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Elis [28]
2 years ago
7

Show all work to identify the asymptotes and zero of the function f of x equals 4 x over quantity x squared minus 16.

Mathematics
1 answer:
wlad13 [49]2 years ago
3 0

9514 1404 393

Answer:

  • asymptotes: x = ±4, y = 0
  • zero: x = 0

Step-by-step explanation:

The function factors as ...

  f(x)=\dfrac{4x}{(x-4)(x+4)}

The vertical asymptotes are found where the denominator factors are zero:

  x-4 = 0   ⇒   x = 4

  x+4 = 0   ⇒   x = -4

The zero of the function is where the numerator is zero:

  4x = 0   ⇒   x = 0

The horizontal asymptote of the function is the value of 4x/x² when x tends to infinity. That value is zero. The equation of the horizontal asymptote is ...

  y = 0

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A rectangular picture frame has a width of 9 cm and a length of x cm.
Fantom [35]

Answer:

x+9

Step-by-step explanation:

the perimeter of any polygon is the sum of all the sides

7 0
3 years ago
The diagonals of a quadrilateral are of lengths 6cm and 8cm. If the diagonals bisect each other at the right angles. Find the le
maks197457 [2]

Answer:

Each side is 5 cm

Step-by-step explanation:

What you are being told is that the figure is a rhombus. The two sides of a right triangle are 1/2 the size of the diagonals.

a = 3

b = 4

c = the side length of the rhombus.

a^2 + b^2 = c^2

3^2 + 4^2 = c^2

9 + 16 = c^2

25 = c^2

Take the square root of 25

sqrt(c)^2 = sqrt(25)

c = 5

5 0
3 years ago
HELP help HELP help HELP help HELP help HELP help HELP help HELP help
Morgarella [4.7K]

\text{mass of freight train} = 9.98 \times  {10}^{6} kg

\text{mass of aircraft carrier} = 7.3 \times  {10}^{7}  \: kg

\text{difference of masses of aircraft and train: } \\  \\ 7.3 \times  {10}^{7}  - 9.98 \times  {10}^{6}  \\  \\  = 73 \times  {10}^{6}  - 9.98 \times  {10}^{6}

= (73 - 9.98 )\times  {10}^{6}  \\  \\  = 63.02 \times  {10}^{6}  \\  \\  = 6.302 \times  {10}^{6}  \: kg \\  \\  \approx 6.3 \times  {10}^{6}  \: kg

Approximately, aircraft carrier is 6.3 × 10^6 kg heavier than the freight train.
7 0
3 years ago
-15x=-4x... How to move the x to the left?
Delvig [45]
-15x=-4x

We know that adding zero wouldn’t change the value

-15x=-4x+0

Now we can add 4x (since that’s the opposite of the negative sign) to the other side

-11x=0

0 divided by 11 is 0

x=0
4 0
3 years ago
Write a linear factorization of the function. f(x) = x4 + 64x2
german
F(X) = x^4 +64x^2 

x^4 +64x^2 = x^2(x^2 +64)

hope this will help you 
7 0
3 years ago
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