ticket sale on Saturday night is triple the ticket sale on Friday night.
Therefore
ticket sales on Saturday night = 3 x 12425 = 37275
Then
ticket sales for both nights = 12425 + 37275 = 49700
A ticket costs 35.
Let the number of people that attended the carnival on both nights be n.
Then, we have
Therefore 1420 people attended the carnival on both nights
Answer:
Children: $13
Adults: $18
Step-by-step explanation:
Well for both sets we can set up the following system of equations,
So first we need to solve for a in the first equation.
3a + 4c = 106
-4c to both sides
3a = -4c + 106
Divide 3 by both sides
<u>a = -4/3c + 35 1/3</u>
Now we plug in that a for a in 2a + 3c = 75.
2(-4/3c + 35 1/3) + 3c = 75
-8/3c + 70 2/3 + 3c = 75
Combine like terms
1/3c + 70 2/3 = 75
-70 2/3 to both sides
1/3c = 4 1/3
Divide 1/3 to both sides
c = 13
Now we can plug in 13 for c in 3a + 4c = 106,
3a + 4(13) = 106
3a + 52 = 106
-52 to both sides
3a = 54
Divide 3 by both sides.
a = 18
<em>Thus,</em>
<em>an adult ticket is $18 and a children's ticket is $13.</em>
<em />
<em>Hope this helps :)</em>
Answer:
A
Step-by-step explanation:
So we have the quadratic equation and it's written in three equivalent forms:
Let's determine the characteristics of the quadratic equation with the given equations.
From the first equation, since the leading coefficient (0.5) is positive, we can be certain that the graph opens upwards.
Also, the constant term is -1.5, so the y-intercept is (0,-1.5).
The second equation is the vertex form. Vertex form has the format:
Where (h,k) is the vertex. From the second equation we know that h is -1 (because (x+1) is the same as (x-(-1))) and k is -2. Therefore, the vertex is (-1,-2).
And since the graph points upwards, this means that (-1,-2) is the minimum point of the function. In other words, the range of the function is greater than or equal to -2. In interval notation, this is:
This also means that the end behavior of the graph as a x approaches negative and positive infinity is positive infinity because the graph will always go straight up.
Also, the third form is the factored form. With that, we can solve for the zeros of the quadratic. The zeros are:
Therefore, the graph crosses the x-axis at x=-3 and x=1.
So, from the three equations, we gathered the following information:
1) The graph curves upwards.
2) The roots of zeros of the function is (-3,0) and (1,0).
3) The y-intercept is (0,-1.5).
4) The vertex is (-1,-2). This is also the minimum point.
5) Therefore, the range of the graph is all values greater than or equal to -2.
6) The end behavior of the graph on both directions go towards positive infinity.
Therefore, our correct answer is A.
B is not correct because the line of symmetry (or the x-coordinate of the vertex) here is -1 and not 1/2.
C is not correct because the graph goes towards <em>positive </em>infinity since it shoots straight up.
And D is not correct because the y-intercept is (0,-1.5).