How many roots does the equation (8/(x^2 - 16) )+ 1 = 1/(x -4) have?

Plz show ALL STEPS

Given:

The function is:

[tex]f(x)=\dfrac{1}{x+3}-2[/tex]

To find:

The graph of the given function.

Solution:

We have,

[tex]f(x)=\dfrac{1}{x+3}-2[/tex]

It can be written as:

[tex]f(x)=\dfrac{1-2(x+3)}{x+3}[/tex]

[tex]f(x)=\dfrac{1-2x-6}{x+3}[/tex]

[tex]f(x)=\dfrac{-2x-5}{x+3}[/tex]

Putting [tex]x=0[/tex] to find the y-intercept.

[tex]f(0)=\dfrac{-2(0)-5}{(0)+3}[/tex]

[tex]f(0)=\dfrac{-5}{3}[/tex]

So, the y-intercept is [tex]\dfrac{-5}{3}[/tex].

Putting [tex]f(x)=0[/tex] to find the x-intercept.

[tex]0=\dfrac{-2x-5}{x+3}[/tex]

[tex]0=-2x-5[/tex]

[tex]2x=-5[/tex]

[tex]x=\dfrac{-5}{2}[/tex]

[tex]x=-2.5[/tex]

So, the x-intercept is [tex]-2.5[/tex].

For vertical asymptote, equate the denominator and 0.

[tex]x+3=0[/tex]

[tex]x=-3[/tex]

So, the vertical asymptote is [tex]x=-3[/tex].

The degrees of numerator and denominator are equal, so the horizontal asymptote is the ratio of leading coefficients.

[tex]y=\dfrac{-2}{1}[/tex]

[tex]y=-2[/tex]

So, the horizontal asymptote is [tex]y=-2[/tex].

End behavior of the given function:

[tex]f(x)\to -2[/tex] as [tex]x\to -\infty[/tex]

[tex]f(x)\to -\infty[/tex] as [tex]x\to -3^-[/tex]

[tex]f(x)\to \infty[/tex] as [tex]x\to -3^+[/tex]

[tex]f(x)\to -2[/tex] as [tex]x\to \infty[/tex]

Using all these key features, draw the graph of given function as shown below.

Answer:

The Answer Is A.

Step-by-step explanation:

Answer: 1865

Step-by-step explanation:

Given

Claimed strains of virus is 1700

If it is increased by 9.7%

Estimated value can be given by

[tex]\Rightarrow 1700+1700\times 9.7\%\\\Rightarrow 1700(1+0.097)\\\Rightarrow 1700\times 1.097\\\Rightarrow 1864.9\approx 1865[/tex]

Thus, the estimated number is [tex]1865[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

Reflection across the line y = -x is accomplished by the transformation ...

  (x, y) ⇒ (-y, -x)

Then the images of the given points are ...

  A(-1, 1) ⇒ A'(-1, 1) . . . . this point is on the line of reflection, so doesn't move

  B(-2, -1) ⇒ B'(1, 2)

  C(-1, 0) ⇒ C'(0, 1)

Answer:

one solution.. your answer is correct

Step-by-step explanation:

discriminate = 900 - (4*9*25)  = 0

thus only one solution

Answer: D

Step-by-step explanation:

m – 11

A. 11 more than a number ( m+11 )

B. the difference of a number and 11 ( 11/m )

C. the quotient of a number and 11  ( m/11 )

D. 11 less than a number ( m-11 )

Answer:

Hence the 90% confidence interval estimate of the population mean is [tex](79.24 , 97.44)[/tex]

Step-by-step explanation:

Given that,  

Point estimate = sample mean = [tex]\bar x[/tex] = 88.34  

sample standard deviation = s = 19.22  

sample size = n = 14  

Degrees of freedom = df = n - 1 = 13  

Critical value =[tex]t\alpha /2,[/tex] df = 1.771

Margin of error

[tex]E = t\alpha/2,df \times (\frac{s}{\sqrt{n} } )\\= 1.771 \times (19.22 / \sqrt 14)[/tex]  

Margin of error = E = 9.10  

The 90% confidence interval estimate of the population mean is,  

[tex]\bar x - E < \mu < \bar x + E\\\\88.34 - 9.10 < \mu < 88.34 + 9.10\\\\79.24 < \mu < 97.44\\(79.24 , 97.44)[/tex]

Step-by-step explanation:

Given, x = 5

y = 5

= 6(5)^2 +7(5)(5) +3(5)

= 6(25)+7(25) +15

= 150+175 + 15

= 150 + 190

=340

Answer:

x = 12 y = 7

Step-by-step explanation:

6x^2 + 7xy + 3y

6(5)^2+ 7(5) + 7(8)y

6(5+5)+25+35 + 7(8)-7y

60+25+35+ 56-7y

y - 5 = 120 + 35 - 5 (+49y)

sqrt 150 + sqrt 49

x = 12 y = 7

Supplementary angles are those angles which make a sum of 180°.

Complementary angles are those angles which make a sum of 90°.

The supplementary angles are given by the straight lines making angles of 180°.

There are two straight lines CB and DE

The angles DAF and FAE are the two angles making a straight line DE

The angles CAF and FAB are the two angles making a straight line CB

The complementary angles are given by angles formed between the perpendicular lines making angles of 90°.

Angle BAF is formed by angle BAE and angle AEF

Supplementary Angle given by the straight line DE is formed by the angles DAF and FAE.

Complementary Angle BAF is formed by angle BAE and angle AEF.

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Answer:

76 degrees

Step-by-step explanation:

First, we can draw a picture. Two of the sides are 110 feet and 55 feet. In a triangle, the smallest angle is opposite the smallest side and vice versa. Therefore, if I have my triangle arranged in the way shown, the smallest angle of 29 degrees will be opposite of the smallest side of 55 feet.

The law of sines states that a/sinA=b/sinB=c/sinC , with corresponding angles being opposite of its corresponding side. Therefore, we can say that

55 feet/ sin(29 degrees) = 110 / sin(largest angle).

If we say that the largest angle is equal to x, we can say

55 / sin(29°) = 110/sin(x)

multiply both sides by x to remove a denominator

55 * sin(x)/ sin(29°) = 110

multiply both sides by sin(29°) to remove the other denominator

55 * sin(x) = 110 * sin(29°)

divide both sides by 55 to isolate the sin(x)

sin(x) = 110 * sin(29°) / 55

For an angle, if sin(x) = y, we can say that arcsin(y) = x. Therefore, we can say

x = arcsin(110 * sin(29°)/55)

x ≈ 76 degrees

Answer:

Castles made:    N         day 1

                           N - 4    day 2

                           N - 8     day 3

                           N - 12     day 4

                           N - 16      day 5

Total   5 N - 40 = 80

              N = 24  total  castles day 1

Total castles = 24 + 20 + 16 + 12 + 8 = 80

In the largest triangle, the missing side has length

√((11 + 5)² - x ²) = √(256 - x ²)

But it's also the hypotenuse of the triangle with side lengths 11 and y, so that its length can also be written as

√(11² + y ²) = √(121 + y ²)

so that

√(256 - x ²) = √(121 + y ²)

or, by taking the squares of both sides,

256 - x ² = 121 + y ²

y ² = 135 - x ²

In the smallest triangle, you have

5² + y ² = x ²   ==>   x ² = 25 + y ²

Substitute this into the previous equation and solve for y :

y ² = 135 - (25 + y ²)

y ² = 110 - y ²

2y ² = 110

y ² = 55

y = √55

Answer:

1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Assume that there is a 0.905 probability that a passenger with a ticket will show up for the  flight.

This means that [tex]p = 0.905[/tex]

Also assume that the airline sells 200 tickets

This means that [tex]n = 200[/tex]

Question 1:

Exactly, so we can use the P(X = x) formula, to find P(X = 180).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910[/tex]

0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.

Now we have to use the approximation.

Mean and standard deviation:

[tex]\mu = E(X) = np = 200*0.905 = 181[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15[/tex]

Using continuity correction, this is [tex]P(X \leq 180 + 0.5) = P(X \leq 180.5)[/tex], which is the p-value of Z when X = 180.5. Thus

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{180.5 - 181}{4.15}[/tex]

[tex]Z = -0.12[/tex]

[tex]Z = -0.12[/tex] has a p-value of 0.4522.

0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.

Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So

[tex]p + 0.4522 = 1[/tex]

[tex]p = 1 - 0.4522 = 0.5478[/tex]

0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

Answer:

8

Step-by-step explanation:

11 + x = 19

Subtract 11 from each side

11+x -11 = 19-11

x = 8

Answer:

8

Step-by-step explanation:

11 + box = 19

=> box = 19 - 11

.°. box = 8

Answer:

down by 1 unit and left by 4 units

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift left of a units

• If a < 0 then a shift right of a units

Then

g(x) = (x + 4)² - 1

is f(x) shifted down by 1 unit and shifted left by 4 units

Answer:

VERTEX: (0.75,25)    

Step-by-step explanation:

the vertex will be at [-b/2a, f(-b/2a)]

−16x2 + 24x + 16

4(-4x^2 + 6x +4)

a = -4, b=6,c=4

-6/-8 = 3/4

f(3/4) = 25

Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.

He wants to end up with a 44 mL solution, so

x + y = 44 mL

Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain

0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL

of acid.

Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives

0.04x + 0.15 (44 mL - x) = 5.28 mL

0.04x + 6.6 mL - 0.15x = 5.28 mL

1.32 mL = 0.19x

x ≈ 6.95 mL

==>   y ≈ 37.05 mL

Answer:

[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]

Step-by-step explanation:

An arithmetic sequence is of the form:

[tex]A_n = A_{n-1} + d[/tex]

While a geometric sequence is of the form:

[tex]A_n = A_{n-1}*r[/tex]

notice that first, we have a change of sign in our sequence, so we already can discard the arithmetic sequence.

In fact, the pattern is kinda easy to see.

The first term is:

A₁ = 2

the second term is:

A₂ = -10

notice that:

A₂/A₍ = r = -10/2 = -5

The third term is:

A₃ = 50

the quotient between the third term and the second term is:

A₃/A₂ = 50/-10 = -5

Whit this we can already conclude that the n-th term of our sequence will be:

[tex]A_n = A_{n-1}*(-5)[/tex]

Then the summation will be something like:

[tex]\sum_{n = 1} A_n = A_1 + A_2 + A_3 + ... = 2 - 10 + 50 - ...[/tex]

We can write:

[tex]A_n = A_{n-1}*(-5) = (A_{n-2}*(-5))*(-5)) = A_1*(-5)^{n-1} = 2*(-5)^{n-1}[/tex]

Then the summation is just:

[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]

Answer:

The mean of the data is 21.41

Step-by-step explanation:

To find the mean of a data set you must...

Add up all data values to get the sum

Count the number of values in your data set

Divide the sum by the count

The mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

We have a data set:

{21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2}

As we know from the definition of the mean:

The mean can be calculated using the formula:

Mean = sum of the data set/number of the data in the data set

Mean = 471/22

Mean = 21.409  ≈ 21.41

Thus, the mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.

Learn more about the mean here:

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#SPJ5

Answer:

S = 38.4 centimeters.

Step-by-step explanation:

Given the following data;

To find the length of the arc of a circle;

A full circle measures an angle of 360 degrees.

π = 180°

So; Angle, A = 360° = 2π

Therefore, a full circle is equal to 2π in terms of radians (rads).

Also, the circumference (the length of an arc) of a circle is equal to 2πr or Ar.

Mathematically, the length of the arc of a circle is given by the formula;

S = rA

Where;

Substituting into the formula, we have;

S = 12 * 3.2

S = 38.4 centimeters.

Answer:

d 12

Step-by-step explanation:

27-3=24÷3=12 do the mathssssss

Answer:

If it was 11, it would be 33 dollars which is over the total so its not a.

It can't be b because that would be 27, and that would be on just notebooks not magazine

24 is correct because he baught one magazine so + 3 which is the total so it is C

Step-by-step explanation:

Answer:

each movie costs $2.75, each video game costs $6.75

Step-by-step explanation:

x = movies, y = video games

7x + 9y = 80

5x + 3y = 34

simplified to

x = 11/4 , y = 27/4

Answer: 12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Check the picture below

Step-by-step explanation:

The answer is 5/8 + 1/3

Answer = 5*3 /(8*3) +8/24 =23/24

Answer = 23/24

Answer:

2.1n-2.1

Step-by-step explanation:

The increase is

1.10 (n-1)= 1.1n -1.1

Add this to the original amount

(n-1) + 1.1n - 1.1

2.1n-2.1

Answer:

D) 13

[tex]\sqrt{169} = 13[/tex]

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The correct answer is A

Answer:

C. 58ft

Step-by-step explanation:

An imaginary triangle is described here. The hypotenuse is 60, and one of the other sides is 15.

60*60=3600

15*15=225

3600-225=3375

sqrt3375=58.09

round that to get 58ft

Answer:

Speed of canoiest is 10 miles/hour.

Speed of current is 2 miles/hour.

Step-by-step explanation:

Let the speed of canoiest is v and the speed of current is u.

distance = speed x time

24 = (v + u ) x 2

v + u = 12 ..... (1)

Now

24 = (v- u) x 3

v - u = 8 .... (2)

By solving (1) and (2)

2 v = 20

v = 10 miles/hour

u = 2 miles/hour

Answer:

22.5

Step-by-step explanation:

 percent is any number over 100, so 25% is 25 over 100, this means that 25% can be written as:

25100

Now, any number in fractional form (a number over a number) is the same as division so 25% can also be written as a decimal, we just move the decimal point 2 places to the right of 25, like this:

25100=0.25

Now we have two ways that we can solve this problem! I'll start with the fractional method of solving.