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kipiarov [429]
3 years ago
6

Solve

%7Bx%7D%20%3D%20%5Cdfrac%7B1%7D%7Bp%20%2B%20q%20%2B%20x%7D" id="TexFormula1" title="\sf \dfrac{1}{p} + \dfrac{1}{q} + \dfrac{1}{x} = \dfrac{1}{p + q + x}" alt="\sf \dfrac{1}{p} + \dfrac{1}{q} + \dfrac{1}{x} = \dfrac{1}{p + q + x}" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Nostrana [21]3 years ago
3 0

Answer:

\displaystyle   \begin{cases} \displaystyle  {x} _{1} =  - p \\   \displaystyle x _{2}   =  -  q \end{cases}

Step-by-step explanation:

we would like to solve the following equation for x:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}  +  \frac{1}{x}  =  \frac{1}{p  + q + x}

to do so isolate \frac{1}{x} to right hand side and change its sign which yields:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}    =  \frac{1}{p  + q + x}  -  \frac{1}{x}

simplify Substraction:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}    =  \frac{x - (q + p +  x)}{x(p  + q + x)}

get rid of only x:

\displaystyle  \frac{1}{p}  +  \frac{1}{q}    =  \frac{  - (q + p )}{x(p  + q + x)}

simplify addition of the left hand side:

\displaystyle  \frac{q + p}{pq}     =  \frac{  - (q + p )}{x(p  + q + x)}

divide both sides by q+p Which yields:

\displaystyle  \frac{1}{pq}     =  \frac{  -1}{x(p  + q + x)}

cross multiplication:

\displaystyle    x(p  + q + x)  =   - pq

distribute:

\displaystyle    xp  + xq +  {x}^{2} =   - pq

isolate -pq to the left hand side and change its sign:

\displaystyle    xp  + xq +  {x}^{2} + pq =  0

rearrange it to standard form:

\displaystyle   {x}^{2} +    xp  + xq  + pq =  0

now notice we end up with a <u>quadratic</u><u> equation</u> therefore to solve so we can consider <u>factoring</u><u> </u><u>method</u><u> </u><u> </u>to use so

factor out x:

\displaystyle  x( {x}^{} +   p ) + xq  + pq =  0

factor out q:

\displaystyle  x( {x}^{} +   p ) +q (x + p)=  0

group:

\displaystyle  ( {x}^{} +   p ) (x + q)=  0

by <em>Zero</em><em> product</em><em> </em><em>property</em> we obtain:

\displaystyle   \begin{cases} \displaystyle  {x}^{} +   p  = 0 \\   \displaystyle x + q=  0 \end{cases}

cancel out p from the first equation and q from the second equation which yields:

\displaystyle   \begin{cases} \displaystyle  {x}^{}   =  - p \\   \displaystyle x  =  -  q \end{cases}

and we are done!

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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The
Delvig [45]

10 small boxes and 11 large boxes were shipped.

Step-by-step explanation:

Given,

Total boxes shipped = 21

Total volume of shipped boxes = 342 cubic feet

Volume of each small box = 10 cubic feet

Volume of each large box = 22 cubic feet

Let,

Number of small boxes = x

Number of large boxes = y

According to given statement;

x+y=21     Eqn 1

10x+22y=342    Eqn 2

Multiplying Eqn 1 by 10

10(x+y=21)\\10x+10y=210\ \ \ Eqn\ 3

Subtracting Eqn 3 from Eqn 2

(10x+22y)-(10x+10y)=342-210\\10x+22y-10x-10y=132\\12y=132

Dividing both sides by 12

\frac{12y}{12}=\frac{132}{12}\\y=11

Putting y=11 in Eqn 1

x+11=21\\x=21-11\\x=10

10 small boxes and 11 large boxes were shipped.

Keywords: linear equation, subtraction

Learn more about linear equations at:

  • brainly.com/question/4793866
  • brainly.com/question/4824362

#LearnwithBrainly

3 0
3 years ago
Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36
Kamila [148]

A. 2x3=6 and 6x12=72 so 78 is greater than 36

6+72=79 which is less than 90

3 0
3 years ago
Read 2 more answers
Polynomial in standard form 7x+3+5x squared
lesya692 [45]
7x+3+5x²
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Hoped this helped!
6 0
3 years ago
The Wall Street Journal reported that automobile crashes cost the United States $162 billion annually (2008 data). The average c
ivanzaharov [21]

Answer:

n=(\frac{2.326(500)}{120})^2 =93.928 \approx 94

So the answer for this case would be n=94 rounded up to the nearest integer

Step-by-step explanation:

Information given

\bar X represent the sample mean

\mu population mean (variable of interest)

\sigma= 500 represent the population standard deviation

n represent the sample size  

Solution to the problem

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{s}{\sqrt{n}}    (a)

And on this case we have that ME =120 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The confidence2 level is 98% or 0.98 then the significance level would be \alpha=1-0.98=0.02 and \alpha/2=0.01, the critical value for this case would be z_{\alpha/2}=2.326, replacing into formula (b) we got:

n=(\frac{2.326(500)}{120})^2 =93.928 \approx 94

So the answer for this case would be n=94 rounded up to the nearest integer

8 0
3 years ago
Look at this set of 5 numbers: 21471 By how much would the mode decrease if the number 1 were added to the set?
Fofino [41]

Answer:

  • Zero

Step-by-step explanation:

The mode is the number of most repeated data in the set.

Given set 2, 1, 4, 7, 1 has mode 1 (repeated twice).

If we add 1 to the set the mode will remain 1 as it will repeat three times, so the mode won't change.

There is no change in mode, so the mode decrease is zero.

6 0
2 years ago
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