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dangina [55]
3 years ago
12

PLEASE HELP FAST ILL GIVE 5 STARS!!!!

Mathematics
2 answers:
MArishka [77]3 years ago
8 0
I believe it's Line y=-x+2 and y=3x+1 intersect the y-axis. From what I've gathered, they are parallel lines, and both are set on the y-axis.
hodyreva [135]3 years ago
7 0
Both are st on the y axis
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<img src="https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Cfrac%7Bx%5E%7B3-8%7D%20%7D%7Bx%5E%7B2%7D%20-6x%2B8%7D" id="TexFormula1" ti
Firlakuza [10]

Answer:

  • Domain: All the real values except x = 2 and x = 4: R - {2, 4}
  • Holes: x = 2
  • VA, vertical asymptores: x = 4
  • HA: horizontal asymptotes: there are not horizontal asymptotes
  • OA: oblique asymptotes: x + 6 [note that OH does not stand for any known feature, and so it is understood that it was intended to write OA]
  • Roots: x = 2
  • Y-intercept: -1

Step-by-step explanation:

1. <u>Given</u>:

f(x)=\frac{x^3-8}{x^2-6x+8}

  • Note that the number 8 in the numerator is not part of the power.
  • Type of function: rational function

2. <u>Domain</u>: is the set of x-values for which the function is defined.

The given function is defined for all x except those for which the denominator equals 0.

  • Denominator:  x² -6x + 8 = 0
  • Solve for x:

        Factor. (x - 4 )(x - 2) = 0

        Zero product property: (x - 4) = 0 or (x - 2) = 0

        x - 4 = 0 ⇒ x = 4

        x - 2 = 0 ⇒ x = 2

  • Domain:

        All the real values except x = 2 and x = 4: x ∈ R / x ≠ 2 and x ≠ 4.

3. <u>Holes</u>:

The holes on the graph of a rational function are at those x-values for which both the numerator and denominator are zero.

  • Find the values for which the numerator is zero:

        Numerator: x³ - 8 = 0

        Factor using difference of cubes property:

                   a³ - b³ = (a - b)(a² + ab + b²)

                   x³ - 8 = (x - 2)(x² + 2x + 4) = 0

        Zero product property:  (x - 2)(x² + 2x + 4) = 0

                    x - 2 = 0 ⇒ x = 2                    

                    x² + 2x + 4 = 0 (this has not real solution)

  • The values for which the denominator is zero were determined above: x = 2 and x = 4.

  • Conclusion: for x = 2 both numerator and denominator equal 0, so this is a hole.

4. <u>VA: Vertical asymptotes</u>.

The vertical asymptotes on the graph of a rational function are the vertical lines for which only the denominator (and not the numerator) equals zero.

  • In the previous part it was determined that happens when x = 4.

5. <u>HA: Horizontal asymptotes</u>.

In rational functions, if the numerator is a higher degree polynomial than the denominator, there is no horizontal asymptote.

6. <u>OA: oblique asymptotes</u>

  • Find the quotient and the remainder.

                       x + 6

                  _______________

x² - 6x + 8 )   x³ + 0x² + 0x - 8

                  - x³ + 6x² - 8x

                   ___________

                          6 x² -   8x -  8

                        - 6x² + 36x - 48

                        _____________

                                    28x  - 56

Result: (x + 6) + (28x - 56) / (x² - 6x + 8)

  • Find limit x → ∞

\lim_{x \to \infty}(x + 6) + \frac{28x-56}{x^2-6x+8}=x+6

<u>7. Roots</u>:

Roots are the values for which f(x) = 0.

That happens when the numerator equals 0, and the denominator is not 0.

As determined earlier: x³ - 8 = 0 ⇒ x = 2.

8. <u>Y-Intercept</u>

The y-intercepts of any function are the y-values when x = 0

  • Substitute x = 0 into the function:

         f(x)=\frac{x^3-8}{x^2-6x+8}=\frac{0^3-8}{0^2-6(0)+8}}=\frac{-8}{8} =-1

3 0
3 years ago
A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 4 types of drinks to choose fr
Temka [501]

To answer this question, multiply all given numbers together.

4*3*3

12*3

36

36 different value meal packages are possible.

Hope this helps!

8 0
3 years ago
Read 2 more answers
The perimeter of a rectangular field is 60 meters. Its area is 200 square meters. Find its dimensions.
Vanyuwa [196]

Answer:

20 m by 10 m

Step-by-step explanation:

let w be width and l be length , then

2(l + w) = 60 ( divide both sides by 2 )

l + w = 30 ( subtract w from both sides )

l = 30 - w → (1)

lw = 200 → (2)

Substitute l = 30 - w into (2)

w(30 - w) = 200 ← distribute parenthesis on left side

30w - w² = 200 ( subtract 200 from both sides )

30w - w² - 200 = 0 ( multiply through by - 1 )

w² - 30w + 200 = 0 ← in standard form

(w - 10)(w - 20) = 0 ← in factored form

Equate each factor to zero and solve for w

w - 10 = 0 ⇒ w = 10

w - 20 = 0 ⇒ w = 20

Substitute these values into (1)

l = 30 - 10 = 20

l = 30 - 20 = 10

dimensions of field is 20 m by 10 m

4 0
2 years ago
Read 2 more answers
Write a ratio to compare the amounts below. Simplify
frutty [35]

Answer:

6/25

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
En un experimento de laboratorio se mezcla dextrosa y agua en varios recipientes, con la condición de que la concentración de de
sashaice [31]

Answer:

4give me I need the points T_T

6 0
3 years ago
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