George C.
Jul 24, 2018
(
x
+
2
)
(
x
+
6
)
2
=
0
Explanation:
Given:
x
3
+
14
x
2
+
60
x
+
72
=
0
By the rational roots theorem, any rational zeros of the given cubic are expressible in the form
p
q
for integers
p
,
q
with
p
a divisor of the constant term
72
and
q
a divisor of the coefficient
1
of the leading term.
That means that the only possible rational zeros are:
±
1
,
±
2
,
±
3
,
±
4
,
±
6
,
±
8
,
±
9
,
±
12
,
±
18
,
±
24
,
±
36
,
±
72
In addition, note that all of the coefficients are positive and the constant term is non-zero. As a result, any real zero (rational or otherwise) of this cubic must be negative.
So that leaves rational possibilities:
−
1
,
−
2
,
−
3
,
−
4
,
−
6
,
−
8
,
−
9
,
−
12
,
−
18
,
−
24
,
−
36
,
−
72
We find:
(
−
2
)
3
+
14
(
−
2
)
2
+
60
(
−
2
)
+
72
=
−
8
+
56
−
120
+
72
=
0
So
x
=
−
2
is a zero and
(
x
+
2
)
a factor:
x
3
+
14
x
2
+
60
+
72
=
(
x
+
2
)
(
x
2
+
12
x
+
36
)
Without trying any more of our "possible" zeros, we can recognise the remaining quadratic factor as a perfect square trinomial:
x
2
+
12
x
+
36
=
x
2
+
2
(
x
)
(
6
)
+
6
2
=
(
x
+
6
)
2
So the factored form of the given cubic equation can be written:
(
x
+
2
)
(
x
+
6
)
2
=
0
Answer: 20%
Step-by-step explanation:
20% black dresses or suits
.35 = 35% wearing brown
1/4 = 25% wearing navy
100% -20% - 35% - 25% = 20% left
Answer:
see explanation
Step-by-step explanation:
Calculate the slope m using the slope formula
m = 
(8)
with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (8, 2)
m = 
= 
= 0
A slope of zero indicates the line is horizontal and parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through
The line passes through (- 3, 2) and (8, 2) with y- coordinates 2, thus
y = 2 ← equation of line
(9)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
with (x₁, y₁ ) = (- 6, 1) and (x₂, y₂ ) = (- 3, 2)
m = 
= 
, then
y = x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 3, 2) , then
2 = - 1 + c ⇒ c = 2 + 1 = 3
y = x + 3 ← equation of line
Answer:
I think it might be d
Step-by-step explanation:
Im not completely sure, BUT YOU GOT THIS
