1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elena-14-01-66 [18.8K]
3 years ago
13

Solve this identifying holes, vertical asymptotes, and horizontal asymptotes for

Mathematics
1 answer:
USPshnik [31]3 years ago
6 0

x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{Vertical asymptotes:}\\\\(x+4)(x-1)=0\iff x+4=0\ \vee\ x-1=0\\\\\boxed{x=-4\ and\ x=1}\\\\\text{Horizontal asymptotes:}

\lim\limits_{x\to\pm\infty}\dfrac{x^2+7x+12}{-x^2-3x+4}=\lim\limits_{x\to\pm\infty}\dfrac{x^2\left(1+\dfrac{7}{x}+\dfrac{12}{x^2}\right)}{x^2\left(-1-\dfrac{3}{x}+\dfrac{4}{x^2}\right)}=\dfrac{1}{-1}=-1\\\\\boxed{y=-1}

You might be interested in
Math on khan academy
IRINA_888 [86]
The answer is b I believe
5 0
2 years ago
If y = kx, where k is a constant,<br> and y = 30 when x = 6, what is<br> the value of y when x = 3?
Svetradugi [14.3K]

Answer:

Step-by-step explanation:

Actually it's 11 because 11 is technically the same when added to constant of x =6 = 11

7 0
2 years ago
How do you use an egg machine?
Daniel [21]

Answer:

like what kind of egg machine because theres a lot of different types

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please help with #19!
ikadub [295]

Answer:

a) yes

b) 2560

Step-by-step explanation:

An exponential function has a common ratio between points uniformly spaced. Here, the data points are 10 years apart.

The ratio of the first two values is 4000/5000 = 0.8.

The ratio of the next two values is 3200/4000 = 0.8.

These ratios are the same, so the data is consistent with an exponential function.

The common ratio can be used to predict the next value. The next value is predicted to be ...

  3200 × 0.8 = 2560

8 0
3 years ago
a roller coaster train with 6 passenger cars and the front decoration has a mass of 3500 kg. when the train has the front decora
Arada [10]

Answer:

The mass of each passenger is 550 kg.

The mass of front decoration is 200 Kg.

Step-by-step explanation:

Given : A roller coaster train with 6 passenger cars and the front decoration has a mass of 3500 kg. when the train has the front decoration and only 4 passenger cars, it has a mass of 2400 kg.

To find : What is the mass of the decoration and of each passenger car?

Solution :

Let the mass of each passenger is x.

Let the mass of front decoration is y.

  • When the number of passenger = 6

Mass of 6 passengers and front decoration = 3500 kg.

The equation form is 6x+y=3500 ..........[1]

  • When the number of passengers = 4

Mass of 4 passengers and front decoration = 2400 kg.

The equation form is 4x+y=2400  ........[2]

Solving equation [1] and [2]

Subtract equation [2] from [1],

6x+y-4x-y=3500-2400

2x=1100

x=550

Put value in [1],

6(550)+y=3500

3300+y=3500

y=200

Therefore, The mass of each passenger is 550 kg.

The mass of front decoration is 200 Kg.

8 0
3 years ago
Other questions:
  • Question 1 WRONG With what number must 3.475817 be multiplied in order to obtain the number 34,758.17? A 100 1,000 10,000 D 100,
    14·1 answer
  • Quadrilateral qrst has diagonals that are perpendicular but not congruent. which type of quadrilateral could describe quadrilate
    7·1 answer
  • Solve the system <br> thank you
    5·1 answer
  • Help asap. need the answer ASAP
    8·1 answer
  • 6. What’s the answer to this question?
    8·1 answer
  • Jada fills the bathtub before taking a bath and then allows the water to drain
    5·1 answer
  • Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the g
    6·2 answers
  • State the x- and y-intercepts of each equation<br> 15x + 20y = 1,800
    6·1 answer
  • I’ll give brainlest if you help me with this!
    6·1 answer
  • Can sombody explain this and give me the answer please and thank you
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!