Answer:
Step-by-step explanation:
Answer:
the quantities do NOT vary directly
Step-by-step explanation:
A graph showing a proportional relationship is a straight line through the origin. This graph goes through (0, 100), so does NOT show a proportional relationship. y does NOT vary directly with x.
We don’t know the value of the shorter side, so we will categorize it as x. Side 2 is just 4 feet longer than x, so we would add 4 on to it. Side 3 has double the x, so we would multiply it be 2 for 2x, and subtract the 4 feet from it.
Side 1: x
Side 2: x + 4
Side 3: 2x - 4
If the perimeter is 64 feet, then all of the sides have to add up to it. Therefore, first we add all of the side lengths up:
x + x + 4 + 2x - 4 = 4x.
Now we put 4x, the amount of all these sides added up, equal to the perimeter of 64.
4x = 64. Divide both sides by 4 to get x by itself.
x = 16.
Now that we know x is 16, we will substitute it in for all the side lengths’ equations.
We know that Side 1 was just x, so that will be 16. Since Side 2 was 4 more than x, we’d do 16 + 4 = 20. We substitute 16 in for x in Side 3’s equation: 2(16) - 4 = 32 - 4 = 28.
Therefore, the final lengths of all the sides are:
Side 1: 16
Side 2: 20
Side 3: 28
To find the perpendicular slope, we simply flip the fraction (aka reciprocal) and flip the sign (go from positive to negative, or vice versa)
So for problem 1a) we flip the fraction to go from 4/3 to 3/4. Then we flip the sign to go from +3/4 to -3/4. The final answer to problem 1a) is -3/4
The answer to problem 1b) is 7/3 following the same basic steps: -3/7 ---> -7/3 ---> 7/3
The answer to problem 1c) is -1/4. You can think of 4 as 4/1 which flips to 1/4 and it becomes -1/4
I'll let you try out the rest 1d and 1e. Tell me what you get so I can check your answers.
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]}
