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4 years ago

I'm making a great dodecahedron for geometry and I'm failing at putting it together! Any tips?!

Mathematics

2 answers:

Neko [114]4 years ago

8 0

$dodecahedron\ grid\ in\ Annex$

vagabundo [1.1K]4 years ago

8 0

If you have any instructions, please look them over carefully.
Take your time and DO NOT RUSH
It might be very confusing at first but take it step by step and don't stress.

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We define the relation =m (read "equal mod m") on Z x Z to be the set: {(p,q): m|(p-q)}. Please show work.

Slav-nsk [51]

Step-by-step explanation:

a) Give two pairs which are in the relation $\equiv \mod 4$ and two pairs that are not.

As stated before, a pair $(x,y)\in \mathbb{Z}\times\mathbb{Z}$ is equal mod m (written $x\equiv y\mod m$ ) if $m\mid (x-y)$ . Then:

x=0 and y=4 is an example of a pair $\equiv \mod 4$
x=0 and y=1 is an example of a pair $\not \equiv \mod 4$

b) Show the $\equiv \mod m$ is an equivalence relation.

An equivalence relation is a binary relation that is reflexive, symmetric and transitive.

By definition $\equiv \mod m$ is a binary relation. Observe that:

Reflexive. We know that, for every m, $m\mid 0$ . Then, by definition, $x\equiv x \mod m$ .
Symmetry. It is clear that, given x,y and m such that $m\mid (x-y)$ , then $m\mid (y-x)$ . Therefore $x\equiv y \mod m \iff y\equiv x \mod m$
Transitivity. Let x,y,z and m such that $x\equiv y \mod m$ and $y\equiv z \mod m$ . Then, $m\mid (y-x)$ and $m\mid (z-y)$ . Therefore:

$m\mid [(y-x)+(z-y)] \implies m\mid (z-x) \implies x\equiv z \mod m$ .

In conclusion, $\equiv \mod m$ defines an equivalence relation.

6 0

3 years ago

15 3/4% is equal to which decimal? A- 0.1575 B- 157.25 C-15.25 D- 15.34

eimsori [14]

15 3/4% = 15.75%
15.75% = 0.1575
The answer is A.

6 0

3 years ago

Read 2 more answers

4.Find the area of the irregular figure. (Please help ASAP <3!!)

Ivanshal [37]

From my understanding the answer is .d

5 0

3 years ago

Read 2 more answers

A motorboat takes 5 hours to travel 100mi going upstream. The return trip takes 2 hours going downstream. What is the rate of th

Temka [501]

The boat went 5hours upstream, let's say it has a "still water" speed rate of "b", it went 100miles... however, going upstream is going against the current, let's say the current has a speed rate of "c"

so, when the boat was going up, it wasn't really going "b" fast, it was going " b - c " fast, because the current was eroding speed from it

now, when coming down, the return trip, well the length is the same, so the distance is also 100miles, it only took 2hrs though, because, the boat wasn't coming down "b" fast, it was coming down " b + c " fast, because the current was adding speed to it, so it came down quicker

now, recall your d = rt, distance = rate * time

$\bf \begin{array}{lccclll}
&distance&rate&time\\
&-----&-----&-----\\
upstream&100&b-c&5\\
downstream&100&b+c&2
\end{array}
\\\\\\
\begin{cases}
100=(b-c)5\\
\qquad \frac{100}{5}=b-c\\
\qquad 20=b-c\\
\qquad 20+c=\boxed{b}\\
100=(b+c)2\\
\qquad 50=b+c\\
\qquad 50=\boxed{20+c}+c
\end{cases}$

solve for "c", to see what's the current's speed

what's "b"? well 20+c = b

4 0

3 years ago

What is the slope of the line that passes through the points shown in the table?

bonufazy [111]

The slope formula is y2-y1/x2-x1, this is considered rise over run. Simply subtract the y2 variable from the y1 variable, 1-(-1) =2 and then subtract the x2 variable from the x1 variable, 2-1 = 1. From there, ride (y) is on top and run(x) is on the bottom. Divide 2/1 which equal 2. The slope of this line is 2.
Hope this helped :)

4 0

3 years ago