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Vsevolod [243]
3 years ago
15

Write an equation for the line that passes through the points (0, -6) and (-3, 0).

Mathematics
1 answer:
Dmitry [639]3 years ago
3 0

Answer:

\displaystyle y = -2x -6

Step-by-step explanation:

x-intercept → Plug in 0 for <em>y</em><em> </em>to get −3 for <em>x</em>

y-intercept → When <em>x</em><em> </em>is set equal to 0 [(0, −6)]

I am joyous to assist you anytime.

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Graph the function g.<br> f(x) = -2(x-4)² +4<br> g(x) = f(x) - 1<br> O
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Answer:

19

Step-by-step explanation:

fx=16+4

fx=20

gx= 20-1

gx=19

19

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2 years ago
What is the value of x in the equation below?<br><br> 7x + 8 = -13
ivann1987 [24]

Answer:

x=-3

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7x=-13-8

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2 years ago
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[10 points] A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimens
MissTica

Answer:

  6 inches square by 3 inches high

Step-by-step explanation:

For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².

That is, the bottom is 6 inches square, and the sides are 3 inches high.

_____

Let x and h represent the base edge length and box height, respectively. Then we have ...

  x² +4xh = 108 . . . . box surface area

Solving for height, we get ...

  h = (108 -x²)/(4x) = 27/x -x/4

The volume is the product of base area and height, so is ...

  V = x²h = x²(27/x -x/4) = 27x -x³/4

We want to maximize the volume, so we want to set its derivative to zero.

  dV/dx = 0 = 27 -(3/4)x²

  x² = (4/3)(27) = 36

  x = 6

  h = 108/x² = 3

The box is 6 inches square and 3 inches high.

_____

<em>Comment on maximum volume, minimum area</em>

In the general case of<em> an open-top box</em>, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².

If the box has a <em>closed top</em>, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.

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3 years ago
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478.8u^3 should be the answer
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What is the complete factorization of the polynomial below x^3+x^2+4x+4?
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B. 

It can first be factored by splitting to:

(x + 1)(x^2 +4)

And (x^2 + 4) splits to x +/- 2i
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