A toy cost 0.85p in January.
Step-by-step explanation:
Given,
Mark down in January = 15%
Let,
Price in December = p
Mark down in January = 15% of price in December
Mark down in January = 
Mark down in January = 0.15p
Price of toy in January = Price in December - Mark down
Price of toy in January = p - 0.15p = 0.85p
A toy cost 0.85p in January.
Keywords: mark down, subtraction
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Answer:
PQ = 20
Step-by-step explanation:
Theorem: The length of the median of a trapezoid is the average of the base lengths.
PQ + 12 = 32
PQ = 20
See how easy that is if you know the theorem!
Answer: the service charge per hour for premium services is $5.5
the service charge per hour for regular services is $3
Step-by-step explanation:
Let x represent the service charge per hour for premium services.
Let y represent the service charge per hour for regular services.
One customer was charged $38 after spending 2 h in premium areas and 9 regular hours. It means that
2x + 9y = 38- - - - - - - - - - - 1
Another customer spent 3 h in premium areas and 6 regular hours and was charged $34.50. It means that
3x + 6y = 34.5- - - - - - - - - - -2
We would eliminate x by multiplying equation 1 by 3 and equation 2 by 2. It becomes
6x + 27y = 114
6x + 12y = 69
Subtracting, it becomes
15y = 45
y = 45/15
y = 3
Substituting y = 3 into equation 1, it becomes
2x + 9 × 3 = 38
2x + 27 = 38
2x = 38 - 27 = 11
x = 11/2 = 5.5
Answer:
sin(2A) = (2√2 + √3) / 6
Step-by-step explanation:
2A = (A+B) + (A−B)
sin(2A) = sin((A+B) + (A−B))
Angle sum formula:
sin(2A) = sin(A+B) cos(A−B) + sin(A−B) cos(A+B)
sin(2A) = 1/2 cos(A−B) + 1/3 cos(A+B)
Pythagorean identity:
sin(2A) = 1/2 √[1 − sin²(A−B)] + 1/3 √[1 − sin²(A+B)]
sin(2A) = 1/2 √(1 − 1/9) + 1/3 √(1 − 1/4)
sin(2A) = 1/2 √(8/9) + 1/3 √(3/4)
sin(2A) = 1/3 √2 + 1/6 √3
sin(2A) = (2√2 + √3) / 6
12 16/56 + 3 35/56 = 15 51/56
