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Afina-wow [57]
2 years ago
15

`

Mathematics
1 answer:
Allisa [31]2 years ago
4 0

Answer:

~~~~~~~~~~~~~~~~~~~~~~~~~.~~~~~~~~~~~~~~~~~~~~~~~~~

Step-by-step explanation:

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Which is equivalent to V180x11 after it has been simplified completely?
inna [77]

Question:

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

Answer:

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

Step-by-step explanation:

Given

\sqrt{180x^{11}}

Required

Simplify

We start by splitting the square root

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

Replace 180 with 36 * 5

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

Further split the square roots

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

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

Replace power of x; 11 with 10 + 1

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

From laws of indices; a^{m+n} = a^m * a^n

So, we have

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

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

Further split the square roots

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

From laws of indices; \sqrt{a} = a^{\frac{1}{2}}

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}

So, we have

\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>

Hence, \sqrt{180x^{11}} is equivalent to 6x^{5}\sqrt{5x}

7 0
2 years ago
Read 2 more answers
50 Points What is the value of r? 6.4r−5.9r=−3.25 Question 1 options: A -6.5 B 6.5 C -3
Oliga [24]

Answer:

Option A. -6.5

Step-by-step explanation:

we have

6.4r-5.9r=-3.25

Solve for r

That means ---> isolate the variable r

Combine like terns left side of the equation

0.5r=-3.25

Divide by 0.5 both sides

0.5r/0.5=-3.25/0.5

r=-6.5

4 0
3 years ago
Rounded to the nearest tenth, what is the area of rectangle ABCD?
m_a_m_a [10]
AC = x, CD = 2x cause of 30° angle. Use pythagoras then
7 0
2 years ago
The graph below shows graph of f (x), its derivative f '(x), and its second derivative f "(x). Which of the following is the cor
Jet001 [13]

Answer:

A is f ", B is f, C is f '.

Step-by-step explanation:

Your answer is correct.  B is the original function f.  It has a local maximum at x=0, and local minimums at approximately x=-3/2 and x=3/2.

C is the first derivative.  It crosses the x-axis at each place where B is a min or max.  C itself has a local maximum at approximately x=-3/4 and a local minimum at approximately x=3/4.

Finally, A is the second derivative.  It crosses the x-axis at each place where C is a min or max.

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3 years ago
In the 7th grade, 132 students take Spanish as an elective. If there are 330 seventh graders, what percent of
klasskru [66]

Answer:

Step-by-step explanation: 40% 132/330=0.4 and 0.4 as a percent is 40%

8 0
3 years ago
Read 2 more answers
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