What is polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Since we know that complex solutions ALWAYS come in pairs, the minimal polynomial must include the root of 4-i as an acceptable root..
This leads to a polynomial of ...
p(x) = (x - 5)(x - (4+i))(x - (4-i))
Now we can simplify...
(x - (4+i))(x - (4-i)) --> x2 + [(4+i)+(4-i)]x + (4+i)(4-i) --> x2 + 8x + [ 16 -4i + 4i -i2 ] = x2 + 8x +17
Take this quadratic and multiply by (x-5) to get the final, minimal polynomial...
p(x) = (x-5)(x2 + 8x +17) = x3 + 8x2 + 17x -5x2 + 40x - 85 = x3 + 3x2 + 57x - 85
So p(x) = x3 + 3x2 + 57x - 85
p(x) has only real coefficients, the leading coefficient of 1, and is the smallest to allow for the two solutions requested
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0.11 times 734 Answer please.
Answer:80.74
Step-by-step explanation: lol
These two polygons are similar.
4
2
9
16
15
w
w = [? ]
45 points asap for anyone who can answer
Are the triangles congruent ? Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!
Answer:
no
Step-by-step explanation:
they are not
Answer:
No
Step-by-step explanation:
because the angles are not equal. If they were they would have the same numbers.
Haley borrows 1000 dollars from her bank.She will pay the loan at a simple annual interest rate of 4% over 4 years.How much will she pay back altogether
Answer: $49.85
No explanation needed
hello help please i’ll give brainliest
Answer:
Erosion by groundwater.
Step-by-step explanation:
Sinkholes are formed when groundwater dissolves rocks underneath the land surface.
Answer:
Erosion of groundwater because the water goes through the rock and "weekends" them into collapsing. Almost like tripping if you will.
Step-by-step explanation:
10+15+6+15+5+15+7+13
Answer:
I think its 86
Step-by-step explanation:
I used a calculator.
An artist used silver wire to make a square that has a perimeter of 40 inches. She then used copper wire to make the largest circle that could fit in the square, like the drawing above.
How many more inches of silver wire did the artist use compared to copper wire? (remember that = 3.14)
Answer:
1.4 inches
Step-by-step explanation:
if I'm wrong please tell me right away I would like to help you good day.
Select all of the angles that are congruent to \angle 5.
Answer:
<5 = <8 b/c of vertical angles
<5 = <4 because of alternate interior angles
<5 = <1 because of corresponding angles
Help I’ll give Brainly est
Answer:
60 square centimeters
Step-by-step explanation:
8*15/2 = 60
Answer:
Ugh A bad B but C and D seem correct to fit in into your own a jar of yellow
Michael is buying new tile for his bathroom. The bathroom is 6 feet wide and 7 feet long. It costs $1.75 per square foot of material for the bathroom. If Michael goes to the store with $70, will he have enough money to buy the material. Why or why not.
Answer: yes because all the math adds up to 22.75 and he has 70
Step-by-step explanation:
Need help once again!!!
Answer:
the answer to this question is seven
Solve for x. Give explanation
Answer:
x = 47 degrees.
Step-by-step explanation:
The angles in a triangle add up to 180 degrees, therefore:
x + 43 + 90 = 180
x = 180 - 43 - 90
x = 180 - 133
= 47 degrees.
Help, I am unsure about what to do exactly
What is 73/48 simplified
Answer:7348 is already in the simplest form. It can be written as 1.520833 in decimal form (rounded to 6 decimal places).
Step-by-step explanation:
Answer: it’s already at its lowest form
Step-by-step explanation:
Describe a real world situation where you might use the Pythagorean Theorem. Help due today :))
how do i find the surface area and volume of this shape?
Answer:
3,761.46 m³
Step-by-step explanation:
Volume of a cone = 1/3πr²h
π = 3.14
radius, r = diameter/2
= 25/2 = 12.5 m
Height, h = 23m
Volume of a cone = 1/3πr²h
= 1/3 * 3.14 * 12.5² * 23
= 1/3 * 3.14 * 156.25 * 23
= 11,284.375 / 3
= 3761.4583333333
Approximately,
Volume of the cone = 3,761.46 m³
what equation is equal to y-34=x(x-12)
Answer: I don’t know how to solve for x but I know how to solve y for y=x^2-12x+34
Step-by-step explanation: Hope this help :D
How many tiles will be in figure 100? EZ COME UP ON POINTS
.
[tex]f(100) = 498[/tex]
.
Explain.
[tex]f(2) = 8[/tex]
[tex]f(3) = 13[/tex]
.
Find b[tex]3b - 2b = 13 - 8[/tex]
[tex]b = 5[/tex]
.
Find f(1)[tex]f(1) = f(2) - b[/tex]
[tex]f(1) = 8 - 5[/tex]
[tex]f(1) = 3[/tex]
.
Find f(100)[tex]f (x)= f(1) + (x - 1)b[/tex]
[tex]f(100) = 3 + (100 - 1)5[/tex]
[tex]f(100) = 3 + (99)5[/tex]
[tex]f(100) = 3 + 495[/tex]
[tex]f(100) = 498[/tex]
.
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Which of the following systems of equations creates the graph of (-3.4, 2.3)?
Option 1 : y= 2x+4
y= -1/3x-8
Option 2 : y= 1/2x-8
y= -3x-8/3
Option 3 : y= 1/2x+4
y= -3x-8
Option 4 : y= 2x-8
y= -1/3x-8/3
I need an answer ASAP, I will mark u brainliest if the answer is valid! thx
Answer:
C
Explanation:
The answer is C because when you plug in (-3.4) as x in that equation, you get 2.3 as an answer which means that option is correct.
[tex]y = \frac{1}{2} x + 4[/tex]
[tex] = \frac{1}{2} ( - 3.4) + 4[/tex]
[tex] = 2.3[/tex]
When you plug in x for other options, you do not get the correct value for y so this is the only answer.
No links!
Factor 5/6 out of 5/6z+15
Answer:
5/6z+15
heart if it helped!
what is the answer of 2m^2 * 2m^3
Answer:
4m^5
Step-by-step explanation:
Answer:
4m^5
Step-by-step explanation:
Rachel buys a bag of apples for $3.21. She pays for the bag with a $20 bill. How much change should Rachel receive?
Answer:
$16.79
Step-by-step explanation:
20 - 3.21 = 16.79
A class collects data on the number of movie tickets purchased and total cost of those tickets. The class plots the data on a scatter plot. Which statement best interprets their results
Answer:
what are your options?
Step-by-step explanation:
Dannon has $10.80 in dimes and quarters. If Dannon has 32 more quarters than dimes, how many dimes does he have?
Answer:
Dannon has 8 dimes.
Step-by-step explanation:
32 divided 10 - 8 divided 2 - 3
Answer:
-3.8
Step-by-step explanation:
Answer:
-3.8 i think sorry this is the first one im not sure with.
Step-by-step explanation:
32/10=2.4
3-2=1
2.4-8=5.6
5.6/1=5.6
=-3.8
Find the length of side X in simplest radical form with a rational denominator.
X
Answer:
given in the figure an isosceles right triangle
hence
x = √3
√3 is a surd it can't be simplified furtherFind mDE. Round your answer to the nearest hundredth.
Answer:
[tex]50.04[/tex]
Step-by-step explanation:
Use this formula for arc length
[tex]2\pi \times r( \frac{x}{360} )[/tex]
where r is the radius and x is the arc measure.
We know Arc de is 8.73 so we are finding x.
R equal 10.
[tex]2\pi \times 10( \frac{x}{360} ) = 8.73[/tex]
[tex]20\pi( \frac{x}{360} ) = 8.73[/tex]
[tex]20\pi \times x = 3142.8[/tex]
[tex]x = \frac{3142.8}{20\pi} [/tex]
x=50.04
The value of the angle will be 50.04.
What will be the angle?It is given in the question that
The arc of the circle A=8.73 In
The radius of the circle =10 In
Now from the formula of arc
[tex]A=2\pi r(\dfrac{\theta}{360} )[/tex]
[tex]8.73=2\pi 10\times \dfrac{\theta }{360}[/tex]
[tex]\theta = \dfrac{8.73\times 360 }{ 2\pi\times 10} =50.04[/tex]
[tex]\theta=50.04[/tex]
Thus the value of the angle will be 50.04
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Priscilla received 240 votes in the election for student council president. That was 60% of the students who voted in the election. How many students voted in the election? *
A) 400 students
B) 300 students
C) 185 students
D) 455 students
Answer:
I think its c
!
Step-by-step explanation:
I need help on this test. Will give Brainliest to whoever answers first!
Answer:
C and G.
Step-by-step explanation:
Need help on this, I have no idea what should go on the first line or the second line
Answer:
1.) 120
2.)120
Step-by-step explanation:
1.) Do length times width
2.) For the number 120 you don't have to round, so it just stays the same