Answer:
Step-by-step explanation:
height of water = ¾×12 = 9 inches
volume of water = 30×10.5×9 = 2,835 in³
For the case of a line through
(
2
,
7
)
and
(
1
,
−
4
)
we have
slope
m
=
Δ
y
Δ
x
=
−
4
−
7
1
−
2
=
−
11
−
1
=
11
Using the point
(
2
,
7
)
we can write the equation of the line in point slope form as:
y
−
7
=
m
(
x
−
2
)
where the slope
m
=
11
.
That is:
y
−
7
=
11
(
x
−
2
)
To get point intercept form, first expand the right hand side so...
y
−
7
=
11
x
−
(
11
⋅
2
)
=
11
x
−
22
Then add
7
to both sides to get:
y
=
11
x
−
15
=
11
x
+
(
−
15
)
This is point intercept (
y
=
m
x
+
c
) form with slope
m
=
11
and intercept
c
=
−
15
.
From your equation, you can see that you have a difference of two cubes (aka two cubes being subtracted): 64, which is

, and

.
There is rule for the difference of two cubes:
The difference of two cubes is equal to the difference of the cube roots times a binomial, which is the sum of the squares of the roots plus the product of the roots.
That sounds pretty confusing, but it's much easier to understand when put mathematically. Let's say our two cubes are

and

. The difference of those two cubes is:

In our problem, a = 4 (since

= 64) and b = y (since

. Plug these values into the rule to find the factor of

:

-----
Answer:
Use the factor theorem to determine whether the first polynomial is a factor of the second polynomial x-3;2x^2-4x+30
x−3,2x^2−4x+30
Answer:3+(-6)
Step-by-step explanation: