Answer:
x=10/c
Step-by-step explanation:
3(cx-7)=9
(cx-7)=3
cx=10
x=10/c
15x - 30 = 105 is the mathematical statement
Answer:
(-67/3, -13/3)
Step-by-step explanation:
Basically, you try to find 2 numbers that divide to 3/2. So, using trial and error, plug in numbers for x in this expression: x/24=3/2, and solve to find the number that makes it true. You end up getting 36/24=3/2. Hope that 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.
