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GrogVix [38]
4 years ago
7

If x+y+z=9, xy+yz+zx =26; find x²+y²+z²

Mathematics
2 answers:
alekssr [168]4 years ago
8 0
<em>we know,</em>
<em>(x + y + z)² = x² + y² + z² + 2(xy + yz + xz)</em>
<em>9²  = x² + y² + z² + 2 X 26</em>
<em> 81 = x² + y² + z² + 52       </em>
<em>81 - 52 = x² + y² + z²</em>
<em>therefore, x² + y² + z² = 29</em>
vichka [17]4 years ago
7 0
<em>First, we must expand  and simplify :</em>
x + y+z = 9

(x + y+z)^{2} = (9)^{2}

x^{2} + y^{2}+z^{2} + 2(xy + yz+zx) = 81

<em>And Than, Enter the value :</em>

x^{2} + y^{2}+z^{2} + 2(26) = 81

x^{2} + y^{2}+z^{2} + 52 = 81

x^{2} + y^{2}+z^{2} = 81- 52

\boxed{x^{2} + y^{2}+z^{2} = 29}

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3 years ago
Theresa Morgan a chemist has a 10% hydrochloric acid solution and a 65% hydrochloric acid solution. How many liters of each shou
prisoha [69]

<u>ANSWER: </u>

170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution to obtain 1870 liters of 60% solution.

<u>SOLUTION: </u>

First, set up a table. Fill in the unknowns with variables x and y. The table is attached below

From this, we can easily set up the two equations.  

Sum of values of two acids = Value of mixture  

0.1x + 0.65y = 1122  

For convenience, we'll multiply the entire equation by 100,

10x + 65y = 112200   ------ (1)  

Now, Sum of amounts of each acid = Amount of mixture  

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multiply (2) with 10 for easy calculation and derive the equation into one variable.

10x + 10y = 18700  

Subtracting equation (2) from (1),  

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( − ) 10x + 10y = 18700

we get the solution as,

0 + 55y = 93500

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x  = 1870 - 1700  

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So, we have x = 170 and y = 1700

We can conclude that 170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution  to obtain 1870 liters of 60% solution.

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3 years ago
I need points 3+4%34
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Answer:

I do too :(

Step-by-step explanation:

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