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marin [14]
3 years ago
15

A van travels 150 miles on 6 gallons of gas. How many gallons will it need to travel 325 miles?

Mathematics
1 answer:
diamong [38]3 years ago
8 0

Answer:

C. 13 gallons

Step-by-step explanation:

150 divided by 6 is 25. 325 divided by 25 is 13.

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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

4 0
3 years ago
Simplify the expression! :D :P
mario62 [17]
54-30/3=54-10=44
The blanks are 30, 10 and 44
6 0
3 years ago
Rewrite in mathematical language. Every negative integer J is less than or equal to its inverse.
Luda [366]

Answer:

-J \leq J

Step-by-step explanation:

Given

Negative integer J

Required

Represent as an inequality of its inverse

The question didn't state if it's additive inverse or multiplicative inverse;

<em>Since the question has to do with negation, I'll assume it's an additive inverse</em>

<em></em>

The inverse of -J is +J

To represent as an inequality (less than or equal), we have:

-J \leq +J

Solving further, it gives

-J \leq J

3 0
3 years ago
Ella played a math game and had the five cards shown.
wlad13 [49]

4Step-by-step explanation:

5 0
3 years ago
Three x squared plus seventeen x plus ten
Sindrei [870]

Answer:

(3x+2)(x+5)

Step-by-step explanation:

3 0
3 years ago
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