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Mumz [18]
3 years ago
6

825 tickets were sold for a game for a total of $1,462.50. If adult tickets sold for $2.50 and children's tickets sold for $1.00

, how many of each kind of ticket were sold?
Mathematics
2 answers:
Shtirlitz [24]3 years ago
7 0

Answer:

greater etext they'd hereafter greatest note count defective justification

In-s [12.5K]3 years ago
7 0
Let the number of adults tickets = a
Let the number of children’s tickets = c

Form 2 equations:

825 tickets total:
a + c = 825 (1)

Cost of tickets:
2.50a + 1.00c = 1,462.50
c = 1462.50 - 2.5a (2)

Solve equations (1) & (2) simultaneously:

Sub (2) into (1):
a + (1462.5 - 2.5a) = 825
a - 2.5a = -637.5
-1.5a = -637.5
a = 425

Sub a=425 into (1):
425 + c = 825
c = 400

Therefore 450 adults tickets and 400 children’s tickets were sold
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Answer:

1. <em>Axis of symmetry</em>: x = 3

2. <em>Vertex:</em> (3,5)

3. <em>Solution of the equation</em>:

<u />

  • x-intercepts:

               (3-\sqrt{5},0) \\\\(3+\sqrt{5},0)

  • y-intercept: (0, -4)

Explanation:

<u>1. Equation:</u>

    y=-x^2+6x-4

<u>2. </u><em><u>Axis of symmetry:</u></em>

That is the equation of a parabola, whose standard form is:

                 y=ax^2+bx+c

Where:    

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The axis of symmetry is the vertical line with equation:

               x=-b/2a

Substitute  a=-1,\text{ and }b=6

          x=-6/[(2)(-1)]=-6/(-2)=3

Thus, the axis of symmetry is:

            x=3

<em><u>3. Vertex</u></em>

<em><u /></em>

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

               y=-x^2+6x-4\\\\y=-(3)^2+6(3)-4=-9+18-4=5

Therefore, the vertex is (3, 5)

<u>4. Find the x-intercepts</u>

The x-intercepts are the roots of the equation, which are the points wher y = 0.

        y=-x^2+6x-4=0

Use the quadratic equation:

       x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\x=\frac{-6\pm\sqrt{(-6)^2-4(-1)(-4)} }{2(-1)}\\\\x_1=3-\sqrt{5} \\\\x_2=3+\sqrt{5}

<u>5. Find the y-intercept</u>

<u />

The y-intercet is the value of y when x=0:

         y=-x^2+6x-4\\\\y=-(0)^2+6(0)-4=-4

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Answer:

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Step-by-step explanation:

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