(hc)the quote below was written by a prominent figure in 1889:
"while the law [of competition] may be sometimes hard for the individual, it is best for the race, because it insures the survival of the fittest in every department. we accept and welcome, therefore, as conditions to which we must accommodate ourselves, great inequality of environment, the concentration of business, industrial and commercial, in the hands of a few, and the law of competition between these, as being not only beneficial, but essential for the future progress of the race."
which philosophy is represented by this quote?

The mentioned quote was written by Andrew Carnegie, who was a great admirer of Herbert Spencer, one of the developers of the Social Darwinism theory; and this quote reflects that philosophy.

Social Darwinism is a social theory that defends that the theory of natural selection of Charles Darwin has social applications in human communities. It is based on the idea of the survival of the fittest conceived as a mechanism of social evolution and the belief that the Darwinian concept of natural selection can be used for the management of human society, insisting on competition (ethnic, national, class, etc.) by natural resources or various social positions.

Social Darwinism is based on interpretations of Darwin's writings, which were originally put forward by Herbert Spencer, and later used for political purposes, with numerous supporters. Social Darwinism enjoyed great acceptance in academic circles and was a great influence in imperialist countries at the end of the 19th century and in the first half of the 20th century.

on this day in 1939, in response to hitler’s invasion of poland, britain and france, both allies of the overrun nation declare war on germany.

the first casualty of that declaration was not german—but the british ocean liner athenia, which was sunk by a german u-30 submarine that had assumed the liner was armed and belligerent. there were more than 1,100 passengers on board, 112 of whom lost their lives. of those, 28 were americans, but president roosevelt was unfazed by the tragedy, declaring that no one was to “thoughtlessly or falsely talk of america sending its armies to european fields.” the united states would remain neutral.

as for britain’s response, it was initially no more than the dropping of anti-nazi propaganda leaflets—13 tons of them—over germany. they would begin bombing german ships on september 4, suffering significant losses. they were also working under orders not to harm german civilians. the german military, of course, had no such restrictions. france would begin an offensive against germany’s western border two weeks later. their effort was weakened by a narrow 90-mile window leading to the german front, enclosed by the borders of luxembourg and belgium—both neutral countries. the germans mined the passage, stalling the french offensive.

no statements but ok.

the statement that best describes the idea of manifest destiny that was used in the 19th century would be that "it was fate that the united states would continue to  expand westward," since people thought the us was "destined" to do so.