The range is the difference between the highest and lowest numbers in the given set of numbers.
Highest number= 80
Lowest number= 28
Range
= 80 - 28
= 52
ANSWER: The range is 52.
Hope this helps! :)
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:
27.60
Step-by-step explanation:
Answer:
Answer:
For converging lens
object distance u = - 2.0cm
Focal length f = 5.0cm
From lens formula
m=
m=
=3
Size of image = size of object x Magnification
= 2 x .10 = 2.0cm
For diverging lens
object distance u = 140 - 120 = 20 cm
focal length f = -30 cm
frac{1}{v}+\frac{1}{20}=-\frac{1}{30}
v = -12 cm
m = 12/20 = 0.6
size of final image = .6 x 30 = 18 cm
In this triangle, we know base & perpendicular are 300 & 400 'cause 500 is the longest side which is hypotenuse
Now, Area of a triangle = ab/2 = (300)(400)/2 = 120000/2 = 60000
As cost for 1 ft² = $0.60
cost for 60000 ft² = 60000 * 0.60 = $36000
In short, Your Answer would be Option A
Hope this helps!
