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3 years ago

What is the counterclockwise rotation shown below? 13 pts.

Mathematics

1 answer:

AveGali [126]3 years ago

6 0

Answer:

270° around the origin

Step-by-step explanation:

As shown at the graph

ΔABC is translated to ΔA'B'C'

A(0,3) , B(-2,2) , C(-1,1)

A'(3,0) , B'(2,2) , C'(1,1)

So, if the coordinate of the pre-image is (x,y)

The coordinate of the image will be (y, -x)

Which mean the rule will be (x,y)→(y,-x)

The previous rule is the rule of rotation 270° counterclockwise

So, the answer is 270° around the origin

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The degree of the numerator (4) is larger than the degree of the denominator (3), so first you need to divide. (Added screenshot of long division procedure.)

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Now the second term can be decomposed into partial fractions.

$\dfrac{4x^2-17x+10}{x(x^2-3)}=\dfrac{r_1}x+\dfrac{r_2x+r_3}{x^2-3}$
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Gold pieces the first leprechaun has: x
Gold pieces the second leprechaun has: y

The first leprechaun says to the other, ‘Give me seven of your gold pieces and I will have twice as many as you!’:
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(1) x-2y=-21
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Using the method of substitution, we can isolating y in the second equation:
(2) x-y=14
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(1) -x+28=-21
(1) -x+28-28=-21-28
(1) -x=-49
(1) (-1)*(-x=-49)
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