12 x − 15 = 6 − 3 x

Mathematics

1 answer:

11Alexandr11 [23.1K]2 years ago

5 0

Answer:

x= 7/5 (1 2/5 or 1.4)

Step-by-step explanation:

Move the variable to the left-hand side and change its sign.

12x-15+3x=6

Move the constant to the right-hand side and change its sign.

12x+3x=6+15

Collect like terms.

15x=21

Divide both sides of the equation by 15.

x=7/5 (1 2/5 or 1.4)

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The owner of a cattle ranch would like to fence in a rectangular area of 3000000 m^2 and then divide it in half with a fence dow

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If you notice the picture below, the amount of fencing, or perimeter, that will be used will be 3w + 2l

now $\bf \begin{cases}
A=l\cdot w\\\\\
A=3000000\\
----------\\
3000000=l\cdot w\\\\
\frac{3000000}{w}=l
\end{cases}\qquad thus
\\\\\\
P=3w+2l\implies P=3w+2\left( \cfrac{3000000}{w} \right)\implies P=3w+\cfrac{6000000}{w}
\\\\\\
P=3w+6000000w^{-1}\\\\
-----------------------------\\\\
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\begin{cases}
0=w^2\\\\
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solve for "w", to see what critical points you get, and then run a first-derivative test on them, for the minimum

notice the $0=w^2\implies 0=w$ so. you can pretty much skip that one, though is a valid critical point, the width can't clearly be 0

so.. check the critical points on the other