Here we are given the expression:
Now let us equate it to zero to find x first,
Now subtracting 18 from the other side,
taking square root on both sides,
So we will get two values of x as ,
Now we can write square root -1 as i,
So our factors become,
Answer:
The final factored form becomes,
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
<span>A) y=-2x+19
B) y=x+7
Multiplying B) by -1
B) -y = -x -7 then adding it to A)
A) y = -2x + 19
3x = 12
x = 4
y = 11
</span>
They are not parallel because the slopes are different (slope of 4 and slope of 0.25)
Neither are they perpendicular. If they were then m1*m2 ( the product of their slopes) would be -1 ). The product of these slopes = 4*0.25 = 1)
So choice A is the correct one.
