?The side length of a square can be expressed as 2x+3. if the area of the square is 121 square meters, what is the value of x?

x = 4 meters

Explanation:

The area of the square is 121 sq meters. 121 is 11 squared. The shape is a square so the side must be 11 meters.

2x + 3 = 11

2x = 8

x = 4

A longer, more complicated algebrai-ish way if to solve the equation:

(2x + 3)^2 = 121

which would give the same answer. But the shape was a square, so use that fact for a simple and elegant solution.

by 1890, the united states had by far the world's most productive economy. american industry produced twice as much as its closest competitor--britain. but the united states was not a great military or diplomatic power. its army numbered less than 30,000 troops, and its navy had only about 10,000 seamen. britain's army was five times the size of its american counterpart, and its navy was ten times bigger. the united states' military was small because the country was situated between two large oceans and was surrounded by weak or friendly nations. it faced no serious military threats and had little interest in asserting military power overseas.

answer:   migrations were important in the neolithic period. "two major migrations passing through southeastern europe were confirmed by the means of archaeo-genetic studies."

the first migration was the early neolithic period -- 6,000 before common era (bce) -- when the first farmers, from anatolia -- asia minor -- spread through europe. the second migration occurred during the early bronze age (3,000-2,500 bce) when the so-called "steppe population," from the eurasian steppe, replaced much of northern europe's previous population.

the first farmers of northern and western europe passed through southeastern europe with limited hunter-gatherer genetic admixture, which occurs when two or more previously isolated populations begin interbreeding. however, some groups that remained mixed extensively -- without the male-biased, hunter-gatherer admixture that prevailed later in the north and west, according to latest discoveries. southeastern europe continued to be a nexus between east and west, with intermittent genetic contact with the steppe people up to 2,000 years before the migrations that replaced much of northern europe's population.

"in some places, hunter-gatherers and incoming farmers seem to have mixed very quickly," says iain mathieson, a geneticist at the university of pennsylvania, who was first author of the paper. "but, mostly, the two groups remained isolated, at least for the first few hundred years. these hunter-gatherers had been living there for thousands of years, and it must have been quite a shock to have these new people show up -- with a completely different lifestyle and appearance."