The cost of each senior ticket is $ 5 and cost of each child ticket is $ 12
<em><u>Solution:</u></em>
Let "a" be the price of each senior ticket
Let "b" be the price of each child ticket
<em><u>On the first day of ticket sales the school sold 4 senior tickets and 4 child tickets for a to total of 68</u></em>
Thus a equation is framed as:
4 senior tickets x price of each senior ticket + 4 child tickets x price of each child ticket = 68
4a + 4b = 68 ---------- eqn 1
<em><u>The school took in 120 on the second day by selling 12 senior tickets and 5 child tickets</u></em>
Similarly, we frame a equation as:
12a + 5b = 120 ---------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
<em><u>Multiply eqn 1 by 3</u></em>
12a + 12b = 204 -------- eqn 3
<em><u>Subtract eqn 2 from eqn 3</u></em>
12a + 12b = 204
12a + 5b = 120
( - ) --------------
7b = 84
b = 12
<em><u>Substitute b = 12 in eqn 1</u></em>
4a + 4(12) = 68
4a + 48 = 68
4a = 20
a = 5
Thus cost of each senior ticket is $ 5 and cost of each child ticket is $ 12
Answer:
20
Step-by-step explanation:
n > -6 is the inequality for 16 plus 5 times a number is more than the number minus 8
<em><u>Solution:</u></em>
Given statement is:
16 plus 5 times a number is more than the number minus 8
We have to write a inequality
From given statement,
16 plus 5 times a number is more than the number minus 8
Let the number be "n"
Therefore,
16 plus 5 times "n" is more than "n" minus 8
Here, "plus" means addition and "minus" means subtraction and "times" means multiplication
Thus the statement is translated into inequality as:
Simplify the inequality
Thus the soultion is n > -6
<h2>
Answer:</h2><h3>
A. Domain </h3>
The domain of a function is the x-values that the graph applies to. This means that the domain is whatever x-values the graph crosses. All vertical parabolas (like the one pictured) have a domain of all reals. This is because any x-value could be plugged into the function and provide a y-value. while it may not seem like it, that graph will cover every single x-value in existence.
<h3>
B. Range</h3>
The range is similar to the domain but is for y-values. So, the range is whatever y-values the graph applies to and crosses. As you can see from the graph, there are no y-values above 1. This means the range is y≤1.
<h3>
C. Increasing Interval</h3>
A graph is increasing when the y-values are increasing. So, on the parent function of a parabola, the graph increases to the right and decreases to the left. However, this graph is inverted and shifted to the left, so the interval will also be flipped and shifted. In this case, the graph increases from -∞ to 2.
- Increasing Interval = [-∞, 2]
<h3>
D. Decreasing Interval</h3>
The decreasing interval is very similar to the increasing interval. This interval applies when the y-values are decreasing as the x-values increase. For a parabola, the increasing and decreasing intervals always meet at the x-value of the vertex, which is 2 on this graph. The y-values decrease during the interval 2 to ∞.
- Decreasing Interval = [2, ∞]
<h3>
E. Opening</h3>
The direction of a parabola is decided by the sign (+ or -) of the leading coefficient. Positive coefficients open up and negative opens down. As you can see from the graph, the sides of the parabola point downwards. This means that the leading coefficient must be negative.
<h3>
F. Min and Max</h3>
A parabola will always only have a min or a max, never both. If a graph opens up it has a min because there is one y-value which is the minimum possible y-value. Graphs that open downwards have a maximum because there is one y-value that is the largest possible. So, this graph has a maximum of 1 because that is the largest possible y-value.
