Answer:
PPF, PFF
Step-by-step explanation:
There are several ways you can list all the possible combinations. A couple of my favorite are a) use a binary counting sequence; b) use a gray code counting sequence.
Using the first method, the binary numbers 000 to 111 can be listed in numerical order as 000, <em>001</em>, 010, <em>011</em>, 100, 101, 110, 111. Letting 0=P and 1=F, the ones missing from your list are the ones in italics in my list.
Using the second method, we change the right-most character, then the middle one, and finally the left-most character so there is one change at a time: 000, <em>001</em>, <em>011</em>, 010, 110, 111, 101, 100.
After you have a list of all possible combinations, it is a simple matter to compare the given list to the list of possibilities to see which are missing.
Answer:
M = -2
Step-by-step explanation:
Answer: D
Explanation: It’s going from least to greatest.
OPTION A is the correct answer.
hope it helps you...
Answer:
(-1 (3 y + 17))/2
Step-by-step explanation:
Simplify the following:
y/4 - (1 + 3/4) y - 12 + 1/2 + 1 + 2
Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:
y/4 - 4/4 + 3/4 y - 12 + 1/2 + 1 + 2
4/4 + 3/4 = (4 + 3)/4:
y/4 - (4 + 3)/4 y - 12 + 1/2 + 1 + 2
4 + 3 = 7:
y/4 - 7 y/4 - 12 + 1/2 + 1 + 2
Put each term in y/4 - (7 y)/4 - 12 + 1/2 + 1 + 2 over the common denominator 4: y/4 - (7 y)/4 - 12 + 1/2 + 1 + 2 = y/4 - (7 y)/4 - 48/4 + 2/4 + 4/4 + 8/4:
y/4 - (7 y)/4 - 48/4 + 2/4 + 4/4 + 8/4
y/4 - (7 y)/4 - 48/4 + 2/4 + 4/4 + 8/4 = (y - 7 y - 48 + 2 + 4 + 8)/4:
(y - 7 y - 48 + 2 + 4 + 8)/4
Grouping like terms, y - 7 y - 48 + 2 + 4 + 8 = (y - 7 y) + (4 + 2 + 8 - 48):
((y - 7 y) + (4 + 2 + 8 - 48))/4
y - 7 y = -6 y:
(-6 y + (4 + 2 + 8 - 48))/4
4 + 2 + 8 - 48 = -34:
(-34 - 6 y)/4
Factor -2 out of -6 y - 34:
(-2 (3 y + 17))/4
The gcd of -2 and 4 is 2, so (-2 (3 y + 17))/4 = ((2 (-1)) (3 y + 17))/(2×2) = 2/2×(-(3 y + 17))/2 = (-(3 y + 17))/2:
Answer: (-1 (3 y + 17))/2
