Given:
An exponential function goes through points (0,12) and (3,6144).
To find:
The exponential function.
Solution:
The general exponential function is:
...(i)
The function goes through point (0,12). Substituting 
, we get
The function goes through point (3,6144). Substituting 
in the general exponential function, we get
Putting 
in (i), we get
Therefore, the required exponential function is .
The value of x is equal to 14.
Since the bottom side is equal to 3 of the small triangle and the side of the larger triangle is equal to 9, that means that it was dilated by a factor of 3, since 3 * 3 = 9
So, the other side of 5, of the smaller triangle needs to be also be dilated by a factor of 3, so the new side is 15.
The larger triangle tells us that the side is x + 1, but we know that it is equal to 15. Since they are the same, we make them equal and solve for x
So, 15 = x + 1
We subtract 1 to isolate x and we get
14 = x
So, x is equals to 14.
I hope this helps.
YOU'RE WELCOME :D
Answer: Non of the option.
Step-by-step explanation:
The given equation is
4x^3 - 6x^2 + 15x + 2 = 0
Let's test 1, if it's one of the root. I.e
If x = 1
4 - 6 + 15 + 2 = 15
Positive 1 is not a root to the equation
If x = - 1
-4 - 6 - 15 + 2 = - 23
Negative 1 is not a root
If x = 2
4x8 - 6×4 + 15×4 + 2
32 - 24 + 30 + 2 = 40
Positive 2 is not a root
If x = - 2
4×(-8) - 6×4 - 15×2 + 2
-32 - 24 - 30 + 2 = -84
Negative 2 is not a root
If x = 3
4×27 - 6×9 + 15×3 + 2
108 - 54 + 45 + 2 = 101
Since non of them tend to zero, non of the option is a root of the equation
Let us say that:
K = age of Kristen
B = age of Ben
From the problem, we make the equations:
eqtn 1: K + B = 32
eqtn 2: (K – 4) = 2 (B – 4)
Simplifying eqtn 2:
K – 4 = 2 B – 8
K = 2 B – 4
Plugging in this to eqtn 2:
(2 B – 4) + B = 32
3 B – 4 = 32
3 B = 36
B = 12
From eqtn 2:
K = 2 B – 4 = 2 (12) – 4 = 20
So Kristen is 20 while Ben is 12.
The first thing you should do in this case is to compose both functions:
f (x) = x + 7
g (x) = 1 / (x-13)
Making the composition
f (g (x)) = (1 / (x-13)) + 7
f (g (x)) = (7 (x-13) +1) / (x-13)
Answer:
The domain of the function is:
x other than 13
(option 4)
