Hi,
Concept: This is work & time related problem which can be solved in their inverse proportions.
Let Lisa can do a work in x hours.
Lisa's one hour work = 1 / x
According to the problem, Justin can do the same work in 2x hours.
Justin's one hour work = 1 / (2x)
Now, we shall find both 1 hour work just by adding their 1 hour's work.
Both 1 hour's work = (1 /x) + [1 / (2x)] = 3 / (2x)
Full works time = (2x /3) hours.
Again, according to the problem,
2x / 3 = 8
or, x= 12 hours.
Hence Justin will take 2x = 24 hours to complete work as alone.
Answer:
yes
Step-by-step explanation:
Answer:
A. b2 – 4ac = –12
Step-by-step explanation:
discriminant must be minus cause the graph doesn't cross the x-axis .in other words it doesn't have an answer.plus , the "a" of the equation is minus too.
Answer:
A)
Step-by-step explanation:
1) To answer this question, we must remember what this discriminant stands for:
2) We must plug in this discriminant, in the square root of Quadratic Formula, to find its roots, i.e.:
The discriminant is a radicand.
3) The graph above shows us no Real roots for this equation then we have roots ∈ Complex Numbers, in other words:
4) So, it's A.
Answer: The correct conclusion is(B) The functions f(x) and g(x) are reflections over the y-axis.
Step-by-step explanation: Two functions f(x) and g(x) are given as follows:
We know that if f(-x) = g(x), then the functions are reflections over Y-axis and if - f(x) = g(x), then the functions are reflections over X-axis.
We have,
So, the function g(x) is a reflection of f(x) over Y-axis.
The graph of f(x) and g(x) are drawn in the attached file. From there, it is clear that the functions are reflections over Y-axis, not reflections over X-axis.
So, options (A) is incorrect and option (B) is correct.
From the table, we have
So, as the value of 'x' increases, the value of f(x) increases and value of y(x) decreases.
Therefore, f(x) is an increasing function and g(x) is a decreasing function. So, option (C) is incorrect.
Also, we have
So, both the functions have same initial value. So, option (D) is also incorrect.
Thus, the correct conclusion is (B) The functions f(x) and g(x) are reflections over the y-axis.
The profit function is .https://tex.z-dn.net/?f=P%28t%29%3D20000%280.866%29%5Et
Step-by-step explanation:
The exponential decay function is defined as
https://tex.z-dn.net/?f=P%28t%29%3Da_0%281-r%29%5Et
Where, a₀ is initial value, r is rate of change and t is time (in year).
From the given information it is noticed that the initial profit is $20,000 and it decreases by 13.4% each year.
The profit function is defined as
https://tex.z-dn.net/?f=P%28t%29%3D20000%281-%5Cfrac%7B13.4%7D%7B100%7D%29%5Et
https://tex.z-dn.net/?f=P%28t%29%3D20000%281-0.134%29%5Et
https://tex.z-dn.net/?f=P%28t%29%3D20000%280.866%29%5Et
Therefore the profit function is .
https://tex.z-dn.net/?f=P%28t%29%3D20000%280.866%29%5Et