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3 years ago

Please solve this proportion with steps (I'm stuck) (9x+6)/18= (20x+4)/3x

2 answers:

7 0

$\frac{9x+6}{18}=\frac{20x+4}{3x}$

Cross multiply. Distribute...
$3x(9x+6)=18(20x+4)\\27x^2+18x=360x+72\\27x^2-342x-72=0\\3x^2-38x-8=0$

OH GOD IT'S A QUADRATIC
(our equation is in ax² + bx + c = 0 form. a=3. b= -38. c= -8.
plug these values into the quadratic formula and simplify.)
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-(-38)\pm\sqrt{(-38)^2-4(3)(-8)}}{2(3)}=\frac{38\pm\sqrt{1444+96}}6\\\\\sqrt{1444+96}=\sqrt{1540}=\sqrt{4\times345}=2\sqrt{345}\\\\\frac{38\pm2\sqrt{345}}6=\boxed{x=\frac{19\pm\sqrt{345}}3}$

Approximate values for x: -0.20714 or 12.874

attashe74 [19]3 years ago

4 0

First, distribute your like terms, which in this case is 'x'

you should get (9x+6)/18= 60x + 12

then you have to multiply both sides by 18 to get rid of the fraction

you should then get 9x+6= 1080x + 206

next, subtract 9x from 1080x, you should get 1071x

then subtract 206 on the side the 6 is on and you should get -200=1080x

divide both sides by 1080 and you should get x=0.19

For future preferences use PEMDAS = Parentheses, exponents, multiplication, division, addition, and subtraction. (Yeah, I know I didn't do it in that order)

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3 years ago

Find the next term in this arithmetic sequence: 2/3, 2, 3 1/3, ____

mihalych1998 [28]

Answer:

Problem 1: $4\frac{2}{3}$

Problem 2: 2.5

Problem 3: 0

Step-by-step explanation:

If it tells you it is arithmetic, it is give you a huge hint. Arithmetic sequences have common differences. That means if you do:

$\text{term}-\text{ term right before}$ you will get the same number.

Problem 1:

$\text{Term}-{Previous}$

$2-\frac{2}{3}$

$1\frac{1}{3}$

So the common difference is $1\frac{1}{3}$ .

The next term can be found by adding $1\frac{1}{3}$ to the previous.

$3\frac{1}{3}+1\frac{1}{3}=4\frac{2}{3}$ .

Problem 2:

0.5 , 0.7 , ....

Start with finding the common difference:

$0.7-0.5$

$0.2$ is the common difference.

The common difference can be used to find the next term given it's previous term.

So you have:

First term is 0.5 .

Second term is 0.7 .

Third term is 0.7+ 0.2=0.9 .

Fourth term is 0.9 + 0.2=1.1 .

You could find a pattern so you don't have to find all the terms before the 11th.

So let's start over:

First term is 0.5 .

Second term is 0.5+0.2 .

Third term is 0.5+0.2(2).

Fourth term is 0.5+0.2(3).

.............

nth term is 0.5+0.2(n-1).

The thing in parenthesis was always one less than term number we wanted to find.

The 11th term is given by 0.5+0.2(10).

Let's simplify:

0.5+0.2(10)

0.5+2

2.5

2.5 is the 11th term.

Problem 3:

We are going to do something similar that we did for the problem before this one.

First common difference is given by:

Term-Previous

24-27

-3

The common difference is -3. (It is going down by 3 each time.)

The tenth will be given by 27+-3(9).

Let's simplify:

27+-3(9)

27+-27

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