MCA High School / MCA EOC 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 $(x - 1)^2 + (y - 2)^2 = 49$.

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

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

$\sin\theta = \tan\theta \cdot \cos\theta = \dfrac{5}{12} \cdot \dfrac{12}{13} = \dfrac{5}{13}$.

A rotation is a rigid transformation that turns a figure around a fixed point, called a center of rotation, by a specific angle in a specific direction. All points remain equidistant from the center of rotation, keeping the image congruent to the preimage. In this example, the image is congruent to the preimage and is located at a different angle around that center point.

In a $30^{\circ}$-$60^{\circ}$-$90^{\circ}$ triangle, the short leg is half the hypotenuse: $\dfrac{14}{2} = 7\textsf{.}$