Answer:
I cant see a table, but go ahead and pick c
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:
c. 4y -x = 8
Step-by-step explanation:
Each of the equations can be put into slope-intercept form (solved for y) as follows:
a: y = 4x +9
b: y = 4x -8
c: y = (1/4)x +2
d: y = 4x -4
___
The equations containing the term "4x" all describe parallel lines. The equation containing (1/4)x describes a line that intersects the given line. It is not parallel to the others.
Let 'x' represent the volume of 6% saline solution
Let 'y' represent the volume of 8% saline solution
Form 2 equations.
Eq. 1: 20+x=y
Meaning 20 cm³ + x cm³=y cm³
Eq 2: 0.06x+0.1(20)=0.08y
Meaning: 6% of x + 10% of 20= 8% of y
Use substitution or elimination to solve this linear system. I used substitution.
Sub. Eq. 1 (20+x=y) into Eq. 2 (0.06x+0.1(20)=0.08y)
0.06x+ 0.1(20)=0.08(20+x)
0.06x+2+1.6=0.08x
-0.02x= -0.4
x=20
Substitute x=20 into equation 1 (you can also use 2 but in this case equation 1 is simpler)
20+x=y
20+20=y
40=y
To check, substitute x=20 and y=40 into equation 2
0.06x + 0.1(20)= 0.08y
0.06(20) +2 = 0.08(40)
1.2+2= 3.2
3.2=3.2
Therefore, Kim would need 20cm³ of 6% saline solution and 40cm³ of 10% saline solution to make 8% solution.
