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3 years ago

Find the next three terms of the geometric sequence -8, 12, -18,27

Mathematics

1 answer:

Pie3 years ago

3 0

Answer:

-40.5, 60.75, -91.125

Step-by-step explanation:

first you want to find the common difference. So just divide 12 by -8, which is -1.5 and then multiply 27 by -1.5, which is -40.5 and continue two more times.

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marta [7]

Answer:

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Step-by-step explanation:

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3 years ago

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Travka [436]

Step-by-step explanation:

$\sqrt{(x + 6) ^{2} } = \sqrt{18} \\ x + 6 = + - \sqrt{18} \\ x + 6 = + - \sqrt[3]{2}$

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3 years ago

Which statement best reflects the solution(s) of the equation?

Inessa [10]

x=2 is only solution while x=1 is extraneous solution

Option C is correct.

Step-by-step explanation:

We need to solve the equation $\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$ and find values of x.

Solving:

Find the LCM of denominators x-1,x and x-1. The LCM is x(x-1)

Multiply the entire equation with x(x-1)

$\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}\\\frac{1}{x-1}*x(x-1)+\frac{2}{x}*x(x-1)=\frac{x}{x-1}*x(x-1)\\Cancelling\,\,out\,\,the\,\,same\,\,terms:\\x+2(x-1)=x^2\\x+2x-2=x^2\\3x-2=x^2\\x^2-3x+2=0$

Now, factoring the term:

$x^2-2x-x+2=0\\x(x-2)-1(x-2)=0\\(x-1)(x-2)=0\\x-1=0\,\,and\,\, x-2=0\\x=1\,\,and\,\, x=2$

The values of x are x=1 and x=2

Checking for extraneous roots:

Extraneous roots: The root that is the solution of the equation but when we put it in the equation the answer turns out not to be right.

If we put x=1 in the equation, $\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$ the denominator becomes zero i.e

$\frac{1}{1-1}+\frac{2}{1}=\frac{1}{1-1}\\\frac{1}{0}+2=\frac{1}{0}$

which is not correct as in fraction anything divided by zero is undefined. So, x=1 is an extraneous solution.

If we put x=2 in the equation,

$\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$

$\frac{1}{2-1}+\frac{2}{2}=\frac{2}{2-1}\\\frac{1}{1}+1=\frac{2}{1}\\1+1=2\\2=2$

So, x=2 is only solution while x=1 is extraneous solution

Option C is correct.

Keywords: Solving Equations and checking extraneous solution

Learn more about Solving Equations and checking extraneous solution at:

#learnwithBrainly

5 0

3 years ago

(7/8)(?)=21<br><br> please help!

alukav5142 [94]

7/8 x = 21
7x = 21×8
7x = 168
x = 24

6 0

3 years ago

Read 2 more answers

What does it mean when two lines are perpendicular? What does it tell you about the equations?

Vaselesa [24]

When lines are perpendicular it’s called parallel, it’s when the lines never touch

3 0

3 years ago