A music festival offers one-day and three-day passes. A one day pass costs $100 and a three-day pass costs $250. write an expression for the total ticket sales if (n) one day passes and (t) three day passes are sold.
Answers
The expression for the total ticket sales if (n) one day passes and (t) three day passes are sold is n + t = $350.
What is an expression?
An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
Cost of one-day passes, n = $100
Cost of three-day passes, t = $250
So, Total ticketssold = Cost of one-day passes + Cost of three-day passes
⇒ Total ticketssold = n + t
⇒ n + t = $100 + $250
⇒ n + t = $350
which is the required expression for total tickets sold.
Thus, the expression for the total ticket sales if (n) one day passes and (t) three day passes are sold is n + t = $350.
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Answer:
100n+250t
Step-by-step explanation:
cost of the1 one day pass=100
cost of n one day passes=100n
cost of the 1 three day pass=250
cost of t three day passes=250t
Total sale= 100n+250t
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Answers
a) VERTEX
We need to find out where the parabola opens. You can predict the equation by tabulating any values of x and f(x). The table is shown:
x f(x)
_____
0 -7
1 -2
2 1
3 2
4 1
5 -3
As you plot it, the parabola opens downward. The vertex is (3,2) because that is the maximum point. The rest of the values are lesser than 2.
However, there is an easier technique to find the opening parabola and vertex rather than you plot it.
b) AXIS OF SYMMETRY
The axis of symmetry is a line that divides the parabola into two congruent halves. There is a formula for the axis of symmetry which is x = -b/2a.
Note: That is only applied if the parabola opens upward or downward and their axis of symmetry is a vertical line.
To get a and b, arrange the given equation first.
f(x) = -(x - 3)^2 + 2
= -(x^2 - 6x + 9) + 2
= -x^2 + 6x - 7 + 2
= -x^2 + 6x -5
The general form of the quadratic equation is ax^2 + bx + c. Setting a = -1, b = 6, c = -5, the axis of symmetry is
x = -6/(2*-1) = 3.
But anyway, you find it out the table above. We know that the coordinate of the vertex is (3,2). For instance, that is x = 3.
c) MAXIMUM or MINIMUM
Remember that the maximum refers to a vertex where the parabola opening downward. Otherwise, it is a minimum if the parabola opens upward. The maximum or minimum must have a certain value.
We know the answer will be a maximum. Since the axis is symmetry is a vertical line, the value for a maximum is 2.
d) DOMAIN and RANGE
Based on the given equation, the domain will be (-∞, ∞) because all values of x, the parabola continually spreads out.
The range will be (-∞, 2] because the maximum point is 2 and the rest of the values goes negative.