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2 years ago

Points A(-2, 4), B(1, 3), C(4, -1) and D form a parallelogram. What are the coordinates of D?

Mathematics

1 answer:

Dominik [7]2 years ago

7 0

Answer: The coordinates of D are Option c (1,-2)

<u>explanation: </u>

The Parallelogram is a quadrilateral whose opposite sides are equal and parallel. The location of a parallelogram on a coordinate plane is determined based on its four vertices.

A coordinate plane is a two-dimensional plane formed by the intersection of two lines one is a vertical line and the other is horizontal. The vertical line is the y-axis and horizontal line x-axis.

Four points of parallelogram ABCD are A(-2,4),B(1,3), C(4,-1), D(1,-2)

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A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

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2 years ago

B. The area of another sheet of paper is 200 square inches. Write an equation that

nata0808 [166]

Answer:

200/3n

Step-by-step explanation:

It is a strangely worded question but you are dividing the paper in 3's n times so 3n will be part of the answer and you are dividing 200. So, the answer is 200/3n.

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How to do geometry ex determining angle measures

stiks02 [169]

Answer:

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Jlenok [28]

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mafiozo [28]

Answer:

Yes

Step-by-step explanation:

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2x+17y+48=0

x+8y-6=0 --> multiply 2 times, so 2x+16y-12=0

and now you can use it as if they are coefficients for both variables

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3 years ago