Write the equation of the mirror line for the segment with endpoints (5, 4) and (-1, -1).

Explanation:

{\displaystyle {}^{n}x}{}^{n}x, for n = 2, 3, 4, …, showing convergence to the infinitely iterated exponential between the two dots

In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. It is the next hyperoperation after exponentiation, but before pentation. The word was coined by Reuben Louis Goodstein from tetra- (four) and iteration.

Under the definition as repeated exponentiation, the notation {\displaystyle {^{n}a}}{\displaystyle {^{n}a}} means {\displaystyle {a^{a^{\cdot ^{\cdot ^{a{\displaystyle {a^{a^{\cdot ^{\cdot ^{a, where n copies of a are iterated via exponentiation, right-to-left, I.e. the application of exponentiation {\displaystyle n-1}n-1 times. n is called the "height" of the function, while a is called the "base," analogous to exponentiation. It would be read as "the nth tetration of a".

Tetration is also defined recursively as

{\displaystyle {^{n}a}:={\begin{cases}1&{\text{if }}n=0\\a^{\left(^{(n-1)}a\right)}&{\text{if }}n>0\end{cases}}}{\displaystyle {^{n}a}:={\begin{cases}1&{\text{if }}n=0\\a^{\left(^{(n-1)}a\right)}&{\text{if }}n>0\end{cases}}},

allowing for attempts to extend tetration to non-natural numbers suc

water   molecules stay close to each other through cohesion, the collective action of hydrogen bonds between water molecules. cohesion plants draw water upwards from the root through the stem's transport tubes (xylem) to the leaf. this transport occurs even in large trees and against gravity. transpiration, evaporation of water from plant leaves, creates a tension on water molecules being pulled up from the stem and roots.

water also has high (the attraction of one substance to another) properties because of its polar nature. adhesion of water molecules to plant cell walls counteract gravity while water is transported from roots to leaves.

water exhibits a very high surface tension when compared to other liquids. surface tension is a property of a liquid that holds the surface together and allows it to resist an external force. by capillary action, the water forms concave menisci inside the pores. the high surface tension of water pulls the concavity outwards, generating enough force to lift water from the roots to the leaves of plants.

thus, cohesion, along with adhesion and surface tension creates a capillary action that keeps water molecules interacting and moving through the plants out to the leaf cells.

therefore, option d) is the correct answer.

explanation:

b is the correct answer

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