Answer:
number 1 is 2 number 2 is 15 number 4 is 30
Step-by-step explanation:
Answer:
The solutions are x = 1.24 and x = -3.24
Step-by-step explanation:
Hi there!
First, let´s write the equation:
log[(x² + 2x -3)⁴] = 0
Apply the logarithm property: log(xᵃ) = a log(x)
4 log[(x² + 2x -3)⁴] = 0
Divide by 4 both sides
log(x² + 2x -3) = 0
if log(x² + 2x -3) = 0, then x² + 2x -3 = 1 because only log 1 = 0
x² + 2x -3 = 1
Subtract 1 at both sides of the equation
x² + 2x -4 = 0
Using the quadratic formula let´s solve this quadratic equation:
a = 1
b = 2
c = -4
x = [-b± √(b² - 4ac)]/2a
x = [-2 + √(4 - 4(-4)·1)]/2 = 1.24
and
x = [-2 - √(4 - 4(-4)·1)]/2 = -3.24
The solutions are x = 1.24 and x = -3.24
Have a nice day!
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:
Your Answer is ...
x > 3 or x < -7
Step-by-step explanation:
1. x > 3 worked out
|X + 2| > 5
Solve absolute Value
|X + 2| > 5
We know either |X + 2| > 5 or x + 2 < - 5
_________________________________

2. x < -7 Worked out

Hope this Helps!
Take Care!
