Answer:
A rotation is a rigid transformation, sometimes called an isometric transformation, that moves every point of the pre-image through an angle of rotation about the center of rotation to create an image. Rotations preserve size, rotations of 360 map a figure to itself, and lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.
Step-by-step explanation:
Here man this is right
Area ABD = 16*12/2
area ABC = 9*12/2
------------------------------
so the ratio of the area ABC to the area of ABD = (9*12/2)/(16*12/2) =
= 9/16
hope helped
Answer:
31.76 ft and 58.64 ft
Step-by-step explanation:
The radius measures between 13 feet and 24 feet.
The wheel is able to turn 7π/9 radians before getting stuck.
We need to find the range of distances that the wheel could spin before getting stuck. That is, the length of arc.
Length of an arc is given as:
where θ = central angle = 7π/9 radians
r = radius of the circle
Therefore, for 13 feet:
For 24 feet:
The wheel could spin between 31.76 ft and 58.64 ft before getting stuck.
Answer:
Option A. is correct
Step-by-step explanation:
The circumcenter is a point of intersection of all the perpendicular bisectors of a triangle.
The incenter is a point of intersection of all the angle bisectors of a triangle.
The orthocenter is a point of intersection of all the altitudes of a triangle.
The centroid is a point of intersection of all the medians of a triangle.
The incenter, orthocenter, and centroid always lie inside a triangle.
However, a circumcenter does not always lie inside a triangle.
In an acute-angled triangle, the circumcenter may lie inside or outside the triangle.
So,
Option A. is correct
Check the picture below.
so, let's notice, is really just a 2x20 rectangle with a quarter of a semicircle with a radius of 11.
![\bf \stackrel{\textit{area of a circle}}{A=\pi r^2}~~ \implies A=\pi 11^2\implies A=121\pi \implies \stackrel{\textit{one quarter of that}}{\boxed{A=\cfrac{121\pi }{4}}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\underline{\textit{area of the figure}}}{\stackrel{\textit{rectangle's area}}{(2\cdot 20)}+\stackrel{\textit{circle's quart's area}}{\cfrac{121\pi }{4}}\qquad \approx \qquad 135.03\implies \stackrel{\textit{rounded up}}{135}}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20a%20circle%7D%7D%7BA%3D%5Cpi%20r%5E2%7D~~%20%5Cimplies%20A%3D%5Cpi%2011%5E2%5Cimplies%20A%3D121%5Cpi%20%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bone%20quarter%20of%20that%7D%7D%7B%5Cboxed%7BA%3D%5Ccfrac%7B121%5Cpi%20%7D%7B4%7D%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Cunderline%7B%5Ctextit%7Barea%20of%20the%20figure%7D%7D%7D%7B%5Cstackrel%7B%5Ctextit%7Brectangle%27s%20area%7D%7D%7B%282%5Ccdot%2020%29%7D%2B%5Cstackrel%7B%5Ctextit%7Bcircle%27s%20quart%27s%20area%7D%7D%7B%5Ccfrac%7B121%5Cpi%20%7D%7B4%7D%7D%5Cqquad%20%5Capprox%20%5Cqquad%20135.03%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Brounded%20up%7D%7D%7B135%7D%7D)
