PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!

Mathematics

1 answer:

Kisachek [45]3 years ago

5 0

Answer: (A) vertical asymptote: x = 2, horizontal asymptote: y = 1

Step-by-step explanation:

$f(x) = \dfrac{1}{x-2}+1$

Vertical Asymptote is the restriction on the x-value. The denominator cannot be zero, so x - 2 ≠ 0 ⇒ x ≠ 2

The restricted value on x is when x = 2 which is the vertical asymptote

Horizontal Asymptote (H.A.) is the restriction on the y-value. This is a comparison of the numerator (n) and denominator (m). There are 3 rules that will help you:

n > m No H.A. (use long division to find slant asymptote)
n = m H.A. is the coefficient of n divided by coefficient of m
n < m H.A. is 0

In the given problem, n < m so y = 0, however there is also a vertical shift of up 1 so the H.A. also shifts up. This results in H.A. of y = 1

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An exterior angle of a regular convex polygon is 40°. What is the number of sides of the polygon?

seraphim [82]

Answer:

option B

Step-by-step explanation:

Sum of interior angles of a polygon with n sides:

$= (n - 2 )\times 180$

$Therefore, Each \ interior \ angle = (\frac{n - 2}{n} )\times 180$

$Sum \ of \ one \ of \ the \ interior \ angle \ with \ its \ exterior \ angle \ is \ 180^\circ$

$[ \ because \ straight \ line \ angle = 180^\circ \ ]$

That is ,

$Exterior \ angle + Interior \ angle = 180^\circ\\\\40^ \circ + (\frac{n-2}{n}) \times 180 = 180^\circ\\\\40 n + 180n - 360 = 180n\\\\40n = 180n - 180n + 360 \\\\40n = 360 \\\\n = 9$