Solve for the radius of a circle, find the value of k, determine the values for which a rational expression is undefined, and solve an exponential equation.

Given $c = 12$ cm and $\theta = 150^\circ$.

$$12 = 2r \sin\left(\frac{150^\circ}{2}\right)$$ $$12 = 2r \sin(75^\circ)$$

$$r = \frac{12}{2 \sin(75^\circ)}$$ $$r = \frac{6}{\sin(75^\circ)}$$

Using $\sin(75^\circ) \approx 0.9659$:

$$r = \frac{6}{0.9659}$$ $$r \approx 6.2118 \text{ cm}$$

Rounding to one decimal place, $r \approx 6.2$ cm.

The final answer is $\boxed{\text{D. 6.2 cm}}$.

42.

Here, $x=3$ and $y=1$.

$$1 = (3)^2 - 5(3) + k$$

$$1 = 9 - 15 + k$$ $$1 = -6 + k$$

$$k = 1 + 6$$ $$k = 7$$

The final answer is $\boxed{\text{C. 7}}$.

43.

Set the denominator to zero.

$$3x^2 - 12 = 0$$

$$3x^2 = 12$$ $$x^2 = \frac{12}{3}$$ $$x^2 = 4$$ $$x = \pm\sqrt{4}$$ $$x = \pm 2$$

So, the values for which the expression is not defined are $x = 2$ and $x = -2$.

The final answer is $\boxed{\text{B. } x = -2, 2}$.

44.

Express 1024 as a power of 4.

$$4^5 = 1024$$

$$x = -5$$

The final answer is $\boxed{\text{D. -5}}$.