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Readme [11.4K]
3 years ago
9

Given A'B'C' and ABC.

Mathematics
2 answers:
Viefleur [7K]3 years ago
4 0

Because the transformation is a rotation of 180 ° about the origin, the resulting image is a reflection of the original image. Since the rotation is 180 degrees there is a movement of 2 quadrants for the coordinates of A, B,and C.  There for this means that if point A's coordinate is in the quadrant of (x,y) then the coordinates point of A' would be in the quadrant where (-x,-y) coordinates are present.

Dovator [93]3 years ago
3 0

Since the transformation occurring is rotation at 180 degrees about the origin, then the resulting image would be a reflection of the original image. Additionally, since the rotation is 180 degrees, then there is a movement of 2 quadrants for the corners A, B and C.

<span>Therefore this would also mean that if point A is in coordinate (x, y) then point A’ would be in coordinate (-x, -y). Similar is true with point B and point C and their corresponding reflection corners point B’ and point C’. So for example if point A is located at (-5, 3) then point A’ must be at (5, -3).</span>

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3 0
3 years ago
What is the greatest integer a, such that a^2 + 3b is less than (2b)^2, assuming that b is 5? Please answer and have a nice day!
solniwko [45]
<h3>Answer: Largest value is a = 9</h3>

===================================================

Work Shown:

b = 5

(2b)^2 = (2*5)^2 = 100

So we want the expression a^2+3b to be less than (2b)^2 = 100

We need to solve a^2 + 3b < 100 which turns into

a^2 + 3b < 100

a^2 + 3(5) < 100

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after substituting in b = 5.

------------------

Let's isolate 'a'

a^2 + 15 < 100

a^2 < 100-15

a^2 < 85

a < sqrt(85)

a < 9.2195

'a' is an integer, so we round down to the nearest whole number to get a \le 9

So the greatest integer possible for 'a' is a = 9.

------------------

Check:

plug in a = 9 and b = 5

a^2 + 3b < 100

9^2 + 3(5) < 100

81 + 15 < 100

96 < 100 .... true statement

now try a = 10 and b = 5

a^2 + 3b < 100

10^2 + 3(5) < 100

100 + 15 < 100 ... you can probably already see the issue

115 < 100 ... this is false, so a = 10 doesn't work

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2 years ago
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