Given the points A(0,4), B(3,0), determine the coordinates of the point C that lies on the line x+y=0.The area of triangle ABC is 5 square units.

We'll determine the area of the triangle ABC , calculating
the determinant formed from the coordinates of the given
points.

The coordinates of C are :
C(a,b)

                | 0   4   1
|

A = (1/2)*| 3   0   1
|

                | a   b   1
|

We'll compute the
determinant:

A = (1/2)*(0*0*1 + 3*b*1 + 4*1*a - a*0*1 -
b*1*0 - 3*4*1)

A = (1/2)*(3b + 4a -
12)

But , from enunciation, the area of triangle ABC is: A
= 5 square units.

5 = (1/2)*(3b + 4a -
12)

3b + 4a - 12 = 10

We'll
add 12 both sides:

4a + 3b = 22
(1)

We know, from enunciation, that C is located on the
line x + y = 0.

a + b = 0
(2)

We'll subtract 3*(2) from
(1):

4a + 3b - 3a - 3b =
22

We'll combine and eliminate like
terms:

a = 22

From (2), a =
-b

b = -22

The
coordinates of the point C are: C(22 ,
-22).

Note: The line x + y = 0 represent the
bisectrix of the 2nd and 4th quadrants.

Compare and Contrast the processes and purposes of mitosis, meiosis, and binary fission.I need to write a 14 sentence accordian paragraph comparing...

Each process is the replication of cells.  Mitosis and
meosis both take place in multicellular, eukaryotic organisms whereas binary fission is
for unicellular, prokaryotic organisms. Mitosis and binary fission are both asexual
processes that result in two genetically identical cells and meosis is the part of
sexual reproduction that yields four genetically different sperm cells, or one egg and
three polar bodies.

The purpose of mitosis is to replace
dead or damaged cells in an organism.  Mitosis is a small part of the cell cycle, or the
life span of a cell.  During interphase the DNA in the nucleus replicates.  The
first step of mitosis is prophase where the DNA condenses into chromatin the chromosomes
are termed tetrads (tetra referring to the four legs on the tetrad) and the nucleus
disintegrates, next the tetrads line up in the center of the cell during metaphase,
thirdly in anaphase the tetrads are pulled apart and move towards the poles of the cell
by spindle fibers that are attached to the centrioles, next the two new nuclei form with
exact copies of the DNA in each nucleus during telophase and finaly cytokinesis (cell
division) occurs.  The result is two genetically identical diploid cells. Diploid
meaning it has a full set of chromosomes.

Meosis occurs to
create gametes or sex cells for sexual reproducing organisms.  Meosis consists of two
rounds of mitosis, however, in between the first and second round "crossing over" occurs
where the genetic material is jumbled.  Segments of the chromosomes cross with each
other to change the genetic code leading to genetic variation.  This process takes place
so that offspring are not genetic clones of their parents.  The result of meosis is 4
genetically different haploid sperm cells, or one egg with three genetically
different haploid polar bodies (cells that provide nutrients for the egg).  Haploid
cells, or gametes contain half the number of chromosomes so that when the egg is
fertilized the resulting embryo has a full set of chromosomes, half from each
parent.

Binary fission occurs in prokaryotic cells, or
bacteria.  This is a very simplistic process compared to meosis and mitosis.  This is an
asexual process where the DNA that is just floating in the cell makes a copy of itself
and the cell splits in two with one set of DNA in each cell.  The purpose of binary
fission is for rapid growth of single celled organisms.    

Does Snowball have a dream that envisions the ideal animal society?

No.  Snowball is not the one who has a dream that shows
the animals living happily without human beings around.  The pig that has that dream is
called Old Major.  Old Major has the dream, but then dies before the revolution can
happen.

After the revolution, Snowball becomes important. 
He and another pig named Napoleon are the leaders of the revolution and of the
government that is created after the animals get rid of Farmer Jones.  But Snowball is
not the one with the original dream -- he is one of the main pigs who tries to make the
dream into reality.

What new philosophy motivates Hamlet in Act 5?

Hamlet has been so concerned through the first four acts
of play about making good choices and the potential consequences of all of his actions
that he has been slow to take action against Claudius and avenge his father's murder. 
But in Act 5 he realizes that he doesn't have control over everything in his life and he
needs to just respond to the moment.  He specifically says to Horatio that he realizes
that "there is a divinity that shapes our ends rough hew them how we will."  What he
means is that we humans can make choices and take actions that give shape to our lives,
but that there is a fate/destiny/Providence that is also in play that will also give
shape to our lives -- probably some of the finer points of our lives are out of our
immediate control.  Hamlet follows this thought up later when Horatio is cautioning

What are x and y given that x + 2y = 5 and 2x +4y = 6?

Given the system of
equations:

x+2y =
5........(1).

2x+4y =
6......(2).

To solve for the solution for
(x,y).

We see that two lines a1x+b1y=c1 and a2x+b2y= c2 = 0
are parallel or have the same slope if a1/a2 = b1/b2 but not equal to
c1/c2.

a1 = 1, b1 = 2, and c1 = 5.  a2 = 2, b2 = 4 and c2 =
6. So a1/a2 = b1/b2 = 1/2. But c1/c2 = 5/6.

Therefore the
given lines  x + 2y = 5 and 2x +4y = 6 are parallel. So the lines do not
intersect.

Therefore there is
no solution which satisfy both system of
equations.equations.

What does the man wear in Jack London's "To Build a Fire"?

I think, given the setting of this excellent story of
survival, that we can safely assume he wasn't wearing a swimsuit! If you look at the
text carefully, you can see that in the opening paragraphs of this story the dress of
the man, who interestingly remains nameless, is described to us, in a paragraph that
also makes clear the man's central failing in underestimating the power of
nature:

Fifty
degrees below zero stood for a bite of frost that hurt and that must be guarded against
by the use of mittens, earflaps, warm moccasins, and thick socks. Fifty degrees below
zero was to him just precisely fifty degrees below zero. That there should be anything
more to it than that was a thought that never entered his
head.

Thus, obviously, the
man is dressed extremely warmly for the weather, but also note how this paragraph makes
it clear the limitation of the man in treating the temperature and the intense cold very
literally and precisely, being blind to the might of nature and the inherent weakness of
mankind in response to the overwhelming power of the natural
world.

In chapter 3 of the novel 'Of Mice and Men' by John Steinbeck, why is Lennie reluctant to fight Curley? What injury does he inflict upon...

In Of Mice and Men, Lennie doesn't
want to fight Curley because he's afraid he'll get in trouble with
George. 

Lennie isn't a fighter anyway, and never wants to
cause trouble.  So he isn't inclined to want to fight.  But he is terrified of fighting
because he thinks George won't let him tend the rabbits on their imaginary farm if he
gets in trouble.

Once he does understand that George says
it's okay if he does fight back, he quickly catches Curley's fist in his hand and
smashes Curley's fist--fight over.

readability="11">

Curley's fist was swinging when Lennie reached
for it.  The next minute Curley was flopping like a fish on a line, and his closed fist
was lost in Lennie's big hand.  George ran down the room, "Leggo of him, Lennie, Let
go."