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Alekssandra [29.7K]
4 years ago
13

A farmer needs to mix 12 ounces of fertilizer for every 10 pounds of soil. How many pounds of fertilizer fill the farmer

Mathematics
1 answer:
Olegator [25]4 years ago
8 0
100lbs of soil= 120 oz of fertilizer
20lbs of soil= 24oz of fertilizer
120+24= 144oz of fertilizer
120lbs of soil needs 114oz of fertilizer
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lesantik [10]
+8 means that it is a positive number
-8 means that it is a negative number
I think what you mean by: {8}, is |8| which is absolute value which means no matter the answer it is the absolute value from 0 so it’s always +
4 0
4 years ago
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Part 4: Use the information provided to write the vertex formula of each parabola.
sergey [27]

Answer:  1. x = (y - 2)² + 8

              \bold{2.\quad x=-\dfrac{1}{2}(y-10)^2}+1

               3. y = 2(x +9)² + 7

<u>Step-by-step explanation:</u>

Notes: Vertex form is: y =a(x - h)² + k    or      x =a(y - k)² + h

  • (h, k) is the vertex
  • point of vertex is midpoint of focus and directrix:   \dfrac{focus+directrix}{2}

     \bullet\quad a=\dfrac{1}{4p}

  • p is the distance from the vertex to the focus

1)

focus = \bigg(\dfrac{-31}{4},2\bigg)\qquad directrix: x=\dfrac{-33}{4}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{-31}{4}+\frac{-33}{4}}{2}=\dfrac{\frac{-64}{4}}{2}=\dfrac{-16}{2}=-8\\\\\text{The y-value of the vertex is given by the focus as: 2}\\\\\text{vertex (h, k)}=(-8,2)

Now let's find the a-value:

p=focus-vertex\\\\p=\dfrac{-31}{4}-\dfrac{-32}{4}=\dfrac{1}{4}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{4})}=\dfrac{1}{1}=1

Now, plug in a = 1   and    (h, k) = (-8, 2) into the equation x =a(y - k)² + h

x = (y - 2)² + 8

***************************************************************************************

2)

focus = \bigg(\dfrac{1}{2},10\bigg)\qquad directrix: x=\dfrac{3}{2}\\\\\text{Since directrix is x, then the x-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{1}{2}+\frac{3}{2}}{2}=\dfrac{\frac{4}{2}}{2}=\dfrac{2}{2}=1\\\\\text{The y-value of the vertex is given by the focus as: 10}\\\\\text{vertex (h, k)}=(1,10)

Now let's find the a-value:

p=focus-vertex\\\\p=\dfrac{1}{2}-\dfrac{2}{2}=\dfrac{-1}{2}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{-1}{2})}=\dfrac{1}{-2}=-\dfrac{1}{2}

Now, plug in a = -1/2   and    (h, k) = (1, 10) into the equation x =a(y - k)² + h

\bold{x=-\dfrac{1}{2}(y-10)^2}+1

***************************************************************************************

3)

focus = \bigg(-9,\dfrac{57}{8}\bigg)\qquad directrix: y=\dfrac{55}{8}\\\\\text{Since directrix is y, then the y-value of the vertex is:}\\\\\dfrac{focus+directrix}{2}=\dfrac{\frac{57}{8}+\frac{55}{8}}{2}=\dfrac{\frac{112}{8}}{2}=\dfrac{14}{2}=7\\\\\text{The x-value of the vertex is given by the focus as: -9}\\\\\text{vertex (h, k)}=(-9,7)

Now let's find the a-value:

p=focus-vertex\\\\p=\dfrac{57}{8}-\dfrac{56}{8}=\dfrac{1}{8}\\\\\\a=\dfrac{1}{4p}=\dfrac{1}{4(\frac{1}{8})}=\dfrac{1}{\frac{1}{2}}=2

Now, plug in a = 2   and    (h, k) = (-9, 7) into the equation y =a(x - h)² + k

y = 2(x +9)² + 7

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3 years ago
Break the numbers 0-9 into 3 groups. Each group needs to equal the same number when added! Write out the groupsand the sum of ea
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we must do the following:

0

1

2

3

4

5

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select the major, the minor and the half and add, like this:

9+0+5+1=15

therefore:

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also:

\begin{gathered} 8+4+3=15 \\  \end{gathered}

the groups are:

(9,0,1,5); (7,6,2); (8,4,3)

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