Answer:
Adjacent
Step-by-step explanation:
Find where the expression
x
−
5
x
2
−
25
x
-
5
x
2
-
25
is undefined.
x
=
−
5
,
x
=
5
x
=
-
5
,
x
=
5
Since
x
−
5
x
2
−
25
x
-
5
x
2
-
25
→
→
−
∞
-
∞
as
x
x
→
→
−
5
-
5
from the left and
x
−
5
x
2
−
25
x
-
5
x
2
-
25
→
→
∞
∞
as
x
x
→
→
−
5
-
5
from the right, then
x
=
−
5
x
=
-
5
is a vertical asymptote.
x
=
−
5
x
=
-
5
Consider the rational function
R
(
x
)
=
a
x
n
b
x
m
R
(
x
)
=
a
x
n
b
x
m
where
n
n
is the degree of the numerator and
m
m
is the degree of the denominator.
1. If
n
<
m
n
<
m
, then the x-axis,
y
=
0
y
=
0
, is the horizontal asymptote.
2. If
n
=
m
n
=
m
, then the horizontal asymptote is the line
y
=
a
b
y
=
a
b
.
3. If
n
>
m
n
>
m
, then there is no horizontal asymptote (there is an oblique asymptote).
Find
n
n
and
m
m
.
n
=
1
n
=
1
m
=
2
m
=
2
Since
n
<
m
n
<
m
, the x-axis,
y
=
0
y
=
0
, is the horizontal asymptote.
y
=
0
y
=
0
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
This is the set of all asymptotes.
Vertical Asymptotes:
x
=
−
5
x
=
-
5
Horizontal Asymptotes:
y
=
0
y
=
0
No Oblique Asymptotes
This is a proportion problem that involves cross multiplication
3/5 = x/650
650 x 3 = 1950
1950/ 5 =390
Or you could have done 650 x .6 (which is the decimal form of 3/5) and got 390 as your answer
Answer:
x = 9/8
Step-by-step explanation:
The triangles are similar so we can use ratios to solve
AB BC
---- = -----------
AD ED
x 1
---- = -----------
x+9 9
Using cross products
9*x = 1(x+9)
9x = x+9
Subtract x from each side
9x-x = x+9-x
8x = 9
Divide by 8
8x/8 = 9/8
x = 9/8
