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steposvetlana [31]

4 years ago

10

Complete the table to make this a proportional relationship

1 answer:

vitfil [10]4 years ago

8 0

Answer:

21

Step-by-step explanation:

y-y over x-x

12-3=9 8-2=6 change in y over change in x is 9/6 or 3/2. 3/2 times 14 is 21...or adding 6 to the x causes adding 9 to the y. 6 is added again to 8 to make fourteen. since the same thing is happening. then do the same to the x. add 9. 12 plus 9 is 21. tell me if this helps

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vovikov84 [41]

Answer:

The simplified expression to the given expression is $\frac{4x^6}{y^2}$

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Step-by-step explanation:

Given fractional expression is $\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}$

To simplify the given expression as below :

$\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}$

$=\frac{2(2x^3y^4)^4}{(2x^2y^6)^3}$

$=\frac{2[(2)^4(x^3)^4(y^4)^4]}{(2)^3(x^2)^3(y^6)^3}$ ( using the property $(a^m)^n=a^{mn}$ )

$=\frac{2[(2)^4(x^{12})(y^{16})]}{(2)^3(x^6)(y^{18})}$

$=2[(2)^4(x^{12})(y^{16})](2)^{-3}(x^{-6})(y^{-18})$ ( ( using the property $a^m=\frac{1}{a^{-m}}$ )

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$=2[2^1x^6y^{-2}]$

$=\frac{4x^6}{y^2}$ ( using the property $a^m=\frac{1}{a^{-m}}$ )

Therefore the simplified expression is $\frac{4x^6}{y^2}$

Therefore $\frac{4(2x^3y^4)^4}{2(2x^2y^6)^3}=\frac{4x^6}{y^2}$

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