Two lines passing through the point (2 , 3) intersect each other at an angle of 60° . If slope of one line is 2, then find the e
2 answers:
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Domain of a function
<h2>STEP 3: finding the x values that make x²-6x-55>0 (factoring)</h2>
<h2>STEP 4: finding the x values that make (x+5)(x-11)>0 (factoring)</h2>
We want to find the domain of the following function:
This means that we want to find the x-values that it can take.
<h2>STEP 1: analyzing the simplies form of the function</h2>Let's analyze the simpliest form of the function:
Its graph is:
Then, for the simpliest form of the function, the x-values can only be higher than 0.
This means that its domain is
domain = x > 0
<h2>STEP 2: domain of the given function</h2>Based on the above we can deduce that for the <em>ln(x)</em> function, what is inside the parenthesis should be higher than 0 on this kind of functions.
This is that for
then
In order to find the values of x that make
we must factor it.
We want to find a pair of numbers that when multiplied give the last term (-55) and when added together give the second term (-6).
For the last term of the polynomial: -55, we have that
(-5) · 11 = 55
5 · (-11) = 11
If we add them:
-5 + 11 = 6
5 - 11 = -6
The pair of numbers that when multiplied give the last term (-55) and when added together give the second term (-6), are: 5 and -11
We use them to factor the polynomial:
Then,
In order to find them, we are going to separate the factors (x+5) and (x-11) and analyze when they are positive or negative:
Combining them:
Since we are going to multiply both factors:
We use the diagram to analyze the sign of their product:
Then
when x < -5 and when x > 11. This is the domain.
Therefore, expressed in set notation:
domain = {x|x∈(-∞, -5)∪(11, ∞)}
<h2>Answer: domain = {x | x ∈ (-∞, -5)∪(11, ∞)}</h2>Answer:
Part 7) Adjacent angles
m<SUR and m<RUN
m<TUP and m<PUQ
Part 8) Vertical acute angles
m<SUR and m<PUQ
m<RUN and m<TUP
Part 9) Supplementary angles
m<SUT and m<TUQ
m<SUR and m<QUR
Part 10)
Part 11) m<RUQ is greater than m< TUR
Part 12)
Part 13)
Step-by-step explanation:
Part 7) we know that
we know that
Two angles are Adjacent when they have a common side and a common vertex
In this problem
m<SUR and m<RUN ----> are adjacent angles
because have a common side UR and a common vertex U
m<TUP and m<PUQ ----> are adjacent angles
because have a common side UP and a common vertex U
Part 8) we know that
An angle is acute when is measure is less than degrees
Vertical Angles are the pair of congruent angles opposite each other when two lines cross
In this problem
------> by vertical angles
------> by vertical angles
Part 9) we know that
Two angles are supplementary if its sum is equal to degrees
In this problem
------> by supplementary angles
------> by supplementary angles
Part 10) Find m<QUR
we know that
------> by supplementary angles
we have
substitute
Part 11) which is greater m<TUR or m< RUQ
we know that
m<TUR=m<TUS+m<SUR
substitute the values
----> see the procedure problem 10
therefore
m<RUQ is greater than m< TUR
Part 12) Find the measure angle x
------> by vertical angles
solve for x
Part 13) m<KMH
we know that
-----> by supplementary angles