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Elis [28]
3 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]3 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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in a school gym, the ratio of the number of boys to the number of girls was 4:3 . after 160 boys left the gym, the ratio became
Annette [7]

Answer:

300 girls were there in the gym.

Step-by-step explanation:

Given:

The ratio of the number of boys to the number of girls was 4:3, after 160 boys left the gym, the ratio became 4:5.

Now, to find the number of girls in the gym.

The girls in the gym does not left, their quantity is same before and after.

So, we multiply the both ratios to make the girls ratio same:

4:3 × 5 = 20:15

4:5 × 3 = 12:15

Now, <em>we find the units of the ratio</em>.

<em>The ratio of boys dropped down by 160</em>:

20 - 12 = 8 units.

160 = 8 units

Now, dividing both sides by 8 we get:

20 = 1 unit

So, 1 unit = 20.

Now, girls = 15 units

So, 15 × 20 = 300.

Therefore, 300 girls were there in the gym.

3 0
4 years ago
In 2007, there were more than 8.14 million cars for sale. Over the next 3 years, the number of cars decreased by 23%. Write an e
Nina [5.8K]

Answer:

c = 8.14 million×(0.9166)^t

4.83 million  

Step-by-step explanation:

Data:

  t = y - 2007

c₀ = 8.14 million

c₃  = 23 % less than c₁

Part 1. Calculate c₃

c₃ = c₀(1 - 0.23) = 0.77c₀

Part 2. Calculate r

      c₃ = c₀r^t

0.77c₀ = c₀r³

   0.77 = r³              Divided each side by c₀

         r = 0.9166     Took the cube root of each side

The explicit decay model is c = 8.14 million×(0.9166)^t

Part 3. Prediction

t = 2013 - 2007 = 6

c = c₀r^t = 8.14 million×(0.9166)⁶ = 8.14 million × 0.5929 = 4.83 million

The model predicts that there will be 4.83 million cars for sale in 2013.

7 0
3 years ago
John Cena buys a new pair of DC shoes every month to wrestle. (Each pair costs $58.99)
Lerok [7]

Answer:

A. $707. 88

B. $12,033.96

Step-by-step explanation:

A. 58.99 × 12 = 707.88

B. 707.88 × 17 = 12,033.96

Hope this helps!

6 0
4 years ago
Round the following 8.388 to 2 decimal places
Roman55 [17]
The answer will be 8.39 because the third number (8) is above 5 so you have to round up. Good luck!
3 0
3 years ago
The velocity of a body is increases from 10 m/s ti 15 m/s in 5seconds calculate its acceleration​
larisa [96]

Answer:

accelaration =  \frac{change \: in \: veloity}{time}  \\  =  \frac{15 - 10}{5}  \\  =  \frac{5}{5}  \\  = 1 \frac{m}{ {s}^{ - 2} }

3 0
3 years ago
Read 2 more answers
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