Is the ordered pair (5,8) a solution to the system y=x+3 and 3x + 2y =25?

When graphed, which function has a horizontal asymptote at 4?

galben [10]

Answer:

Correct answer: C. f(x) = 2(3)x + 4

(please note we changed the expression of the function to exponential form which we believe is the correct form of the question)

Step-by-step explanation:

Horizontal Asymptote

The graph of a function is said to have a horizontal asymptote at y=a if one or both the following limits exist

$\lim\limits_{x \rightarrow \infty}f(x)=a$

$\lim\limits_{x \rightarrow -\infty}f(x)=a$

The horizontal asymptotes are horizontal lines to which the function tends when x increases or decreases without limits.

Let's analyze each one of the options provided:

A. f(x) = 2x -4

$\lim\limits_{x \rightarrow \infty}(2x-4)=+\infty$

$\lim\limits_{x \rightarrow -\infty}(2x-4)=-\infty$

No horizontal asymptote

B. f(x) = -3x + 4

$\lim\limits_{x \rightarrow \infty}(-3x+4)=-\infty$

$\lim\limits_{x \rightarrow -\infty}(-3x+4)=\infty$

No horizontal asymptote

C. f(x) = 2\cdot 3^x + 4

$\lim\limits_{x \rightarrow \infty}(2\cdot 3^x + 4)=2\cdot 3^\infty + 4=\infty$

$\lim\limits_{x \rightarrow \infty}(2\cdot 3^x + 4)=2\cdot 3^{-\infty} + 4=0+4=4$

This function has a horizontal asymptote at y=4

D. 3\cdot 2^x -4

$\lim\limits_{x \rightarrow \infty}(3\cdot 2^x - 4)=3\cdot 2^\infty - 4=\infty$

$\lim\limits_{x \rightarrow \infty}(3\cdot 2^x- 4)=3\cdot 2^{-\infty} - 4=0-4=-4$

This function has a horizontal asymptote at y=-4

Correct answer: C.

8 0

2 years ago

Need help with courseReplace 250 with 575 and -3 with -5.

Svetlanka [38]

Given

The demand function

$p(x)=\frac{250}{\sqrt{x}}-5$

To determine:

a) The revenue function.

b) The marginal revenue.

c) The marginal revenue when x=200.

d) The equation of tangent, and its derivation.

Explanation:

It is given that,

$p(x)=\frac{250}{\sqrt{x}}-5$

a) The revenue function is given by,

$\begin{gathered} R(x)=x\cdot p(x) \\ R(x)=x\times(\frac{250}{\sqrt{x}}-5) \\ R(x)=250\sqrt{x}-5x \end{gathered}$

b) The marginal revenue function is,

$\begin{gathered} R^{\prime}(x)=\frac{d}{dx}(R(x)) \\ =\frac{d}{dx}(250\sqrt{x}-5x) \\ =250\times(\frac{1}{2}\times x^{-\frac{1}{2}})-5 \\ =\frac{125}{\sqrt{x}}-5 \end{gathered}$

c) The marginal revenue when x=200 is,

$\begin{gathered} R^{\prime}(200)=\frac{125}{\sqrt{200}}-5 \\ =\frac{125}{10\sqrt{2}}-5 \\ =8.8388-5 \\ =3.8388 \\ =3.84 \end{gathered}$

Hence, the marginal revenue is 3.84.

d) Let y=mx+c is the tangent.

Then,

$y=3.84x+c$

That implies, for y=12.68, and x=200,

$\begin{gathered} 12.68=3.84\times200+c \\ 12.68=768+c \\ c=12.68-768 \\ c=-755.32 \end{gathered}$

Hence, the equation of tangent is,

$y=3.84x-755.32$

8 0

5 months ago

Solve with subsitution y-3x=2 y=-2x-8 show ur work HURRY PLSS

IRINA_888 [86]

Answer:

y-3x=2......1

y=-2x-8 ......2

substituting value of y in equation 1

-2x-8-3x=2

-5x=2+8

x=10/-5=-2

substituting value of x in equation 1

y-3×(-2)=2

y+6=2

y=2-6=-4

x=-2

y=-4

(

5 0

2 years ago

Read 2 more answers

What is the value of c in the equation 12 c minus 53 = 91?

dmitriy555 [2]

Answer:

c=12

Step-by-step explanation:

12c - 53= 91

12c=144

c=12

5 0

3 years ago

On a map. 1 inch equals 15 miles. Two cities are 6 inches apart on the map. What is the actual distance between the cities?

WARRIOR [948]

Answer:

90 miles

Step-by-step explanation:

The person who answered first explained it well, so I dont have to.

have a nice day :)

5 0

2 years ago