The general solution for the given equation is 40°+120°n.
The period of g(x) is π.
The range of f(x) is [-1, 1].
- sin(x-30°) = cos 2x
- sin(x-30°) = sin(90°-2x)
- (x-30°) = (90°-2x) + 360°n
- x + 2x = 90° + 30° + 360°n
- 3x = 120° + 360°n
- x = (120° + 360°n)/3
- The general solution (x) is 40° + 120°n.
- g(x) = cos 2x
- The period of cos x is 2π.
- If the multiplying factor of x is 'n', then it decreases the period by n times.
- Here, in g(x), n is 2.
- The period of g(x) is equal to half the period of cos x.
- The period of g(x) = 2π/2
- The period of g(x) is π.
- f(x) = sin(x-30°)
- "Sin" is a trigonometric function which has a range from -1 to 1.
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90 games since each team would be playing 9 games (one against every other team)
Answer:
x= -5 y= -1
Step-by-step explanation:
So, both equations are essentially linear equations.
Linear equations are written in the format
y = mx+b, where
m represents the
slope/slope intercept and
b represents the
y-intercept.
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Part Athe slope and y-intercept
y = mx +b
m - the slope; b- y-intercept
therefore;
y = 6x - 4
m = 6; b = -4y = 5x - 3
m = 5; b = -3The coordinates of the point where the lines are crossed are the solution to the system of linear equations.
How to graph the lines:
y = 6x - 4
y-intercept (0; -4)
for x = 1 ⇒ y = 6 · 1 - 4 = 6 - 4 = 2 ⇒ (1; 2)
y = 5x - 3
y-intercept (0; -3)
for x=1 ⇒ y = 5 · 1 - 3 = 5 - 3 = 2 ⇒ (1; 2)
***look at the img for graph reference***Part B:
x = 1; y = 2
To find the length of a side of a square fins the square root of the area.
Area = 200 cm^2
Side = √200
Side = 10√2 (Exact length)
or 14.142 cm's ( round the decimal answer as needed.)