Answer:
The first pair shows equivalent expressions.
Step-by-step explanation:
3(x+2), you would have to distribute 3 among x and 2, also known as expanding the expression. So you'd do 3*x + 3*2, which equals 3x+6
The first equation is 3(x+2)=3x+6
Therefore, the first pair shows equivalent expressions.
Answer:
45
Step-by-step explanation:
To know how many 1/5 s are in 9, we will take the ratio of both numbers as shown;
9:1/5
= 9 ÷ 1/5
= 9 * 5/1
= 9 * 5
= 45
Hence there are 45 1/5s in 9
4=4 6=5 7=9 8=4 9=2 10=8 11=3 12=9
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
Answer:
Under compound interest, not only does the principal generate interest, so does the previous accumulated interest. The future value F of P dollars compounded annually for t years with an annual percentage rate (APR) r expressed as a decimal is .
