When using the 30° - 60° - 90° method, the side lengths will always be x and x√3 for the legs and 2x for the hypotenuse.
Because the hypotenuse is 12, the equation is:
2x = 12
And now you find x to get the length of the shortest leg.
2x = 12
x = 6
Now that we know the length of x, you just add √3 in order to find the longest leg.
Therefore, the length of the longest leg would be 6√3.
-3 is actually less than -1
it can't be equal because they are 2 different values
and it can't be greater than because if you place -3 and -1 in a number Line, -1 is closer to 0 which equals that -1 is greater than -3
<h3>
Answer: 180 degrees</h3>
note: it doesn't matter if its clockwise or counterclockwise when it comes to 180 degree rotations.
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Explanation:
The rule for 180 degree rotations is
(x,y) ---> (-x, -y)
So the x and y coordinates flip in sign from positive to negative, or vice versa.
Point D ' (-3, 5) rotates to D ' (3, -5) following this rule
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A further detailed break down might look like this
x = -3 becomes -x = -(-3) = 3
y = 5 becomes -y = -5
(-3, 5) ----> (3, -5)
From the given description it seems that the small shaded circle lies within the larger circle as shown in image below:
The probability that a point choosen at random lies within the shaded area = Area of shaded region / Total area of the bigger cricle
So,
Probability = 78.5/314 = 0.25
Thus there is 0.25 or 25% probability that the point chosen at random will lie inside the shaded region.