Answer:
Prove set equality by showing that for any element
,
if and only if
.
Example:
.
.
.
.
.
Step-by-step explanation:
Proof for
for any element
:
Assume that
. Thus,
and
.
Since
, either
or
(or both.)
- If
, then combined with
,
. - Similarly, if
, then combined with
,
.
Thus, either
or
(or both.)
Therefore,
as required.
Proof for
:
Assume that
. Thus, either
or
(or both.)
- If
, then
and
. Notice that
since the contrapositive of that statement,
, is true. Therefore,
and thus
. - Otherwise, if
, then
and
. Similarly,
implies
. Therefore,
.
Either way,
.
Therefore,
implies
, as required.
Answer:
x = 7 hope this helps !!!
Step-by-step explanation:
Type 1: You know the short leg (the side across from the 30-degree angle). Double its length to find the hypotenuse. You can multiply the short side by the square root of 3 to find the long leg.
Type 2: You know the hypotenuse. Divide the hypotenuse by 2 to find the short side. Multiply this answer by the square root of 3 to find the long leg.
Type 3: You know the long leg (the side across from the 60-degree angle). Divide this side by the square root of 3 to find the short side. Double that figure to find the hypotenuse.
this is a type 3 triangle, and you can find the length of y from it, it being 14, and x is half of y, being 7
Answer:
Step-by-step explanation:
A vertex is a corner or a point where two lines meet.
the vertex represents the highest point on the graph, or the maximum value.
A knitter with 14 skeins of yarn can make 7 scarves
Explanation:
We can use a proportion to solve this
4 skeins of yarn
-----------------------
2 scarves
That is the information we know. What we want to do is find out how many scarves for 14 skeins of yarn, like this
4 14
-- = ---
2 ?
To get from 4 to 14, you multiply by 3.5. We must to the same thing to the bottom as well. So we multiply 2 by 3.5, which gives us 7
x3.5
4 14
-- = ---
2 7
x3.5