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4 years ago

What is the width of a poster board if the length is 28 inches and the diagonal is 35 inches?

Mathematics

1 answer:

Rudiy274 years ago

4 0

Answer:

$W=21\ in$

Step-by-step explanation:

we know that

The diagonal of a rectangular poster board is given by the Pythagorean Theorem

$D^2=L^2+W^2$

where

D is the diagonal

L is the length

W is the width

we have

$L=28\ in\\D=35\ in$

substitute the given values

$35^2=28^2+W^2$

$W^2=35^2-28^2$

$W^2=441$

$W=\sqrt{441}=21\ in$

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answer

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Step-by-step explanation:

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A rectangle has vertices E(-4, 8), F(2, 8), G(2, -2) and H(-4, -2). The rectangle is dilated with the origin as the center of di

Marizza181 [45]

Answer:

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Step-by-step explanation:

From Linear Algebra, we define the dilation of a point by means of the following definition:

$G'(x,y) = O(x,y) +k\cdot [G(x,y)-O(x,y)]$ (1)

Where:

$G(x,y)$ - Coordinates of the point G, dimensionless.

$O(x,y)$ - Center of dilation, dimensionless.

$k$ - Scale factor, dimensionless.

$G'(x,y)$ - Coordinates of the point G', dimensionless.

If we know that $O(x,y) = (0,0)$ , $G(x,y) =(2,-2)$ and $G'(x,y) =(5,-5)$ , then scale factor is:

$(5,-5) = (0,0) +k\cdot [(2,-2)-(0,0)]$

$(5,-5) = (2\cdot k, -2\cdot k)$

$k = \frac{5}{2}$

The dilation on any point of the rectangle is:

$P'(x,y) = (0,0) + \frac{5}{2}\cdot [P(x,y)-(0,0)]$

$P'(x,y) = \frac{5}{2}\cdot P(x,y)$ (2)

The dilation on any point of the rectangle is $P'(x,y) = \frac{5}{2}\cdot P(x,y)$ .

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3 years ago

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Answer:

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Step-by-step explanation:

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_____

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