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Scilla [17]
11 months ago
13

What is the equation of the slant asymptote of the rational function?

Mathematics
1 answer:
marta [7]11 months ago
6 0

The equation of the slant asymptote of the rational function is; y = 2x - 3

<h3>What is the equation of the slant asymptote of the rational function?</h3>

We want to find the equation of the slant asymptote of the rational function given as;

f(x) = (10x³ - 15x² + x - 1)/(5x² - 2)

To solve this question, we will divide the numerator by the denominator.  The result (not including the remainder) will be the equation of the slant asymptote.

We can tell the first term of the quotient will be 2x since 10x³/5x² = 2x. Thus, the answer from the given options will be either 2x − 3 or 2x − 11/5.

The easiest method to apply here is to simply multiply these options by the denominator to get;

(5x² − 2) (2x − 3) = 10x³ − 15x² − 4x + 6

(5x² − 2) (2x − 11/5) = 10x³ − 11x² − 4x + 22/5

So the answer must be 2x − 3

Thus, the equation of the slant asymptote of the rational function is; y = 2x - 3

Read more about Equation of Slant Asymptote at; brainly.com/question/17256965

#SPJ1

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Geometric mean <br> Pls help thank u
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Answer:

Step-by-step explanation:

1). Geometric mean of a and b = \sqrt{a\times b}

   Therefore, geometric mean of 2 and 50 = \sqrt{2\times 50}

                                                                       = 10

2). By geometric mean theorem,

   \frac{JM}{KM}=\frac{KM}{ML}

   \frac{6}{e}=\frac{e}{24}

   e² = 6 × 24

   e = √144

   e = 12

  Similarly, \frac{JL}{KJ}=\frac{KJ}{JM}

   \frac{6+24}{d}=\frac{d}{6}

   d² = 6 × 30

   d = √180

   d = 6√5

   And \frac{JL}{KL}=\frac{KL}{ML}

   \frac{6+24}{c}=\frac{c}{24}

   c² = 30 × 24

   c = √720

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3 0
2 years ago
At a bake sale for every 8 cupcakes sold you earn 5.00. If u made 45 how many cupcakes did you sell?
grandymaker [24]
45 divided by 5 is 9 and 9 times 8 is 72 so the answer is 72.
3 0
3 years ago
Please help me on this question
STALIN [3.7K]
The Answer is 240 yes
5 0
2 years ago
a high school stage collapsed in Fullerton, California, when 250 students got on stage for the finale of a musical production. T
Lera25 [3.4K]

Answer:

91

Step-by-step explanation:

In this question, the important information we get from this is that the stage can support 12,750 students. We are asked, if the average weight of a student is 140 pounds, what is the maximum number of students that can be on the stage safely?

To solve, we simply divide 12,750 by 140.

x=\frac{12,750}{140}

x= 91.07

We get 91.07 as our answer. Since we are considering the maximum number of students, then we must round 91.07 to the nearest whole number which would be 91.

The maximum number of students who could safely be on the stage is 91.

6 0
2 years ago
For the rational expression 2x^2-7x-15/x^2-25, do both of the following,
Mrrafil [7]

Answer:

a. \frac{2x + 3}{x+5}

b. x ≠ -5 (Vertical asymptote) and x ≠ 5 (Hole)

Step-by-step explanation:

Factor the numerator (Grouping):

2x^2 - 7x - 15              

Two numbers that multiply to -30 and add to -7 = -3 and 10

[2x^2 - 10x] + [3x - 15]

(2x + 3)(x - 5)

Factor the denominator (Difference of Two Squares):

x^2 - 25 = (x +5)(x-5)

Factored Expression:

(x - 5) can be factored out of top and bottom as a hole-

\frac{(2x + 3)(x - 5)}{(x + 5)(x - 5)} = \frac{2x + 3}{x+5}

Variable Restrictions:

Denominator ≠ 0

x + 5 = 0\\x = -5

Vertical asymptote at x = -5 ⇒ x ≠ -5

3 0
3 years ago
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