Answer:
Step-by-step explanation:
Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.
The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).
The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320
(0+4)^3*(0-1)*k = 320
-64k = 320
k = -5
Combining all three conditions, f(x)
= -5(x+4)^3*(x-1)
= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)
= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)
= -5(x^4 + 11x^3 + 36x^2 + 16x -64)
= -5x^3 -55x^3 - 180x^2 - 80x + 320
1/4 hour because since it took him 3/4 hr to milk 3 groups, it is reasonable to divide 3/4 by 3. So in 1/4 hour.
Answer:
Option B.
Step-by-step explanation:
It is given that a delivery truck driver charges a fixed base price of $6 for 2 miles.
After 2 miles, he charges an additional $2 for every mile and after 6 miles, he charges an additional $4 for every mile.
We need to describe the cost of the delivery truck between 1 mile and 2 miles.
In the given graph x-axis represents the distance in miles and y-axis represents the cost in dollars.
From the given graph it is clear that the value of function is constant between x=1 and x=2.
It means the cost of the delivery truck between 1 mile and 2 miles is constant.
Therefore, the correct option is B.
Given:
The two functions are:
To find:
The type of transformation from f(x) to g(x) in the problem above and including its distance moved.
Solution:
The transformation is defined as
.... (i)
Where, a is horizontal shift and b is vertical shift.
- If a>0, then the graph shifts a units left.
- If a<0, then the graph shifts a units right.
- If b>0, then the graph shifts b units up.
- If b<0, then the graph shifts b units down.
We have,
The function g(x) can be written as
...(ii)
On comparing (i) and (ii), we get
Therefore, the type of transformation is translation and the graph of f(x) shifts 2 units up to get the graph of g(x).
98 - 14x + 1
-14x + (98 + 1)
-14x + 99
Answer: -14x + 99.
