-3x + 9 - 4 = x + 3 + 2x
-3x + 9 - 4 = 3x + 3
9 - 4 = 6x + 3
5 = 6x + 3
2 = 6x
1/3 = x
2y + 4 + 5y + 8=
7y + 4 + 8=
7y + 12=
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:
-3b³ - 5b² + 10b
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define Expression</u>
(10b + 7b² - 6b³) - (12b² - 3b³)
<u>Step 2: Simplify</u>
- Distribute negative: 10b + 7b² - 6b³ - 12b² + 3b³
- Combine like terms (b³): -3b³ + 10b + 7b² - 12b²
- Combine like terms (b²): -3b³ - 5b² + 10b
Difference of a number and 17: x - 17
eight times that = 8(x - 17)
8(x - 17) = 30
divide both sides by 8
x - 17 = 30/8
x = 30/8 + 17 which is 20.75
