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3 years ago

Holiday dinners at June’s house are always a festive occasion. One particular holiday, June has 16 guests.

Mathematics

1 answer:

Semmy [17]3 years ago

3 0

Answer:

a. 3

Step-by-step explanation:

We solve this question gathering the information given in the question.

June serves 8 guests slices of both pies.

This is soon going to be used

June serves a total of 10 slices of apple pie

This includes the 8 guests which got served both pieces. So 10 - 8 = 2 guests were served only apple pie.

11 slices of blueberry pie.

By the same logic as above, 11 - 8 = 3 guests were served only blueberry pie.

8 + 2 + 3 = 13 guests were served at least one pie.

16 - 13 = 3 guests had no pie at all.

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3 years ago

Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

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

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

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3 years ago

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alexdok [17]

Answer:

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hope this helps :)

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