Answer:
-75
Step-by-step explanation:
Let us consider the first odd number to be 'x'.
Thus:
- 1st odd number: x
- 2nd odd number: x+2
- 3rd odd number: x+3
According to the question, the sum of these three consecutive ODD numbers should be equal to -219
So,
x + x + 2 + x + 4 = -219
3x + 6 = -219
3x = -225
x = -75
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]
Make f(x) = y
y = (15x + 50)/(x + 5)
Swap the x and y and make y the subject again
x = (15y + 50)/(y + 5)
x(y + 5) = 15y + 50
xy + 5x = 15y + 50
xy - 15y = 50 - 5x
y(x - 15) = 50 - 5x
y = (50 - 5x)/(x - 15)
So inverse function f^-1(x) = (50 - 5x)/(x - 15)
Answer:
y = -2x +15
Step-by-step explanation:
The point-slope form of the equation for a line through (h, k) with slope m is ...
... y - k = m(x - h)
For your point (h, k) = (5, 5) and slope m = -2, the equation in point-slope form is ...
... y - 5 = -2(x - 5)
Simplifying, we get
... y - 5 = -2x +10
Adding 5 puts the equation into slope-intercept form, as you want.
... y = -2x +15
Answer:
Step-by-step explanation:
