Since the point lies on the unit circle, it satisfies
Solving for
gives two possible solutions:
Given that
is in quadrant IV, you know that its value must be positive, so
Reasons:
(1) Given
(2) their 2 non-common sides in 1 ray
(3) definition of: supplemental angles
(4) Substitution
(5) Opposite angles are congruent (equal)
(6) Substitution
(7) Definition of supplementary angles
Let D = the amount of money Deanna has after x games.
We know Deanna started with $15 and she spends 0.75 per game, so we can make the following equation:
D = 15 - 0.75x
Let L = the amount of money Lisa has after x games.
We know Lisa started with $13 and she spends 0.50 per game, so we can make the following equation:
L = 13 - 0.5x
The question is asking how many games need to be played for L and D to be equal, so just equate L and D and solve for x:
D = L
15 - 0.75x = 13 - 0.5x
15 - 13 = -0.5x + 0.75x
2 = 0.25x
2 = (1/4)x
8 = x
Therefore they need to play 8 games each to have the same amount of money.
