Line 1 to 2: Commutative Property of Multiplication, because all that changed was the order of the things being multiplied.
Line 2 to 3: Commutative Property of *Addition*, because all that changed was the order of the things being added.
All that changed in either step was the ordering of the things being multiplied or added. That’s the commutative property.
Answer:
1-3x+8y
Step-by-step explanation:
Multiply y and 2
Multiply y and 1
The y just gets copied along.
2*y evaluates to 2y
Multiply x and 4
Multiply x and 1
The x just gets copied along.
The answer is x
4*x evaluates to 4x
2*y-4*x evaluates to 2y-4x
The answer is 2y-4x+8
2*y-4*x+8 evaluates to 2y-4x+8
Multiply y and 6
Multiply y and 1
The y just gets copied along.
The answer is y
6*y evaluates to 6y
2y + 6y = 8y
The answer is 8y-4x+8
2*y-4*x+8+6*y evaluates to 8y-4x+8
-4x + x = -3x
The answer is -3x+8y+8
2*y-4*x+8+6*y+x evaluates to -3x+8y+8
8 - 7 = 1
The answer is 1-3x+8y
2*y-4*x+8+6*y+x-7 evaluates to 1-3x+8y
Answer:
(-5, 0) ∪ (5, ∞)
Step-by-step explanation:
I find a graph convenient for this purpose. (See below)
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When you want to find where a function is increasing or decreasing, you want to look at the sign of the derivative. Here, the derivative is ...
f'(x) = 4x^3 -100x = 4x(x^2 -25) = 4x(x +5)(x -5)
This has zeros at x=-5, x=0, and x=5. The sign of the derivative will be positive when 0 or 2 factors have negative signs. The signs change at the zeros. So, the intervals of f' having a positive sign are (-5, 0) and (5, ∞).
