Answer:
18x^4 − 12x^3 + 57x^2 − 28x + 35
Answer:
512
Step-by-step explanation:
Suppose we ask how many subsets of {1,2,3,4,5} add up to a number ≥8. The crucial idea is that we partition the set into two parts; these two parts are called complements of each other. Obviously, the sum of the two parts must add up to 15. Exactly one of those parts is therefore ≥8. There must be at least one such part, because of the pigeonhole principle (specifically, two 7's are sufficient only to add up to 14). And if one part has sum ≥8, the other part—its complement—must have sum ≤15−8=7
.
For instance, if I divide the set into parts {1,2,4}
and {3,5}, the first part adds up to 7, and its complement adds up to 8
.
Once one makes that observation, the rest of the proof is straightforward. There are 25=32
different subsets of this set (including itself and the empty set). For each one, either its sum, or its complement's sum (but not both), must be ≥8. Since exactly half of the subsets have sum ≥8, the number of such subsets is 32/2, or 16.
Answer:
m<1 = 105°
m<2 = 75°
very simple explanation:
a and b are perpendicular. line t intersects these perpendicular lines. the given 75° is, in short, an intersect of a line, which is 180°. 75-180=105. angles 1 and 2 are duplicates of what is shown
Answer:
935 grams
Step-by-step explanation:
1 day = 55 grams
17 days = 55 x 17 = 935 grams
