Lets use proportion
let the perimeter of the smaller figure be 'x'
8:18::x:24
Product of means=product of extreames
24 x 8= 18 x 'x'
192=18x
x=10.6666667 units
Ans: the perimeter of the smaller figure is 10.6666667 units
7,485 just do long division
The answer will be 10 because you plug in y=-×+12 in the equation 4x-2y=36. After you solve and do distributive property your new equation should be 4x+2x-24=36, then you add the like terms of 4x and 2x which will equal to 6x and your new equation should be 6x-24=36. Add 24 from both sides and your equation should be 6x=60, then you divide 60 by 6 and your final answer will be x=10 or 10
Answer: C
Step-by-step explanation: There are 9 cards. 3 are vowels. 3/9 reduces to 1/3
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
