Recall the sum identity for cosine:
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
so that
cos(a + b) = 12/13 cos(a) - 8/17 sin(b)
Since both a and b terminate in the first quadrant, we know that both cos(a) and sin(b) are positive. Then using the Pythagorean identity,
cos²(a) + sin²(a) = 1 ⇒ cos(a) = √(1 - sin²(a)) = 15/17
cos²(b) + sin²(b) = 1 ⇒ sin(b) = √(1 - cos²(b)) = 5/13
Then
cos(a + b) = 12/13 • 15/17 - 8/17 • 5/13 = 140/221
Amount Earned (E) = 8.25*Hours (H)
Since he wants to buy a game system you can also write this as an inequality, if the amount of the game system has any relevance in the problem.
8.25*H >= 206.25
A. Always
These lines<span> are </span>perpendicular<span> since their slopes are negative reciprocals.</span>
The independent variable (the one they want) is the # of hours worked, since that determines the price.
All the other answers contain information not included in the problem
Answer:

Step-by-step explanation:
To factor the equation, break it into two binomials which multiply to make the equation. To write these binomials (x+a)(x+b), find factors which multiply to -20 and add to -1 for a and b.
20: 1, 2, 4, 5, 10, 20
-5+4 = -1
