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:
25 years
Step-by-step explanation:
To find the mean you need to find the sum of all numbers and divide by the number of terms there are.
In this case you would need to multiply the mean ages by the number of people used to find the mean:
35 * 3 = 105
23 * 12 = 276
Then add the total ages together:
105 + 276 = 381
Then divide by the number of total people in the office:
12 + 3 = 15
381/15 = 25.4
rounded to 25
Answer:
x =5
Step-by-step explanation:
Tangents from same external point have equal length.
KJ = LJ
4x - 1 = 2x + 9
Add 1 to both sides
4x = 2x + 9 + 1
4x = 2x + 10
Subtract '2x' from both side
4x - 2x = 10
2x= 10
Divide both sides by 2
x = 10/2
x = 5
Answer:
Ac=14 is you answer i think
Step-by-step explanation:
Hope this helps
