History, 23.09.2019 03:30 taylorwhitfield6

What did the declaration of independence do?

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The Declaration fo Independence was a formal document sent to the King of England to inform him the American colonies no longer wanted to stay under Britain's rule.

Answer from: sswaqqin

The Declaration of Independence formally declared the American colonies' intention to separate themselves from British rule.

The Declaration of Independence starts with a title, asserting it as the unanimous assertion of all 13 colonies, declaring their independence as the United States of America. This is the way it is titled:

In Congress, July 4, 1776, a declaration by the representatives of the United States of America, in General Congress assembled.

Then, the opening paragraph of the Declaration says, "When in the Course of human events it becomes necessary for one people to dissolve the political bands which have connected them with another and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation. "

Following that are the lines from the document that are probably the most famous: "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."

The Declaration asserted the legitimacy of the new United States of America in establishing itself. The document laid out numerous "facts to be submitted to a candid world" -- points that demonstrated that the British king had been seeking to establish "an absolute Tyranny over these States" (the colonial states which were declaring their independence).

Answer from: Quest

answer

$x = \pm 2\sqrt{2} \: \: or \: \: x = \pm 1$

explanation

the given equation is

${x}^{4} - 9 {x}^{2} + 8 = 0$

we can rewrite this as:

$({x}^{2})^{2} - 9 {x}^{2} + 8 = 0$

let

$u = {x}^{2}$

then the equation becomes:

${u}^{2} - 9 {u}^{2} + 8 = 0$

the factors of 8 that sum up to -9 are {-1,-8}

we split the middle term with these factors to obtain,

${u}^{2} - u - 8u+ 8 = 0$

we factor by grouping to obtain:

$u(u - 1) - 8(u - 1) = 0$

$(u - 8)(u - 1) = 0$

apply the zero product property to get:

$u - 8 = 0 \: \: or \: \: u - 1 = 0$

$u = 8 \: or \: u = 1$

but

$u = {x}^{2}$

${x}^{2} = 8 \: or \: {x}^{2} = 1$

$x = \pm \sqrt{8} \: \: or \: \: x = \pm \: \sqrt{ 1}$

$x = \pm 2\sqrt{2} \: \: or \: \: x = \pm 1$

Answer from: Quest

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