Answer:
The simplest polynomial function is [tex]y = x^{4}-(7+\sqrt{13})\cdot x^{3}+(27+7\sqrt{13})\cdot x^{2}-(189+27\sqrt{13})\cdot x + 189\sqrt{13}[/tex].
Step-by-step explanation:
A n-th order polynomial in factorized form is defined by:
[tex]y = (x-r_{1})\cdot (x-r_{2})\cdot ...\cdot (x-r_{n-1})\cdot (x-r_{n})[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]r_{1}[/tex], [tex]r_{2}[/tex],..., [tex]r_{n-1}[/tex], [tex]r_{n}[/tex] - Roots of the polynomial.
We know that three roots, two real and a complex root. By Quadratic Formula, a second order polynomial has two conjugated complex number of the form [tex]a + i\,b[/tex] and [tex]a - i\,b[/tex]. Hence, there is an additional zero: [tex]-i\,27[/tex].
By applying (1), we have the following polynomial when all roots are used:
[tex]y = (x-7)\cdot (x-\sqrt{13})\cdot (x-i\,27)\cdot (x+i\,27)[/tex]
By factorization and algebraic handling we have the simplest polynomial function:
[tex]y = [x^{2}-(7+\sqrt{13})\cdot x +7\sqrt{13}]\cdot (x^{2}+27)[/tex]
[tex]y = x^{2}\cdot (x^{2}+27)-(7+\sqrt{13})\cdot [(x^{2}+27)]\cdot x+7\sqrt{13}\cdot (x^{2}+27)[/tex]
[tex]y = x^{4}+27\cdot x^{2}-(7+\sqrt{13})\cdot x^{3}-(7+\sqrt{13})\cdot 27\cdot x +7\sqrt{13}\cdot x^{2}+189\sqrt{13}[/tex]
[tex]y = x^{4}-(7+\sqrt{13})\cdot x^{3}+(27+7\sqrt{13})\cdot x^{2}-(189+27\sqrt{13})\cdot x + 189\sqrt{13}[/tex]
The simplest polynomial function is [tex]y = x^{4}-(7+\sqrt{13})\cdot x^{3}+(27+7\sqrt{13})\cdot x^{2}-(189+27\sqrt{13})\cdot x + 189\sqrt{13}[/tex].
Draw a ring around the point which does not lie on the line y = 3x + 2 * 1 point (100, 302) (2, 8) (0, 4) (9, 29)
Answer:
(0,4)
Step-by-step explanation:
Given the line equation:
y = 3x + 2
Given the points :
(100, 302)
x = 100 ; y =302
302 = 3(100) + 2
302 = 300 + 2
(2, 8)
8 = 3(2) + 2
8 = 6 + 2
(0, 4)
4 = 3(0) + 2
4 ≠ 2
(9,29)
29 = 3(9) + 2
29 = 17 + 2
I really need help??
How many gallons of milk containing 1% fat is mixed with milk containing 4% fat to obtain a 15 gallon mixture
containing 2% fat?
Answer:
5%
Step-by-step explanation:
milk dont have fat but it contains 5% of milk
find the perimeter of WXYZ
Answer:
40 but see below.
Step-by-step explanation:
You have to assume that the figure is a parallelogram. That is never a safe assumption, but you have to make it because there is nothing else you can do.
That being the case, to get the perimeter, you just add the sides. If say well y could be just about any value with some limitations, you would be correct.
Per = 12 + 12 + 8 + 8 = 40
Hey guys please help me!
Answer: Option 2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Because it is
Kayla made a full pot of coffee she poured out 52 ounces she now has 18 ounces left how many ounces were in a full pot of coffee
Mafhvjfifjdfjujufugjfdu5\6 + 3\4 = ?
what is the initial value of the function:
f(x)=3/2(2)^x
Answer:
the initial value -- f(0) -- results in a value of 1.5
Step-by-step explanation:
f(0) = [tex]\frac{3}{2}[/tex] · [tex]2^{x}[/tex] (any value raised to the power of zero equals one)
f(0) = [tex]\frac{3}{2}[/tex] · 1
f(0) = 3/2 or 1.5
An equation is different from an expression because it has...
Answer:
Because it bears an equal sign
Expressions don't have a definite solution to the problem.
what is the diagonal of a solid square. each side is 7.
Answer:
9. 89
Step-by-step explanation:
A squared + B squared = C squared
7 squared + 7 squared = 98 squared
Find the square root of 98 (I recommend using a calculator)
You should get 9.89 as an answer.
What is the value of x ?
Enter your answer in the box.
Answer:
43.8
Step-by-step explanation:
Charlotte needs to order some new supplies for the restaurant where she works. The restaurant needs at least 535 glasses. There are currently 321 glasses. If each set on sale contains 20 glasses, write and solve an inequality which can be used to determine s, the number of sets of glasses Charlotte could buy for the restaurant to have enough glasses.
Answer:
sadafsa a a a a a aa. a heehehwhwhwh hehehheeheheh im going to bed ehehebbebeeb for al jfdjskalsm or worse expelled harry potter
PLEASE HELP! GIVING POINTS :)!
Answer:
1 and 1/8
Step-by-step explanation:
If using the method of completing the square to solve the quadratic equation x^2-13x+14=0, which number would have to be added to "complete the square"?
Answer:
169/4
Step-by-step explanation:
Take the coefficient of the x term. Here it's -13. Now halve that, obtaining -13/2. Finally, square this result. We get 169/4. This is the desired number.
x^2 - 13x + 169/4 - 169/4 + 14 = 0
need help. PLEASE! I dont understand
what is this angle? plz help
Answer:
56 degrees
Step-by-step explanation:
a straight angle is 180 degrees so you subtract 180 and 124 and get 56
Answer: 56 degrees
Step-by-step explanation:
Line AD is supplementary, therefore subtracting 180 from 124 is 56 degrees.
Brainiest help
Alex wrote the equation y = 2x + 3 to describe a tile pattern. Use his equation to complete the table. how would you graph it
5 times a number increased by 2 is the
same as 8 more than 3 times the number.
Find the number.
Answer:
Step-by-step explanation: 5*x + 2 = 3*x + 8
5x - 3x = 8 - 2. Which yields. 2x = 6. Therefore, x = 3. QED
PLease help the question is in the photo
Conserve Tree Foundation is trying to increase the number of trees in a region that has suffered deforestation. It plants a certain number of trees each year, resulting in a linear growth model, y1 = 5t, where t represents the time that has passed in years and y1 represents the number of trees planted. In the same region, the number of trees remaining, y2, is inversely proportion to the time elapsed, t. This is represented by . The graphs of the two equations are shown.
The answer will be 4
Need help ASAP plz
What is the slope of (1,4) (7,2)
Answer:
3 or 3/1
Step-by-step explanation
the equation for finding the slope when given two coordinate pairs is (y₂ - y₁)/(x₂ - x₁), aka change in y over change in x.
pick one of your coordinate pairs to be y₂ and x₂. it doesn't matter which coordinate pair you choose. the remaining coordinate pair will be your y₁ and x₁.
for this example, i'll use the coordinate pair (7, 2) as my y₂ and x₂ and (1, 4) as my y₁ and x₁.
first, substitute the x-value and y-value from the first coordinate pair.
(y₂ - y₁)/(x₂ - x₁) ⇒ (7 - y₁)/(2 - x₂)
then substitute the y-value and x-value from the remaining coordinate pair.
(7 - y₁)/(2 - x₂) ⇒ (7 - 4)/(2 - 1)
subtract 7 - 4.
(7 - 4)/(2 - 1) ⇒ (3)/(2 - 1)
subtract 2 - 1.
(3)/(2 - 1) ⇒ (3)/(1) or 3/1
simplify.
3/1 ⇒ 3
i hope this helps! have a great day <3
pls help me with this multiple choice !
Answer:
C
Step-by-step explanation:
[tex] \sin(30) = \frac{y}{32} \\ y = 16 \\ \cos(30) = \frac{x}{32} \\ x = 16 \sqrt{3} [/tex]
Harry and Luna together ate 56 Chocolate Frogs. Harry ate 6 more Chocolate Frogs than Luna. How many Chocolate Frogs did Luna eat?
Answer: 25 chocolate frogs eaten by Luna
Step-by-step explanation:
let the amount of chocolate frogs eaten by Luna = x
and the amount of chocolate frogs eaten by Harry = 6+ x
Such that total a,mount of chocolate frogs eaten by both of them
= x +( 6+x) = 56
Step 2- Solving
x+6+x=56
6 + 2x= 56
2x= 56-6
2x= 50
x= 50/2
x= 25
x= 25 chocolate frogs eaten by Luna
6 +x= 6+ 25= 31 chocolate frogs eaten by Harry.
PLEASE HURRY AND ANSWER
can you find the area for this?
Answer:
I think it's C) 18.5ft^2
it's just an educated guess though I haven't worked on area in a while
Answer:
[tex]18.5ft^{2}[/tex]
Step-by-step explanation:
[tex]A=(5*2.1)+(.5*2*5)+(.5*1.2*5)=18.5ft^{2}[/tex]
What is the value of the missing angle ? HELPPP PLSSS
Answer:
The angle of a straight line is 180 degrees.
180 degrees-71 degrees=109 degrees
Step-by-step explanation:
Evaluate the sum from n equals four to ten of quantity five n plus two.
202
207
254
259
Answer:
The answer is D. 259
Step-by-step explanation:
Step 1: [tex]\sum _{n=4}^{10}5n+2[/tex]
Step 2: [tex]\sum _{n=1}^{10}5n+2-\sum _{n=1}^35n+2[/tex]
Step 3:
[tex]\sum _{n=1}^{10}5n+2=\sum _{n=1}^{10}5n+2-\sum _{n=1}^35n+2\\\sum _{n=1}^{10}5n+2=295[/tex]
[tex]\sum _{n=1}^35n+2=\sum _{n=1}^35n+\sum _{n=1}^32=36\\[/tex]
Step 4: [tex]295-36=259[/tex]
43x34x7x34x21x32 please help me i really need an answer
Answer:
233826432
Step-by-step explanation:
7,21,63
what’s the common ratio, recursive function, explicit formula, and the 12 term
Answer:
See explanations below
Step-by-step explanation:
The given sequence 7,21,63... is geomertic in nature
The nth term is expressed as;
Tn = ar^n-1
a is the first term = 7
r is the common ratio = 21/7 = 63/21 = 3
n is the number of terms
Substitute
Tn = 7(3)^n-1
For the 12th term, when n = 12
T12 = 7(3)^12-1
T12 = 7(3)^11
T12 = 7(177,147)
T12 = 1,240,029
Hence the 12th terms is 1,240,029
For the recursive function
First term = 7(1)
2nd term T2 = 21 = 7(3)
3rd term T3 = 63 = 7(9) = 7(3^2)
Tn = 7(3^n)
Hence the recursive function is 7(3^n)
Sign out Fred's bedroom has an area of 54 square feet. The bedroom is 6 times as many square feet as Fred's closet. If the closet is 3 feet wide, what is the length of the closet?
Answer:
3 feet
Step-by-step explanation:
Area of bedroom = 54 square feet.
Area of closet = Area of bedroom / 6= 54/6= 9 square feet.
Area = length * breadth
9 = length *3
length = Area/ width
length = 9/3= 3 feet.
As the bedroom is having 6 times the area of the closet we will divide the area of the bedroom by 6 to get the area of the closet ( 54/6= 9) . Area is obtained by multiplying the length and the breadth so we have the width which 3 feet , we divide the area with the width ( 9/3= 3) to get the length = 3 feet.