Answer:
B.
The solution of |2x + 8| > 6 includes all values that are less than –7 or greater than –1.
The solution of |2x + 8| < 6 includes all values that are greater than –7 and less than –1.
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Step-by-step explanation:
You can find the solution by "unfolding" the absolute value, then dividing by 2 and subtracting 4:
-6 > 2x +8 > 6 . . . . . read this as -6 is less than 2x+8 or 2x+8 is greater than 6
-3 > x +4 > 3 . . . . . . .divide by 2
-7 > x > -1 . . . . . . . . . solution to the first inequality: x is less than -7 or greater than -1.
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The solution to the other inequality is identical, except the direction of the comparison is reversed. It is read differently, because the segments overlap, rather than being disjoint.
-7 < x < -1 . . . . . . . . solution to the second inequality: x is greater than -7 and less than -1.
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These descriptions match choice B.
Answer:
off course D
Step-by-step explanation:
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A 3x3 matrix has a characteristic polynomial of degree 3. If all the elements of the matrix are real, then the polynomial has up to 3 distinct complex roots. If one of these roots is complex (in particular, has a non-zero imaginary part), then a second root would be that first root's complex conjugate. Then the remaining root has to be real.
We are asked to determine how many marbles must be in the seventh line but the condition stated in the problem must be followed such that "starting with a number in every consecutive line it has a number one more than the previous line".
We start with 3, followed by 3+1 = 4, followed by 4+1=5, followed by 5+1=6, followed by 6+1=7, followed by 7+1=8, followed by 8+1=9
The sequence is:
3,4,5,6,7,8,9
In the seventh, there are 9 total marbles.