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Sedaia [141]
3 years ago
11

Help me solve⬇️ Plzzzzzzzz

Mathematics
1 answer:
LekaFEV [45]3 years ago
5 0

The inequalities that match the number line are

10.x≥-2

11.x<-2

Explanation

The inequalities can be determined from the number line. In the first number line the arrow starts from the point -2 and then extends to infinity. The point -2 is marked by a solid circle which means that the point too is included.

so x≥-2 becomes the inequality corresponding to the number line.

In the next number line the arrow starts from the point -2 but the point  is marked by an unshaded circle which indicates that the point  is not included .

therefore the inequlity x<-2 represents the number line.

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Answer:

x-intercepts = 1,2, and 4, y-intercept = -8

Step-by-step explanation:

x^3 - 7x^2 - 14x - 8 in factored form is equal to (x-1)(x-2)(x-4).

Solving for x-intercepts:

  • We are actually able to solve for all x-intercepts without the given factor. But since we are given one of the factors, our job becomes much easier.
  • Using synthetic division, or long division, we factor out the x-intercept 4. Which leaves us with the polynomial x^2 - 3x + 2.
  • From here we can separate the polynomial into two binomials.
  • x^2 - 3x + 2 = (x-1)(x-2). Giving us all 3 x-intercepts.
  • Using Descartes' rules we can identify before even starting the problem how many real x-intercepts there are (Not needed for this problem).

Solving for y-intercept:

  • The y-intercept is always the coefficient that does not have any assigned x-variables.
  • The coefficient is -8, thus the y-intercept.
  • If unsure of the y-intercept, you can always plug in x = 0. Solving for the y-intercept will give you the value of f(0).
  • If there is no coefficient, the y-intercept is equal to zero.
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