Answer:
The regular price of the ticket was $12.
Step-by-step explanation:
Let us call 
the regular price of the tickets, and if she had bought tickets at this price, the total cost would have been
.
But Holly got $4 off the regular ticket price, that means one ticket cost her
and if she bought 23 tickets it cost her
and we are told this equals $184; therefore we have
now we solve this equation the following way:
Thus, the regular price was $12.
The solution of a system of linear equations is the point where the two lines meet. Note that for the given equations, both lines have the same slope (4/5). If two lines have the same slope, it means that those lines are parallel. Parallel lines do not meet at any point, they stay parallel to the infinite.
Therefore, since this two lines are parallel, they don't meet and the system has no solution.
Answer:
- building: 222.61 ft
- flagpole: 32.15 ft
Step-by-step explanation:
The tangent function of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, the adjacent side is 500 ft, so we have ...
tan(24°) = (building height)/(500 ft)
building height = (500 ft)tan(24°) ≈ 222.61 ft
__
Similarly, the height to the top of the flagpole is ...
total height = (500 ft)tan(27°) ≈ 254.76 ft
The length of the flagpole is the difference of these heights:
flagpole length = 254.76 ft -222.61 ft = 32.15 ft
The height of the building is 222.61 ft; the length of the flagpole is 32.15 ft.
Answer:
The candles will be the same height at 10 pm.
Step by step explanation:
12 - 0.5x = 18 - 2x
12 + 1.5h = 18
1.5h = 6
h = 4
4 hours
4 hours after 6 pm. is 10pm.
