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3 years ago

Which is a graph of f(x)=5x-2/x+2,with any vertical or horizontal asymptotes indicated by dashed lines?

Mathematics

1 answer:

Whitepunk [10]3 years ago

4 0

Answer:

The graph of the given function f(x) is attached below :

$f(x)=\frac{5\cdot x -2}{x+2}$

To find vertical asymptotes :

Since the given function is rational so the vertical asymptotes of the function will be zeroes of the denominator

Vertical Asymptotes : x + 2 = 0

⇒ x = -2

To find horizontal asymptotes :

As the degree of numerator is s equal to the degree of denominator. Therefore,

$\text{Horizontal asymptote, y = }\frac{\text{Numerator's leading coefficient}}{\text{Denominator's leading coeeficient}}\\\\\bf\implies y = \frac{5}{1}=5$

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Sean has a collection of coins. One tenth of the coins are from Europe. Thirty-two hundredth are from Asia. The rest are from Af

Tema [17]

Lets write each part, the total will be x:
(1/10)x = Europe
3200 = Asia
x - <span>(1/10)x - 3200 = Africa

Europe + Asia = </span><span>(1/10)x + 3200 = x/10 + 3200
= (320x + 1)/3200
that would be expressed as a fraction, and depends on the total of coins, x</span>

7 0

3 years ago

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You are situated 300 feet from the base of Tower Glitz Plaza watching an external elevator descend down the side of the building

nordsb [41]

Answer:

18.66 ft/s

Step-by-step explanation:

The distance between you and the elevator is given by:

$h=\sqrt{x^2+y^2}$

The rate of change for the distance between you and the elevator is given by:

$\frac{dh}{dt}=\frac{dh}{dy}*\frac{dy}{dt}$

$-16=\frac{dh}{dy}*\frac{dy}{dt}$

$\frac{dh}{dy}=\frac{d}{dy} (\sqrt{x^2+y^2})\\$

Applying the chain rule:

$u=x^2+y^2\\\frac{dh}{dy}=\frac{d\sqrt u}{du} *\frac{du}{dy}\\\frac{dh}{dy}=\frac{1}{2\sqrt u} *2y\\\frac{dh}{dy}=\frac{y}{\sqrt {(x^2+y^2)}}$

Therefore, at x=300 and y = 500, dy/dt is:

$-16=\frac{y}{\sqrt {(x^2+y^2)}}*\frac{dy}{dt}\\-16=\frac{500}{\sqrt {(300^2+500^2)}}*\frac{dy}{dt}\\\frac{dy}{dt}=-18.66\ ft/s$

The elevator is descending at 18.66 ft/s.

7 0

3 years ago

If sec(theta) =25/24, find cot(theta) (Picture provided)

larisa [96]

Answer:

Step-by-step explanation:

By the definition,

$\sec \theta=\dfrac{\text{hypotenuse}}{\text{adjacent leg}}.$

If $\sec \theta=\dfrac{25}{24},$ we can consider right triangle with hypotenuse 25 un. and adjacent leg 24 un. By the Pythagorean theorem,

$\text{hypotenuse}^2=\text{adjacent leg}^2+\text{opposite leg}^2,\\ \\\text{opposite leg}^2=25^2-24^2,\\ \\\text{opposite leg}^2=625-576,\\ \\\text{opposite leg}^2=49,\\ \\\text{opposite leg}=7\ un.$

So,

$\cot \theta=\dfrac{\text{adjacent leg}}{\text{opposite leg}}=\dfrac{24}{7}.$

8 0

3 years ago

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2. Yahir was going up the stairs when he noticed that the first step was taller, so he measured

goblinko [34]

Answer:

6.5

Step-by-step explanation:

This answer makes sense because i subtracted the 8 inches from the total 60 then i used the number i got in the result (52)then i divided 52 by 8 wich are the rest of the steps. getting 6.5

3 0

3 years ago

A triangle has the area of 1/2(4x^2+29x+30)ft^2. If the base of the triangle is (x+6) ft, find the height of the triangle.

Paul [167]

Answer:

4x+5 ft

Step-by-step explanation:

1/2(4x²+29x+30) = 1/2 (x+6) * Height

Height = (4x²+29x+30) / (x+6) = (x+6) (4x+5) / (x+6) = 4x+5

3 0

3 years ago