What is the complete factorization of the polynomial function over the set of complex numbers?
f(x)=x3−5x2+4x−20
Enter your answer in the box.
Answer:
[tex]x^3-5x^2+4x-20=(x-5)(x+2\mathbf{i})(x-2\mathbf{i})[/tex]
Step-by-step explanation:
Factorization of polynomials
Factor:
[tex]f(x)=x^3-5x^2+4x-20[/tex]
There are several techniques to factor polynomials. We'll use algebraic manipulation and common factor:
Separate in groups:
[tex](x^3-5x^2)+(4x-20)[/tex]
Factor out 4 from 4x-20:
[tex]=(x^3-5x^2)+4(x-5)[/tex]
Factor out [tex]x^2[/tex] from [tex]x^3-5x^2[/tex]
[tex]=x^2(x-5)+4(x-5)[/tex]
Factor out x-5:
[tex]=(x-5)(x^2+4)[/tex]
The roots of
[tex]x^2+4=0[/tex]
Are two complex numbers:
[tex]x=2\mathbf{i}, x=-2\mathbf{i}[/tex]
The complete factorization is:
[tex]\boxed{x^3-5x^2+4x-20=(x-5)(x+2\mathbf{i})(x-2\mathbf{i})}[/tex]
of
Simplify.
1.
4^4
2^5
Answer:
4x4x4x4, 256
2x2x2x2x2, 32
Step-by-step explanation:
can i have brainlies plzz
Rona filled out this information on her monthly statement. Find Rona's revised statement balance. Does her account reconcile?
Checking Account Summary
Ending Balance
$ 72571
Deposits
+ $610.00
Checks Outstanding - $ 471.19
Revised Statement Balance
Check Register Balance $ 864.52
Answer:
Revised statement balance=$ 864.52
Yes Rona's is account reconcile
Step-by-step explanation:
Calculation to Find Rona's revised statement balance
Using this formula
Revised statement balance=Ending balance+Deposits-Checks Outstanding
Let plug in the formula
Revised statement balance=$ 725.71+$610.00-$ 471.19
Revised statement balance=$ 864.52
Based on the above calculation the Revised statement balance of the amount of $ 864.52 is equal to the balance from checkbook which simply means that Rona's ACCOUNT is RECONCILE
Point P' is the image of P(-2,4) under a translation by 2 units to the left and 5 units down.
Answer:
(-4,-1)
X value: -2 - 2 = -4.
Y value: 4 - 5 = -1
find the scale factor of the dilation
Step-by-step explanation:
The scale factor of the dilation determines how much larger or smaller the image will be (compared to the original object). when the absolute value of the scale factor is greater than one, an expansion occurs.
Which student correctly translated the phrase "twice the sum of a number cubed and nine" and evaluated it for r = 3?
Antonio's work Jessica's work Maria's work Mark's work
2(r + 9)
2(r+ 9) 2+p3 +9 2 + 3r + 9
2(3 + 9)
2(3' + 9)
2 + 3² +9 2 + 3(3) +9
O
2(9+ 9)
2(27+ 9) 2 + 27 + 9
2 + 9 + 9
2(18)
2(36)
29 + 9
11 + 9
36
(72
38
20
O
Answer:
answer is B
Step-by-step explanation:
i did it in e2022
person above me gets brainliest
The mapping diagram shows a functional relationship.
Complete the statement.
f(3) is
Domain
Range
0
3
Tomos
-1
9
9
Answer:
its -1
Step-by-step explanation:
cuz
Answer: it’s -1
Step-by-step explanation:
I just did the test
what is vertex of the graph of the function below y=x^2-10x+21
Answer:
(-4,5)
Step-by-step explanation:
Answer:
Step-by-step explanation:
it is (5,-4) the first answer is backwards
Which inequality is true?
Answer:
2 1/3 > 2 1/6
Step-by-step explanation:
2.33 > 2.17 True
How do you know if it is inequality or not w/ fraction?
An equation or an inequality that contains at least one variable is called an open sentence. When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.
To solve an inequality using the following steps:
1) Eliminate fractions by multiplying all terms by the least common denominator of all fractions.
2) Simplify by combining like terms on each side of the inequality.
3) Add or subtract quantities to obtain the unknown on one side and the numbers on the other.
Answer:
B
Step-by-step explanation:
I did the quiz
A new television set was recently purchased for the common room in a Residence Hall for $408.00 including tax. If the tax rate is 2% , find the price of the television set before taxes.
Answer:
399.84
Step-by-step explanation:
408.00 x .98 (2% reduction from 100) = 399.84
(2x^4 + 3x^3 – 5x - 19)+(x^2 + 1)
Answer:
2x 4 +3x 3 +x 2 −5x−18
Step-by-step explanation:
what is the sum of the place values of the number 6,453
Answer:
Thousands Hundreds Tens Ones6 4 5 3
Step-by-step explanation:
Number x Multiplier = Value6 x 1,000 6,000
4 x 100 400
5 x 10 50
3 x 1 3
Add up all of the values and you get 6,453.
A contractor purchases ceramic tile to remodel a kitchen. Each tile costs $4, and the adhesive and grouting material costs $17.82. If the contractor is charged a total of $581.82, how many ceramic tiles did the contractor purchase?
Answer:
The answer is 145 ceramic tiles
Step-by-step explanation:
$4 Divided by $581.82 = 145.455
Use the square to answer the question.
5 in.
What is the perimeter of the square?
A 10 inches
B. 15 Inches
ОО
O c. 20 Inches
O D. 25 inches
Answer:
20 inches
Step-by-step explanation:
The correct answer is 20 because there is 4 sides and each side is worth of the length 5 so 5 times 4 - is what 20 . So the answer 20 is right . Hope this helps, you are welcome.
Evaluate. 68.14 + 0.0007
Answer:
68.1407 us the answer
Step-by-step explanation:
Just add
w = 8.75h
What is an impossible value for h?
Answer:
h = 0.1 142857 w
Step-by-step explanation:
Answer:
hayy
Step-by-step explanation:
Solve 12-5x-4kx=y for x
Answer:
x = - y-12/5+4k
Step-by-step explanation:
Solve 12-5x-4kx=y for x
12-5x-4kx = y for x
substract 12 from both side
-5x-4kx = y-12
Factor of -5x-4kx = -x(5+4k)
-x(5+4k) = y-12
Solve for x
-x = y-12/(5+4k)
Therefore x = - y-12/5+4k
5/6 divide (-13/7)
what does this equal?
Answer:
i think -35/78
Step-by-step explanation:
What are the values of x and y if this equation is true?
22(x + yi) + (28 + 4i) 72 – 62i
Answer:
x = 2
y = -3
Step-by-step explanation:
The given equation is,
22(x + yi) + (28 + 4i) = 72 - 62i
By solving this equation further,
22x + 22yi + 28 + 4i = 72 - 62i
(22x + 28) + (22y + 4)i = 72 - 62i
Now both the sides of the equation is in the form of complex number,
By comparing real and imaginary parts given on both the sides,
22x + 28 = 72
22x = 72 - 28
22x = 44
x = 2
22y + 4 = -62
22y = -62 - 4
22y = -66
y = -3
Therefore, x = 2 and y = -3 are the values for which the given equation is true.
Convert
40.7% to fraction
Answer:
Decimal Fraction Percentage
0.407 407/1000 40.7
Step-by-step explanation:
The equation p = 3.25b can be used to find the price, p, in dollars, of b pounds of blueberries at a particular supermarket. Each of the tables gives the prices of various pounds of blueberries at a different supermarket. Which of these tables represents blueberries that are more expensive than those represented by the equation? Select all that apply.
Answer:
Table C, Table D, Table E
Step-by-step explanation:
See attachment for tables
Given
[tex]p = 3.25b[/tex]
Required
Which of the tables is more expensive than the given function
To answer this question, we simply determine the equation of each table and then compare the equation with [tex]p = 3.25b[/tex]
Table A:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (1,2.75)[/tex]
[tex](b_2,p_2) = (4,11)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{11 - 2.75}{4 - 1}[/tex]
[tex]m = \frac{8.25}{3}[/tex]
[tex]m = 2.75[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 2.75 = 2.75(b-1)[/tex]
[tex]p - 2.75 = 2.75b-2.75[/tex]
[tex]p = 2.75b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]2.75 < 3.25[/tex]
Hence:
This equation is less expensive than [tex]p = 3.25b[/tex]
Table B:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (1.5,3.75)[/tex]
[tex](b_2,p_2) = (6,15)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{15 - 3.75}{6 - 1.5}[/tex]
[tex]m = \frac{11.25}{4.5}[/tex]
[tex]m = 2.5[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 3.75 = 2.5(b-1.5)[/tex]
[tex]p - 3.75 = 2.5b- 3.75[/tex]
[tex]p = 2.5b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]2.5 < 3.25[/tex]
Hence:
This equation is also less expensive than [tex]p = 3.25b[/tex]
Table C:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (2,7)[/tex]
[tex](b_2,p_2) = (4,14)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{14 - 7}{4 - 2}[/tex]
[tex]m = \frac{7}{2}[/tex]
[tex]m = 3.5[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 7 = 3.5(b - 2)[/tex]
[tex]p - 7 = 3.5b - 7[/tex]
[tex]p = 3.5b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3.5 > 3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table D:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (2.5,10)[/tex]
[tex](b_2,p_2) = (5,20)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{20 - 10}{5 - 2.5}[/tex]
[tex]m = \frac{10}{2.5}[/tex]
[tex]m = 4[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 10 = 4(b - 2.5)[/tex]
[tex]p - 10 = 4b - 10[/tex]
[tex]p = 4b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]4 > 3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table E:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (6, 22.5)[/tex]
[tex](b_2,p_2) = (12,45)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{45 - 22.5}{12 - 6}[/tex]
[tex]m = \frac{22.5}{6}[/tex]
[tex]m = 3.75[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p - 22.5 = 3.75(b - 6)[/tex]
[tex]p - 22.5 = 3.75b - 22.5[/tex]
[tex]p = 3.75b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3.75>3.25[/tex]
Hence:
This equation is more expensive than [tex]p = 3.25b[/tex]
Table F:
Consider two corresponding points in the table, we have:
[tex](b_1,p_1) = (7, 21)[/tex]
[tex](b_2,p_2) = (14,42)[/tex]
Determine the slope
[tex]m = \frac{p_2 - p_1}{b_2 - b_1}[/tex]
[tex]m = \frac{42 - 21}{14 - 7}[/tex]
[tex]m = \frac{21}{7}[/tex]
[tex]m = 3[/tex]
The equation is determined as follows:
[tex]p - p_1 = m(b-b_1)[/tex]
[tex]p -21 =3(b -7)[/tex]
[tex]p -21 =3b -21[/tex]
[tex]p = 3b[/tex]
Comparing this equation to [tex]p = 3.25b[/tex], we have that:
[tex]3 < 3.25[/tex]
Hence:
This equation is less expensive than [tex]p = 3.25b[/tex]
A ball is thrown directly upward from a height of 3 ft with an initial velocity of 20 ft/sec. The function s(t)=-16t^2+20t+3 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.
Answer:
#1: s'(t)= -32t+20
#2: -32t+20=0
t=2/3
#3: s(2/3)=-16(2/3)^2+20(2/3)+3=83/9
Step-by-step explanation:
first find the derivative of the original funtion #1
set the equation equal to 0 because when s't=0 is the maximum height
put the t at highest point into the funtion to solve for distance
Hayleigh took a long multiple-choice, end-of-year math test. The ratio of the number of problems Hayleigh got incorrect to the number of problems she got correct is 2:9. If Hayleigh missed 8 questions, how many did she get correct?
Answer:
36
Step-by-step explanation:
If sh missed 8, then 8/2 is 4, 4x9 is 36
You are given a set of data with a mean of 50 and standard deviation of 8. Using the normal curve, give an example of an outlier and explain why.
Answer:
Anything less than 26, and greater than 74.
Step-by-step explanation:
In normal distribution, the outlier is more than e ≈ 2.72 standard deviations above quartile 3, and e standard deviations below quartile 1. These quartiles are divisions that make up what is known as the innerquartile range(IQR). Which defines the variability of a data set given by IQR = Q3-Q1.
Given that the mean of this data is 50, and the standard deviation is 8.
Our outliers are anything less than 26, and anything greater than 74. Since outliers are anything outside the mean plus and minus the standard deviation times 3
[tex] outliers :/ = :/ mean :/ \pm [/tex]
Please help with the middle question!!
Answer: D) The relation R is a function because for each input there is exactly one output
There's not much else to say other than what choice D already does. Visually we can use the vertical line test to confirm if we have a function or not. If we can pass a single vertical line through more than one point on a curve, then the curve isn't a function. The graph is said to have failed the vertical line test. Otherwise, the relation passes the vertical line test and we have a function.
13 and 5/8 plus 7/8 please answer quickly
13 5/8 + 7/8 = 14 1/2
5/8 + 7/8 = 1 4/8 = 1 1/2
1 1/2 + 13 = 14 1/2
Evaluate -2 x 2y , if x = -3 and y = -1.
Answer:
-12
Step-by-step explanation:
hope this helps
Answer:
-12
Step-by-step explanation:
i did math
Marrisa went to target to buy a sweater. She was exited that all the sweaters were 40% off She picked out a sweater with the original price of $28.99 How much money did marrissa save? How much did she pay for the sweater?
Please helpppp
In a group of 90 seventh
graders, 80% like hot chocolate.
How many students do not like
hot chocolate?
Answer: 18
Step-by-step explanation:
90 / 10 = 9 (10%)
9 x 8 = 72 (80%)
90 - 72 = 18 (20%)
Write the expression in radical form. (x + 1) 2/3