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Reptile [31]
3 years ago
8

Love this called sketch a graph of the polynomial function f(x)=x^3-6x^2+3x+10. Use it to complete the following:

Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
6 0

Answer:

  • increasing
  • positive
  • negative

Step-by-step explanation:

You can actually answer this question without graphing the equation, but a graph confirms the answers.

__

A cubic with a positive leading coefficient will be <em>negative</em> and <em>increasing</em> on any interval* whose left end is -∞. Similarly, it will be <em>positive</em> and <em>increasing</em> on any interval whose right end is +∞.

The answer choices tell you ...

  • there are zeros at -1, 2, 5
  • there are turning points at 0.27, 3.73

The function is increasing up to the first turning point and after the second one.

The function is negative up to the first zero and between the last two.

  • f is <u>increasing</u> on the intervals (-∞, 0.27) and (3.73, ∞).
  • f is <u>positive</u> on the intervals (-1,2) and (5, ∞).
  • f is <u>negative</u> on the intervals (-∞, -1) and (2,5).

_____

* We say "any interval" but we mean any interval whose boundary is a zero or turning point, and which properly describes an interval where the function is one of <em>increasing</em>, <em>decreasing</em>, <em>positive</em>, or <em>negative</em>.

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Answer:

∠C = 80 ° ; ∠ T = 40°.

Step-by-step explanation:

Triangle CRS is isosceles because it has two sides of equal length. (CR and CS are radii).

An isosceles triangle has also two equal angles, which means that ∠CRS= ∠CSR.

Therefore, ∠C = 80 ° (180° – 50° - 50°)  because the sum of angles in a triangle is 180 degrees.  

∠C is the central angle of the arc RS.

∠ T is the inscribed angle of the arc RS.

An inscribed angle is half of a central angle that subtends the same arc on the circle, so the inscribed angle ∠ T is half of the central angle ∠C. Since ∠C = 80 °, we can easily determine the measure of ∠ T:  

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Answer:

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Step-by-step explanation:

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the length of a rectangle is 3 times the width. If the length is increased by 4 cm and the width is decreased by 1 cm, the perim
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Step-by-step explanation:

In the attached file

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