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mezya [45]
3 years ago
10

If you can buy 1⁄4 pizza for 5 dollars, how much can you purchase for 8 dollars? Write your answer as a fraction.

Mathematics
1 answer:
N76 [4]3 years ago
6 0
This is a problem using proportions.

a/b = c/d where: ad = bc

1/4 : 5 = x : 8

a = 1/4 ; b = 5 ; c = x ; d = 8

get the cross products: ad = bc

1/4 * 8 = 5 * x
8/4 = 5x
2 = 5x
2/5 = x

2/5 of a pizza can be purchased for 8 dollars.

to check:

1/4 : 5 = 2/5 : 8

1/4 * 8 = 5 * 2/5
8/4      = 10/5
  2       = 2
  
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Y=-x^2+6x-4<br> Find the Axis of Symmetry and the Vertex, Also solve the whole equation.
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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:    

                 a=-1;b=6;c=-4

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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