If you want the intersect of M and N, then:
M∩N = {4,7} (common part in M AND N)
Remove parentheses
3m - 7m+12 = 2 m-3
collect like terms
3m-7m-12 = 2m-6
move terms
-4m - 12 = 2m-6
collect the like terms and calculate
-4m-2m = -6+12
divide both sides by -6
-6m=6
m= -1
Answer:
Perimeter of the smaller triangle = 1.75x
Step-by-step explanation:
Let the two equal sides of an isosceles triangle = x
Therefore, length of the base = 
Perimeter of this isosceles triangle = x + x + 
= 2x + 
= 2x + x + 
= 
Since, smaller triangle has a perimeter that is half the perimeter of the larger triangle,
Length of each corresponding side of smaller triangle will be half of the larger triangle.
Length of sides of the smaller triangle = 
Perimeter of the smaller triangle = 
= x + 
= 
= 
= 
= 1.75x
Therefore, expression that represents the perimeter of the smaller triangle is (1.75x)
We can say that exchanging one couple's ticket for an individual's ticket would increase the money in the cash box from 200 to 202 and it would result in an even number of couples tickets sold.
<u>Step-by-step explanation:</u>
Let the number of tickets sold to the individuals = s
Let the number of tickets sold to the couples = c
According to the question,
s + c = 46 ( Equation 1)
Since each individual's ticket is $6, the total amount of money made by selling tickets to individuals is 6s.
Similarly, since each ticket sold to couples is $8, the total amount of money made by selling tickets to couples is 8c.
So,
6 s + 8 c = 200 ( Equation 2)
On solving both the equations, we get
c = 38 and s = 8
Therefore, 8 tickets were sold to individuals and 38 tickets were sold to the couples.