We want to
solve the given system of equations by graphing and locating the point of intersection (if it
exists). The system:
y = x - 1
y = 3x -
9
A system of two linear equations in two variables can
have 0, 1, or infinite solutions. If the lines are parallel, there are no solutions. (The system
is said to be inconsistent.) If the lines intersect at a single point, there is one solution.
(The system is said to be consistent and independent.) If the two lines are actually the same
line, there are an infinite number of solutions for the system. (The system is said to be
consistent and dependent.)
The first line, y = x - 1, has slope 1 and
y-intercept of -1. This means that the line includes the point (0, -1), as this is the
y-intercept. To find another point on the line we can use the slope: for every unit to the
right, we go we should go up 1 unit. Points on this line include (0,-1), (1,0), (2,1), (3,2),
and so on.
The second line, y = 3x - 9, has slope 3 and y-intercept -9. Once
we plot (0,-9) (the y-intercept), for every 1 unit to the right we must go up 3 units. Points on
this line include (0,-9), (1,-6), (2,-3),(3,0), and so on.
The graphs: y = x
- 1 in blue and y = 3x - 9 in red (see attached).
It
appears that the lines intersect at (4,3). We can verify this algebraically:
If x = 4 then y = x - 1 = 4 - 1 = 3
If x = 4 then y = 3x -
9 = 3(4) - 9 = 3 as required.
The solution
is the point (4,3).
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What is the tone of the poem "Africa" by David Diop?
This
intriguingly unique poem has an
overall tone and a secondary,
middle
tone along with a tertiary (third)
tone.
The overall
tone is heard in the first six and last two
lines. In between
are the two other tones, the secondary and the tertiary.
The overall tone begins with the first line then
melds
into the secondary tone part way through
the seventh line:
"Your beautiful black blood that irrigates the fields." The
secondary
tone carries on from there to "But a
grave voice answers me," which
introduces the tertiary
tone before the poem returns to the
original, overall tone.
Knowing where these divisions are will you
help
you to identify the tones when you reread the poem and look for these tones yourself.
Now,
what are these tones?
Tone is the feeling or
emotion
expressed by the poetic speaker or persona toward the subject or characters
being
written about: tone is what the speaker feels about what is being said.
The first
tone, the first expression of the
speaker's feeling, is triumphal. A triumphal
feeling is a celebratory
feeling. The speaker feels triumphal when he reflects on Africa because
it is
a proud homeland lineage full of images of might and greatness, as his grandmother
sings
of it.
The secondary
tone in "Your
beautiful black blood that irrigates the
fields," is a tone sadly desperate. The speaker is
saddened by the images of
backbreaking labor under the whip of slavery and desperate to know if
this
whipped Africa is the same Africa that his grandmother triumphally sings about, the
Africa
that flows through his veins.
The
tertiary tone
is spoken by "a grave voice"
(perhaps a collective voice from the grave) and is a
gentle yet earnest tone
that gently reprimands while earnestly exhorting. This gentle, earnest
tone
expresses the feeling of the "grave voice" as it points the speaker, who is
like
an "impetuous child," toward the correct present-day image of Africa:
Africa is not
the image of bent and whipped backs but the image a tree,
"young and strong," that is
acquiring and bearing the fruit of
liberty:
That is your
Africa springing
up anew
Springing up patiently, obstinately
Whose fruit
bit
by bit acquires
The bitter taste of liberty.
Dehumanization In Night
Dehumanization is a theme that is consistently present throughout
. The Nazis enacted countless horrors upon the people they imprisoned and
executed in the concentration camps and ghettos during the Holocaust. Examples of the
dehumanization in the actions of the Nazis throughout the book include the systematic forced
relocation of Jews from their homes into ghettos and concentration camps, the extermination of
people via mostly gas chambers and mass shootings, the beatings and torture of prisoners, the
tattooing of numbers onto concentration camp prisoners, the separating of families
and...
What was the reason for an increase in voters over the period between 1924 and 1828? What led to the Nullification Crisis?
During the 1820s, a
decade that historians have called "The Age of the Common Man," voting increased
because many states removed property requirements for voting. These changes meant that most
white men could now vote, regardless of their economic status. In addition, several northern
states allowed freed African-American men to vote. Most African-Americans and all women,
however, still could not vote. Voting procedures were also changed so that voting by voice was
replaced by paper ballots; these changes encouraged people to vote the way they wanted and to
feel less pressured to vote in the way their social superiors did. These changes in the
electorate helped Andrew Jackson win the Presidency in 1828.
The
Nullification Crisis of 1832 involved the refusal of South Carolina to pay the Tariff of 1832
(and the earlier Tariff of 1828), which they referred to as "The Tariff of
Abominations." They objected to a high tariff (a tax on imported goods) that made
manufactured goods from Europe very expensive. By stating that they could nullify, or declare
void, a federal law, South Carolina set a dangerous precedent (which had been used earlier by
New Englanders during the Hartford Convention) that southern states would use later during the
outbreak of the Civil War. However, Andrew Jackson passed a Force Bill through Congress in 1833
that authorized the use of force to collect the tariff, and a compromise was reached that
lowered the tariff. As a result, South Carolina, though backed by Jackson's Vice-President, John
Calhoun, relented and paid the tariff.
How does Jonathan Edward challenge one's self?
One way
in which Edwards can be seen as issuing
a challenge to the individual that they can place on
themselves is in seeking
to move closer to God. Edwards does not make any distinctions. He
makes it
fairly clear that all human beings are in some level of guilt in terms of how they
have
turned from the divine. Edwards lumps all human beings into a realm
where each individual has
to make a clear spiritual choice to stop what has
happened and embrace a new vision of what
should be happening in their lives:
All wicked men's
pains
and contrivance which they use to escape hell, while they
continue...
What advantages allowed Spain and Portugal to expand overseas first?
As Spain expanded
into the Americas and Portugal moved into West Africa, Brazil and India, their military strength
played an important role in their expansion. Military innovations such as firearms and well
built and militarized ships gave these European countries an advantage over the indigenous
people of their acquired colonies. Monetary strength from both financial endowments and trade
kept the colonies financially strong. Both Spain and Portugal enslaved many of the original
occupants of their conquests. Although slavery is considered immoral, at the time it helped
secure these counties hold on their expansions by increasing the labor force. Spain especially
benefited from the use of slaves to mine silver which greatly supported their economy in the
16th century. And finally, Spain and Portugal were successful in their expansions because they
really didnt have any additional European competition. Political weakness plagued Italy,
England wasnt interested in the Southern Hemisphere, and France was preoccupied with other
matters.