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RideAnS [48]
3 years ago
14

Which expression is equivalent to 3/56x^7y^5 , if x ≠0 and y≠0

Mathematics
1 answer:
Mariulka [41]3 years ago
3 0

Answer:

2x^2y\sqrt[3]{7xy^2}

Step-by-step explanation:

Given

\sqrt[3]{56x^7y^5}

Required

Solve

Expand

\sqrt[3]{8*7*x^6*x*y^3*y^2}

Rewrite as:

\sqrt[3]{8*x^6*y^3*7*x*y^2}

Split

\sqrt[3]{8*x^6*y^3} *\sqrt[3]{7*x*y^2}

Express 8 as 2^3

\sqrt[3]{2^3*x^6*y^3} *\sqrt[3]{7*x*y^2}

Apply law of indices

2^{(3/3)}*x^{(6/3)}*y^{(3/3)} *\sqrt[3]{7*x*y^2}

2*x^2*y *\sqrt[3]{7*x*y^2}

2x^2y *\sqrt[3]{7xy^2}

2x^2y\sqrt[3]{7xy^2}

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Answer:

The y-intercept of the equation is 100 and represents the initial studio-use fee.

Step-by-step explanation:

In this equation, our t variable (time) is the equivalent of the x-variable on a graph. This is because it is the variable that we 'change' to see its impact on y. We see how the amount of hours affects the price. So our P variable (price) is the equivalent of y on a graph. The y-intercept is where the line crosses the y-axis on a graph. At this point, x=0.

Since P is our y, and t is our x, to find the y-intercept, we simply need to make t = 0.

P = 50(0) + 100

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Therefore the y-intercept is 100.

In this context, t represents time, so even though the studio has been used for 0 hours, the price is still 100. This is because the 100 represents the initial studio-use fee, and using it for certain amounts of time adds onto the initial fee of $100. The hourly fee is represented by 50t so it costs $50 more for each hour of use.

Hope this helped!

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3 years ago
Which answer describes the transformation of f(x)=x^2−1 to g(x)=(x+4)^2−1
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Hope this helps
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3 years ago
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