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svp [43]
2 years ago
12

Is the equation y=85x-600 linear? Explain why or why not.

Mathematics
2 answers:
USPshnik [31]2 years ago
6 0
Yes, it has a slope and a y-intercept, using the linear equation, y=mx+b.

Not sure if this answer is in depth enough, but its definitely a linear function.
Pani-rosa [81]2 years ago
5 0
Yes the equation is linear because the linear equation is y=mx+b and y=85x-600 is linear.
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Question:

Which is equivalent to \sqrt{180x^{11}} after it has been simplified completely?

Answer:

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Step-by-step explanation:

Given

\sqrt{180x^{11}}

Required

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\sqrt{180x^{11}} = \sqrt{36 * 5} *  \sqrt{x^{11}}

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\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10 + 1}}

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\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x^1}

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Further split the square roots

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10}} * \sqrt{x}

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So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{10*\frac{1}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{\frac{10}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{5} * \sqrt{x}

Rearrange Expression

\sqrt{180x^{11}} = 6 *  x^{5} * \sqrt{5} * \sqrt{x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}

From laws of indices; \sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}

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\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

<em>The expression can no longer be simplified</em>

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