MCAS Grade 10 Geometry. Practice it free.

Consecutive angles are supplementary: $(4x+6)+(2x+24)=180$, so $6x+30=180$ and $x=25$. Then $m\angle P=4(25)+6=106°$.

The endpoints share the same $x$-coordinate, so the diameter is vertical with length $|7 - (-1)| = 8\textsf{.}$ The radius is half the diameter, so $r = \dfrac{8}{2} = 4\textsf{.}$

Circle A has center $(1, -4)$ and radius $7$. Shifting up $6$ moves the center to $(1, 2)$, so Circle B is $(x - 1)^2 + (y - 2)^2 = 49$.

The center is $(-1, -10)$ and the radius is $12\textsf{.}$ A point on the circle must satisfy $-1 - 12 \le a \le -1 + 12\textsf{,}$ so $-13 \le a \le 11\textsf{.}$ The value $6$ is in this interval.

Both variables are squared with positive coefficients and different denominators: this is an ellipse.

Set up the proportion $\dfrac{x\text{ packages}}{1\text{ cubic foot}} = \dfrac{4{,}800\text{ packages}}{160\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $160x = 4{,}800\textsf{,}$ so $x = 30\text{ packages per ft}^{3}\textsf{.}$

$(y - 7)^{2}$ means $k = 7\textsf{,}$ so the center is $(-1, 7)\textsf{.}$

Since $\dfrac{2 + x}{2} = 5$, we get $x = 10 - 2 = 8$.