Answer:
![\circledast \ \ f\circ f\left( x\right) = x](https://tex.z-dn.net/?f=%5Ccircledast%20%5C%20%5C%20f%5Ccirc%20f%5Cleft%28%20x%5Cright%29%20%3D%20x)
![\circledast \ \ g\circ g\left( x\right) =4x - 21](https://tex.z-dn.net/?f=%5Ccircledast%20%5C%20%5C%20g%5Ccirc%20g%5Cleft%28%20x%5Cright%29%20%20%3D4x%20-%2021)
Step-by-step explanation:
![f(x)=\frac{5}{2x}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B5%7D%7B2x%7D)
g(x) = 2x - 7
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![f\circ f\left( x\right) =\frac{5}{2\left( f\left( x\right) \right) }](https://tex.z-dn.net/?f=f%5Ccirc%20f%5Cleft%28%20x%5Cright%29%20%20%3D%5Cfrac%7B5%7D%7B2%5Cleft%28%20f%5Cleft%28%20x%5Cright%29%20%20%5Cright%29%20%20%7D)
![=\frac{5}{2\left( \frac{5}{2x} \right) }](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B2%5Cleft%28%20%5Cfrac%7B5%7D%7B2x%7D%20%20%5Cright%29%20%20%7D)
![=\frac{5}{\left( \frac{5}{x} \right) }](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B%5Cleft%28%20%5Cfrac%7B5%7D%7Bx%7D%20%20%5Cright%29%20%20%7D)
![=5\times\frac{x}{5}](https://tex.z-dn.net/?f=%3D5%5Ctimes%5Cfrac%7Bx%7D%7B5%7D)
![=x](https://tex.z-dn.net/?f=%3Dx)
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![g\circ g\left( x\right) =2(g(x)) - 7](https://tex.z-dn.net/?f=g%5Ccirc%20g%5Cleft%28%20x%5Cright%29%20%20%3D2%28g%28x%29%29%20-%207)
= 2(2x - 7) - 7
= 4x - 14 - 7
= 4x - 23
Answer:
y = (1/6)x - 11
Step-by-step explanation:
y = (1/6)x + 7; Point: (12, -9)
(x₁, y₁)
y - y₁ = m (x - x₁)
y - (-9) = (1/6) (x - 12)
y + 9 = (1/6)x - 2
-9 -9
y = (1/6)x - 11
I hope this helps!
Answer:
-4
Step-by-step explanation:
Subtract 10g from both sides
8 = -2g
divide by negative 2
g = -4
T=5w
T= total cost
W= weeks
It can't be W= because the question is asking for total cost in dollars, so two options are cancelled out.
Can't be t=5+w because it's 5 per week and if, let's say calculating dollars for 2 weeks, the answer would be t=5+2=7 and that wouldn't be right
Answer:
θ = 36.9°, 90°, 216.9°, or 270°
Step-by-step explanation:
4 sin 2θ − 3 cos 2θ = 3
Use double angle formulas:
4 (2 sin θ cos θ) − 3 (cos²θ − sin²θ) = 3
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3
Use Pythagorean identity:
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3 (sin²θ + cos²θ)
8 sin θ cos θ − 3 cos²θ + 3 sin²θ = 3 sin²θ + 3 cos²θ
8 sin θ cos θ − 6 cos²θ = 0
2 cos θ (4 sin θ − 3 cos θ) = 0
2 cos θ = 0
θ = 90° or 270°
4 sin θ − 3 cos θ = 0
4 sin θ = 3 cos θ
tan θ = 3/4
θ = 36.9° or 216.9°