LEAP 2025 Geometry Expressing Mathematical Reasoning. Practice it free.

Same-side interior angles are supplementary: $(6x-5)+(4x+15)=180$, so $10x+10=180$ and $x=17$.

A reflection is a rigid transformation that maps the points from a preimage, over a line of reflection, to the points of an image that are equidistant to the line. In this example, that line is the perpendicular bisector of a line segment from a point to its image, so the segment maps onto itself.

The center is $(4, -5)$ and the radius is $6\textsf{.}$ A point on the circle must satisfy $4 - 6 \le a \le 4 + 6\textsf{,}$ so $-2 \le a \le 10\textsf{.}$ The value $3$ is in this interval.

$x$-coordinate $= \dfrac{2 + 6}{2} = \dfrac{8}{2} = 4$.

Parallel lines have the same slope, so $m = -1$. Substitute $(4, -2)$ into $y = -x + b$: $-2 = -4 + b$, so $b = 2$. The equation is $y = -x + 2\textsf{.}$

Parallel lines have the same slope. In $y = \dfrac{3}{4}x + 8$, the slope is $\dfrac{3}{4}$, so the slope of line $n$ is also $\dfrac{3}{4}\textsf{.}$

$V = \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 3 \times 4 \times 9 = 36$.

$V = \pi r^{2} h = \pi (4)^{2}(10) = 160\pi$ cubic feet.