It’s the second option, (x,y) —> (3x,3y) since you have to multiply each coordinate by a certain number called the scale factor (in this case, it’s 3)
The first option won’t work because the scale factor has to be same for both coordinates. The third option is a translation, and the fourth won’t work either because you have to multiply each coordinate by the same variable.
Answer:
They ate
of the pizza
Step-by-step explanation:
Carolyn and Joyce at 4 slices of pizza altogether, and since there are 12 slices of pizza, they ate
of the pizza.
The cosine of an angle is the x-coordinate of the point where its terminal ray intersects the unit circle. So, we can draw a line at x=-1/2 and see where it intersects the unit circle. That will tell us possible values of θ/2.
We find that vertical line intersects the unit circle at points where the rays make an angle of ±120° with the positive x-axis. If you consider only positive angles, these angles are 120° = 2π/3 radians, or 240° = 4π/3 radians. Since these are values of θ/2, the corresponding values of θ are double these values.
a) The cosine values repeat every 2π, so the general form of the smallest angle will be
... θ = 2(2π/3 + 2kπ) = 4π/3 + 4kπ
b) Similarly, the values repeat for the larger angle every 2π, so the general form of that is
... θ = 2(4π/3 + 2kπ) = 8π/3 + 4kπ
c) Using these expressions with k=0, 1, 2, we get
... θ = {4π/3, 8π/3, 16π/3, 20π/3, 28π/3, 32π/3}
Answer:
1/2 - 3(1/2 + 1)²
simplify the expression (1/2 + 1)
1/2 - 3•(3/2)²
using PEMDAS, we see we have to evaluate the exponent first
(3/2)² = 9/4
rewrite the equation
1/2 - 3 • (9/4)
multiply 3 by (9/4)
1/2 - (27/4)
subtract
-25/4
(1 + 1/3)² - 2/9
simplify the expression (1 + 1/3)
(4/3)² - 2/9
using PEMDAS, we see we have to evaluate the exponent first
(4/3)² = 16/9
rewrite the equation
(16/9) - (2/9)
subtract
14/9