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Arlecino [84]
3 years ago
10

What are the discontinuities of the function f(x) = the quantity x squared minus 16 over the quantity 4x minus 24?

Mathematics
2 answers:
ANEK [815]3 years ago
4 0
Dividing x^2 - 16 by 4x - 24  gives the quotient (1/4)x + 3/2

y = (1/4)x + 3/2  would be an asymptote  ( discontinuity)

Another would be a vertical discontinuity  when x =  6  (this would make the denominator 4x-24  = 0.
Ilya [14]3 years ago
3 0

Answer:

x=6 is only the point of discontinuity for the function f(x).      

Step-by-step explanation:

Given a function f(x)=\frac{x^2-16}{4x-24}.

We have to find the discontinuities of the function.

Point of discontinuities are the points at which the function is not defined.

To find the point of discontinuities we have to put the denominator 0 to find the value of x or to find the point of discontinuity.

∴ 4x-24=0

⇒ 4x=24 ⇒ x=6

Ar x=6 the denominator becomes 0 and the function f(x) is not defined.

Hence, x=6 is only the point of discontinuity for the function f(x).

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dlinn [17]
B. sqrt(441) is rational
4 0
3 years ago
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Scores on a final exam taken by 1200 students have a bell shaped distribution with mean=72 and standard deviation=9
SVETLANKA909090 [29]

Answer:

a. 72

b. 816

c. 570

d. 30

Step-by-step explanation:

Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.

Please refer the figure for a better understanding.

a. In a normal distribution, Mean = Median = Mode

Therefore, Median = Mean = 72

b. We have to know that 68% of the values are within the first standard deviation of the mean.

i.e., 68% values are between Mean $ \pm $ Standard Deviation (SD).

Scores between 63 and 81 :

Note that 72 - 9 = 63 and

72 + 9 = 81

This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.

Now, Scores between 63 and 81 = $ \frac{68}{100} \times 1200 $

= 68 X 12 = 816.

That means 816 students have scored between 63 and 81.

c. We have to know that 95% of the values lie between second Standard Deviation of the mean.

i.e., 95% values are between Mean $ \pm $ 2(SD).

Note that 90 = 72 + 2(9) = 72 + 18

Also, 54 = 63 - 18.

Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to $ \frac{95}{2} \% $ of the values.

Therefore, Scores between 72 and 90 = $ \frac{95}{2(100)} \times 1200 = \frac{95}{200} \times 1200  $

$ \implies 95 \times 12 $ = 570.

That is a total of 570 students scored between 72 and 90.

d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.

In this case, 5 % of the values lie between below 54 and above 90.

Since, we are asked to find scores below 54. It should be 2.5% of the values.

So, Scores below 54 = $ \frac{2.5}{100} \times 1200 $

= 2.5 X 12 = 30.

That is, 30 students have scored below 54.

8 0
3 years ago
Estimate the area of the top of a round pizza that has a diameter of 16 inches.
notsponge [240]
the are would be 64 inches pi or approximately  200.96 inches squared

Hope this helps!
4 0
3 years ago
Read 2 more answers
On a timed session please help I have one more question after this.....
olya-2409 [2.1K]

The coffee shop used 52 pounds of Type A coffee.

Step-by-step explanation:

Cost of Type A coffee per pound = 5.25

Cost of Type B coffee per pound = 4.10

Total pounds used in blend = 142

Total cost = 642.00

Let,

x be the pounds of Type A coffee used

y be the pounds of Type B coffee used

According to given statement;

x+y=142      Eqn 1

5.25x+4.10y=642.00   Eqn 2

Multiplying Eqn 1 by 4.10

4.10(x+y=142)\\4.10x+4.10y=582.20\ \ \ Eqn\ 3

Subtracting Eqn 3 from Eqn 2

(5.25x+4.10y)-(4.10x+4.10y)=642.00-582.20\\5.25x+4.10y-4.10x-4.10y=59.80\\1.15x=59.80\\

Dividing both sides by 1.15

\frac{1.15x}{1.15}=\frac{59.80}{1.15}\\x=52\\

The coffee shop used 52 pounds of Type A coffee.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/10677255
  • brainly.com/question/10689103

#LearnwithBrainly

5 0
3 years ago
Find the measure of the missing angles.
Alenkinab [10]

Answer:

d = 69°, e = 32°, f = 79°

Step-by-step explanation:

the 69° angle and d are vertical angles, so d is 69°.

same with e and the 32° angle, so e is 32°.

the 69° angle and f are on a straight angle, which means they, and e, add up to 180° when combined.

69 + 32 = 101

180 - 101 = 79

so f is 79°.

8 0
2 years ago
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