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Zielflug [23.3K]
3 years ago
13

Show all work to identify the asymptotes and zero of the faction f(x) = 4x/x^2 - 16.

Mathematics
1 answer:
Reptile [31]3 years ago
5 0

Answer:

  • asymptotes: x = -4, x = 4
  • zeros: x = 0

Step-by-step explanation:

The vertical asymptotes of the rational expression are the places where the denominator is zero:

  x^2 -16 = 0

  (x -4)(x +4) = 0 . . . . . true for x=4, x=-4

  x = 4, x = -4 are the equations of the vertical asymptotes

__

The zeros of a rational expression are the places where the numerator is zero:

  4x = 0

  x = 0 . . . . . . divide by 4

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Use the following information for problems 1 – 3. Suppose you sign a contract for an annual salary of $50,000 with a guaranteed
erik [133]

Initial salary =  $50,000 .

Rate of raise = 5% each year.

Therefore, each next year salary would be 105% that is 1.05 times.

5% of 50,000 = 0.05 × 50000 = 2500.

Therefore raise is $2500 each year.

According to geometric sequence first term 50000 and common ratio 1.05.

Applying geometric sequence formula

a_n = ar^{n-1}

1) a_n = 50000(1.05)^{n-1}

2) In order to find salary in 5 years we need to plug n=5, we get

a_5 = 50000(1.05)^{5-1}= 50000(1.05)^4

= 50000(1.21550625)

<h3>=$60775.3125.</h3>

3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.

S_n = \frac{a(1-r^n}{1-r}

Plugging n=10, a = 50000 and r= 1.05.

S_10 = \frac{50000(1-(1.05)^{10}}{1-1.05}

S_10 = \frac{50000(0.050)^{10}}{0.05}

= 628894.62678.

<h3>Therefore , you will have earned $ 628894.62678 in total salary by the end of your 10th year.</h3>



7 0
3 years ago
PLEASE HELP WILL MARK BRAINLIEST NO FAKE ANSWERS OR WILL BE REPORTED
GarryVolchara [31]

Answer:

height is 15

Y = L = Length

therefore 15y = (-x^2) +(300/20)

Step-by-step explanation:

15 = -x^2 +(300/20)

is the same as;

15 = (300/20) - (x^2)

we just add y to 15 and that can represent a division for x

y = L

Where area cm^2 can be shown as 300 as 15 x 20 = 300

when we divide by length we get the height as asked in the question.

7 0
3 years ago
2. Simplify:<br> b. 3(2x + 4y)
Nutka1998 [239]

Answer:

(6x+12y)

Step-by-step explanation:

answer is helpful or not

3 0
3 years ago
Read 2 more answers
How do you find the tenth term in this sequence
slava [35]

Answer:

should be none of the about because each time you multiple by 1/2, i got 1/64 for the 10th

Step-by-step explanation:

7 0
3 years ago
3 (x-5) =5<br> what is x?
azamat

Answer: 20/3

So when solving this equation first distribute our 3,we will now have   3x-15=5.

Next we will Add 15 to both sides of our equation. Now we have 3x=20.Then divide our terms,and you will have 3x/3 = 20/3

<u>This will leave you with  1x=20/3. </u>

So the X is 20/3.

      Hope that helped!

8 0
3 years ago
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