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Igoryamba
3 years ago
5

Which expression is equivalent to 4(x^3)(2x)^-4

Mathematics
1 answer:
AVprozaik [17]3 years ago
3 0

Answer:

=\frac{4x^{3}}{16 x^{4}}

Step-by-step explanation:

4(x^{3} )(2x)^{-4}

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

=\frac{4x^{3}}{2^{4} x^{4}}

=\frac{4x^{3}}{16 x^{4}}

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hi, i dont undertand number 20 because i was absent in class today and i rerally need help, i will appraciate with the help, and
Mariulka [41]

Given:

The equation is,

2\log _3x-\log _3(x-2)=2

Explanation:

Simplify the equation by using logarthimic property.

\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{      \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}

Simplify further.

\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}

Solve the quadratic equation for x.

\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

\begin{gathered} x-6=0 \\ x=6 \end{gathered}

For (x - 3) = 0,

\begin{gathered} x-3=0 \\ x=3 \end{gathered}

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

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1 year ago
There are 565 sheets of paper in a book
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565 sheets/ 1 book* 2,000 books= 1,130,000 sheets.

The final answer is 1.13*10^(6) sheets.

Hope this helps~
4 0
2 years ago
Daniel's basic cell phone rate each month is $29.95. Add to that $5.95 for voice mail and $2.95 for text messaging. This past mo
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5.95 + 2.95 = 8.9
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3 years ago
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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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