Answer:

Step-by-step explanation:
Given
Lines x and y
Transversal b

Required
Find 
From the attachment,
and
are vertically opposite.
This means that

Similarly
and
are supplementary angles
So:

Make
the subject



The relationship between
and
is that they are supplementary angles because:

Answer:
461 adults and 864 students
Step-by-step explanation:
We can set-up a system of equations to find the number of adults. We know students and adults attended. We will let s be the number of students and a be the number of adults. Since 1,325 tickets were purchased, then s+a=1325.
We also know that a total of $3,169 was collected and adult tickets cost $5 each and students cost $1 each. We can write 1s+5a=3169.
We will solve by substituting one equation into the other. We first solve the first equation for s which is s=1325-a. Substitute s=1325-a into 1s+5a=3169. Simplify and isolate the variable a.
1(1325-a)+5a=3169
1325-a+5a=3169
1325+4a=3169
1325-1325+4a=3169-1325
4a=1844
a=461
This means that 461 adults attended and 864 students attended since 864+461=1325.
Inequalities are used to show the relationship between unequal expressions
- <em>The set notation of (5) and (6) are: </em>
<em> and </em>
<em>.</em> - <em>See attachmen</em>t for the graphs
The following should be notated when plotting the graph of an inequality
- < and > are represented with open circles, while
and
are represented with closed circles - The arrows of
and
point to the left, while the arrows of
and
point to the right.
So, we have:

Rewrite as:
The graph of
will point to the right, and it will use an open circle

Split the inequality:
and 
<em>It is not possible for -6 to be less than x and at the same time, x is greater than or equal to -2.</em>
<em />
Hence.
cannot be represented on a graph

Split the inequality:
and 
means that -4 is less than x or x is greater than -4.
So, we have:
and 
If
and
, then we make use of
because it contains more values of x.
The graph of
will point to the right, and it will use an open circle
Read more about inequalities at:
brainly.com/question/11612965