a number, half of that number, and one-third of that number are added. The result is 22. What is the original number
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<h3>Answer:</h3>
- C. (9x -1)(x +4) = 9x² +35x -4
- B. 480
- A. P(t) = 4(1.019)^t
Step-by-step explanation:
1. See the attachment for the filled-in diagram. Adding the contents of the figure gives the sum at the bottom, matching selection C.
2. If we let "d" represent the length of the second volyage, then the total length of the two voyages is ...
... (d+43) + d = 1003
... 2d = 960 . . . . . . . subtract 43
... d = 480 . . . . . . . . divide by 2
The second voyage lasted 480 days.
3. 1.9% - 1.9/100 = 0.019. Adding this fraction to the original means the original is multiplied by 1 +0.019 = 1.019. Doing this multiplication each year for t years means the multiplier is (1.019)^t.
Since the starting value (in 1975) is 4 (billion), the population t years after that is ...
... P(t) = 4(1.019)^t
The line is called the directrix. Here we have a vertical directrix, so a parabola sideways from usual.
Geometry is best done with squared distances. The squared distance from an arbitrary point (x,y) to the vertical line x=2 is
We equate that to the squared distance of (x,y) to the focus (-2,0):
We could call that done. A more standard form might be
Geometry is best done with squared distances. The squared distance from an arbitrary point (x,y) to the vertical line x=2 is
We equate that to the squared distance of (x,y) to the focus (-2,0):
We could call that done. A more standard form might be