Rom

$\alpha+\beta \in \mathbb{R} \Rightarrow Im(\alpha)+2=0 \Rightarrow Im(\alpha)=-2\\ \alpha-2\beta \in i \cdot \mathbb{R}\Rightarrow Re(\alpha) - 6 = 0 \Rightarrow Re(\alpha)=6\\ \alpha = 6-2i$

$\text{in a frictionless system linear momentum is conserved}\\ 15.0 + (-35.0) = (-12.0) + m_{bf}\\ m_{bf} = -8 kg*m/s$

$\dfrac 2 3 t - 1 < t + 7 \leq -2t+15\\ \dfrac 2 3 t -8< t \leq -2t+8\\~\\ \text{left side}\\ \dfrac 2 3 t -8 < t\\ -\dfrac 1 3 t < 8\\ t > -24$

$\text{Right side}\\ t \leq -2t+8\\ 3t\leq 8\\ t\leq \dfrac 8 3$

$\text{final result}\\ -24 < t \leq \dfrac 8 3 \\ t \in \left(-24, \dfrac 8 3 \right]$

$f(g(x)) = 4g(x) + c = \\ 4(cx+2)+c = \\ 4cx+(8+c) = 12x+d\\~\\ 4c=12\\ 8+c=d\\~\\ c=3\\ d=11$

$6\frac 1 8 < 7 < 8=\sqrt{64}$

$\dfrac{150 (63) + (500-150)h_b}{500} = 67.8\\ 9450 + 350h_b = 33900\\ 350h_b = 24450\\ h_b \approx 69.86~inches$

 A price for a good or service that is equal to the cost of production.

really?

63 + 6 x 27 = ?

the object exerts a force on Earth in the direction of Earth towards the object.  (Gravity is attractive)

This would be considered an upwards force on Earth.

The cost before tax is cost=50h

and then we apply an 8% tax to that to get tax = 0.08 cost = 0.08(50h)

and we add the two together to get the total cost

total = tax + cost = 0.08(50h) + 50h