Step-by-step explanation:
a rectangle has two pairs of equally long sides and each of the 4 angles between the sides is 90 degrees.
given that ABCDEF is a regular hexagon, it means that all its sides are equally long, and therefore also all internal angles are the same size.
that means for ACDF that the sides DC and FA are equally long.
DEF and ABC are congruent triangles, as the sides DE = BC, EF = AB, and the angle E is congruent to angle B.
based on the SAS criteria this confirms that DF is congruent to AC.
the angles ACB, CAB, EDF and EFD have to be all the same, and therefore also the angles FDC, DCA, CAF and DFA.
so, all 4 angles of the parallelogram ACDF are the same, and the sum of all these angles has to be 360 degrees, we have
360 = 4×angle
angle = 90 degree.
so, all angles are 90 degrees and we have two pairs of equally long sides : this process that ACDF us a rectangle
Answer:
18f - 6 bottles
Step-by-step explanation:
Amanda, Bruno and Carla collected bottle caps for charity. Amanda collected (4f – 3) bottle caps. Bruno collects twice as many bottle caps as Amanda. Carla collects 3(5 + 2f) bottles. How many bottles did they collect altogether in terms of f ?
From the question
Amanda collected (4f – 3) bottle caps. Bruno collects twice as many bottle caps as Amanda.
= 2(4f - 3)
= 8f - 6 bottle caps
Carla collects 3(5 + 2f) bottles.
= 15 + 6f bottles
The number of bottles they collected altogether in terms of f is calculated as:
(4f – 3) bottle + 8f - 6 bottle + 15 + 6f bottle
4f - 3 + 8f - 6 + 15 + 6f
= 18f - 6
This is an example of a Circle Graph, a circle graph is like a Pie chart, and In graph theory, a circle graph is the intersection graph of a set of
chords of a circle. That is, it is an undirected graph whose vertices
can be associated with chords of a circle such that two vertices are
adjacent if and only if the corresponding chords cross each other.
Look at the graph I showed you
Hope it helped
Answer:
A nice way to show it is through the unit circle.
In the unit circle, the point at angle theta from the origin has a y value of sin theta.
If you rotate a point 360-theta degrees from the origin, that is like rotating it theta degrees "backwards", or downwards, which is going to yield the same exact point, reflected through the x-axis. In other words, the y value, or sin(360-theta), is exactly -sin(theta).
The answer would be 14
Explanation:
If you look on a number line and start from 15 then from there you minus 6 which equals 9 then you minus 5 which equals 4 and add 10 which equals 14 and that 14 is on the positive side of the number line. So 14 is your answer.
