What does it mean to say that algebra is a written language? How would I express an algebraic expression such as for example, numerator displaystyle{3}{x}^{2}+{5}{y} and 2 as the denominator, in words?

Question
Math Word Problem
What does it mean to say that algebra is a written language? How would I express an algebraic expression such as for example, numerator $$\displaystyle{3}{x}^{2}+{5}{y}$$ and 2 as the denominator, in words?

2021-02-26
Step 1
To explain the connection (in algebra) between the written and symbolic language
Step 2
Historically, problems (in algebra, or arithmetic or geometry) were expressed completely as word problems in the corresponding languages (Greek, Latin, Arabic,...). It was only much later that symbols were introduced and mathematrical expressions began to be expressed in the compact symbolic form that we are used to. Even operations like addition,multiplication (+, -, * ,/) were expressed only in words (plus, minus,...). In fact , the history of algebraic notation is a fascinating and important subject of research on its own
Step 3
Powers like $$\displaystyle{x}^{3},{x}^{2},{x}^{{\frac{1}{{2}}}}{\left(\square{\sqrt[{o}]{{f}}}{x}\right)}$$ were also expressed as words (cubus, quadratum ). , radix quadrata,.
Step 4
ANSWER: Coming to the present problem, the expression displayed would be described in words as "Three times the square of x plus five times y , the whole divided by 2"
$$\displaystyle\frac{{{3}{x}^{2}+{5}{y}}}{{2}}$$

Relevant Questions

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Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
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At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
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Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
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