1. Translation of a units to the right and b units up has rule:
(x,y)→(x+a,y+b).
Then the function is
![T(x,y)=(x+a,y+b).](https://tex.z-dn.net/?f=T%28x%2Cy%29%3D%28x%2Ba%2Cy%2Bb%29.)
2. Reflection across the y-axis acts in following way:
(x,y)→(-x,y).
Then the function is
![R_y(x,y)=(-x,y).](https://tex.z-dn.net/?f=R_y%28x%2Cy%29%3D%28-x%2Cy%29.)
3. Reflection across the x-axis acts in following way:
(x,y)→(x,-y).
Then the function is
![R_x(x,y)=(x,-y).](https://tex.z-dn.net/?f=R_x%28x%2Cy%29%3D%28x%2C-y%29.)
4. Rotation of 90 degrees counterclockwise about the origin, point O acts bu the rule:
(x,y)→(-y,x).
Then the function is
![R_{O,90^{\circ}}(x,y)=(-y,x).](https://tex.z-dn.net/?f=R_%7BO%2C90%5E%7B%5Ccirc%7D%7D%28x%2Cy%29%3D%28-y%2Cx%29.)
5. Rotation of 180 degrees counterclockwise about the origin, point O acts bu the rule:
(x,y)→(-x,-y).
Then the function is
![R_{O,180^{\circ}}(x,y)=(-x,-y).](https://tex.z-dn.net/?f=R_%7BO%2C180%5E%7B%5Ccirc%7D%7D%28x%2Cy%29%3D%28-x%2C-y%29.)
6. Rotation of 270 degrees counterclockwise about the origin, point O acts bu the rule:
(x,y)→(y,-x).
Then the function is
![R_{O,270^{\circ}}(x,y)=(y,-x).](https://tex.z-dn.net/?f=R_%7BO%2C270%5E%7B%5Ccirc%7D%7D%28x%2Cy%29%3D%28y%2C-x%29.)
Answer:
5/16 as a decimal is 0.3125.
Answer:
Don
Step-by-step explanation:
1. We make the fractions have common denominators so it is easier to compare them. We can do this buy multiplying 2/3 by a factor of 16, so it becomes 32/48. For 11/16, we multiply by a factor of 3 so it becomes 33/48. It is now apparent that Don has the longer pipe.
Answer:
X = -2
Step-by-step explanation:
1/2 X (5X-8) = -9
multiply both sides of the equation by 2
2 X 1/2 X (5X - 8) = 2 X (-9)
1 X (5X - 8) = 2 X (-9)
Reduce the numbers with the greatest common divisor 2
5 x -8 = 2 x (-9)
5 x -8 = -18
Move constant to the right by adding its opposite to both sides
5X -8 + 8=-18 + 8
Then eliminate the opposites
5X = -18 + 8
Calculate the sum
5X = -10
Divide both sides of the equation by 5
5X DIVIDE 5 = -10 DIVIDE BY 5
X = -10 DIVIDE BY 5
X = -2