Answer:
Step-by-step explanation:
Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,
 
 
Firstly convert it into <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>i</em><em>n</em><em>t</em><em>e</em><em>r</em><em>c</em><em>e</em><em>p</em><em>t</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line which is <u>y</u><u> </u><u>=</u><u> </u><u>m</u><u>x</u><u> </u><u>+</u><u> </u><u>x</u><u> </u>, as ;
 
 
 
 
On comparing it to <em>y</em><em> </em><em>=</em><em> </em><em>m</em><em>x</em><em> </em><em>+</em><em> </em><em>c</em><em> </em>, we have ,
 
 
 
 
Now as we know that the <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>o</em><em>f</em><em> </em><em>t</em><em>w</em><em>o</em><em> </em><em>p</em><em>a</em><em>r</em><em>a</em><em>l</em><em>l</em><em>e</em><em>l</em><em> </em><em>l</em><em>i</em><em>n</em><em>e</em><em>s</em><em> </em><em>i</em><em>s</em><em> </em><em>s</em><em>a</em><em>m</em><em>e</em><em> </em>. Therefore the slope of the parallel line will be ,
 
 
Now we may use <em>p</em><em>o</em><em>i</em><em>n</em><em>t</em><em> </em><em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line as ,
 
 
On substituting the respective values ,
 
 
 
 
 
 
 
 
 
 
 
 
Again the equation can be rewritten as ,
 
 
 
 
 
 

 
        
             
        
        
        
"Contains four right angles" is the one among the following choices given in the question that is <span>not a property of a parallelogram. Parallelograms can have angles that are not ninety degrees. The correct option among all the options that are given in the question is the second option or option "B". </span>
        
             
        
        
        
4/3 /......................................................../
        
             
        
        
        
Answer:
   both kinds of tickets are $5 each
Step-by-step explanation:
Let s and c represent the dollar costs of a senior ticket and child ticket, respectively. The problem statement describes two relationships:
   12s + 5c = 85 . . . . . revenue from the first day of sales
   6s + 9c = 75 . . . . . . revenue from the second day of sales
Double the second equation and subtract the first to eliminate the s variable.
   2(6s +9c) -(12s +5c) = 2(75) -(85)
   13c = 65 . . . . . simplify
   65/13 = c = 5 . . . . . divide by the coefficient of c
Substitute this value into either equation. Let's use the second one.
   6s + 9·5 = 75
   6s = 30 . . . . . . . subtract 45
   30/6 = s = 5 . . . divide by the coefficient of s
The price of a senior ticket is $5; the price of a child ticket is $5.