}{[0.08 + (1 - 0.08)e^{-4k}]}$

$\frac{0.08}{[0.08 + 0.92e^{-4k}]} = \frac{1}{2}$

$0.08 + 0.92e^{-4k} = 0.16$

$0.92e^{-4k} = 0.16 - 0.08$

$0.92e^{-4k} = 0.08$

$e^{-4k} = \frac {0.08}{0.92}$

$k = - \frac{1}{4} In(\frac {0.08}{0.92})$

k ≈ 0.06106

Calculating time, t when y(t) = 90%

⇒ y(t) = 0.9

$\frac{0.08}{[0.08 + 0.92e^{-0.06106t}]} =0.9$

$0.08 + 0.92e^{-0.06106t} = \frac {0.9}{0.08}$

$0.08 + 0.92e^{-0.06106t} = 0.089$

$0.92e^{-0.06106t} = 0.089 - 0.08$

$0.92e^{-0.06106t} = 0.0089$

$t = - \frac{1}{0.06106}In (\frac{0.0089}{0.92})$

t = 7.59 hours

⇒ 7 hours 36 minutes

From 8 A.M. plus 7 hours 36 minutes = 3:36 PM

At 3:36 PM will 90% of the population have heard the rumor

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3 years ago

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4 years ago

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RUDIKE [14]

Answer:

B solving by factoring
A the quadratic formula

Step-by-step explanation:

The "zero product principle" or "zero product rule" tells you a product will be zero if and only if one or more of the factors is zero. This fact is used to solve quadratic equations by factoring.

Factoring the equation y = ax² +bx +c to the form y = a(x -r)(x -s) allows you to immediately identify the solutions of y=0 as x=r and x=s. These are the values of x that make the factors zero, hence making the product zero.

Finding the values of x that satisfy ax² +bx +c = 0 by rearranging it to the form a(x -r)(x -s) = 0 is called "solving by factoring."

When the process of "completing the square" is applied to the standard-form quadratic y = ax² +bx +c, the result is a formula for the two solutions to y = 0:

$x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

This quadratic formula tells you the solutions based on the coefficients of the original equation, so <em>does not require rearranging</em> the equation in any way.

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2 years ago