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3 years ago

Which expression is equivalent to sqrt8x^7y^8? assume x>0

Mathematics

2 answers:

Ilia_Sergeevich [38]3 years ago

8 0

Answer:

$\sqrt{8x^7y^8$ $= 2x^3y^4 * \sqrt{2x}$

Step-by-step explanation:

Given

$\sqrt{8x^7y^8$

Required

Evaluate

$\sqrt{8x^7y^8$

Separate each factor with multiplication sign

$\sqrt{8*x^7*y^8$

Express 8 as 4 * 2 and $x^7$ as $x^6 * x$

$\sqrt{4 * 2 *x^6 * x*y^8$

Split each factor

$\sqrt{4} * \sqrt{2} *\sqrt{x^6} * \sqrt{x}*\sqrt{y^8}$

Evaluate $\sqrt4$

$2 * \sqrt{2} *\sqrt{x^6} * \sqrt{x}*\sqrt{y^8}$

Apply law of indices:

$2 * \sqrt{2} * x^{6*\frac{1}{2}} * \sqrt{x} * y^{8*\frac{1}{2}}$

$2 * \sqrt{2} * x^3 * \sqrt{x} * y^4$

Reorder

$2* x^3 * y^4 * \sqrt{2} * \sqrt{x}$

$2x^3y^4 * \sqrt{2} * \sqrt{x}$

$2x^3y^4 * \sqrt{2*x}$

$2x^3y^4 * \sqrt{2x}$

$2x^3y^4 \sqrt {2x$

Hence:

$\sqrt{8x^7y^8$ $= 2x^3y^4 * \sqrt{2x}$

Sindrei [870]3 years ago

5 0

Answer: It is C or 2x^3y^4 square root2x.

Step-by-step explanation: Checked on my calculator it is correct.

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Daniela is a stain glass artist; she created the window below for her living room. What is

OLga [1]

The window has a shape of a semi-circle (half of a circle).

We know the diameter d = 12 ft.

The area of a (complete) circle is given by the formula:
A = π × r²

The radius can be found by halving the diameter:
r = d ÷ 2
= 12 ÷ 2
= 6 ft

Therefore the area of the circle will be:
A = π × r²
= 3.14 × 6²
= 3.14 × 36
= 113.04 ft²

And the area of the semi-circle:
A = 113.04 ÷ 2
= 56.52 ft²

Hence, the area of the window will be 56.52 ft².

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3 years ago

The vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). what is the perimeter and area in square units

ad-work [718]

Check the picture below.

the triangle has that base and that height, recall that A = 1/2 bh.

now as for the perimeter, you can pretty much count the units off the grid for the segment CB, so let's just find the lengths of AC and AB,

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&A&(~ 2 &,& 8~) 
% (c,d)
&C&(~ 6 &,& 2~)
\end{array}~~~ 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AC=\sqrt{(6-2)^2+(2-8)^2}\implies AC=\sqrt{4^2+(-6)^2}
\\\\\\
AC=\sqrt{16+36}\implies AC=\sqrt{52}\implies AC=\sqrt{4\cdot 13}
\\\\\\
AC=\sqrt{2^2\cdot 13}\implies AC=2\sqrt{13}$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&A&(~ 2 &,& 8~) 
% (c,d)
&B&(~ 16 &,& 2~)
\end{array}\\\\\\
AB=\sqrt{(16-2)^2+(2-8)^2}\implies AB=\sqrt{14^2+(-6)^2}
\\\\\\
AB=\sqrt{196+36}\implies AB=\sqrt{232}\implies AB=\sqrt{4\cdot 58}
\\\\\\
AB=\sqrt{2^2\cdot 58}\implies AB=2\sqrt{58}$

so, add AC + AB + CB, and that's the perimeter of the triangle.

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3 years ago

What is an equation of the parabola with vertex at the origin and focus (0, 0.75)?

morpeh [17]

Answer:

$x^{2} =3y$

Step-by-step explanation:

Notice that the focus is a points on the vertical axis, that means the parabolla opens vertically, and has the form

$x^{2} =4py$

Because the parameter $p$ is positive and equal to 0.75. Additionally, the vertex is at the origin, that's why the equation is this simple.

Replacing the parameter value, we have

$x^{2} =4(0.75)y\\x^{2} =3y$

Therefore, the equation of a parabolla with vertex at the origin and focus at (0, 0.75) is $x^{2} =3y$ .

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babunello [35]

If x is the amount that Tanya paid for each item, then Tony's items would be x-2.25. So:
3x=4(x-2.25)

3x=4x-9
x=9
x-2.25=6.75
Tanya spent $9 on each item; Tony spent $6.75 on each of his items

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belka [17]

Answer:

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Step-by-step explanation:

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