Show all work to identify the asymptotes and zero of the function f(x)= 5x/x^2-25. Please answer ASAP!!!

The asymptotes and zero of the function are ±5 and 0 respectively

Given the function below;

The vertical asymptotes occur at the point where the function goes large that is the denominator is zero.

If the denominator is zero, hence;

x^2 - 25 = 0

x^2 = 25

x = ±√25

x = ±5

Hence the asymptotes of the function is ±5

For the zero of the function;

Hence the zero of the function is 0

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Answers:

The term "root" is another way of saying "zero of a function"

Explanation:

To find the roots, we need to solve f(x) = 0 for x

f(x) = 0

5x/(x^2 - 25) = 0

5x = 0*(x^2-25)

5x = 0

x = 0/5

x = 0

Plugging x = 0 into f(x) leads to f(x) = 0.

The root is x = 0 meaning the x intercept is at 0 on the x axis number line. This is the origin (0,0).

To find the vertical asymptotes, set the denominator equal to 0 and solve for x

x^2 - 25 = 0

x^2 - 5^2 = 0

(x-5)(x+5) = 0 ... difference of squares rule

x-5 = 0 or x+5 = 0

x = 5 or x = -5

If either x = 5 or x = -5, then then the denominator x^2-25 is zero

We cannot divide by zero, so these values are excluded from the domain, and this produces the vertical asymptotes.

The horizontal asymptote is y = 0 because the degree of the numerator is 1, while the degree of the denominator is 2. The denominator's degree is larger, which leads to y = 0. The rules for finding the horizontal asymptote are

For those rules above, m and n are the degrees of the numerator and denominator respectively. The a,b refers to the leading coefficients of the numerator and denominator.

angle addition postulate

2x=56

step-by-step explanation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47