The polynomial f(x) of degree 3 with real coefficients and the given zeros 2 and 1-2i is f(x) = (x - 2)(x - (1 - 2i))(x - (1 + 2i)).
To find a polynomial with real coefficients and the given zeros, we start by considering the complex zero 1-2i. Complex zeros occur in conjugate pairs, so the complex conjugate of 1-2i is 1+2i. Thus, the factors involving the complex zeros are (x - (1 - 2i))(x - (1 + 2i)).
Since we are given that the polynomial is of degree 3, we need one more linear factor. The other zero is 2, so the corresponding factor is (x - 2).
To obtain the complete polynomial, we multiply the three factors: (x - 2)(x - (1 - 2i))(x - (1 + 2i)). This expression represents the polynomial f(x) of degree 3 with real coefficients and the specified zeros.
Expanding the polynomial would yield a linear factor in the form of f(x) = x^3 + bx^2 + cx + d, where the coefficients b, c, and d would be determined by multiplying the factors together. However, the original factorized form (x - 2)(x - (1 - 2i))(x - (1 + 2i)) is sufficient to represent the polynomial with the given zeros.
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The graph shows a function. Is the function linker or non linear?
Answer:
It is linear since it is a straight line.
01:53:18
Which inequality represents the sentence below?
Two more than a number is less than 14.
2 + n less-than-or-equal-to 14
2 + n less-than 14
2 + n greater-than-or-equal-to 14
2 + n greater-than 14
Answer: It's the second option
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
edge 2020-2021 <3
-30-0.6k
what does k equal?
Answer:
K would equal to:
K= 50
Hope that helps! :)
Step-by-step explanation:
Sami lights up a candle every 10 minutes. Every candle burns for exactly 40 minutes. How many candles are burning exactly 55 minutes after Sami lit up the first candle?
Answer:
4
Step-by-step explanation:
Candle is lit every 10 minutes :
Number of candles lit in 55 minutes:
Starting from 0 minute ; Numbe rod candles lit on 55 minutes = 6
1st candle burns out after 40 minutes
Second burns out after 50 minutes
Third will burn out after 60 minutes
Hence Number of candles still burning :
Number of candles lit - Number of candle burnt out
6 - 2 = 4 candles
explain why the expression 2y-y can be written as why
Answer:
y
Step-by-step explanation:
2y-y=y
Answer: 2y-y can be written as y because 2y means you have 2 y’s and 2y’s minus 1 y is just 1 y
Step-by-step explanation:
Two side of a triangle have the following measure 11 and 12. Find the range of possible measure for the third side.
A) 2
B) 3
C) 1
D) 1
HELP it is due tomorrow and I am super super stuck I have been doing this one for the last 2 days and did I make any progress? NOOOOOOOOOO I GIVE UP
Step-by-step explanation:
First thing you need to do is Slope - intercept form of the line going through point A and B.
Slope-intercept form: y = mx + b (m = slope, b = y-intercept)
To get slope: [tex]\frac{y2 - y1}{x2-x1}[/tex]
Lets set point A as point1 (x1, y1) and point B as point2(x2, y2).
x1 = -4
x2 = 8
y1 = 6
y2 = 3
If you plug these numbers in the slope equations:
[tex]\frac{3 - 6}{8 - 4}[/tex] = [tex]\frac{-3}{4}[/tex]
m = [tex]\frac{-3}{4}[/tex]
So a parallel line is a line that has a different b value but the same slope value.
To get b for the parallel line : we need to substitute the x and y for a given point (0,-2).
which will make -2 = 0([tex]\frac{-3}{4}[/tex] ) + b
now we solve for b:
-2 = 0 +b
b = -2
So the whole Slope-intercept form of the parallel line is: y = [tex]\frac{-3}{4}[/tex] x -2
Ashley and Carmen are both saving money for college. They each deposit a constant amount from their paychecks into their savings accounts. Which girl saves more money per paycheck? Explain how you know.
You have to use slopes
Lewis scored 0.15 of the points in a basketball game. How many of the team's 120 points did Lewis score
Write the converse, inverse and contrapositive of each conditional statement, and tell if the resulting statement is True or false
2. If mA = 100, then is not a right angle.
Converse:
Inverse:
Contrapositive:
Answer:
See below.
Step-by-step explanation:
It's good to recall what these terms mean:
Conditional statement: if p then q
Converse: if q then p
Inverse: if not p then not q
Contrapositive: if not q then not p
Conditional statement:
If m<A = 100, then <A is not a right angle.
p = m<A = 100
q = <A is not a right angle
Converse:
If angle A is not a right angle, then m<A = 100.
False. An angle that is not a right angle can have many measures other than 100 degrees.
Inverse:
If the measure of <A is not 100 degrees, then <A is a right angle.
False. If an angle has a measure of other that 100 degrees, it can have many measures in addition to 90 degrees, so it is not necessarily a right angle.
Contrapositive:
If angle A is a right angle, then m<A is not 100 degrees.
True. Only a right angle has a measure of 90 degrees, so an angle with measure 100 deg cannot be a right angle.
Graph the image of △JKL after a reflection over the line y=x
Answer:
K (2,-4)
L (4,-6)
J (2,-9)
Step-by-step explanation:
The required graph of the image of △JKL after a reflection over the line y=x has been attached below.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The triangle △JKL is given in the represented graph, which vertices are as follows :
J (-9, 2)
K (-4, 2)
L (-6, 4)
The image of △JKL after a reflection over the line y = x will be triangle △J'K'L' that vertices are as follows :
K' (2,-4)
L' (4,-6)
J' (2,-9)
Hence, the required graph of the image of △JKL after a reflection over the line y=x has been attached below.
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This cylinder has a volume of 392\pi392π cubic inches and a diameter of 14 inches. Find the radius and the height.
Answer:
15688
Step-by-step explanation:
Can someone please help me ASAP? What are the points? Point: (_, _)
Answer:
Step-by-step explanation:
I believe the point is 2:5
Hope this helps
1. 3x + 2y - Z-6
a) 3 terms
b) 5 terms
c) 4 terms
d) 6 terms
PLEASE HELP
Answer:
c) 4 terms
Step-by-step explanation:
3x is 1 term ,2y is 1 term,z is 1 term,6 is also 1 term
so in all there are 4 terms
Help with math
Find CE.
Answer:
6
Step-by-step explanation:
if DB equal to 6 then look down at CE, it has the same distance as D to B so CE equal to 6.
9514 1404 393
Answer:
CE = 10
Step-by-step explanation:
Assuming BC is parallel to DE, that segment divides the sides proportionally.
CE/CA = BD/BA
CE/25 = 6/15
CE = 25(6/15) . . . . multiply by 25
CE = 10
X+ 6
X+ 3
=
x + 2
x-5
a.
I = x
c.
X= -9
b.
S = x
d. x= -8
Step-by-step explanation:
x+6/x+2=x+3/x-5 x<>2 and x<>5
(x+6)(x-5)=(x+3)(x+2)
x2-5x+6x-30=x2+2x+3x+6
-5x+6x-30=2x+3x+6
x-30=5x+6
x-5x=6+30
-4x=36
x=-9
Note* x2=x in the power of 2
Plz help ill mark brainlest
Answer:i believe its 3 correct me if im wrong
Step-by-step explanation:
Answer:
either 6/10 or 7/10
Step-by-step explanation:
HELP PLS I WILL GIVE BRIANLY!
The students will paint 4 rooms on the first floor and the conference room on the second floor. Each room on the first-floor room is 4m x 5m.
1. Calculate the area of one of the rooms.
Answer:
20m
Step-by-step explanation:
The rooms are 4m x 5m.
To find the area, multiply length by width: 4*5=20
The Area of one room is 20 m².
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
Given:
First, Area of one room= lw
= 4 x 5
= 20 m²
Now, Area of four room = 4 x 20
= 80 m²
Thus, area of one room is 20 m².
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Which of these rational numbers is also an integer?
1. 2/4
2. 0.24
3. 4/2
4. 2.4
Answer:
Ce clasă ești sa văd daca te pot ajuta
Answer:
3. 4/2
Step-by-step explanation:
Easier way to explain it is the numerator or the top number is higher then the denominator or the bottom number.
What are the solutions to the equation (x−32)2=56?
x=±2√22
x=32±2√ 14
x=4√5±2√14
x=±2√6
Answer:
[tex]\bold{ x=32\pm2\sqrt{14}}[/tex]Step-by-step explanation:
[tex](x-32)^2=56\\\\x-32=\pm\sqrt{56}\\\\x=32\pm\sqrt{4\cdot14}\\\\ x=32\pm2\sqrt{14}[/tex]
what is the answer to 4 - (-4)
HELP please can you answer this please
Answer:
1. 2x² - 8x - 7
2. x³+ x + 30
Step-by-step explanation:
[tex]2 {x}^{2} - 9x - 2 +x - 5[/tex]
[tex]2 {x}^{2} - 8x - 7[/tex]
2x² has no other like terms to add or substract with so it stays as is.
(-9x) + x = -8
(-2) - 5 = -7
or
(-2) - (-5) = 3
Watch out for the ones on top. I'm a bit confused about them but those ones are your possible options.
//
[tex] {x}^{3} + 27 + x + 3[/tex]
[tex] {x}^{3} + x + 30[/tex]
x³ stays as is and so does x.
27 + 3 = 30
chase bought his dream car ,a chevy corvette, for $58,735. sales tax is 5% where chase lives what is the total price chase paid for the corvette?
Answer:
$61,671.75
Step-by-step explanation:
There is a calculator called "Sales Tax Calculator" and if you put in your Before Tax Price and your Sales Tax Rate you will receive your answer of $61,671 and 75 Cents. ($61,671.75)
How many distinct, real solutions does the following equation have?
x^2=49
A) Two distinct, real solution
B) One distinct, real solution
C) No solutions
Answer:
A) two (they are 7 and -7)
Step-by-step explanation:
angles
B
D
The AAS Triangle Congruence sch
Theorem can be used to show that ABE CDE
Choose...
Vertical Angles
Alternate Interior Angles
AAS Triangle Congruence
SSS Triangle Congruence
Answer:
Using the right angles, we can establish AAS making the triangles congruent. Or using the Pythagorean Theorem, we can find the missing side, and then use SSS, SAS, or ASA to make the triangles congruent.
Step-by-step explanation:
Add.
-1 + 2 = 1
- 6 + (-5)
Answer:
-6 + -5 = -11
Step-by-step explanation:
b/4 = 3.2 help me plz
Answer:
Step-by-step explanation:
B/4=3.2
B=12.8
please help
How are transformations related to congruence?
Answer:
Congruence transformations
transformations that are performed on an object that can create a congruent object
Please asnwer the picture
What is the equation of the line that represents the horizontal asymptote of the function f(x)=25,000(1+0.025)^(x)?
Answer:
The answer is below
Step-by-step explanation:
The horizontal asymptote of a function f(x) is gotten by finding the limit as x ⇒ ∞ or x ⇒ -∞. If the limit gives you a finite value, then your asymptote is at that point.
[tex]\lim_{x \to \infty} f(x)=A\\\\or\\\\ \lim_{x \to -\infty} f(x)=A\\\\where\ A\ is\ a\ finite\ value.\\\\Given\ that \ f(x) =25000(1+0.025)^x\\\\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} [25000(1+0.025)^x]= \lim_{x \to \infty} [25000(1.025)^x]\\=25000 \lim_{x \to \infty} [(1.025)^x]=25000(\infty)=\infty\\\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} [25000(1+0.025)^x]= \lim_{x \to -\infty} [25000(1.025)^x]\\=25000 \lim_{x \to -\infty} [(1.025)^x]=25000(0)=0\\\\[/tex]
[tex]Since\ \lim_{x \to -\infty} f(x)=0\ is\ a\ finite\ value,hence:\\\\Hence\ the\ horizontal\ asymtotes\ is\ at\ y=0[/tex]