What is the equation of the line that passes through (-3,7) and parallel to the line 2y-4x +2 = 0

Given the point (-3,7) passes through the
line.

Then we know that:

y-y1
= m(x-x1)

==> y-7 =
m(x+3)

Now we will determine the
slope.

Since the line is parallel to the line 2y-4x +2 = 0,
then the slopes are equal.

==> We will rewrite into
the slope form.

==> y= 2x
-1

==> Then the slope is m=
2

==> y-7=
2(x+3)

==> y-7 = 2x +
6

==> y= 2x +
13

Then the equation of the line is y=
2x+13.

Prove Pascal's rule(n,k)+(n,k+1)=(n+1,k+1)

We'll use combinatorial way to prove this
identity.

We'll recall the factorial formula of
combinations of n elements taken k at a time:

C(n,k) =
n!/k!*(n-k)!

Now, we'll write the factorial formula of
combinations of n elements taken k+1 at a time:

C(n,k+1) =
n!/(k+1)!*(n-k-1)!

Now, we'll write the factorial formula
of combinations of n+1 elements taken k+1 at a
time:

C(n+1,k+1) =
(n+1)!/(k+1)!*(n+1-k-1)!

We'll reduce like terms within
brackets form denominator:

C(n+1,k+1) =
(n+1)!/(k+1)!*(n-k)!

Now, we'll re-write the identity that
has to be demonstrated:

n!/k!*(n-k)! + n!/(k+1)!*(n-k-1)! =
(n+1)!/(k+1)!*(n-k)!

We'll create the same denominator at
the fractions from the left side:

[n!*(k+1) +
n!*(n-k)]//(k+1)!*(n-k)!

We'll remove the brackets from
numerator:

(n!*k + n! + n!*n -
n!*k)/(k+1)!*(n-k)!

We'll eliminate like terms within the
brackets:

(n! +
n!*n)/(k+1)!*(n-k)!

We'll factorize by
n!:

n!*(n +
1)/(k+1)!*(n-k)!

But n!*(n + 1) =
(n+1)!

The left side will
become:

n!*(n + 1)/(k+1)!*(n-k)! =
(n+1)!/(k+1)!*(n-k)!

We notice that the LHS =
RHS, therefore the Pascal's rule is verified, so that n!/k!*(n-k)! + n!/(k+1)!*(n-k-1)!
= (n+1)!/(k+1)!*(n-k)!.

How do we write and solve the statement " the difference between a number and 3 is less than 15" What are possible values of the number?

Let us assume that the number required is
x.

Then we need to find the
difference.

==> l x - 3l <
15

Now we will solve the inequality with the absolute
value.

We will
rewrite:

==> -15 < x-3 <
15

Now we will add 3 to both
sides.

==> -12 < x <
18

Then the values of the number are the
interval (-12, 18).

The function f is defined as f(x)=(2x+1)/(x-3). Find the value of k so that the inverse of f is f^-1(x)=(3x+1)/(x-k).

We'll determine the inverse function
f^-1(x).

Let f(x)=y, such
as:

y = (2x+1)/(x-3)

We'll
multiply both sides by (x-3):

xy - 3y =
2x+1

We'll move 3y to the
right:

xy = 2x + 3y +1

We'll
subtract 2x both sides:

xy - 2x = 3y +
1

We'll factorize by x to the
left:

x(y - 2) = 3y + 1

We'll
divide by (y-2):

x =
(3y+1)/(y-2)

The inverse function is: f^-1(x) =
(3x+1)/(x-2)

Comparing with the given
expression of f^-1(x) = (3x+1)/(x-k), we'll identify k =
2.

reflect on what pip's reaction reveals about his character when he meets the true benafactor magwitch

Pip is horrified (to put it mildly) and devestating when
he learns Magvitch is his benefactor. He is devestated because he truly believed Miss
Havisham was his benefactor, and that she was arranging it so Pip could marry Estella.
As for being horrified, Pip's true character is revealed at this point: he has become a
snob. He has allowed his new position in life (gentleman) to ruin his true person. Pip
was once a boy/teenager who knew what it meant to have to work for something, but
because of his benefactor, he has grown lazy and greedy. He feels he deserves the money
he received; he feels it is his destiny to be a gentleman and to be with Estella. By
revealing the truth to him, Magvitch has crushed all of Pip's expectations. Pip feels
that Magvitch's money and intent are below him. He despises the criminal in spite of all
the criminal has done for him. At the start of the book, the crinimal appears hard and
cruel; now it is Pip who is the cruel one.

In Othello, who is responsible for Desdemona's death?

Desdemona is killed by her husband, Othello. He smothers
her in the belief that she has been unfaithful to him with a Cassio, a member of
Othello's staff. Desdemona tells us of her innocence in Act V Scene
ii- 

O,
falsely, falsely
murdered!

And indeed Othello
confesses to his crime-

readability="5">

She's like a liar gone to burning hell;

'Twas I that kill'd
her.

However, it is through
the cruel machinatios of Othello's ensign, Iago, that Othello has believed the tale that
Desdemona was unfaithful. Once Emilia is able to piece together Iago's wicked plot, she
directs the guilt squarely at her husband -

And
your reports have set the murder on.

In
the final lines of the play it is clear whom Lodovico, as representative of the Venetian
government, believes is responsible for the tragedy which has befallen as he addresses
Iago-

O Spartan dog;
More fell than anguish,
hunger, or the sea!
Look on the tragic loading of this bed;
This
is thy work.

Is there a commutative property of addition, subtraction, multiplication, or division and does order matter when doing any of them, why or why not?

Addition and Multiplication ARE commutative, while
Subtraction and Division are NOT commutative.

e.g, in
simple addition and multiplication, no matter what the order, the result is still the
same. Whereas, subraction and division need to have a particular order or the result
will change.

When doing more complex expressions and
equations, order IS important or the answer will change
completely.

An easy way to remember order is
BIMDAS

B -
Brackets
I -
Indices
M - Multiplication (from
left of expression to right)
D - Division (from
left of expression to right)
A - Addition(Left of
expression to right)
S- Subtraction (Left of
expression to right)

Hope that
helped.