Can someone help me solve this? Thanks!

Can Someone Help Me Solve This? Thanks!

Answers

Answer 1

9514 1404 393

Answer:

  p(x) = x³ -3x²+4x -2

Step-by-step explanation:

When the polynomial has real coefficients, the complex roots come in conjugate pairs. You are given one root as 1+i, so there is another that is 1-i.

Each root r gives rise to a factor (x -r). Then the three roots tell you the factorization is ...

  p(x) = (x -1)(x -(1+i))(x -(1-i))

The last two factors can be recognized as the factors of the difference of squares:

  ((x -1) +i)((x -1) -i) = (x -1)² -i²

  = (x² -2x +1) -(-1) = x² -2x +2

Now the whole polynomial can be seen to be ...

  p(x) = (x -1)(x² -2x +2) = x(x² -2x +2) -1(x² -2x +2)

  p(x) = x³ -2x² +2x -x² +2x -2 . . . . eliminate parentheses

  p(x) = x³ -3x²+4x -2


Related Questions

If a business borrows $12,600 and repays $23,940 in 5 years, what is the simple interest rate? ​

Answers

Answer:

18%

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Simple Interest Rate Formula: A = P(1 + rt)

P is principle amountr is ratet is time

Step-by-step explanation:

Step 1: Define

Identify variables

P = 12600

A = 23940

t = 5

Step 2: Solve for r

Substitute in variables [Simple Interest Rate Formula]:                                 23940 = 12600(1 + 5r)[Division Property of Equality] Divide 12600 on both sides:                         19/10 = 1 + 5r[Subtraction Property of Equality] Subtract 1 on both sides:                         9/10 = 5r[Division Property of Equality] Divide 5 on both sides:                                  9/50 = rRewrite:                                                                                                             r = 9/50Evaluate:                                                                                                           r = 0.18Convert:                                                                                                            r = 18%

Land costing $140,000 was sold for $173,000 cash. The gain on the sale was reported on the income statement as other income. On the statement of cash flows, what amount should be reported as an investing activity from the sale of land?

Answers

Answer:

Amount should be reported in investing activities = $173,000

Step-by-step explanation:

Given:

Amount of land costing = $140,000

Sold amount of land = $173,000

Find:

Amount should be reported in investing activities

Computation:

Amount should be reported in investing activities = $173,000

The cash flow statement shows how much money is coming in and going out. The whole amount of cash received, which is 173,000 dollars, will be recorded as proceeds from the sale of land in the investment activity. As a result, the right answer is 173,000.

What is the value of q?
2/5
2/14

Answers

Answer:

2√14 prob I'm not 100% sure

2) There are 40 boys and 16 girls in a class of students. What is the ratio of girls to students?

Answers

Add boys and girls together for total students:

40 + 16 = 56 total students

Girls to total students is 16/56

Divide both numbers by 8 to get 2/7

The ratio is 2/7

[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]

There are 40 boys and 16 girls in a class of students. ⠀⠀⠀⠀

[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]

⠀What is the ratio of girls to students?⠀⠀⠀

[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]

In a class,

boys=40

girls =16

So,

The students of the class =

boys+girls 40+1656

According to the question,

we have to find the ratio of girls to the total students

ratio=[tex]\sf{\dfrac{girls}{students} }[/tex]

ratio=[tex]\sf{\dfrac{16}{56} }[/tex]

ratio=[tex]\sf{\dfrac{\cancel{16}}{\cancel{56}} }[/tex]

ratio=[tex]\sf{\dfrac{2}{7} }[/tex]

ratio=[tex]\sf{2:7 }[/tex]

⠀⠀⠀⠀

[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]

⠀⠀⠀⠀

Hence,the ratio of girls to students is 2:7

⠀⠀⠀⠀

3p + 2q = 14
10p + 6q = 44
What is p and what is q

Answers

Answer:

p = 2 ; q = 4

Step-by-step explanation:

Given tbe equation :

3p + 2q = 14 - - - (1)

10p + 6q = 44 - - -(2)

What is p and what is q

This is a simultaneous equation ; using elimination method :

Multiply (1) by 6 and (2) by 2

18p + 12q = 84 - - - - (3)

20p + 12q = 88 - - - (4)

Subtract (3) and (4)

-2p = - 4

p = 4/2

p = 2

Put p = 2 in (1)

3p + 2q = 14

3(2) + 2q = 14

6 + 2q = 14

2q = 14 - 6

2q = 8

q = 8/2

q = 4

p = 2 ; q = 4

To test for the significance of a regression model involving 3 independent variables and 51 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.

Answers

Answer:

numerator degree of freedom = 3

Denominator degree of freedom = 47

Step-by-step explanation:

The numerator degree of freedom is given by :

p - 1 ; where p = number of predictors ;

p = number of independent variables + 1

Number of independent variables = 3

p = 3 + 1 = 4

Numerator degree of freedom = p - 1 = 4 - 1 = 3

The denominator degree of freedom = n - p ; where n = number of observations

Number of observations, n = 51

Denominator degree of freedom = n - p = 51 - 4 = 47

uppose that the walking step lengths of adult males are normally distributed with a mean of 2.8 feet and a standard deviation of 0.2 feet. A sample of 76 men’s step lengths is taken. Step 1 of 2 : Find the probability that an individual man’s step length is less than 2.5 feet. Round your answer to 4 decimal places, if necessary.

Answers

Answer:

.0668

Step-by-step explanation:

Formula:

z=(x-average)/standard deviation

(2.5-2.8)/.2= -1.5

Go to a ztable and find the value for 1.5  (.9332) and take the compliment of this (we can do this because the normal distribution is symmetrical)

1-.9332= .0668

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7 is:_________
a. 0.0069
b. 0.000
c. 0.4931
d. 0.9931

Answers

Answer:

0.0069

Step-by-step explanation:

According to the Question,

Given That, X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7

We have, μ=22 , σ= 5 , P(X<9.7)=Area to the left of 9.7.

Z = (x-μ)/σ

Z = (9.7-22) / 5 ⇒ -2.46

Thus,

P(X<9.7)=P(Z < -2.46) ⇒ 0.0069 (From z-table)

An automobile purchased for ​$38000 is worth ​$2300 after 7 years. Assuming that the​ car's value depreciated steadily from year to​ year, what was it worth at the end of the third​ year?
The value 3 years after it was purchased is

Answers

Answer:

11422.46

Step-by-step

2300=38000x⁷

x=.669872323

38000*.669872323³=11422.4614

Pls answer this last question in full method​

Answers

Answer:

if the sum of two angles is 90° they are said to be complementary

If one angle is x

the other should be (90 - x)°

so the complementary angle of x is (90 - x)

For any real number √a²
a
- |al
lal.
-a

Answers

Answer:

|a|

Step-by-step explanation:

For any positive or negative a, when you square it, the answer is positive.

The square root symbol means the principal square root. For a positive number, the principal square root is positive. To make sure the square root is always non-negative, use absolute value.

Answer: |a|

The graphs below have the same shape. Complete the equation of the blue
graph. Enter exponents using the caret (-1); for example, enter xas x^3. Do
not include "G(x) =" in your answer.

Answers

Step-by-step explanation:

The graphs below have the same shape. What is the equation of the blue graph? A. G(x) = (x + 3)^3 B. G(x) = x^3 + 3 C. G(x) = x^3 - 3 D.

G(x) = (x - 3)^3

The function of the blue curve in the graph is g(x)=(x+3)²+1.

What is the function?

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=x².

In the image, we have two functions, the red one is a parent function, which is the most basic version of it. The blue function is a transformation of the red one, that is, it was only moved to the left and upwards.

From the graph, we can see that the blue function was moved to the left and upwards, that means we have to sum units to x and f(x).

So, g(x)=(x+3)²+1

Therefore, the function of the blue curve in the graph is g(x)=(x+3)²+1.

To learn more about the function visit:

https://brainly.com/question/28303908.

#SPJ7

Find the length of CE

Answers

Answer:

C. 37.8 units

Step-by-step explanation:

ED = 17/ cos(38°) = 17 / 0.7880 = 21.6 units

DF = 17× tan (38°) = 17× 0.7813 = 13.3 units

CD = 10/13.3 × 21.6 = 16.2 units

so, the length of CE = 21.6+16.2 = 37.8 units

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened?

Answers

Answer:

Lf(x) = Lg(x) = Lh(x) =  1 - 2x

value of the functions and their derivative are the same at x = 0

Step-by-step explanation:

Given :

f(x) = (x − 1)^2,  

g(x) = e^−2x ,  

h(x) = 1 + ln(1 − 2x).

a) Determine Linearization of  f, g and h  at a = 0

L(x) = f (a) + f'(a) (x-a)  ( linearization of f at a )

for f(x) = (x − 1)^2  

f'(x ) = 2( x - 1 )

at x = 0

f' = -2  

hence the Linearization at a = 0

Lf (x) = f(0) + f'(0) ( x - 0 )

Lf (x) = 1 -2 ( x - 0 ) = 1 - 2x

For g(x) = e^−2x

g'(x) = -2e^-2x

at x = 0

g(0) = 1

g'(0) = -2e^0 = -2

hence linearization at a = 0

Lg(x) = g ( 0 ) + g' (0) (x - 0 )

Lg(x) = 1 - 2x

For h(x) = 1 + ln(1 − 2x).

h'(x) =  -2 / ( 1 - 2x )

at x = 0

h(0) = 1

h'(0) = -2

hence linearization at a = 0

Lh(x) = h(0) + h'(0) (x-0)

        = 1 - 2x

Observation and reason

The Linearization is the same in every function i.e. Lf(x) = Lg(x) = Lh(x) this is because the value of the functions and their derivative are the same at x = 0

an amount of R3000, Is invested to three years at simple interest rate and it earned R905 interest. determine the simple interest rate at which the money was invested​

Answers

Answer:

Step-by-step explanation:

P=R3000.00

T=3 years

SI=R905

SI=P\times R\times T\\R905=R3000\times \frac{r}{100}\times 3SI=P×R×T

R905=R3000×  

100

r

×3

R905=\frac{R9000r}{100}R905=  

100

R9000r

 

R905=\frac{R905}{R90}R905=  

R90

R905

 

r=\frac{R905}{R90.}r=  

R90.

R905

 

r=10.06\%r=10.06%

ASK YOUR TEACHER A 12-sided die can be made from a geometric solid called dodecahedron. Assume that a fair dodecahedron is rolled. (a) What is the probability of getting a number less than 10 on a single roll

Answers

9514 1404 393

Answer:

  3/4

Step-by-step explanation:

Assuming the faces are numbered 1 to 12, there are 9 faces with values less than 10. Since the outcomes are equally probable and mutually exclusive, the probability of any of the 9 is the sum of their individual probabilities:

  P(n < 10) = 9×1/12 = 9/12 = 3/4

Suppose f(x) = x2. What is the graph of g(x)= 1/4 f(x)?

NEWD HELP ASAP!

Answers

Answer:

g(x) =1/4 x²

The choose (1)

first drawing

What is the inverse of function f? f(x)=10/9+11

Answers

Answer:

Option D is answer.

Step-by-step explanation:

Hey there!

Given;

f(x) = 10/9 X + 11

Let f(X) be "y".

y = (10/9) X + 11

Interchange "X" and "y".

x = (10/9) y + 11

or, 9x = 10y + 99

or, y = (9x-99)/10

Therefore, f'(X) = (9x-99)/10.

Hope it helps!

Solve the equation 2sin^2(x) = 1 for x ∈ [-π,π], expressing all solutions as exact values. please help its urgent !!

Answers

Answer:

2sin.2(x) sd s

Step-by-step explanation:

Help if possible, thanks

Answers

Answer:

C

Step-by-step explanation:

Sara's speed is 10mph while Bob is 8mph

The third option is correct
Sara did 10
Bob did 8
The difference is 2
Hope that helped *smiles*

Given the function
Calculate the following values:
f( - 1) =
f(0)
f(2)=

Answers

-1 is less than 0, so you use the first equation:

3(-1) +2 = -3+2 = -1

f(-1) = -1

For 0 use the 2nd equation:

3(0) + 4 = 0+4 = 4

f(0) = 4

For 2 use the 2nd equation:

3(2) + 4 = 6+4 = 10

f(2) = 10

Write an equation for the function that includes the following points (2,32) and (3,64)

Answers

Answer:

32 = a*2 +b

64 = a*3 + b

Then 32 = a

32 = 32*2 +b

b = - 32

So

Y = 32a - 32

Is the equation

A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 82 months with a standard deviation of 7 months. If the claim is true, what is the probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors

Answers

Answer:

0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

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

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean life of 82 months with a standard deviation of 7 months.

This means that [tex]\mu = 82, \sigma = 7[/tex]

Sample of 71

This means that [tex]n = 71, s = \frac{7}{\sqrt{71}}[/tex]

What is the probability that the mean monitor life would be greater than 83.8 months?

1 subtracted by the p-value of Z when X = 83.8. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{83.8 - 82}{\frac{7}{\sqrt{71}}}[/tex]

[tex]Z = 2.17[/tex]

[tex]Z = 2.17[/tex] has a p-value of 0.985.

1 - 0.985 = 0.015

0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors

Joe bikes at the speed of 30 km/h from his home toward his work. If Joe's wife leaves home 5 mins later by car, how fast should she drive in order to overtake him in 10 minutes.

Answers

Answer:

Joe's wife must drive at a rate of 45km/hour.

Step-by-step explanation:

We are given that Joe leaves home and bikes at a speed of 30km/hour. Joe's wife leaves home five minutes later by car, and we want to determine her speed in order for her to catch up to Joe in 10 minutes.

Since Joe bikes at a speed of 30km/hour, he bikes at the equivalent rate of 0.5km/min.

Then after five minutes, when his wife leaves, Joe is 5(0.5) or 2.5 km from the house. He will still be traveling at a rate of 0.5km/min, so his distance from the house can be given by:

[tex]2.5+0.5t[/tex]

Where t represents the time in minutes after his wife left the house.

And since we want to catch up in 10 minutes, Joe's distance from the house 10 minutes after his wife left will be:

[tex]2.5+0.5(10)=7.5\text{ km}[/tex]

Let s represent the wife's speed in km/min. So, her speed times 10 minutes must total 7.5 km:

[tex]10s=7.5[/tex]

Solve for s:

[tex]\displaystye s=0.75\text{ km/min}[/tex]

Thus, Joe's wife must drive at a rate of 0.75km/min, or 45km/hour.

rotation 180 degrees about the origin.​

Answers

Answer:

Take the picture you uploaded.

Click the rotate button twice.

Done

what is the measure of an angle if it is 120 less than 5 times its own complement

Answers

Answer:

The measure of the angle is 55º.

Step-by-step explanation:

Complement of angle x:

If two angles are complementary, the sum of their measures is of 90º. Thus, the complement of an angle x is 90 - x.

In this question:

Angle is 120 less than 5 times its own complement, so:

[tex]x = 5(90 - x) - 120[/tex]

We have to solve for x

[tex]x = 450 - 5x - 120[/tex]

[tex]6x = 330[/tex]

[tex]x = \frac{330}{6}[/tex]

[tex]x = 55[/tex]

The measure of the angle is 55º.

the average of two number is xy.if one number is x the other i​

Answers

Answer:

z = (2xy-x)

Step-by-step explanation:

Let the first number be x and the other number is z.

According to question,

The average of two number is xy i.e.

[tex]\dfrac{x+z}{2}=xy\\\\x+z=2xy\\\\z=2xy-x[/tex]

So, the value of z is (2xy-x) i.e. the other number is (2xy-x).

Does the expression represents a positive or negative 3(-2 1/3)

Answers

Answer:

Positive

Step-by-step explanation:

This is an equation, with distribution in it. The number on the outside is positive, and the one inside is negative. Furthermore, since the number on the outside is larger than the one inside, the outcome will be positive.

Answer:

positive

Step-by-step explanation:

when both positive and negative will multiply then will  makes negatives. so negative is correct option.

help me with 2 excersise , thanks a lot

Answers

Answer: I do not know what you mean, but you could do burpees, and sit ups.

Christian and Tanae both leave Disneyland at the same time. Christian travels north at 65 mph. Tanae travels south at 55 mph. How long will it take them to be 540 miles apart? Which of the following equations would you use to solve this word problem?
65t + 55(t − 1) = 540.
65t + 55t = 540.
65t + 55(t + 1) = 540.
None of these choices are correct.

Answers

Answer:

Step-by-step explanation:

B looks like it would work.

You add speeds * time when you are travelling in opposite directions.

I don't know why you would add or subtract 1 as in A and C

120 * t = 540

t = 540/120

t = 4.5 hours.

So after 4.5 hours they are 540 miles apart.

Answer:

b

Step-by-step explanation:

Other Questions
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