In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.
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]}
Answer:
D. 4 x -2 - 7/8
Step-by-step explanation:
4 x -2 7/8
2 7/8 can be separated into 2 pieces 2 +7/8
4x - (2+7/8)
Distribute the minus sign
4x - 2 -7/8
Hi there! I can help you with these! For these types of questions, all you have to do is that if there is a markup, multiply by one hundred something to get the new price, because you're including the original price and the markup. For example, if there is a 75% markup on something, you multiply by 175% (1.75). Or, if there is a markdown, basically multiply by the remaining percentage. For example, if the markdown is 35%, you multiply the original price by 65% (0.65), because that is the amount of the price that it's on sale for. With that being said, if you do this correctly, here are the answers:
1. $54
2. $2.25
3. $90
Hopefully if you're talking about the markup or markdown from these prices, those are your answers.
