Answer:
The number of tickets sold at the gate is 
The number of tickets sold in advance is 
Step-by-step explanation:
From the question we are told that
The cost of a tickets at the gate is 
The cost of a ticket in advance is 
Let the number of ticket sold in the gate be G
Let the number of ticket sold in advance be A
From the question we are told that
One hundred more tickets were sold in advance than at the gate and this can be mathematically represented as
From the question we are told that
The total revenue from ticket sales was $1990 and this can be mathematically represented as
substituting for A in the equation above
![5 G + 3[G + 100]= 1990](https://tex.z-dn.net/?f=5%20G%20%20%2B%20%203%5BG%20%20%2B%20%20100%5D%3D%20%201990)
=>
Substituting this for G in the above equation
![5 [211.25] + 3A = 1990](https://tex.z-dn.net/?f=5%20%5B211.25%5D%20%20%2B%20%203A%20%20%3D%20%201990)
=> 
=>
Given the following points:
(1, 4): (2, 2.5): (3, 1) and (4, -0.5).
We are asked to find the average rate of change of the sequence.
The average rate of change for the sequence is the slope and it can be solved using the slope formula.
Slope (m) = y2 - y1
x2 - x1
So, lets choose two points on the line and substitute into the formular.
(1, 4) and (2, 2.5)
where:
x1 = 1
x2 = 2
y1 = 4
y2 = 2.5
m = 2.5 - 4
2 - 1
m = -1.5/1
m = -1.5
m = -1 1/2
Therefore, the correct option is the second option.
Answer:the total number of horses in the herd is 36
Step-by-step explanation:
Let x represent the total number of horses in the herd.
One fourth of the herd of horses was seen in the forest. This means that the number of horses that was seen in the forest would be
1/4 × x = x/4
Twice the square root of the herd had gone to the mountain slopes. This means that the number of horses that had gone to the mountain slopes would be
2 × √x = 2√x
Three times five horses remained on the riverbank. This means that the number that remained would be
3 × 5 = 15
Therefore
x/4 + 2√x + 15 = x
x - x/4 - 15 = 2√x
(4x - x - 60)/4 = 2√x
(3x - 60)/4 = 2√x
Cross multiplying,
3x - 60 = 8√x
Squaring both sides of the equation, it becomes
(3x - 60)(3x - 60) = 64x
9x² - 180x - 180x + 3600 = 64x
9x² - 360x - 64x + 3600 = 0
9x² - 424x + 3600 = 0
Applying the quadratic equation
x = (- b ±√b² - 4ac)/2a
x = ( - - 424 ± √-424² - 4(9 × 3600)/2 × 9
x = (424 ± √179776 - 129600)/18
x = (424 ±√50176)/18
x = (424 + 224)/18 or
x = (424 - 224)/18
x = 36 or x = 11.11
the number of horses must be whole number. Therefore, the number of horses is 36
47 is the answer Since two opposites add up to zero, remove them from the expression, and then you just add up the answers
