Abraham has 6 jawbreakers.
Isaac has 13 lollipops.
Jacob has 9 peanut butter cups.
If Ahmed ... one of Rebecca's camels that can't resist candy ...
makes the rounds in the middle of the night, breaks into each
of their tents, and eats all of the patriarchs' sweets, how many
pieces of candy will Ahmed the camel eat before sunrise ?
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:
0
Step-by-step explanation:
<h2><em>2</em><em>x</em><em>-</em><em>6</em><em>+</em><em>1</em><em>5</em><em>x</em><em>+</em><em>5</em><em>-</em><em>1</em><em>6</em><em>x</em><em>=</em><em>x</em></h2>
<h2><em>2</em><em>x</em><em>+</em><em>1</em><em>5</em><em>x</em><em>-</em><em>1</em><em>6</em><em>x</em><em>-</em><em>x</em><em>=</em><em>6</em><em>-</em><em>5</em></h2><h2 /><h2 /><h2><em>0</em><em>×</em><em>x</em><em>=</em><em>1</em></h2><h2 /><h2 /><h2 /><h2><em>x</em><em>=</em><em>1</em><em>÷</em><em>0</em></h2><h2 /><h2 /><h2><em>x</em><em>=</em><em>0</em></h2>
9514 1404 393
Explanation:
The three Reasons tell you what to look for to put in the Statement blank.
1. We are given that RE = 2AR and RT = 2GR.
2. The only vertical angles in the figure are ...
∠GRA ≅ ∠TRE
3. Using the given relation between the sides, we can write the proportion ...
RE/RA = RT/RG = 2
It is nice, though maybe not absolutely essential, to write the segment names in order of corresponding vertices.
4. Having shown that two sides are proportional and the angle between them is congruent, we can claim similarity using the SAS Theorem.
