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kirza4 [7]
2 years ago
7

Show all work to identify the asymptotes and state the end behavior of the function f(x)=3x/x-9

Mathematics
1 answer:
lorasvet [3.4K]2 years ago
8 0

Using the asymptote concept, we have that:

  • The vertical asymptote is x = 9.
  • The horizontal asymptote is y = 3.
  • The end behavior is that as x \rightarrow \infty, y \rightarrow 3.

<h3>What are the asymptotes of a function f(x)?</h3>

  • The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
  • The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, the function is:

f(x) = \frac{3x}{x - 9}

For the vertical asymptote, we have that:

x - 9 = 0 -> x = 9.

For the horizontal asymptote:

y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{3x}{x - 9} = \lim_{x \rightarrow \infty} \frac{3x}{x} = \lim_{x \rightarrow \infty} 3 = 3

Hence, the end behavior is that as x \rightarrow \infty, y \rightarrow 3.

More can be learned about asymptotes at brainly.com/question/16948935

#SPJ1

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5p/7 - 18 = -43<br> A: -50<br> B: -85 &amp; 2/5<br> C: -31<br> D: -35
Oliga [24]

I'm sorry I really don't know I'm not really good with math that's why I got them brainly for other people's help because I really not that cool math and I'm homeschooled

4 0
4 years ago
A small boat traveled 29.5 miles upstream in 2 hours. The same boat took 3 hours to travel 59.25 miles downstream. If the speed
mel-nik [20]

Answer:

  • boat speed: 17.25 mph
  • current: 2.5 mph

Step-by-step explanation:

Upstream, the speed of the current (c) subtracts from the speed of the boat (b) to give the net speed. Downstream, the speed of the current adds. We can make use of the relation ...

  speed = distance/time

  b-c = 29.5/2 = 14.75 . . . . . miles/hour

  b+c = 59.25/3 = 19.75 . . . .miles/hour

Subtracting the first equation from the second, we get ...

  (b+c) -(b-c) = 19.75 -14.75

  2c = 5

  c = 2.5

Then either equation can be used to find b:

  b = 14.75 +c = 17.25

The speed of the boat in still water is 17.25 miles per hour; the speed of the current is 2.5 miles per hour.

5 0
4 years ago
Factoring quadratics. Not in a rush, but I would appreciate some help on this. It's too late into the day to ask for help from m
Pie

Answer:

  • (y + 10)(2y + 1)

Step-by-step explanation:

<u>Factor the expression:</u>

  • 2y² + 21y + 10 =
  • 2y² + 20y + y + 10 =
  • 2y(y + 10) + (y + 10) =
  • (y + 10)(2y + 1)

4 0
3 years ago
Read 2 more answers
What is the variable "x" in the equation, 7/2=x/2, and why?
love history [14]
X is equal to 7. Since you are trying to make them equal to each other, the denominator is already the same, so you just need to make the numerator the same too.
7 0
3 years ago
Using the picture above find the measure of VPW
elena-14-01-66 [18.8K]

Given:

Measure of arc UV is 56 degrees.

The measure of arc QW is 132 degrees.

To find:

The measure of angle VPW.

Solution:

Intersecting chords theorem: If two chords intersect each other inside the circle, then the measure of angle on the intersection is half of the sum of intercepted arcs.

Using the intersecting chords theorem, we get

m\angle VPU=\dfrac{1}{2}(m(arcQW)+m(arcUV))

Substituting the given values, we get

m\angle VPU=\dfrac{1}{2}(132^\circ+56^\circ)

m\angle VPU=\dfrac{1}{2}(188^\circ)

m\angle VPU=94^\circ

Now,

m\angle VPU+m\angle VPW=180^\circ           [Linear pair]

94^\circ+m\angle VPW=180^\circ

m\angle VPW=180^\circ-94^\circ

m\angle VPW=86^\circ

Therefore, the measure of angle VPW is 86^\circ.

8 0
3 years ago
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