3 x + 4 = 31 ecuación de primer grado ayuda!

Vertical asymptote can be Identites if there is a factor only in the denominator. This means that the function will be infinitely discounted at that point.

For example,

$\frac{1}{x - 5}$

Set the expression in the denominator equal to 0, because you can't divide by 0.

$x - 5 = 0$

$x = 5$

So the vertical asymptote is x=5.

Disclaimer if you see something like this

$\frac{(x - 5)(x + 3)}{(x - 5)}$

x=5 won't be a vertical asymptote, it will be a hole because it in the numerator and denominator.

Horizontal:

If we have a function like this

$\frac{1}{x}$

We can determine what happens to the y values as x gets bigger, as x gets bigger, we will get smaller answers for y values. The y values will get closer to 0 but never reach it.

Remember a constant can be represent by

$a \times {x}^{0}$

For example,

$1 = 1 \times {x}^{0}$

$2 = 2 \times {x}^{0}$

And so on,

and

$x = {x}^{1}$

So our equation is basically

$\frac{1 \times {x}^{0} }{ {x}^{1} }$

Look at the degrees, since the numerator has a smaller degree than the denominator, the denominator will grow larger than the numerator as x gets larger, so since the larger number is the denominator, our y values will approach 0.

So anytime, the degree of the numerator < denominator, the horizontal asymptote is x=0.

Consider the function

$\frac{3 {x}^{2} }{ {x}^{2} + 1}$

As x get larger, the only thing that will matter will be the leading coefficient of the leading degree term. So as x approach infinity and negative infinity, the horizontal asymptote will the numerator of the leading coefficient/ the leading coefficient of the denominator

So in this case,

$x = \frac{3}{1}$

Finally, if the numerator has a greater degree than denominator, the value of horizontal asymptote will be larger and larger such there would be no horizontal asymptote instead of a oblique asymptote.

8 0

2 years ago

Lydia has half of her investments in stock paying an 11% dividend and the other half in a stock paying 14% interest. If her tota

SVETLANKA909090 [29]

Based on the calculations, the amount of money she invested is equal to $3,520.

<h3>How to determine the amount invested?</h3>

First of all, we would assign variables to the amount of money that he invested at different interest rates as follows:

Let x be the amount of money she invested at 11%.

Let y be the amount of money she invested at 14%.

Since Lydia invested the same amount of money in both stocks, we have:

x = y ....equation 1.

At the two interest rates, the total amount Lydia gets is given by:

0.11x + 0.14y = 440 ....equation 2.

Solving the equations simultaneously, we have:

0.11y + 0.14y = 440

0.25y = 440

y = 440/0.25

y = $1,760.

Thus, the total investment is given by:

Total investment = 1760 + 1760

Total investment = $3,520.

Read more on interest rates here: brainly.com/question/16793428

#SPJ1

8 0

1 year ago

The probability distribution of random variable, X, is defined as follows:

stealth61 [152]

Answer and Step-by-step explanation:

A) For the model to be a probability distribution, it has to follow two conditions:

1) The probability of each value of the discrete random variable is between, and included, 0 and 1:

2) The sum of all probabilities is 1;

In the table shown, the probabilities are from 0 to 0.3 - between 0 and 1;

Adding the probabilities: 0 + 0.3 + 0.1 + 0.3 + 0.3 = 1

Therefore, this model is a valid probability distribution model.

B) They are discrete because each value correspond to a finite number of possible values.

C) Expected value is calculated by

$E(X) = \Sigma xP(x)$

$E(X) = 0.0 + 1*0.3 + 2*0.1 + 3*0.3 + 4*0.3$

E(X) = 2.6

D) P(X=3) = P(3), which means probability of 3:

P(X=3) = 0.3

E) P(X<4): probabilities of values of X that are less than 4:

P(X<4) = P(0) + P(1) + P(2) + P(3)

P(X<4) = 0 + 0.3 + 0.1 + 0.3

P(X<4) = 0.7

F) P(X>0) = P(1) + P(2) + P(3) + P(4)

P(X>0) = 0.3 + 0.1 + 0.3 + 0.3

P(X>0) = 1

G) P(X=5) = P(5)

There is no probability of P(5) because the model doesn't "cover" that number.

H) P(X=0) = P(0)

P(X=0) = 0

I) The total area of any density curve is 1 because it represents all the possible values a variable can assume.

3 0

3 years ago