answer:To solve for x by completing the square, we follow these steps: 1. Move the constant term to the right side of the equation: x^{2}+4x = -3 2. Take half of the coefficient of the x term, square it, and add it to both sides of the equation: x^{2}+4x + 4 = -3 + 4 (x + 2)^{2} = 1 3. Take the square root of both sides: x + 2 = pm1 4. Isolate x to find the solutions: x = -2 pm 1 x = -2 + 1 = -1 x = -2 - 1 = -3 Therefore, the solutions are x = -1 and x = -3.

answer:Beta-lactamase inhibitors work by binding to and inhibiting the beta-lactamase enzyme, which is responsible for breaking down beta-lactam antibiotics. This inhibition prevents the degradation of the antibiotic, allowing it to remain effective against the bacteria. The three specific beta-lactamase inhibitors mentioned in the passage are clavulanic acid, sulbactam, and tazobactam.

answer:Professor Dimm's assumption that the compound would have 16 π electrons and thus be non-aromatic was based on including the electrons from the triple bond in the π system. However, the two electrons in the triple bond are part of an orthogonal π orbital, which does not interact with the conjugated π system. Therefore, the conjugated π system only contains 14 electrons, satisfying the 4n+2 rule with n=3. Despite this, the molecule's stability cannot be solely attributed to aromaticity. Crystal structure analysis is crucial for understanding its stability. The compound likely adopts a non-planar conformation due to steric strain, as seen in the figure. This non-planar structure prevents the aromaticity typically associated with planar compounds that follow the Hückel rule. Two geometric isomers of dehydro[14]annulene (the compound in question) have been synthesized and isolated. Their NMR data indicate aromaticity, as the internal hydrogens display shielded chemical shifts, and the outer hydrogens show signals in the aromatic region. In conclusion, while the compound technically meets the 4n+2 rule for aromaticity, its non-planar structure due to steric strain renders it non-aromatic in practice. The stability observed may be a result of this unique conformation rather than aromaticity. Further research, such as that by Santander et al. (2013), has investigated the interconversion mechanisms between the isomers.

answer:To find the sum of two matrices, we add the corresponding elements of each matrix. {left[begin{array}{rr}{1}+{1} & {3}+{4} {1}+{2} & {-2}+{-1} {1}+{0} & {2}+{-1}end{array}right]} Simplifying further, we get: {left[begin{array}{rr}{2} & {7} {3} & {-3} {1} & {1}end{array}right]}