Answer = 2,3,and 4
a rigid transformation is a geometric transformation that preserves the distance between every pair of points. The rigid transformations include rotations, translations, reflections, or any sequence of these (dilation changes the points for a bigger or smaller shape so it is NOT rigid)
Answer:
√
8
≈
3
Explanation:
Note that:
2
2
=
4
<
8
<
9
=
3
2
Hence the (positive) square root of
8
is somewhere between
2
and
3
. Since
8
is much closer to
9
=
3
2
than
4
=
2
2
, we can deduce that the closest integer to the square root is
3
.
We can use this proximity of the square root of
8
to
3
to derive an efficient method for finding approximations.
Consider a quadratic with zeros
3
+
√
8
and
3
−
√
8
:
(
x
−
3
−
√
8
)
(
x
−
3
+
√
8
)
=
(
x
−
3
)
2
−
8
=
x
2
−
6
x
+
1
From this quadratic, we can define a sequence of integers recursively as follows:
⎧
⎪
⎨
⎪
⎩
a
0
=
0
a
1
=
1
a
n
+
2
=
6
a
n
+
1
−
a
n
The first few terms are:
0
,
1
,
6
,
35
,
204
,
1189
,
6930
,
...
The ratio between successive terms will tend very quickly towards
3
+
√
8
.
So:
√
8
≈
6930
1189
−
3
=
3363
1189
≈
2.828427
It is 10x the value of the one in the thousands place
1/2 + 3/4 + 7/8
4/4(1/2)+ 2/2(3/4) + 7/8
4/8 + 6/8 + 7/8
4+ 6 + 7
—————
8
17 1
——. Or 2—-
8 8
He prepared 2 1/8 lbs of trail mix
Answer:
<span>The irrational number between 5.5 and 5.2 is square root of 30. </span>
