Botanical names of plants are treated as in Latin becausea. Rules of nomenclature were framed by Italian botanists and they were speaking Latin b. It is very difficut to pronoumce Latin names and they convey multiple meanings c. Latin was the natural language of many European countries d. Latin was a dead language, its words would convery precise meaning. It was the mother of all European languages and all the early botanical literature was in Latin

Sure, here are some step-by-step solutions using LaTeX: Example 1: Solving a quadratic equation by factoring Given the quadratic equation $x^2+5x+6=0$, we can solve for $x$ by factoring it as $(x+2)(x+3)=0$. This gives us two solutions: $x=-2$ and $x=-3$. Step 1: Write the quadratic equation in standard form, $a{x}^2+bx+c=0$. $x^2+5x+6=0$ Step 2: Factor the quadratic expression. $(x+2)(x+3)=0$ Step 3: Set each factor equal to zero and solve for $x$. $x+2=0$ or $x+3=0$$x=-2$ or $x=-3$ Step 4: Check the solutions by plugging them back into the original equation. $x=-2$: $(-2{)}^2+5(-2)+6=0$, which is true. $x=-3$: $(-3{)}^2+5(-3)+6=0$, which is also true. Therefore, the solutions to the quadratic equation are $x=-2$ and $x=-3$. Example 2: Finding the slope and y-intercept of a linear equation Given the equation $y=2x+3$, we can find the slope and y-intercept using the slope-intercept form. Step 1: Write the equation in slope-intercept form, $y=mx+b$. $y=2x+3$ Step 2: Identify the slope, $m$, and y-intercept, $b$. Slope: $m=2$ Y-intercept: $b=3$ Step 3: Interpret the slope and y-intercept in the context of the problem. The slope of the equation represents the rate of change of $y$ with respect to $x$. In this case, for every increase of one unit in $x$, $y$ increases by two units. The y-intercept of the equation represents the value of $y$ when $x$ is equal to zero. In this case, when $x=0$, $y$ is equal to three. Therefore, the slope of the equation is 2 and the y-intercept is 3.