For , on the left we have , and on the right,
(where we use the double angle identity: )
Suppose the relation holds for :
Then for , the left side is
So we want to show that
On the left side, we can combine the fractions:
Recall that
so that we can write
(another double angle identity: )
Then recall that
which lets us consolidate the numerator to get what we wanted:
and the identity is established.
(y2-y1)/(x2-x1)
(-7-5)/(4-2)
-12/2= -6
Answer:
1:3
Step-by-step explanation:
for every 1 apple, he is packing 3 plums,
therefore,
1 apple to(:) 3 plums
1:3
Answer:
See explanation
Step-by-step explanation:
Let be the number of students and be the number of adults on the show.
1. Tickets cost $15 for students, so x student tickets cost $15x.
Tickets cost $25 for adults, so y adult tickets cost $25y.
Total cost of all tickets is $(15x + 25y).
The charity show is conducted in order to raise at least $3,750, thus
2. The auditorium can accommodate up to 180 spectators, hence
3. We get the system of inequalities:
Plot all solutions sets to each inequality and the common region is the solution set to the system of inequalities. This region is not empty, so the charity will reach its goal. For example, if they sell 50 students tickets and 125 adult tickets, they will raise