Answer:
6(7a + 9b) = 3(14a + 18b)
Step-by-step explanation:
We need to find the equivalent expression for the given expression i.e. 6(7a + 9b).
We can use the distributive property here such that,
a(b+c) = ab + ac
We have, a = 6, b = 7 and c = 9
6(7a + 9b) = 6(7a) + 6(9b)
= 42a + 54b
or taking 3 common from the above expression.
= 3(14a+18b)
Hence, the correct option is (a).
Answer:
A)
Decay
B)
Initial value is 5.
C)
The decay factor is 0.75.
D)
75%
Step-by-step explanation:
An exponential function is given by:
![f(x)=a(r)^x](https://tex.z-dn.net/?f=f%28x%29%3Da%28r%29%5Ex)
Where a is the initial value and r is the rate.
We have the function:
![y=5(1/4)^x](https://tex.z-dn.net/?f=y%3D5%281%2F4%29%5Ex)
So, a = 5 and r = 1/4.
A)
Remember the guidelines:
- It is exponential growth if r > 1.
- And it is exponential decay if r < 1. (And r must be positive.)
Our rate is 1/4 or 0.25.
It is less than 1, so our function is exponential decay.
B)
The initial value is the value in front of our rate.
So, our initial value in this case is 5.
C)
The decay factor will be 1 - r, where r is our rate.
Since our rate is 0.25, our decay factor is 1 - 0.25 = 0.75.
So, we are decaying by a factor of 0.75.
D)
To convert a decimal to a percent, we move the decimal dot two places to the rght and add a percent sign.
So, 0.75 will be 75.0 % or smply 75%.
It is a 75% decay.
Answer:
If the given equation is
comparing with ![y = kx](https://tex.z-dn.net/?f=y%20%3D%20kx)
Therefore, the option
is correct.
Step-by-step explanation:
Given
We know when
varies directly with
, means that when x increases, y increases by the same factor
i.e.
y ∝ x
![y = kx](https://tex.z-dn.net/?f=y%20%3D%20kx)
where k is the 'constant of proportionality.
![k\:=\:\frac{y}{x}](https://tex.z-dn.net/?f=k%5C%3A%3D%5C%3A%5Cfrac%7By%7D%7Bx%7D)
If the given equation is
comparing with ![y = kx](https://tex.z-dn.net/?f=y%20%3D%20kx)
Therefore, the option
is correct.
The equation for the volume of a cylinder is: pi*r^2*h
Plug in the values and you get:
pi * 3^2 * 6 = 54 pi inches cubed.