The polynomial of specified degree is 2x²-8x²+6
Before attempting to answer a polynomial problem, write it out in standard form. Factor it, then when each variable factor reaches zero, set them all to zero. The answers to the derived equations are the solutions to the original equations. Polynomial equations are not always amenable to factoring as a solution.
Polynomials are the sums of terms of the form kxn, where k is any number and n is a positive integer. a description of polynomials, such the polynomial 3x+2x-5. This video covers the ideas of degree, standard form, monomial, binomial, and trinomial.
If √3 is a root
so is -√3
thus, the polynomial is c(x-1)(x+1)(x-√3)(x+√3) = c(x²-1)(x²-3) = c(x⁴-4x²+3)
As the constant term is 6, 3c = 6, so c = 2
2(x4-4x2+3) = 2x⁴-8x²+6
Hence The polynomial of specified degree is 2x²-8x²+6
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Can someone please give me the solution for x (−2)exponent2 = 4(−2).
Answer:
Step-by-step explanation:
Exponent calculator helps you find the result of any base raised to a positive or negative exponent.
Enter the polynomial function f(x) in standard form given that f has leading coefficient 2 and roots 2, sqrt{3}, and -sqrt{3}.
Given that a polynomial function [tex]f(x)[/tex] has,
leading coefficient= 2roots = 2 , √3 , -√3And we need to find [tex]f(x)[/tex]
as we know that if a polynomial has zeroes as [tex]\alpha[/tex] , [tex]\beta[/tex] and [tex]\gamma[/tex] , then the cubic polynomial is given by,
[tex]\longrightarrow f(x)=k (x-\alpha)(x-\beta)(x-\gamma)\\ [/tex]
where ,
k is the leading coefficient.Now substitute the given zeroes, as ;
[tex]\longrightarrow f(x)=2[ (x-2)(x-\sqrt3)(x+\sqrt3)]\\ [/tex]
[tex]\longrightarrow f(x)= 2[(x-2)\{ x^2-(\sqrt3)^2\}][/tex]
[tex]\\\longrightarrow f(x)= 2[ (x-2)(x^2-3)]\\ [/tex]
[tex]\longrightarrow f(x)=2[ x(x^2-3)-2(x^2-3)]\\ [/tex]
[tex]\longrightarrow f(x)= 2[ x^3-3x -2x^2+6]\\ [/tex]
[tex]\longrightarrow \underline{\underline{ f(x)= 2x^3-4x^2-6x+12}}[/tex]
and we are done!
Answer:
[tex]f(x)=2x^3-4x^2-6x+12[/tex]
Step-by-step explanation:
Given characteristics of the polynomial:
leading coefficient = 2roots = 2, √3, and -√3.As the polynomial has 3 roots, it is a cubic polynomial.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a cubic polynomial}\\\\$y=a(x-r_1)(x-r_2)(x-r_3)$\\\\where:\\ \phantom{ww}$\bullet$ $r_n$ are the roots. \\ \phantom{ww}$\bullet$ $a$ is the leading constant.\\\end{minipage}}[/tex]
Substitute the given leading coefficient and roots into the formula:
[tex]f(x)=2(x-2)(x-\sqrt{3})(x+\sqrt{3})[/tex]
Expand to standard form:
[tex]\implies f(x)=2(x-2)(x+\sqrt{3}x-\sqrt{3}x-3)[/tex]
[tex]\implies f(x)=(2x-4)(x^2-3)[/tex]
[tex]\implies f(x)=2x^3-6x-4x^2+12[/tex]
[tex]\implies f(x)=2x^3-4x^2-6x+12[/tex]
You have a plate of 40 cookies. Ten have chocolate chips and 15 have pecans. Of the cookies mentioned in the preceding sentence, two have both chocolate chips and pecans. You select a cookie at random. What is the probability that your cookie has chocolate chips or pecans ?
Answer:
see below
Step-by-step explanation:
23 out of the 40 have cc or pecans
23/40
Does anyone know how to do this? I keep getting stuck on it. Look at this graph. What is the equation of the line in slope-intercept form?
Answer: 4/1
Step-by-step explanation: You go on the y-axis up to 6 then you count up until you get to 10 then you go over 1 so the equation would be 4/1
A plumber charges $75 make a house call. He also charges $32.50 per hour for labor. If the bill from the plumber is $286.25, how many hours did he work at your house?
7 3/4 divided by 1/3
Answer:
23.25 or 23 1/4
Step-by-step explanation:
keep change flip
7 3/4 = 31/4
31/4 x 3/1
31 x 3=93
4 x 1 =4
93/4 simplifies to 23 1/4 or 23.25
1. Calculate the average number of cheeseburgers eaten in a year by the followingpeople: Heidi ate 0. Tom ate 24. Diamond ate 18, Jesse ate 30, Maureen ate 0,and Makayla at 15
Number of people = 6
(0+ 24 + 18 + 30 + 0 + 15)/ 6 = 87/6
. = 14 + 3/6
Then answer IS
Average number of cheeseburgers= 14
In Triangle ABC, AB= 6cm, AC= 8cm, and BC= 12cm.
Angle ACB= 26.4
Calculate the area of triangle ABC
The area of the triangle is 18 cm.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
In Triangle ABC,
AB= 6cm
AC= 8cm
BC= 12cm.
Angle ACB= 26.4
The area of a triangle is given as:
Area = 1/2 x base x height
From the figure below,
Base = BC = 12
D is the midpoint of BC.
BC = BD + DC
DC = 12/2 = 6
Height = Tan 26.4
Tan 26.4 = AD / DC = AD / 6
0.50 = AD / 6
AD = 0.50 x 6
AD = 3
Now,
Area of the triangle ABC:
= 1/2 x base x height
= 1/2 x 12 x 3
= 18 cm
Thus,
The area of the triangle is 18 cm.
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A) Justin bought 27 pounds of sugar for $11. How many pounds of sugar did he get per dollat? Pounds per dollars mearest hundredth. B) A color printer prints 20 pages in 7 minutes. How many minutes does it take per page? Minutes per page nearest hundredth.
A)
[tex]\begin{gathered} \frac{27\text{ pounds }}{11\text{ dollars}}=\text{ } \\ 2.45\text{ pounds per dollar } \end{gathered}[/tex]b)
[tex]\begin{gathered} \frac{20\text{ pages}}{7\text{ minutes}}= \\ 2.86\text{ pages per minutes} \\ \\ Then: \\ If\text{ 2.86 pages are printed in 1 minute, how many minutes does it take for 1 page?} \\ \frac{1\text{ page \lparen1 minute\rparen}}{2.86\text{ pages}}=\text{ } \\ 0.35\text{ minutes takes to print 1 page. } \end{gathered}[/tex]
From problems 1-4 state whether or not the equation is a quadratic equation
1. y = x^(2) + 3x - 15
2. y = 6x^(5) - 0.7 x (pi symbol)
3. y = 9x
4. y = (-4/3)x^(2)
(Chapter 61 in Big Fat Notebook Algebra)
Answer:
1. Quadratic
2. Not quadratic
3. Not quadratic
4. Quadratic
Step-by-step explanation:
A quadratic equation will have a degree of 2. The degree is the highest power of the x term in the equation.
Therefore a quadratic equation will be of the form
y = ax² + bx + c,
where a, b and c are constants
a ≠ 0 but either b or c or both can be 0
if h(x)=10-x^2, then determine the value of h(f(2))
what is the total area of the shaded sections of trapezoid?
The shaded sections of the trapezoid are triangles.
We know how to find the area of triangles
A = 1/2 bh
Lets start with the left triangle
The bases is 1.1 inches and the height is 3.8 inches
A left triangle is
A = 1/2 ( 1.1) * 3.8 = 2.09
The right triangle has the same dimensions
A right triangle is
A = 1/2 ( 1.1) * 3.8 = 2.09
Add the two triangles together
2.09+2.09 = 4.18 in^2
The area of the shaded region is 4.18 in^2
x^3−x^2−2x=0 Help me factory this problem
Answer: x=0 x=2 x=-1
Step-by-step explanation:
[tex]x^3-x^2-2x=0\\\\x(x^2-x-2)=0\\\\x(x^2-2x+x-2)=0\\\\x((x-2)+(x-2))=0\\\\x(x-2)(x+1)=0\\\\x=0\\\\x-2=0\\\\x-2+2=0+2\\\\x=2\\\\x+1=0\\\\x+1-1=0-1\\\\x=-1[/tex]
Answer:
Factored form: x(x-2)(x+1)=0
Solutions: x=0, x=2, x=-1
Step-by-step explanation:
[tex]x^{3} -x^{2} -2x=0\\[/tex]
[tex]x(x^{2} -x-2)=0\\\left \{ {{x=0} \atop {x^{2}-x-2 =0}} \right. \\\left \{ {{x=0} \atop (x-2)(x+1)=0}} \right. \\x=0,x=2,x=-1[/tex]
The graphs of f (x) = x3 + x2 – 6x and g(x) = ex + 2 – 1 have which of the following features in common?
Rational function f of x increases from the left in quadrant 3 passing through the point negative 2 comma 0 and going to a local maximum and then decreasing through the point 0 comma 0 to a local minimum and then increasing through the point 3 comma 0 to the right and the exponential function g of x increases from the left in quadrant 3 asymptotic to the line y equals negative 1 and passes through the points negative 2 comma 0 and increases through the point 0 comma 6 to the right
x-intercept
y-intercept
End behavior
Range
The end behavior of the graphs of the functions f(x) and g(x) are common.
Consider the two functions,
f(x) = x³ + x² - 6x and g(x) = [tex]e^{x+2}[/tex] - 1
Now,
y = x³ + x² - 6x
The x-intercept will be:
0 = x³ + x² - 6x
x( x² + x - 6 ) = 0
x( x - 2 )( x + 3 ) = 0
So, x = 0, 2, - 3
Hence, the x-intercepts are ( 0, 0 ), ( 2, 0 ), and ( - 3, 0 ).
The y-intercept will be:
y = x³ + x² - 6x
y = (0)³ + (0)² - 6(0)
y = 0
Hence, the y-intercept is ( 0, 0 ).
The range of the function f(x) = x³ + x² - 6x is ( - ∞, ∞ ).
Using the degree 3 and the leading coefficient 1 of the function f(x) the end behavior of the function will be:
Falls to the left and rises to the right.
For the function,
y = g(x) = [tex]e^{x+2}[/tex] - 1
The x-intercept will be:
y = [tex]e^{x+2}[/tex] - 1
0 = [tex]e^{x+2}[/tex] - 1
[tex]e^{x+2}[/tex] = 1
[tex]e^{x+2}[/tex] = e⁰
x + 2 = 0
x = - 2
Hence, the x intercept is ( - 2, 0 ).
The y-intercept will be:
y = g(x) = [tex]e^{x+2}[/tex] - 1
y = e² - 1
Hence, the y-intercept will be ( 0, e² - 1 ).
The range of the function g(x) is ( - 1, ∞ ).
The end behavior of the function g(x) constantly rises to the right in the positive y-axis.
Hence, the functions f(x) and g(x) have the end behavior in common.
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Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
12,10,8
We can see here, from the first term to the second term, we minus 2. From the second term to the third term, we minus 2.
So, we're constantly reducing by an amount, therefore making this sequence an arithmetic sequence.
The common difference, said above, is -2 (since if the terms are getting smaller the common difference is a negative number.)
Write the equation of a line parallel to the line shown that has a y-intercept of (0, -6):
The required equations of the line are as follows;
(y + 6) = 1(x - 0); Point-slope form.y = x - 6; Slope-intercept form.x - y = 6; Standard form.Which equations represent the equation of the line on different forms?The line shown in the task content has a slope of 1 as it has a unit rate of change and also, the y-intercept of the graph shown is at the point; (0, 1).
On this note, it follows from line graphs that parallel lines have equal slopes. Hence, the required line would have the same slope, m = 1 too.
The equations are therefore as follows;
In point slope form; (y - y1) = m (x - x1). Hence we have; (y + 6) = 1(x - 0).In slope-intercept form; y = mx + c. Hence we have; y = x - 6.And finally, in standard form; ax + by = c. Hence, we have; x - y = 6.Read more on equations of a line;
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7y+2=11y-3please help me answer
Equation
[tex]\begin{gathered} 7y+2=11y-3 \\ 11y-7y=2+3 \\ 4y=5 \\ y=\frac{5}{4} \\ \end{gathered}[/tex]Steps
1. Group the variables and constants on each side of the equality
2. Operate the variables and operate the constants.
3. Divide both parts by 4 to clear y
The answer would be y = 5/4
Which table shows a function that is increasing only over the interval (–2, 1), and nowhere else?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 6, negative 3, negative 1, 1, 3, 6.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 3, negative 5, negative 7, negative 6, 1, negative 1.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 5, 7, 1, 0, negative 4, negative 2.
A table that shows a function that is increasing only over the interval (–2, 1), and nowhere else:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
In this question, we have been given some table that shows functions.
A 2-column table consists of six rows. The first column is labeled x (input values). The second column is labeled f(x) (output values)
We need to find a function which is increasing only over the interval (–2, 1), and nowhere else.
We can observe that for a second table, the first column x with entries negative 3, negative 2, negative 1, 0, 1, 2 and the second column with entries negative 2, negative 4, negative 1, 1, 4, 3 function f(x) is increasing only over the interval (–2, 1), and nowhere else.
Therefore, a table that shows a function that is increasing only over the interval (–2, 1), and nowhere else:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
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Please help me
:) thank you
Answer:
11 degrees
Step-by-step explanation:
Answer: 28 degrees
Step-by-step explanation: Set the two equations equal to each other, and solve. X equals 4 and then you plug that into 7x. 7x4 is 28.
I need help pls someone -
Answer:
Number above 42 : 14
Number beside 2 : 1
Number above 0: 12
Step-by-step explanation:
which expression is equivalent to 3/4-2/5
15/20-8/20
8/9-6/9
3/20-2/20
3/9-2/9
The expression that can be considered as been equivalent to 3/4-2/5 is 15/20-8/20.
How can the equivalent expression be gotten?The equivalent expression be gotten by finding the values of the given answer one after the other, from the given option, we can see that the value of the difference in the given expression is 0.35, then the value option A is also 0.35 which implies that the option A as well as the given expression have the same value.
It should be noted that the option A can as well be simplified as still get the vale of the given option.
Therefore, option A is correct.
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I need help on this one
△ABC is congruent to △CDA (△ABC ≅ △CDA) under (A) SAS condition.
What is the congruency of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. The five properties SSS, SAS, AAS, ASA, and RHS can be used to demonstrate the congruency of any two triangles.So, to prove that △ABC ≅ △CDA as follows:
BA = DC (given)∠BAC = ∠DCA (given)AC = AC (Common line)So, △ABC ≅ △CDA under SAS condition.
Therefore, △ABC is congruent to △CDA (△ABC ≅ △CDA) under (A) SAS condition.
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HELP If r = -6, s = -2, v = 10, and w = 3; then
vs(r - s) ÷ 2 + rw =
Responses
A -98
B 58
C -22
D 22
E -62
If r = -6, s = -2, v = 10 and w = 3, then the response of the expression vs(r-s) ÷ 2 + rw is option (D) 22
The expression is
vs(r-s) ÷ 2 + rw
The values are
r = -6
s = -2
v = 10
w = 3
Substitute the values in the given expression
= 10×-2 (-6-(-2)) ÷ 2 + -6×3
First we have to do the arithmetic operation in brackets
= 10 × -2 (-4) ÷ 2 + -6×3
Next we have to do the multiplications
= 80 ÷ 2 -18
Do the division
= 40-18
= 22
Hence, if r = -6, s = -2, v = 10 and w = 3, then the response of the expression vs(r-s) ÷ 2 + rw is option (D) 22
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Which graphs are correct?
Question 11
The slope is 7/2 (so the line is increasing), and the y-intercept is 3.
Answer is A.Question 12
The slope is -8/3 (so the line is decreasing), and the y-intercept is -5.
Answer is D.a box contains 6 red, 8 green, 10 blue, 12 yellow and 15 white balls. what is the minimum number of balls we have to choose randomly from the box to ensure that we get 9 balls of same color?
The minimum number of balls that must be chosen randomly from the box to ensure that we get 9 balls of the same color is 39.
Given that a box contains 6 red, 8 green, 10 blue, 12 yellow, and 15 white balls.
As the question says that the minimum number of balls chosen must ensure that we get 9 balls of the same color, so we must consider the balls of those colors which are more than 9 in number.
Here, 10 blue, 12 yellow, and 15 white balls are considered as they are more than 9.
By applying the Pigeon principle,
we can get.,
9 blue + 9 yellow + 9 white – 3 + 1 = 25
As we are picking randomly so we can get all the red and green balls before the above 25 balls.
Therefore we add the balls 6 red + 8 green + 25 = 39
Hence, the minimum number of balls that must be chosen randomly from the box to ensure that we get 9 balls of the same color is 39.
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Susan buys lotion for $2.33. She gives the clerk a $10 bill, three dimes, and three pennies. What was her change? Write one other combination of coins Susan could use with her $10 bill to get only bills.
The change left when Susan buys lotion for $2.33 and gives the bill is $8.
How to calculate the value?Susan buys lotion for $2.33. She gives the clerk a $10 bill, three dimes, and three pennies. The total amount will be:
= $10 + (3 × 0.1) + (3 × 0.01)
= $10.33
The change left will be:
= Total amount - Cost of lotion
= $10.33 = $2.33
= $8
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The cost (in dollars) of a custom-made sweatshirt is represented by 3.5n+29.99, where n is the number of different colors in the design. Write a simplified expression that represents the cost of 15 sweatshirts.
Answer:
3.5n + 29.99 × 15
Step-by-step explanation:
Since it is an expression there are no equals, and since we do not know how many colors there are in the design we leave the variable.
A principle of $300 was deposited in a savings account that pays 3.5 interest compoundedyearly. Find the balance after 5 years. Your answer should be numerical only.
Explanation:
The balance after t years can be calculated using the following equation:
[tex]A=P(1+r)^t[/tex]Where P is the principal amount and r is the rate of interest per year.
So, replacing P by $300, r by 3.5%, and t by 5, we get:
[tex]\begin{gathered} A=300(1+0.035)^5 \\ A=300(1.1877) \\ A=356.3059 \end{gathered}[/tex]So, the balance after 5 years is $356,3059
Answer: $356.3059
7
John is less than half his mother's age, though the sum of their ages is greater than
sixty. John was born on his mother's twenty-sixth birthday.
By expressing these facts as two inequalities and one equation, find the range of
possible ages for John.
Answer:
Step-by-step explanation:
ans is 7
Dave earned $637 last week. He worked 35 hours and earned the same amount rach hour. How much was he paid per hour?
