Answer is C. usual balance
Answer: 3
Step-by-step explanation:
Answer:
its 9.0864
Step-by-step explanation:
Answer:
y = 2sin(x/2 - pi/4) + 1
Step-by-step explanation:
The normal sine has a range of [-1, 1]. This one has a range of [-1, 3], so the amplitude is 2 times higher (4 vs 2).
After that, 2sin(x) has a range of [-2, 2], but this one has a range of [-1, 3], so we need to shift it upwards by 1.
We now know that the answer is 2sin(____)+1.
A normal sine has it's middle point while rising at x = 0, but this one has it at x = pi/2 - so we need to shift a sine to the right by pi/2.
Lastly, a sine has a cycle of length 2pi, but this one has a cycle of length 4pi. We can achieve that by dividing the argument 2.
We now know that the answer is 2sin(x/2 - pi/4) + 1. We can plot it to verify.
Given:
Flights: 4 points per dollar
Hotels: 2 points per dollar
Other: 1 point per dollar.
Total spent = $9,480
Points earned = 14,660
Let
x = money spent on flights
y = money spent on hotels
z = money spent on other purchases.
Because the money spent on flights was $140 more than twice the money spent on hotels, therefore
x = 2y + 140 (1)
Total charges were $9,480, therefore
x + y + z = 9480 (2)
Total points earned was 14,660. Therefore
4x + 2y + z = 14660 (3)
Subtract (2) from (3).
4x + 2y + z - (x + y + z) = 14660 - 9480
3x + y = 5180 (4)
Substitute (1) into (4).
3(2y + 140) + y = 5180
7y + 420 = 5180
7y = 4760
y = 680
From (1), obtain
x = 2y + 140 = 2*680 + 140 = 1500
From (2), obtain
z = 9480 - (x + y) = 9480 - (1500 + 680) = 7300
Answer:
$1,500 was spent on flights,
$680 was spent on hotels,
$7,300 was spent on other purchases.