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Find all solutions of the equation algebraically. Check your solutions. (Enter your answers as a comma-separated list x^4-7x^2-144=0

Answers

Answer 1

Answer:

Answer:

The solutions are: $x=4,\:x=-4,\:x=3i,\:x=-3i$

Step-by-step explanation:

Consider the provided equation.

$x^4-7x^2-144=0$

Substitute $u=x^2\mathrm{\:and\:}u^2=x^4$

$u^2-7u-144=0$

$u^2-16u+9u-144=0$

$(u-16)(u+9)=0$

$u=16,\:u=-9$

Substitute back $\:u=x^2$ and solve for x.

$x^2=16\nx=√(16)\n \quad x=4,\:x=-4$

$x^2=-9\nx=√(-9)\n \quad x=3i,\:x=-3i$

Hence, the solutions are: $x=4,\:x=-4,\:x=3i,\:x=-3i$

Check:

Substitute x=4 in provided equation.

$4^4-7(4)^2-144=0$

$256-112-144=0$

$0=0$

Which is true.

Substitute x=-4 in provided equation.

$(-4)^4-7(-4)^2-144=0$

$256-112-144=0$

$0=0$

Which is true.

Substitute x=3i in provided equation.

$(3i)^4-7(3i)^2-144=0$

$81+63-144=0$

$0=0$

Which is true.

Substitute x=-3i in provided equation.

$(-3i)^4-7(-3i)^2-144=0$

$81+63-144=0$

$0=0$

Which is true.

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Nikki makes $9.50 an hour working at Current Electronics She plans to buy a DVD recorder that costs $269.60. Write and solve an inequalitydescribing how many hours h Nikki will have to work to be able to buy the DVD recorderA. 269,60 -- 29.56; 28 hoursB. 9.50h 2 269,60; 29 hoursC. 269.60 + h 29.50; 31 hoursD. 269.60 2 9,50; 30 hours
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During the period of time that a local university takes phone-in registrations, calls come inat the rate of one every two minutes.
a. What is the expected number of calls in one hour?
b. What is the probability of three calls in five minutes?
c. What is the probability of no calls in a five-minute period?

Answers

Answer:

a) The expected number of calls in one hour is 30.

b) There is a 21.38% probability of three calls in five minutes.

c) There is an 8.2% probability of no calls in a five minute period.

Step-by-step explanation:

In problems that we only have the mean during a time period can be solved by the Poisson probability distribution.

Poisson probability distribution

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

a. What is the expected number of calls in one hour?

Calls come in at the rate of one each two minutes. There are 60 minutes in one hour. This means that the expected number of calls in one hour is 30.

b. What is the probability of three calls in five minutes?

Calls come in at the rate of one each two minutes. So in five minutes, 2.5 calls are expected, which means that $\mu = 2.5$ . We want to find P(X = 3).

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

$P(X = 3) = (e^(-2.5)*(2.5)^(3))/((3)!) = 0.2138$

There is a 21.38% probability of three calls in five minutes.

c. What is the probability of no calls in a five-minute period?

This is P(X = 0) with $\mu = 2.5$ .

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

$P(X = 0) = (e^(-2.5)*(2.5)^(0))/((0)!) = 0.0820$

There is an 8.2% probability of no calls in a five minute period.

Consider each equation and solution. Which solution is NOT correct?

Answers

Answer:

D, or the last answer

Step-by-step explanation:

First, plugin the value of y into the equation, resulting in 12 - 2(-2) = 8.

Second, Simplify as much as you can on the left hand side of the equation, resulting in 12 - (-4), and because of the double negative rule, those two negatives become a plus. 16

Lastly, see if the two sides are equal or not equal. 16 is NOT equal to 8. That means D is your answer.

Create a polygon JKLMNOPQ that is a dilation of polygon ABCDEFGH with a scale factor of 3 about the origin

Answers

The dilated polygon and polygon are created. And the scale factor of the polygon STUVWXYZ to JKLMNOPQ will be 9.

What is dilation?

Dilation is the methodology of expanding the dimensions of an object without impacting its appearance.

The coordinate of the polygon ABCDEFGH is given as,

(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)

a) If the scale factor is 3, then the coordinate of the polygon JKLMNOPQ is given as,

⇒ 3 [(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)]

⇒ (9, -9), (12, -12), (15, -9), (24, -18), (30, -12), (27, -9), (24, -12), (15, -3)

b) If the scale factor is 1/3, then the coordinate of the polygon STUVWXYZ is given as,

⇒ 1/3 x [(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)]

⇒ (1, -1), (4/3, -4/3), (5/3, -1), (8/3, -2), (10/3, -4/3), (3, -1), (8/3, -4/3), (5/3, -1/3)

c) The polygon JKLMNOPQ and STUVWXYZ are similar. Then the scale factor is given as,

Scale factor = 9/1

Scale factor = 9

The diagram is given below.

More about the dilation link is given below.

brainly.com/question/2856466

#SPJ9

What are 567 times 3

Answers

Answer:

1,701

Step-by-step explanation:

the answer is 1,701 :D

There are 11 students in your class. In how many ways a group of 4 students will beselected to participate in a social campaign such that you will always be included in
the group to lead the event?

Answers

Answer:

Step-by-step explanation:

If you are always included to lead, that leaves 10 students to choose from.

If all that is important is being selected, then there are 10C3 = 120 ways to choose them.

If each selection has a unique duty, then there are 10P3 = 720 ways to assign them their jobs.

Answer: 10P3=720

Step-by-step explanation:

Writing on the SAT Exam It has been found that scores on the Writing portion of the SAT (Scholastic Aptitude Test) exam are normally distributed with mean 484 and standard deviation 115. Use the normal distribution to answer the following questions. Required:
a. What is the estimated percentile for a student who scores 425 on Writing?
b. What is the approximate score for a student who is at the 87th percentile for Writing?

Answers

Answer:

a) The estimated percentile for a student who scores 425 on Writing is the 30.5th percentile.

b) The approximate score for a student who is at the 87th percentile for Writing is 613.5.

Step-by-step explanation:

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

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

$Z = (X - \mu)/(\sigma)$

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.

In this question, we have that:

$\mu = 484, \sigma = 115$