Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
First of all we know the
Absolute Value Function that is:

This is called the
Parent Function <em>of the Absolute Value Function.</em>
From the equation:

The term:

means that the the Parent Function is <em>shifted</em>
two units <em>to the left</em>.
On the other hand, the term:

means that the function

is <em>shifted</em>
three units <em>downward. </em>So the result is the graph shown below
Answer:
y = 49 - x
Step-by-step explanation:
Let the other number be y.
Given x + y = 49
x+y-x = 49 - x
y = 49 - x
Answer:
-1875
Step-by-step explanation:
An arithmetic sequence has a common difference as a sequence. Here the common differnece is -11.
So our sequence so far looks like,
(57,46,35,24....). We know the last term of the sequence is -207 and we need to find the nth term of that series so we use arithmetic sequence

where a1 is the inital value,
d is the common differnece and n is the nth term.
We need to find the nth term so




So the 25th term of a arithmetic sequence is last term, now we can use the sum of arithmetic sequence
which is



