3. The system of equations $\left\{\begin{array}{l}y=m(x+2)-4, \\ x^{2}+y^{2}=4(x \geqslant 0)\end{array}\right.$ has real solutions. Then the range of values for $m$ is ( ....).
(A) $[1,3]$
(B) $\left[\frac{3}{4}, 3\right]$
(C) $\left[\frac{3}{4},+\infty\right)$
(D) $(-\infty, 0] \cup\left[\frac{3}{4},+\infty\right)$
3. (B).

As shown in Figure 6, the first equation represents a family of lines passing through the fixed point \( P(-2, -4) \), and the second equation represents the right semicircle. To determine the slopes of the lines in the family that intersect the right semicircle, these lines should lie between the tangent \( PT \) and the secant \( PA \), i.e.,
$$
k_{A T} \leqslant m \leqslant k_{P A} .
$$

It is easy to see that \( A(0, 2) \), so
$$
k_{P A}=\frac{-4-2}{-2-0}=3 \text {. }
$$

Furthermore, the distance from the origin to the line \( PT \) equals the radius 2, thus
$$
\frac{|m \times 0-0+2 m-4|}{\sqrt{m^{2}+1}}=2 \text {. }
$$

This simplifies to \((m-2)^{2}=m^{2}+1\).
Solving for \( k_{P T} = m = \frac{3}{4} \).
Therefore, \(\frac{3}{4} \leqslant m \leqslant 3\).