What is the oblique asymptote of the function f(x) = the quantity x squared plus 5x plus 6 over the quantity x plus 4?

Answers

Answer 1

Answer:

Answer:

$x+1$

Step-by-step explanation:

A slant (oblique) asymptote occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator.

To find the slant asymptote you must divide the numerator by the denominator using either long division or synthetic division.

We are given a function:

$f(x)=(x^2+5x+6)/(x+4)$

Since in the given function the polynomial in the numerator is a higher degree than the polynomial in the denominator.

So, now to find oblique asymptote we will divide the numerator by the denominator

So, on dividing we get :

$f(x)=(x^2+5x+6)/(x+4)=x+1+\frac2{x+4}$ j

Now, As $x\to\pm\infty$ the remainder term disappears

So the oblique asymptote is the line $y=x+1$

Thus, the oblique asymptote of the function $f(x)=(x^2+5x+6)/(x+4)$ is $x+1$

Answer 2

Answer: $f(x)=(x^2+5x+6)/(x+4)=x+1+\frac2{x+4}$

As $x\to\pm\infty$ , the remainder term disappears, so the oblique asymptote is the line $y=x+1$ .

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Which value of x satisfies both -9x + 4y = 8 and -3x - y = 4 given the same value of y?ОА
1
7
ОВ.
7
9
Ос.
8
7
D. -9
OE.
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Answers

Answer:

- $(8)/(7)$

Step-by-step explanation:

-9x+4y=8

-3x-y=4

Multiple the entire second equation by 4

-12x-4y=16

-9x+4y=8

__________

-21x=24

divide each side by -21 and simplify

x= - $(8)/(7)$

When considering linear equations, what is a y-intercept?

Answers

Definition

A y-intercept is the place where a line or curve crosses, or touches, the y-axis - the vertical, often darkened line in the center of a graph. It is also the point at which x = 0.

Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together?5x + 13y = 232
12x + 7y = 218
The first equation can be multiplied by –13 and the second equation by 7 to eliminate y.
The first equation can be multiplied by 7 and the second equation by 13 to eliminate y.
The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.
The first equation can be multiplied by 5 and the second equation by 12 to eliminate x.

Answers

The THIRD sentence is correct.
The first equation can be multiplied by -12 and the second equation by 5, to eliminate x.
Let's do this:
(1st equation) 5*x + 13*y = 232 / *(-12)
(2nd equation) 12*x + 7*y = 218 / *(5)
---------------------------------
When multiplied, we get:
(1st equation) -60*x - 156*y = -2784
(2nd equation) 60*x + 35*y = 1090
---------------------------------
Further, first equation now will be obtained when ADDING 1st and 2nd equation together:
(1st equation) -60x+60x-156y+35y=-2784+1090
2nd equation we get from just writing any equation from the beginning, for example, the second one:
(2nd equation) 12*x + 7*y = 218
-----------------------------------------
(1st equation) 0*x - 121*y = -1694
(2nd equation) 12*x + 7*y = 218
------------------------------------------
(1st equation) -121*y = -1694 [x variable is in this step eliminated]
(2nd equation) 12*x + 7*y = 218
----------------------------------------------
(1st equation) y = 1694/121
(2nd equation) 12*x + 7*y = 218
----------------------------------------------
(1st equation) y = 14
(2nd equation) 12*x + 7*14 = 218
----------------------------------------------
(1st equation) y = 14
(2nd equation) 12*x + 98 = 218
----------------------------------------------
(1st equation) y = 14
(2nd equation) 12*x = 218 - 98
----------------------------------------------
(1st equation) y = 14
(2nd equation) 12*x = 120
----------------------------------------------
(1st equation) y = 14
(2nd equation) x = 120/12
----------------------------------------------
(1st equation) y = 14
(2nd equation) x = 10
----------------------------------------------
So, solution of the system of this two equations is obtained, and it is:
(x,y)=(10,14)

Answer:

The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.

How do i write a fraction or a mixed number as a decimal?

Answers

A decimal is a number divided by 10: 0.x = x/10, whatever the x number might be. If the "decimal" has more digits, then is divided by 100, 1000, and so forth: 0.0y = y/100, 0.00z = z/1000

So the trick for a mixed number to be written as a decimal is first to write the mixed number as a fraction, then, when you have a fraction, you need to make the denominator of the fraction equal to 10, 100, 1000, 10000, etc, and then you have it done.

For example, 4/25 as decimal is:
(4/25) = (4*4)/(25*4)
= 16/100, and that is = 0.16

If x / y is an integer, which of the following statements must be true?A. both x and y are integers
B. x is an integer
C. either x or y is negative
D. y / x is an integer
E. x = ny where n is an integer

Answers

Only E) is true. If I were to arbitrarily pick x = 2.2 and y =1.1, then I could show that A), B), C), and D) to be false, given x/y = 2.2/1.1 = 2 (which is an integer). However for E), if we define x/y = n where n is an integer, then by rearranging terms, we can show x = n*y where n still equals an integer and our original equation is still valid.

A baseball team played 54 games this season. They loss 18 games this season. What is the team's wins to losses ratio

Answers

The ratio would be 2:1 because if there are 18 losses and a total of 54 games, 54-18 is 36 and 36:18 is simplified to 2:1.

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