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Anna [14]
3 years ago
5

Ashley has 9 pizzas .She is serving each person at a party 3/4 of a pizza.How many can she serve at the party?​

Mathematics
1 answer:
shusha [124]3 years ago
8 0

Answer:

Ashley can serve 12 pieces of pizza in the party

Step-by-step explanation:

To solve this question we need to convert the 9 pizzas to decimal:

9 times 4 = 36. That is:

9 pizzas are equal to 36/4 of pizza (36/4 = 9)

As Ashley is serving 3/4 of a pizza she can serve:

36/4 ÷ 3/4 = 36/3 = 12

<h3>Ashley can serve 12 pieces of pizza in the party</h3>
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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh
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A parabola is a mirror-symmetrical U-shape.

  • The equation of the parabola is \mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}
  • The focus is \mathbf{Focus = (80, -1760)}
  • The directrix is \mathbf{y = \frac{1}{640}}
  • The axis of the symmetry of parabola is: \mathbf{x = 80}

From the question, we have:

\mathbf{Vertex: (h,k) = (80,10)}

\mathbf{Origin: (x,y) = (0,0)}

The equation of a parabola is:

\mathbf{y = a(x - h)^2 + k}

Substitute the values of origin and vertex in \mathbf{y = a(x - h)^2 + k}

\mathbf{0 = a(0 - 80)^2 + 10}

\mathbf{0 = a(- 80)^2 + 10}

\mathbf{0 = 6400a + 10}

Collect like terms

\mathbf{6400a =- 10}

Solve for a

\mathbf{a =- \frac{1}{640}}

Substitute the values of a and the vertex in \mathbf{y = a(x - h)^2 + k}

\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}

The focus of a parabola is:

\mathbf{Focus = (h, \frac{k+1}{4a})}

Substitute the values of a and the vertex in \mathbf{Focus = (h, \frac{k+1}{4a})}

\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}

\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}

\mathbf{Focus = (80, -11\times 160)}

\mathbf{Focus = (80, -1760)}

The equation of the directrix is:

\mathbf{y = -a}

So, we have:

\mathbf{y = \frac{1}{640}} ----- the directrix

The axis of symmetry is:

\mathbf{x = -\frac{b}{2a}}

We have:

\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}

Expand

\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}

Expand

\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}

\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }

A quadratic function is represented as:

\mathbf{y = ax^2 + bx + c}

So, we have:

\mathbf{a = -\frac{1}{640}}

\mathbf{b = \frac{1}{4}}

Recall that:

\mathbf{x = -\frac{b}{2a}}

So, we have:

\mathbf{x = -\frac{1/4}{2 \times -1/640}}

\mathbf{x = \frac{1/4}{1/320}}

This gives

\mathbf{x = \frac{320}{4}}

\mathbf{x = 80}

Hence, the axis of the symmetry of parabola is: \mathbf{x = 80}

Read more about parabola at:

brainly.com/question/21685473

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