Answer: b
Step-by-step explanation: I did this on a test before
A quadratic with roots at 8 and 5 is f(x) = x^2 +12x + 20
In order to find an equation given roots you can create statements that equal 0 in order to create parenthesis. For instance we know x = 8 at one point. So, we can solve that to equal 0.
x = -2 ----> add 2 to both sides
x + 2 = 0
We can do the same for the other zero.
x = -10 ----> add 10 to both sides
x + 10 = 0
Now that we have both of these, we can multiply these two things together. This will give us the function we need.
f(x) = (x + 2)(x + 10)
f(x) = x^2 + 10x + 2x + 20
f(x) = x^2 + 12x + 20
Answer:
(a)
(b) There will be 1lb left after 14 hours
Step-by-step explanation:
Solving (a): The equation
Since the substance decomposes at a proportional rate, then it follows the following equation
Where
Initial Amount
rate
time
Amount at time t
Solving (b):
We have:
First, we calculate k using:
This gives:
Substitute:
Divide both sides by 4
Take natural logarithm of both sides
This gives:
Solve for k
So, we have:
To calculate the time when 1 lb will remain, we have:
So, the equation becomes
Divide both sides by 8
Take natural logarithm of both sides
Solve for t
--- approximated
f(x)=-3x+2, for x = 3
Replace x with 3 in the equation and solve:
-3(3) + 2 = -9 + 2 = -7
The answer is -7
Hi there.
I'm just going to put the answer for now. I might come back and edit my answer if I figure out how to solve this the long way.
All I did was figure out what exponent you raise 10 to.
10³ = 1000
So, we now have 8 + 10³ = 1008
Edit:
I did it on paper - here it is broken down.
8 +
= 1008
Subtract 8 from both sides.
= 1000
We know that 10³ = 1000
<em>x</em> = 3
~