What is the perimeter of the rectangle whose width is two third the length and the area is 96

Let the length of the rectangle be L and the width be
W.

Given that the width is 2/3 of the
length.

Then, we will write:

W
= (2/3)*L................(1)

Also, given that the area of
the rectangle is 96.

Then,

A =
w*L = 96..............(2)

Now we will substitute (1) into
(2).

==> W*L =
96

==> (2/3)*L * L =
96

==> (2/3)*L^2 =
96

Now we will multiply by
3/2.

==> L^2 =
96*3/2

==> L^2 =
144

Now we will take the root of both
sides;

==> L = 12
.

==> W = (2/3)L = (2/3)*12 =
8

==> W = 8.

Now we
will calculate the perimeter;

==> P = 2L + 2W = 2*12
+ 2*8 = 24 + 16 = 40.

Then, the perimeter of
the rectangle is 40 units.

Given that the point (1,5) is on the graph of f(x)=3x+b, decide which one from the points (-1,-1), (3,7) are on the graph of f?

According to the rule, a point belongs to the graph of a
function, if and only if it's coordinates verify the expression of the
function.

The point (1,5) is on the graph,
so:

f(1) = 5

f(1) = 3*1 +
b

3 + b = 5

We'll subtract 3
both sides:

b =
5-3

b =
2

The function is determined and it
is:

f(x) = 3x +
2

To verify if the given points belong to
the graph of f(x), we'll substitute their coordinates into the expression of the
function.

(-1,-1), (3,7)

First
we'll verify if f(-1) = -1

f(-1) = 3*(-1) +
2

f(-1) = -3 + 2

f(-1) =
-1

So, the point (-1 , -1) belongs to the graph of
f(x).

Now, we'll verify if the point  (3,7) belongs to the
graph of f(x).

f(3) = 3*3 +
2

f(3) = 9 + 2

f(3) =
11

Since the value of f(3) is not 7, but 11, the point
(3,7) doesn't belong to the graph of f(x) = 3x + 2.

Explain the destruction man has on the environment throughout the novel Lord of the Flies.

In the first chapter, references run rampant to the "scar"
that the plane caused on the island in scratching the surface of the earth there.
Obviously in this case, the technology of man combined with man that was in the plane
later littered up the island tremendously destroying the
land.

In chapter 5, Ralph called a meeting that called
attention to the boys lack of respect for the land:

readability="21">

 “I said if you’re taken short you keep away
from the fruit. That’s dirty!” Laughter rose again.

“I said
that’s dirty!”

He plucked at his stiff, grey shirt. “That’s
really dirty. If you’re taken short you go right along the beach to the rocks.
See?”

Piggy held out his hands for the conch but Ralph
shook his head. His speech was planned, point by
point.

“We’ve all got to use the rocks again. This place is
getting dirty.” He paused. The assembly, sensing a crisis, was tensely
expectant. 

Taking short
meant going to the bathroom. The boys began letting loose wherever and whenever they
felt like it. This really made the place filthy when they had already had a plan in
place for cleansing the land.

These details taken together
demonstrate the lack of respect the boys had for the environment. Perhaps their civility
made them that way. I think you could use these circumstances to argue that humanity has
a destructive tendency toward nature.

Sophocles’ uses plant symbolism several times in Oedipus Rex. It could not be otherwise: he is crowned with bay,/The chaplet is thick with...

This strikes me as a rather interesting question over
what, at first glance, seems like a minor detail. The suppliant Thebans also have
garlands of bay (also known as laurel) upon their branches at the first of the play. If
Oedipus wears a crown of laurel, too, then this would seem to create a link between him
and his fellow citizens, whom he is hoping to help.

We
should also note that the laurel is a plant that is sacred to Apollo. The laurel crown
also links Oedipus with Apollo, the very god whose prophecies he is trying to
avoid.

A crown of laurel might also have reminded
Sophocles' audience of the laurel crowns awarded to victors at the Pythian games,
competitions held in honor of Apollo at Delphi. Having Oedipus wear a crown of laurel
might have cast him in the figurative role of a victor. Of course, he is the tragic
victor, who ultimately falls by the play's end.

The
thickness of the berries is also interesting. Thickness might indicate ripeness and
vitality, marking Oedipus as a powerful and vigorous person who has the ability to deal
with the blight of the plague that vexes the Thebans.

Copernicus and Galileo opened the door to what is now modern science. What did they do that so profoundly changed the way we think today?

Copernicus altered the model of the solar system that
stood for about 1500 years by placing the sun at the center, rather than the earth. When
he made this change, his model became more useful at explaining observations, making
predictions and opening up new areas of
study.

When Galileo heard about a toy with two
lenses that made things appear closer, he added to the understanding of the solar
system. He modified the toy to create the telescope. With this telescope, he studied
Jupiter. He noticed four objects that moved each night. He made notations of this motion
and concluded that these objects must be moons orbiting Jupiter. This provided support
for Copernicus because objects orbiting Jupiter, couldn't be orbiting Earth. This
provided evidence that the Earth at the center of the solar system couldn't be supported
any longer, therefore, Copernicus had created a model of the solar system that explained
what Galileo observed.

So, the use of technology, the
telescope, helped to demonstrate the heliocentric (sun centered) model was the best
explanation for explaining the solar system.

Romeo and Juliet both express love for each other, but what are Juliet's doubts and what does she say to express her concerns?

I assume that you are referring to Act II, Scene ii, which is
commonly known as the "Balcony Scene."

Juliet expresses several
concerns throughout the conversation she has with Romeo in Act II, Scene ii. Her first fear is
that her family will kill Romeo if he is found in the Capulet orchard, but Romeo dismisses her
worry. Juliet also reveals her anxiety at not adhering to typical rules of convention, such as
having been "too quickly won"; she fears that Romeo will think that she is not being serious or
is not modest. Basically, Juliet is afraid that she should have been more aloof and played "hard
to get."

The most troubling of Juliet's worries is her belief that
she and Romeo should not rush into things. Romeo panics when Juliet tells him of her fear, and
she responds by reiterating that she does, indeed, love him.

What does Frost seem to be saying about humankind in his poem "Mending Wall"?

Out of all of Frost's richly symbolic poems, this appears
to be one of the most controversial in terms of its ambiguity--that is, it is open
to opposing interpretations. The poem presents two mind-sets, and it is unclear which of
the two is being endorsed. The neighbour expresses the view that walls are useful, while
the speaker seems them as barriers that should be torn down. There are also other
ambiguities: for example, if the speaker dislikes walls, why does he begin the wall
mending every spring?

However, given this ambiguity, and
regardless of whether you are for or against walls and their symbolic meaning, I think
one of the most interesting phrases in the poem is when the narrator discusses how to
think about whether to build a wall or not:

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Before I built a wall I'd ask to
know

What I was walling in or walling
out,

And to whom I was like to give
offence.

This, to me, lies at
the heart of the poem, because when we build metaphorical walls in terms of our identity
or who we include, we will always exclude others. It seems to be a truth about wall
building that building a wall necessarily entails keeping some in and others out. One
the one hand, walls are shown to be necessary, in that they promote privacy, define
boundaries and protect rights. On the other hand, walls encourage separateness,
isolation, and suspicion. Walls seem to be helpful in some areas and extremely harmful
in others.