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miss Akunina [59]
3 years ago
9

I need help. this is the problem x^2/3+10=7x^1/3

Mathematics
1 answer:
Arlecino [84]3 years ago
7 0

\it x^{\frac{2}{3}}+10=7x^{\frac{1}{3}} \Leftrightarrow  (x^{\frac{1}{3}})^2-7x^{\frac{1}
  {3}} +10=0 
\\\;\\
We\ note\ x^{\frac{1}{3}} =t \ \ and \ the \ equation \ will \ be:
\\\;\\
t^2-7t+10 = 0 \Leftrightarrow t^2 -2t-5t+10=0 \Leftrightarrow t(t-2) -5(t-2)=0

\it \Leftrightarrow (t-2)(t-5)=0 
\\\;\\
t-2=0 \Rightarrow t=2 \Rightarrow x^{\frac{1}{3}}=2 \Rightarrow (x^{\frac{1}{3}})^3 =2^3 \Rightarrow x = 8
\\\;\\
t-5=0 \Rightarrow t=5 \Rightarrow x^{\frac{1}{3}}= 5  \Rightarrow (x^{\frac{1}{3}})^3 = 5^3 \Rightarrow x = 125

S = {8; 125}


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Answer:

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The number of red marbles = 10

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The prize won for pulling a red marble = 0

The prize won for pulling a purple marble = $2

The prize won for pulling a turquoise marble = $5

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To find the expected value, EV sum the prizes won multiplied by the probability of winning that prize and then subtract the cost of playing the game.

Therefore;

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8 0
3 years ago
Which expression is equivalent to <img src="https://tex.z-dn.net/?f=%5Csqrt128x%5E%7B8%7D%20y%5E%7B3%7D%20z%5E%7B9%7D" id="TexFo
Elis [28]

Answer:

(C)8x^4z^4\sqrt{2yz}

Step-by-step explanation:

We want to determine an expression equivalent to: \sqrt{128x^8y^3z^9}

\sqrt{ab} =\sqrt{a}*\sqrt{b}

Therefore:

\sqrt{128x^8y^3z^9}=\sqrt{128}*\sqrt{x^8}*\sqrt{y^3}*\sqrt{z^9}

=\sqrt{64*2}*\sqrt{x^{4*2}}*\sqrt{y^{2+1}}*\sqrt{z^{8+1}}\\=8\sqrt{2}*\sqrt{x^{4*2}}*\sqrt{y^2*y}*\sqrt{z^{8}*z}}

=8\sqrt{2}*x^4*y \sqrt{y}*z^4\sqrt{z}\\=8*x^4*z^4*\sqrt{2}*\sqrt{y}*\sqrt{z}\\=8x^4z^4\sqrt{2yz}

4 0
3 years ago
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