$\bf \sqrt{108x^5y^6}\qquad 
\begin{cases}
108=2\cdot 2\cdot 3\cdot 3\cdot 3\\
\qquad 2^2\cdot 3^2\cdot 3\\
\qquad (2\cdot 3)^2\cdot 3\\
\qquad 6^2\cdot 3\\
x^5=x^{4+1}\\
\qquad x^4\cdot x^1\\
\qquad x^{2\cdot 2}\cdot x\\
\qquad (x^2)^2\cdot x\\
y^6=y^{3\cdot 2}\\
\qquad (y^3)^2
\end{cases}\implies \sqrt{6^2\cdot 3\cdot (x^2)^2\cdot x\cdot (y^3)^2}
\\\\\\
6x^2y^3\sqrt{3x}$

3 0

3 years ago

The dimensions of a rectangular piece of paper are 8.5 inches and 11 inches. Veronica folded the piece of paper along its diagon

Mashutka [201]

Answer:

D) 13.9 in

Step-by-step explanation:

The diagonal of a rectangle is longer than the longest side. It will never be more than 42% of the shortest side longer than the longest side.

Here, the longest side is 11 inches. 42% of the shortest side is about 3.6 inches, so the diagonal length will be between 11 and 14.6 inches. Only one answer choice is in that range: 13.9 in.

Of course, the length of the diagonal can be figured to any desired accuracy using the Pythagorean theorem.

... √(8.5² +11²) = √193.25 ≈ 13.9014 . . . . inches

_____

<em>Comment on the solution</em>

For this multiple-choice problem, it is sufficient to estimate the length of the diagonal. The estimate we suggested was to add 0.42 times the short side to the long side.

An even closer estimate can be had by multiplying that value (.42×short side) by the ratio of the short to long sides prior to adding it to the long side. This will get you within 1.5% of the correct value without the need for a square root.

3 0

3 years ago

Graph the solution set for this inequaltity: -6x-3y≤18

artcher [175]

Answer:

Step-by-step explanation: Graph it by finding the boundary line y≥ 6-2x