Answer:
C. -1
Step-by-step explanation:
f(x) = 2/ (-x-1)
As we can see, f(x) is a fraction with two components: numerator (2) and denominator (-x-1).
According to the theorem, the fraction only exists when its denominator is different from 0.
So that in this situation, (-x-1) has to be different from 0
- x - 1 ≠0
=> - x≠ 1
=> x ≠ -1
So that if x = -1, (-x-1) = 0, making the fraction not exist.
So the input is not allowed is x = -1
The difference between the 6th term and the 9th term of the sequence is 135
<h3>How to determine the difference</h3>
Given that the nth term is;
3n² + 11
For the 6th term, the value of n is 6
Let's solve for the 6th term
= 3( 6)^2 + 11
= 3 × 36 + 11
= 108 + 11
= 119
For the 9th term, n = 9
= 3 (9)^2 + 11
= 3( 81) + 11
= 243 + 11
= 254
The difference between the 6th and 9th term
= 254 - 119
= 135
Thus, the difference between the 6th term and the 9th term of the sequence is 135
Learn more about algebraic expressions here:
brainly.com/question/4344214
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Answer: Exponential decay model:
y
=
x
(
1
−
r
)
t
, half life of tablet is about
2
hours and after
t
=
3
hours , remaining drug on patient's system is
42.875
mg.
Step-by-step explanation: Initial drug
x
=
125
mg ; rate of decay
r
=
30
100
=
0.3
gm/hour
Exponential model:
y
=
x
(
1
−
r
)
t
=
125
(
1
−
0.3
)
t
=
125
⋅
0.7
t
Half life:
y
=
125
2
=
62.5
mg
∴
62.5
=
125
⋅
0.7
t
or
0.7
t
=
1
2
. Taking logarithm on both sides we get ,
t
log
(
0.7
)
=
log
(
0.5
)
∴
t
=
log
(
0.5
)
log
(
0.7
)
≈
1.94
(
2
d
p
)
hour
The half life of tablet is about
2
hours.
After
t
=
3
hours , remaining drug on patient's system is
y
=
125
⋅
0.7
t
=
125
⋅
0.7
3
=
42.875
mg [Ans]
Answer:
98 ft²
Step-by-step explanation:
There are a couple of ways you can think about this one. Perhaps easiest is to treat it as a square with a triangle cut out of it. The cutout triangle has a base (across the top) of 14 ft and a height of 14 ft, so its area is ...
A = (1/2)(14 ft)(14 ft) = 98 ft²
Of course the area of the square from which it is cut is ...
A = (14 ft)² = 196 ft²
So, the net area of the two triangles shown is ...
A = (196 ft²) - (98 ft²) = 98 ft²
_____
Another way to work this problem is to attack it directly. Let the base of the left triangle be x. Then the base of the right triangle is 14-x, and their total area is ...
A = A1 + A2 = (1/2)(x ft)(14 ft) + (1/2)((14-x) ft)(14 ft)
We can factor out 7 ft to get ...
A = (7 ft)(x ft + (14 -x) ft)
A = (7 ft)(14 ft) = 98 ft²
