3. Which of the following are the characteristics for the graph of the parent linear function?
2 answers:
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Answer:
The angle between vector and
is approximately
radians, which is equivalent to approximately
.
Step-by-step explanation:
The angle between two vectors can be found from the ratio between:
- their dot products, and
- the product of their lengths.
To be precise, if denotes the angle between
and
(assume that
or equivalently
,) then:
.
The first component of is
and the first component of
is also
The second component of is
while the second component of
is
. The product of these two second components is
.
The dot product of and
will thus be:
.
Apply the Pythagorean Theorem to both and
:
.
.
Let represent the angle between
and
. Apply the formula
to find the cosine of this angle:
.
Since is the angle between two vectors, its value should be between
and
(
and
.) That is:
and
. Apply the arccosine function (the inverse of the cosine function) to find the value of
:
.
The plus-minus sign represents that there are two possible outcomes.
In this case, we have
. When we branch out the possibilities we got 2 values: 
and 
Those are the roots of this equation. When they ask their product, they want you to multiply both numbers.
When we multiply them:
When we FOIL the we get:
Simplify:
So the product of the two roots of this equation is 6.
In this case, we have
Those are the roots of this equation. When they ask their product, they want you to multiply both numbers.
When we multiply them:
When we FOIL the we get:
Simplify:
So the product of the two roots of this equation is 6.
First, add 1 on both sides of the equation to begin to isolate x
x/5 = 8
Now, to isolate x, multiply both sides of the equation by 5/1
· 
= 
= x
x= 7 · 5/1 = 7 · 5 = 35
x = 35
x/5 = 8
Now, to isolate x, multiply both sides of the equation by 5/1
x= 7 · 5/1 = 7 · 5 = 35
x = 35