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2 years ago

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Virgil has 1/6 of a birthday cake left over. He wants to share the leftover cake with 3 friends. What fraction of the original c

ake will each of the 4 people receive? Draw a picture to support your response.

1 answer:

klemol [59]2 years ago

3 0

Answer:

Each of the 4 people will get 1/24 of the original cake

Step-by-step explanation:

The fractional part of cake left out is 1/6

This remaining cake is to be divided among four people.

Thus, each person will get

fractional part of cake left/total number of people

i.e 1/6/4

= 1/24

Each of the 4 people will get 1/24 of the original cake

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which statements are true about the graph of the function f(x) = 6x – 4 x2? check all that apply. the vertex form of the functio

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Answer:

The vertex of the function is the point $(-3,-13)$

The graph increase over the interval--------> (-3,∞)

Step-by-step explanation:

we have

$f(x)=6x-4+x^{2}$

<u>1) Convert to vertex form</u>

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+4=x^{2}+6x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)+4+9=x^{2}+6x+9$

$f(x)+13=x^{2}+6x+9$

Rewrite as perfect squares

$f(x)+13=(x+3)^{2}$

$f(x)=(x+3)^{2}-13$ -----> function in vertex form

<u>2) Find the vertex</u>

The vertex of the function is the point $(-3,-13)$

<u>3) Find the axis of symmetry</u>

we know that

In a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertex

The x-coordinate of the vertex in this problem is equal to $x=-3$

therefore

the equation of the axis of symmetry is $x=-3$

<u>4) Find the increase-decrease intervals</u>

The graph increase over the interval--------> (-3,∞)

The graph decrease over the interval--------> (-∞,-3)

see the attached figure to better understand the problem

<u>5) Find the x-intercepts of the function</u>

we know that

the x-intercepts are the values of x when the value of the function is equal to zero

In this problem the x-intercepts are

$(-6.61,0)$ and $(0.61,0)$

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see the attached figure

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Small, because 1 divided by 8 = 0.125, and 3 divided by 4 = .75 Hope this helps!

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Draw at least six different sized rectangles that have an area of 64 square units

olga_2 [115]

Let

x------> the length of the rectangle

y------> the width of the rectangle

we know that

The area of a rectangle is equal to

$A=x*y$

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let's assume different values of x to get the different values of y

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see the draw in the attached figure N 1

<u>case 2)</u> For x=32 units

substitute in the equation 1

$x*y=64$

$y=64/x$

$y=64/32$

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the dimensions of the rectangle are 32 units x 2 units

see the draw in the attached figure N 2

<u>case 3)</u> For x=16 units

substitute in the equation 1

$x*y=64$

$y=64/x$

$y=64/16$

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see the draw in the attached figure N 3

<u>case 4)</u> For x=30 units

substitute in the equation 1

$x*y=64$

$y=64/x$

$y=64/30$

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see the draw in the attached figure N 4

<u>case 5)</u> For x=40 units

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$x*y=64$

$y=64/x$

$y=64/40$

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see the draw in the attached figure N 5

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$y=64/x$

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