Help would be truly appreciated. Write the polynomial in standard form from the given zeroes of lest degree that has rational coefficients, a leading coefficient of 1.
Don't have to answer all just what you can. I would appreciate if work is shown that way I can do the same for the rest. I really just need a tutorial and I'm good. Thank you so much!!!
Answers
Answer:
1) The polynomial in standard form is f(x) = x³ - 9·x² + 23·x - 15
2) The polynomial in standard form is f(x) = x³ - (2 - 2·i)·x² + 4·i·x
3) The polynomial in standard form is f(x) = x² + (3·i - 3)·x + 2 - 6·i
4) The polynomial in standard form is f(x) = x² - (5 + √5)·x + 6 + 3·√5
Step-by-step explanation:
Given that that the polynomial is of least degree, we have;
The standard form is the form, f(x) = a·xⁿ + b·xⁿ⁻¹ +...+ c
1) The zeros of the polynomial are x = 5, 3, 1
Which gives the polynomial in factored form as_f(x) = (x - 5)·(x - 3)·(x - 1)
From which we have;
f(x) = (x - 5)·(x - 3)·(x - 1) = (x - 5)·(x² - 4·x + 3) = x³ - 4·x² + 3·x - 5·x² + 20·x - 15
f(x) = x³ - 9·x² + 23·x - 15
The polynomial in standard form is therefore f(x) = x³ - 9·x² + 23·x - 15
2) The zeros of the polynomial are x = 2, 0, 2·i
Which gives the polynomial in factored form as_f(x) = (x - 2)·(x)·(x - 2·i)
From which we have;
f(x) = (x - 2)·x·(x - 2·i) = (x² - 2·x)·(x - 2·i) = x³ - 2·i·x² + 2·x² + 4·ix
The polynomial in standard form is therefore f(x) = x³ - (2 - 2·i)·x² + 4·i·x
3) The zeros of the polynomial are x = 2, 1 - 3·i
Which gives the polynomial in factored form as_f(x) = (x - 2)·(x - 1 - 3·i)
From which we have;
f(x) = (x - 2)·(x - (1 - 3·i)) = x² - x + 3·i·x - 2·x + 2 -6·i = x² + 3·i·x - 3·x + 2 - 6·i
The polynomial in standard form is therefore f(x) = x² + (3·i - 3)·x + 2 - 6·i
4) The zeros of the polynomial are x = 3, 2 + √5
Which gives the polynomial in factored form as_f(x) = (x - 3)·(x - (2 + √5))
From which we have;
f(x) = (x - 3)·(x - (2 + √5)) = x² - 2·x - x·√5 - 3·x + 6 + 3·√5
f(x) = x² - 5·x - x·√5 + 6 + 3·√5 = x² - (5 + √5)·x + 6 + 3·√5
The polynomial in standard form is therefore f(x) = x² - (5 + √5)·x + 6 + 3·√5.
Related Questions
10. Rewrite into slope-intercept form 7x + y = 25
Answers
To write in slope-intercept form, you first need to get y by itself. To do this, subtract 7x from both sides of the equation.
Doing this gets you: y = 25 - 7x
Now that y is by itself, remember that slope-intercept form looks like this: y = mx + b
So, let's switch the right side.
y = -7x + 25
Slope intercept form is: y = -7x + 25
Rules for y in Slope-Intercept form:
y must be positive
y must be by itself (so, not 2y, or anything with it... just y)
CW: A sheet measures 20cm by 50cm. How many sheets
required to cover a wall of size 4m and 5 m?
!
Answers
Answer:
200 sheets are required
Step-by-step explanation:
We need to calculate the area of both the sheets and the wall
Mathematically,
area of a rectangle = l * b
Area of the sheet = 20 * 50 = 1,000 cm^2
100cm = 1 m
so the area of the wall is 400 by 500 = 200,000 m^2
To know the number of sheets, we now divide the area of the wall by that of the sheet
Mathematically, that will be;
200,000/1,000 = 200 sheets
helpppp meeeeeeeeeeeeee
Answers
Answer:
you have to find gradient
Step-by-step explanation:
[tex] \frac{y2 - y1}{x2 - x1} \\ [/tex]
[tex] \frac{ - 3}{1} [/tex]
HELPPPPPPP!!!!!! THIS IS DUE AT 4:20
Answers
Answer:
B. PK = 15, RJ = 9
Step-by-step explanation:
RQ = 3
PQ = 5
✔️In ∆JKL, Q is the centroid. According to the centroid theorem, thus:
⅓(RJ) = RQ
⅓(RJ) = 3
Multiply both sides by 3
RJ = 3*3
RJ = 9
✔️Also, based on the centroid theorem,
⅓(PK) = PQ
⅓(PK) = 5
Multiply both sides by 3
PK = 5*3
PK = 15
Write the quadratic equation in standard form:
7x + 15 + x^2= -1
Answers
The sum of three numbers is 76. The third number is eight less than the first. The second number is two times the third. What are the numbers?
Answers
Step-by-step explanation:
Read the poem. excerpt from “Spring” by Christina Rossetti Frost-locked all the winter, Seeds, and roots, and stones of fruits, What shall make their sap ascend That they may put forth shoots? Tips of tender green, Leaf, or blade, or sheath; Telling of the hidden life That breaks forth underneath, Life nursed in its grave by Death. Which line from the poem contributes most to a hopeful tone? "Telling of the hidden life" "Frost-locked all the winter," "Life nursed in its grave by Death." "What shall make their sap ascend"
The numbers are 25, 34, and 17.
Let x be the first number, y be the second number, and z be the third number. We know that x + y + z = 76, z = x - 8, and y = 2z.
Substituting the second and third equations into the first equation, we get x + 2(x - 8) + (x - 8) = 76.
Simplifying the right side of the equation, we get 4x - 24 = 76.
Adding 24 to both sides of the equation, we get 4x = 100.
Dividing both sides of the equation by 4, we get x = 25.
Substituting x = 25 into the equation z = x - 8, we get z = 25 - 8 = 17.
Substituting x = 25 and z = 17 into the equation y = 2z, we get y = 2 * 17 = 34.
Therefore, the numbers are 25, 34, and 17.
To learn more about numbers here:
https://brainly.com/question/3589540
#SPJ2
Triangle GHI with vertices G(4, 1), H(5, -4), and I(2, -8) REFLECTED over the line y = x.
Answers
Answer:
Below.
Step-by-step explanation:
This transformation is described by (x,y)---> (y,x).
G(4,1) ---> G'(1,4)
H(5,-4) ---> H'(-4,5)
I(2, -8) ----> I'(-8,2).
Find f (3)for f () = 5* - 12.
3
57
113
125
Answers
Answer:
113
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = 5ˣ - 12
f(3) is x = 3
Step 2: Evaluate
Substitute in x: f(3) = 5³ - 12Exponents: f(3) = 125 - 12Subtract: f(3) = 113Which inequality correctly matches the graph?
Answers
Answer:
The inequality correctly matches the graph is -2 < x < 4 ⇒ B
Step-by-step explanation:
From the given figure
∵ There is a segment drawn from -2 to 4
∴ The starting point of the inequality is -2
∴ The ending point of the inequality is 4
∵ The endpoints of the segments are white circles (not shaded)
→ That means the signs of inequality without sign =
∴ The values of x are between -2 and 4
∴ The inequality is -2 < x < 4
∴ The inequality correctly matches the graph is -2 < x < 4
2. Multiple Choice.
If the perimeter of AFED = 29, what is the
length of FE?
D
A 3
B 5
с 8
D 11
E I need help
6x
x + 2y
F
5x -y E
Answers
Answer:
Ans is y so find y by using formula for isoceles triangle that is 2 right triangles
help please I beg you
Answers
Answer:
a. x= 5
b. x=9
Step-by-step explanation:
a.
2x=10
10/2=5
x=5
b. 3x=27
27/3=9
x=9
Please mark me brainliest
:)
Answer:
a) x=5
b) x=9
Step-by-step explanation:
a) 2x=10
x=10/2
x=5
b)3x=27
x=27/3
x=9
What is the distance between
-24 and 9
on a number line?
Answers
Answer:
the distance is 14 on the number line
The distance between -24 and 9 is; 33.
While determining the distance between two points on the number line;
The absolute value of their difference is considered the distance between the two points.
In this case; the difference is;
-24 - 9 = -33.However, the absolute value of -33 is; 33.
Read more:
https://brainly.com/question/17555743
A recipe calls for 1.5 cups of flour. Sara is making 9 times the recipe for a school fundraiser. How many cups of flour does Sara need?
Answers
Answer:
The answer is 13.5 cups
Step-by-step explanation: One bach requires 1.5 cups so if she is making 9 or those she will have to 1.5 cups 9 times.
Answer: 13.50
Step-by-step explanation:
Sara needs 1.5*9=13.5 cups of flour
14 points A line has a slope of 8 and includes the points (4, -8) and (5, 1). What is the value of f?
f=
Submit
Answers
help someone tell me how to figure out these i forgot
Answers
Answer:
option B is correct
Hope my answer is helpful to you
Plz help answer fast for 20 points
Answers
Answer:
wheres the question
Step-by-step explanation:
5 1/2 x 3 in simplest form
Answers
Answer:
16.5
Step-by-step explanation:
Answer:
33/2
Step-by-step explanation:
Charlie employs his friend Karl to help him prepare the food and to sell it at theevent. He pays Karl $11 per hour. If Karl helped Charlie for five hours, how much profit did Charlie’s business make from the event?
Answers
Anja divides (8x3 – 36x2 + 54x – 27) by (2x – 3) as shown below. What error does Anja make? 2 x minus 3StartLongDivisionSymbol 8 x cubed minus 36 x squared + 54 x minus 27 EndLongDivisionSymbol. minus 8 x cubed minus 12 x squared to get a remainder of negative 24 x squared + 54 x. minus 24 x squared + 36 x to get a remainder of 18 x minus 27. minus 18 x + 27 to get a remainder of 0 and a quotient of 4 x squared minus 12 x + 9
Answers
Answer:
c. she makes a multiplication error.
Step-by-step explanation:
edge:) 2020
Answer:
she makes a multiplication error
Step-by-step explanation:
took the test
If a triangle has an angle of 142 degrees, then what kind of triangle is it? right, acute, obtuse, or isosceles?
Answers
Answer:
It is an obtuse angle
Step-by-step explanation:
It is an obtuse angle because if any angle on a triangle is greater than 90 degrees, then it is called obtuse.
Which of the following inequalities has the solution set shown on the graph?
Answers
Answer:
option A) y > 5/4x + 10
Step-by-step explanation:
Take any point in the shaded region
( -12 , 1)
y > 5/4 x + 10
1 > 5/4 * (-12) + 10
1 > 5*(-3) +10
1 > -15 + 10
1 > -5
(-12 , 5) satisfies the equation.
What is the perimeter of triangle ABC?
Answers
Answer:
18 units
Step-by-step explanation:
Using the midpoint theorem, the perimeter of the triangle formed by joining the midpoints of the original triangle is exactly half the size in perimeter
What we mean in this case is that the perimeter of BAC IS two times the perimeter of EDF
perimeter of EDF is the sum of all the sides = 2 + 4 + 3 = 9
So the perimeter of BAC is 2 * 9 = 18
Write 2x+3y=6 in slope-intercept form.
pls help me!!
Answers
Answer:
Y= [tex]\frac{-2x+6}{3}[/tex]
Step-by-step explanation:
slope intercept formula is
Y=mx+b
Now we want the y isolate so in this case we just subtract 2x on both sides
3Y=6-2x
or in more better terms
3y=-2x+6
Now we want the 3 isolated so we divide 3 on both sides
and you’ll get
[tex]\frac{-2x+6}{3}[/tex]
✨✨✨IDENTIFY THE DOMAIN AND RANGE OF EACH. THEN SKETCH THE GRAPH✨✨✨ PLS HELPPPPPPP
Answers
Answer:
A
Step-by-step explanation:
The graph stops at the point (-1,-3) so
The domain (x) would have to be greater than or equal to -1
The range (y) would be greater than or equal to -3
Diane sold some stuffs at a garage sale. She spent one-half of the money she made on a new bicycle. Next, she spent one-half of what was left on a portable stereo. If Diane had $40.00 left, how much money did she make from the garage sale
Answers
Answer:
$160
Step-by-step explanation:
Diane sold some stuffs at a garage sale.
Let the total value of the money Diane made = x
She spent one-half of the money she made on a new bicycle.
Amount spent on a Bicycle = 1/2 × x = 1/2x
Next,
Amount left
= x - 1/2x = 1/2x
She spent one-half of what was left on a portable stereo.
Amount spent spent on Portable stereo
= 1/2 × 1/2x
= 1/4x
If Diane had $40.00 left,
Hence:
The fraction of what was left is calculated as:
= x - (1/2x + 1/4x)
= x - (3/4x)
= 1/4x
Hence:
1/4x = $40
We can find the value of x now.
1/4 × x = $40
x/4 = $40
x = $40 × 4
x = $160
Therefore, the amount she made from the garage sale is $160
Answer:
Hey hey guys, it is 160.00
Step-by-step explanation:
Tyler and Elena are on the cross country. Tyler's distance and times for a training run are shown on the graph.
Answers
Answer:
shown
Step-by-step explanation:
This is the link to the same question i think with a answer, im not good at these types of math but hopefully this helps you guys out! https://brainly.com/question/13982030
The expression ( x 22)( x 7)3 is equivalent to xp . What is the value of p ?
Answers
Answer:
p = 43
Step-by-step explanation:
I assume you mean an expression with exponents.
In the future, for a to the n power use a^n.
Recall the following two rules of exponents:
[tex] x^a \times x^b = x^{a + b} [/tex]
[tex] (x^a)^b = x^{ab} [/tex]
Now we can answer your question.
[tex] (x^{22})(x^7)^3 = [/tex]
[tex]= (x^{22})(x^{21})[/tex]
[tex] = x^{43} [/tex]
Since
[tex] x^{43} = x^p [/tex]
then
p = 43
Options are:
y = - 5/2x + 1/2
y = 5/2x + 1/2
y = 2/5x + 1/2
y = 2/5x - 1/2
Answers
Answer:
The answer is B
Step-by-step explanation:
A recipe for a loaf of bread calls for 2/3 of a cup of flour. If Milo used 12 cups of flour, how many loaves of bread did he prepare?
Answers
Answer:
8
Step-by-step explanation:
2/3 x 12 = 8
Answer:
the answer was 8 it was on my mid-term
Step-by-step explanation:
2. What is the slope of the line that passes through the points (-5,0) and N(6,8)?
Answers
Answer:
m= 8/11
Step-by-step explanation:
plug into the formula and solve