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<h2><em>hope</em><em> it</em><em> helps</em><em>!</em></h2>
Answer:
Center: (-2, 4)
Radius: 4
Step-by-step explanation:
To find the centre and radius, we require to identify g , f and c
By comparing the coefficients of 'like terms' in the given equation with the general form.
2g = 4 → g = 2 , 2f = -8 → f = -4 and c = 4 → center=(−g,−f)=(−2,4)
radius = √22+(−4)2−4= √4+16−4=4
Center: (-2, 4)
Radius: 4
Hope This Helps! :)
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.
