Answer:
(f·g)(x) = x³ -8x² +20x -16
Step-by-step explanation:
The distributive property is useful for this.
(f·g)(x) = f(x)·g(x) = (x² -6x +8)(x -2)
= x(x² -6x +8) -2(x² -6x +8)
= x³ -6x² +8x -2x² +12x -16
(f·g)(x) = x³ -8x² +20x -16
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<em>Additional comment</em>
I find it convenient to separate the terms of the shortest polynomial. That way, the distributive property doesn't need to be used quite so many times. Of course, any outside minus sign applies to all terms inside parentheses.
<span>A motorboat
travels 222 km in 6 hours going upstream.
Rate = distance/time = 222/6 = 37 km/hr
----------------------
It travels 390 km going downstream in the same amount of time.
Rate = distance/time = 390/6 = 65 km/hr
---------
What is the rate of the boat in still water and what is the rate of the
current?
Equations:
Upstream: b-c = 37 km/hr
Downstrm: b+c = 65 km/hr</span>
<span>Add and solve
for "b":
(2)b = 102 km/hr
b = 51 km/hr (speed of the boat in still water)
-----
Solve for "c":
b+c = 65
51 + c = 65
c = 14 km/hr (speed of the current)</span>
1) It tells you in the question c = cost, so cost would be the answer
2) 2.75 is the fixed rate so we would keep it as is. C is the cost which would the total, so c = ?m + 2.75
0.40 per half mile so you put 0.40m because it varies depending on the amount of miles
That makes the equation c = 0.40m + 2.75
3) Now to find how much it costs for 45 miles, you plug 45 for m
c = 0.4 * 45 + 2.75
c = 20.75
Not sure why it isn't an option
