Find the value of the ratio x ÷ y if the equation is 5x²-13xy+8y²

Mathematics

1 answer:

Maslowich3 years ago

5 0

Answer:

x÷y=8/5 or 1÷1

Step-by-step explanation:

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Please help The dilation DO,2.5 is applied to triangle ABC below. Use the dilation of triangle ABC and its image to prove that t

viva [34]

A dilation $D_{O,\,k}$ is a dilation with a scale factor, k centered at the origin.

A scale factor, k means that the distance of the image from the the center of dilation is k times the distance of the pre-image from the center of dilation and the size of the image is k times the size of the pre-image.

Given triangle ABC with vertices A(-2, 2), B(1, 2) and C(1, -1), a dilation $D_{O,\,k}$ will result in the image with vertices A'2.5(-2, 2) = A'(-5, 5), B'2.5(1, 2) = B'(2.5, 5) and C'2.5(1, -1) = C'(2.5, -2.5)

Now, consider line AC, the equation of the line is given by

$\frac{y-2}{x-(-2)} = \frac{-1-2}{1-(-2)} \\ \\ \Rightarrow \frac{y-2}{x+2} = \frac{-3}{1+2} = \frac{-3}{3} =-1 \\ \\ \Rightarrow y-2=-(x+2)=-x-2 \\ \\ \Rightarrow y=-x$

Notice that line y = -x is a line passing through the origin which is the center of dilation.

Consider line A'C', the equation of the line is given by

$\frac{y-5}{x-(-5)} = \frac{-2.5-5}{2.5-(-5)} \\ \\ \frac{y-5}{x+5} = \frac{-7.5}{2.5+5} = \frac{-7.5}{7.5} =-1 \\ \\ \Rightarrow y-5=-(x+5)=-x-5 \\ \\ \Rightarrow y=-x$

As an be seen the line AC and the line A'C' is the same line.

4 0

2 years ago

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Write an expression in factored form to represent the volume in the canister not occupied by the tennis balls.

olya-2409 [2.1K]

Answer:

$\implies V=\pi r^2(h-4 r)$