Answer:
Step-by-step explanation:
x
2
+
x
−
6
=
(
x
+
3
)
(
x
−
2
)
x
2
−
3
x
−
4
=
(
x
−
4
)
(
x
+
1
)
Each of the linear factors occurs precisely once, so the sign of the given rational expression will change at each of the points where one of the linear factors is zero. That is at:
x
=
−
3
,
−
1
,
2
,
4
Note that when
x
is large, the
x
2
terms will dominate the values of the numerator and denominator, making both positive.
Hence the sign of the value of the rational expression in each of the intervals
(
−
∞
,
−
3
)
,
(
−
3
,
−
1
)
,
(
−
1
,
2
)
,
(
2
,
4
)
and
(
4
,
∞
)
follows the pattern
+
−
+
−
+
. Hence the intervals
(
−
3
,
−
1
)
and
(
2
,
4
)
are both part of the solution set.
When
x
=
−
1
or
x
=
4
, the denominator is zero so the rational expression is undefined. Since the numerator is non-zero at those values, the function will have vertical asymptotes at those points (and not satisfy the inequality).
When
x
=
−
3
or
x
=
2
, the numerator is zero and the denominator is non-zero. So the function will be zero and satisfy the inequality at those points.
Hence the solution is:
x
∈
[
−
3
,
−
1
)
∪
[
2
,
4
)
graph{(x^2+x-6)/(x^2-3x-4) [-10, 10, -5, 5]}
Volume formula: 1/3pir^2h
From this, 1/3(pi)(8^2)(15)= 1005.3
This is not a answer choice but… 1004.8 is the best choice they might have used 3.14 instead of the full pi
Hope this helps
(12 + 3) + 32 = 12 + (3 + 32)
Associative property of addition: if you have to sum three or more terms, you can group them as you like.
14(1/14) = 1
Multiplicative inverse: a number multiplied by its inverse is 1
27 + 0 = 27
Identity element of addition. If you sum any number with zero, the result is the number you started with.
11(4y – 9) = 44y - 99
Distributive property of addition: if you have to multiply a whole sum/subtraction by a number, it is the same as multiplying each term in the sum/subtraction by that number.