Rotate the Axes to Eliminate The $x y$ -Term in the Following Equation

question 12

Multiple Choice

Rotate the axes to eliminate the $x y$ -term in the following equation.
$$18 x ^ { 2 } - 12 \sqrt { 3 } x y + 6 y ^ { 2 } + 12 x + 12 \sqrt { 3 } y = 0$$

• A) \(\left( y ^ { \prime } \right) ^ { 2 } + x ^ { \prime } = 0\)
• B) \(6 \sqrt { 3 } \left( y ^ { \prime } \right) ^ { 2 } + 6 \sqrt { 3 } x ^ { \prime } = 0\)
• C) \(6 \left( x ^ { \prime } \right) ^ { 2 } - 6 y ^ { \prime } = 0\)
• D) \(\frac { \left( y ^ { \prime } \right) ^ { 2 } } { 6 } + \frac { x ^ { \prime } } { 6 } = 0\)
• E) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 12 } + \frac { y ^ { \prime } } { 12 } = 0\)

Identify the unique and common features of prokaryotic cells.

Grasp the evidence supporting the theory of a single origin of life.

Distinguish between Gram-positive and Gram-negative bacteria, including their structural differences.

Understand the monophyletic and non-monophyletic groupings within bacteria.

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Definitions:

Marginal Revenue

The increase in revenue that results from the sale of one additional unit of output, important for making decisions about production and pricing.

Price Segment

A subset of the market tailored to a specific price range, accommodating customers with different willingness to pay.

Sanitary Landfill

A waste management site where garbage is isolated from the environment until it is safe to be integrated into the natural environment, minimizing pollution and health risks.

Standard Deviation

A statistical measure that quantifies the amount of variability or dispersion of a set of data points.