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Delvig [45]
3 years ago
15

Simplify. 16 - 8 + 5x - 3x 16 + 2x 8 + 8x 8 + 2x 10x

Mathematics
2 answers:
KiRa [710]3 years ago
6 0
The answer to this question is 10x
klio [65]3 years ago
3 0

Answer:

8+2x

Step-by-step explanation:

Combine Like Terms:

<u>1</u><u>6</u><u>-</u><u>8</u>+5x-3x

8+<u>5</u><u>x</u><u>-</u><u>3</u><u>x</u>

8+2x

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Graph y = 3(x + 2)3 - 3 and describe the end behavior.
-BARSIC- [3]
1) The function is 3(x + 2)³ - 3

2) The end behaviour is the limits when x approaches +/- infinity.

3) Since the polynomial is of odd degree you can predict that the ends head off in opposite direction. The limits confirm that.

4) The limit when x approaches negative infinity is negative infinity, then the left end of the function heads off downward (toward - ∞).

5) The limit when x approaches positive infinity is positivie infinity, then the right end of the function heads off upward (toward + ∞).

6) To graph the function it is important to determine:
- x-intercepts
- y-intercepts
- critical points: local maxima, local minima, and inflection points.


7) x-intercepts ⇒ y = 0

⇒ <span>3(x + 2)³ - 3 = 0 ⇒ (x + 2)³ - 1 = 0
</span>

<span>⇒ (x + 2)³ = -1 ⇒ x + 2 =  1 ⇒ x = - 1
</span>

8) y-intercepts ⇒ x = 0

y = <span>3(x + 2)³ - 3 = 3(0 + 2)³ - 3 = 0 - 3×8 - 3 = 24 - 3 = 21
</span><span>
</span><span>
</span><span>9) Critical points ⇒ first derivative = 0
</span><span>
</span><span>
</span><span>i) dy / dx = 9(x + 2)² = 0
</span><span>
</span><span>
</span><span>⇒ x + 2 = 0 ⇒ x = - 2
</span><span>
</span><span>
</span><span>ii) second derivative: to determine where x = - 2  is a local maximum, a local  minimum, or an inflection point.
</span><span>
</span><span>
</span><span>y'' = 18 (x + 2); x = - 2 ⇒ y'' = 0 ⇒ inflection point.
</span><span>
</span><span>
</span><span>Then the function does not have local minimum nor maximum, but an inflection point at x =  -2.
</span><span>
</span><span>
</span><span>Using all that information you can graph the function, and I attache the figure with the graph.
</span>


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