To perform a 90° rotation clockwise around the origin, you take the coordinates of the point A(x, y) and transform them to A'(y, -x). Since 180° and 270° are both "steps" of 90°, we can do this in succession and achieve our goal.
1) (5, 2) 90° = (2, -5) [(y, -x)]
2) (5, 2) 180° = two 90° turns = (2, -5) rotated 90° = (-5, -2)
3) (5, 2) 270° = three 90° turns = (-5, -2) rotated 90° = (-2, 5)°
4) (-5, 2) 90° = (y, -x) = (2, 5)
5) (-5, 2) 180° = two 90° turns = (2, 5) rotated 90° = (5, -2)
6) (-5, 2) 270° = three 90° turns = (5, -2) rotated 90° = (-2, -5)
7) (-2, 5) 90° = (y, -x) = (5, 2)
8) (5, -2) 180° = (y, -x) with another 90° turn = (-2, -5) rotated 90° = (-5, 2)
9. The experimental probability that it will rain on any given day in Houston Texas is about 15%.
Thus, out of 365 days, 15% of that are the predicted days the it will rain in the Place.
=> 365 days is the total number of days in a year
=> 15% is the predicted days to rain
=> 365 * .15 = 54.75
Since this is a decimal number, let’s round this off to 55 days.
Why 55 because the value of tenths is more than 5.
Answer:
She will be n+10 years old.
Answer: The answer is 8.
Step-by-step explanation: The first step is to convert the expression into figures. We shall call the unknown number Y. So if we are told “the square of a number,” that means Y squared, or better still, Y^2. Further we are told “the difference between the square of a number and 40” and that can be written as;
Y^2 - 40.
Next we are told that this expression is equal to 3 times that number (that is 3Y). That can now be written out as follows,
Y^2 - 40 = 3Y
If we move all expressions to one side of the equation, what we would have is,
Y^2 - 3Y -40 = 0
(Remember that when a positive value crosses to the other side of an equation it becomes negative and vice versa)
We now have a quadratic equation
Y^2 -3Y - 40 = 0
By factorizing we now have
(Y -8) (Y + 5) = 0
Therefore Y - 8 = 0 or
Y + 5 = 0
Hence, Y = 8 or Y = -5
Since we are asked to calculate the positive solution, Y = 8
Answer:
y= -1/3x + 5
Step-by-step explanation:
