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3 years ago

Write an inequality for the given statement: The product of –3 and a number is no more than 15.

Mathematics

1 answer:

baherus [9]3 years ago

3 0

-3n<_15
the "<_" is a "less than or equal to" sign i just couldn't type it how it looks

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Polygon ABCD is reflected and dilated to give polygon PQRS. The coordinates of the preimage are (2, 2), (6, 8), (12, 8), and (16

HACTEHA [7]

Answer: The scale factor of the dilation is 0.5.

Explanation:

It is given that ABCD is polygon which is reflected and dilated , then we get PQRS.

The vertices of ABCD are (2, 2), (6, 8), (12, 8), and (16, 2) respectively. The vertices of image PQRS are (11, 15),(9, 12), (6, 12), and (4, 15) respectively.

The reflection affects the coordinates but does not affect the length of the sides.

But when we talk about dilation it affects the length of sides according to the scale factor or a constant factor.

If a line segment AB is dilated by scale factor k then length of A'B' is k times length of AB.

$|A'B'|=k\times |AB|$ .... (1)

So we have to find any side length of preimage and the side length of that side in image. it means we have to find AB and PQ.

Use distance formula to find the side length.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$AB=\sqrt{(8-2)^2+(6-2)^2}=\sqrt{36+16}=2\sqrt{13}$

$PQ=\sqrt{(9-11)^2+(12-15)^2}=\sqrt{4+9}=\sqrt{13}$

It is noticed that the size of side in preimage is $2\sqrt{13}$ and the size of same side in image is $\sqrt{13}$ .

Using equation (1), we get

$\sqrt{13}=k \times 2\sqrt{13}$

$k=\frac{1}{2}$

$k=0.5$

Hence, the value of scale factor is 0.5.

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Henrietta solved a rational equation. Her work is shown. How could she solve it in a simpler way?

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