1. . By using factor theorem and long division, completely factorize the polynomial f(x) = x + 2x? - 19x - 20 (CLO2:PLOI:C3) ci 2. Solve the inequality >1. Write your answer in interval notation or set form.
Answers
The completely factorized form of f(x) is f(x) = (x + 1)(x - 5)(x + 4).
To solve the inequality x > 1, we have two options for representing the solution: interval notation or set form.
To factorize the polynomial f(x) = x^3 + 2x^2 - 19x - 20, we can first apply the factor theorem to find one of its factors. We need to find a value of x such that f(x) equals zero. By trial and error, we find that x = -1 is a zero of the polynomial. Therefore, (x + 1) is a factor of f(x).
Next, we can perform long division or synthetic division to divide f(x) by (x + 1). After dividing, we obtain the quotient x^2 - x - 20. This quadratic polynomial can be factored as (x - 5)(x + 4).
Hence, the completely factorized form of f(x) is f(x) = (x + 1)(x - 5)(x + 4).
To solve the inequality x > 1, we have two options for representing the solution: interval notation or set form.
In interval notation, we express the solution as (1, +∞), indicating that x is greater than 1 and extends to positive infinity.
In set form, we write the solution as {x | x > 1}, indicating that x belongs to the set of all real numbers greater than 1.
Both representations convey the same meaning, stating that x is any real number greater than 1.
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Related Questions
Help please!! Due today I'll give brainliest and a 5 star rating to everyone ILL DO ANYTHING JUST HELPADWIEFHRJ
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Answer:
i think the answer would be B i think if its wrong i am sorry
Step-by-step explanation:
equivalent to 3(x+8) ?
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Answer:
3x + 24
Step-by-step explanation:
do 3 * x and 3 * 8 . you get 3x + 24
Answer:
3x + 24
Step-by-step explanation:
expand
first do 3 * x
then 3 * 8
so 3*x + 3*8
=> 3x + 24
The radius of a circle is 9 m. Find its circumference in terms of π.
schoology
Answers
Answer: \(18\pi\)
Step-by-step explanation: The formula to find the circumference is \(2\pi r\) where r represents the radius. Since we are solving in terms of pi we can just multiply the radius of 9 by 2 and leave pi unchanged.
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A polynomial f and a factor of f are given. Factor f completely.
f(x) = 3x³ + 13x²+2x-8; x + 4
Answers
Answer:
(x+4)(3x-2)(x+1)
Step-by-step explanation:
triangle + triangle+triangle =circle+circle triangle +circle =30 wjat is te number of circle and triangle?
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If triangle + triangle + triangle =circle + circle and triangle +circle =30, then there are 15 circles and 15 triangles.
Based on the facts provided, we can say:
triangle + triangle + triangle = circle + circle_______________(1)
triangle + circle = 30_________________(2)
Let's start with equation (2). We can see that the sum of a triangle and a circle is 30. Hence, we can write:
triangle + circle = 30
Now we can substitute this into equation (1), which gives:
triangle + triangle + triangle = (triangle + circle) + (circle)
⇒ 3(triangle) = 2(circle) + triangle
To solve for the number of triangles in terms of the number of circles, we can rearrange this equation as follows:
2(triangle) = 2(circle)
⇒ triangle = circle
As a result, we have discovered that the quantity of triangles and circles is identical. So that we can determine the value of each form, we can substitute this into equation (2) as follows:
triangle + circle = 30
⇒ 2(triangle) = 30
⇒ triangle = circle = 15
Hence, the solution is that there are 15 circles and 15 triangles.
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Can someone help me with this Question.
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The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.
\(P=3W+D\)A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.
B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.
\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.
That leaves \(27-14=13\) matches. These represent the matches team lost.
Finally, the answers are below.
\(A)29\)
\(B)13\)
Answer:
a) 29 points
b) 13 losses
Step-by-step explanation:
You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.
A 8 wins, 5 drawsThe number of points the team has is ...
P = 3W +D
P = 3(8) +(5) = 29
The team has 29 points.
B 54 pointsYou want the number of losses the team has if it has 54 points and 12 draws after 39 games.
The number of wins is given by ...
P = 3W +D
54 = 3W +12
42 = 3W
14 = W
Then the number of losses is ...
W +D +L = 39
14 +12 +L = 39 . . . substitute the known values
L = 13 . . . . . . . . . . subtract 26 from both sides
The team lost 13 games.
__
Additional comment
In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)
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Payton is in charge of the water jugs for the football team. She has 410 ounces of water that she will use to fill plastic cups for the players. If each cup holds 10.25 ounces of water, how many cups can she fill if all are filled completely?
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Answer:
40
Step-by-step explanation:
410 divided by 10.25 = 40
3/4 -0.8 7/10 -3/4 from least to greatest
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Answer:
-0.8 < -3/4 < 7/10 < 3/4
Step-by-step explanation:
theyre decreasing
Answer:
-0.8, -3/4, 7/10, 3/4
Solve for x and y
Select 2 correct answer(s)
Answers
X=15
Y=15
Step-by-step explanation:
The small box is 90 degrees plus 60 degrees is 150 degrees so x is 15 degrees and y is 15 degrees so 15+15+150=180
Answer:
Step-by-step explanation:
x= 15. tan 60°= 15*√3= 15*1.73 = 25.9
y= 15. sec60°= 15*2 =30
A giant balloon i dropped from a plane landing on tahir and zach at point w(42,-15) and ending two friend flying off an equal ditance in oppoite direction. Of tahir end up at coordinate t(-18,36) where would we expect to find zack
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Zack is expected to be at (-12,-10.5) by finding the midpoint of line segment WT and reflecting T over it.
What is coordinate ?
A coordinate is a set of numerical values that are used to identify the position of a point in a specific space, such as a two-dimensional plane or a three-dimensional space. In two-dimensional space, coordinates are commonly represented by an ordered pair (x, y) or (x, y, z) in three-dimensional space.
The problem states that the balloon lands at point W(42,-15) and Tahir ends up at point T(-18,36). We know that Tahir and Zack are flying off in opposite directions from point W at equal distances. To find the point where Zack is expected to land, we can use the midpoint formula which states that the midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates.
We can find the midpoint of line segment WT by taking the average of the x-coordinates and y-coordinates:
x_midpoint = (x1 + x2) / 2 = (42 + -18) / 2 = 12
y_midpoint = (y1 + y2) / 2 = (-15 + 36) / 2 = 10.5
So the midpoint of line segment WT is (12,10.5). Since Zack is flying off in the opposite direction from Tahir at the same distance, we can expect Zack to end up at the point which is the reflection of point T over the midpoint of line segment WT.
This point would be (-12,-10.5)
Therefore , Zack is expected to be at (-12,-10.5) by finding the midpoint of line segment WT and reflecting T over it.
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i need help!! Please ASAP
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Answer:
It would be Square root of 38, and square root of 44 because they are all between 5 and 10. I'm sure you don't need their exact values, but that's them.
If you have nay more questions let me know! :)
Explain why the set of natural numbers {1,2,3,4,...} and the set of even numbers {2, 4, 6, 8, . . .} of positive even numbers
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The set of natural numbers {1,2,3,4,...} and the set of positive even numbers {2, 4, 6, 8, . . .} are different because natural numbers include all positive integers, while even numbers only include those that are divisible by 2 with no remainder.
About the setsTwo important sets of numbers are natural numbers and even numbers. The set of natural numbers consists of numbers that are not negative, beginning with 1 and continuing indefinitely with 2, 3, 4, and so on.
The set of even numbers, on the other hand, consists of numbers that are divisible by 2, beginning with 2, 4, 6, and so on.
Positive integers refer to natural numbers. Any integer greater than zero is a positive integer.
Zero is not a positive integer. Hence, the set of natural numbers consists of {1,2,3,4,…}
On the other hand, the set of even numbers consists of {2, 4, 6, 8, . . .}.
Therefore, {1,2,3,4,…} and {2, 4, 6, 8, . . .} are two different sets of numbers where one set is composed of positive integers (natural numbers) and the other is composed of positive even numbers.
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How many hours is a 7am to 3pm shift?
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Answer:
8 hours shift because you count from 7 am to 3pm
The total number of hours between the 7 am and 3 pm shift is 8 hours.
What is meant by the hour?
Depending on the speed of the Earth's rotation, an hour is a measure of time that is traditionally calculated as 1/24 of a day and scientifically estimated to last between 3,599 and 3,601 seconds. There are 24 hours in a day and 60 minutes in an hour.
The 24-hour day is divided into two sections, a.m. and p.m., according to the 12-hour clock time convention. Latin terminology for the hours of the day, AM and PM, are commonly employed. The abbreviations AM and PM stand for Ante meridiem and Post meridiem, respectively, which indicate before noon or midday and afternoon or midday. AM is used to denote the first 12-hour period, which runs from midnight to noon, and PM is used to denote the following 12-hour period, which runs from noon to midnight.
From 7 am to 12 pm, the number of hours = 5
From 12 pm to 3 pm, the number of hours = 3
Therefore the total number of hours between the 7 am and 3 pm shift is (3+5) = 8 hours.
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In parallelogram FGHJ if m∡ GHJ=55˚ find m∡FGH
Answers
Answer:
∠ FGH = 125°
Step-by-step explanation:
The consecutive angles in a parallelogram are supplementary, then
∠ FGH + ∠ GHJ = 180° , that is
∠ FGH + 55° = 180° ( subtract 55° from both sides )
∠ FGH = 125°
Answer: m∠FGH = 125°
Step-by-step explanation:
In a parallelogram, adjacent angles are supplementary (add up to 180°).
From the diagram, we can see that m∠GHJ and m∠FGH are adjacent.
This means that:
m∠GHJ + ∠FGH = 180° where ∠FGH is ∠x and ∠GHJ = 55°
55° + m∠x = 180° (subtract 55 from both sides)
m∠x = 125°
Ok, I made a mistake on my last question, but this time I have the right one. Solve v, 5/v=2/7.25
Answers
Answer:
\(v=\frac{145}{8}\)
Step-by-step explanation:
\(\frac{5}{v}=\frac{2}{7.25}\)
\(\frac{5}{v}=\frac{2}{\frac{725}{100}}\)
\(v=\frac{2}{\frac{5^2*29}{2^2*5^2}}\)
\(v=\frac{145}{8}\)
At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 percent. Which
expression represents how much she will receive in commission from the sale?
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At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 percent. 569 (0.18) represents how much she will receive in commission from the sale.
suppose that two boys named davis, three boys named jones, and four boys named smith are seated at random in a row containing nine seats. what is the probability that the davis boys will occupy the first two seats in the row, the jones boys will occupy the next three seats, and the smith boys will occupy the last four seats?
Answers
The probability that the Davis boys will occupy the first two seats in the row, the Jones boys will occupy the next three seats, and the Smith boys will occupy the last four seats is 7.937×\(10^{-4}\).
There are \(\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]\) potential arrangements for the nine boys if we do not make a distinction amongst boys with the same last name. We are curious in the likelihood of a specific one of these configurations.
Probability = \(\frac{1}{\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]}\)
= \(\frac{2!3!4!}{9!}\)
= 0.0007937
= 7.937×\(10^{-4}\)
Hence, the probability is 7.937×\(10^{-4}\).
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How is the expression (7 + y) ⋅9 described by its factors and terms?
It is has two factors and the factor (7 + y) has two terms.
It has three factors and the factor (7 + y) has two terms.
It has three factors and the factor (7 + y) has one term.
It has two factors and the factor (7 + y) has one term.
Answers
It has three factors and the factor (7 + y) has two terms.
The given expression is (7 + y) ⋅9.
We need to find how is the expression (7 + y) ⋅9 described by its factors and terms.
What is the factor of algebraic expressions?When algebraic expressions are written as a product of numbers, algebraic variables, or algebraic expressions, each of these numbers and expressions is referred to as a factor of algebraic expressions.
The (7+y).9 expression has two factors other than 1 and the other two factors are (7+y) and 9.
The factor (7+y) has two terms they are 7 and y.
Therefore, the given expression has three factors and the factor (7 + y) has two terms.
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Every day, George goes to church. The distance between church and his house is 15 feet. On a map, 1 inch is equal to 3 feet. How many inches apart would George’s church and home be on the map?
Answers
Answer: Five inches
Step-by-step explanation: If the distance between his home and church is 15 feet and on the map 1 inch = 3 feet then you would need to add three together until you reach 15 feet. 5•3=15
Which is an example of stratified random sampling created from each given population? A. Deciding who should be the president of the senior class by tossing a coin to choose between two candidates. B. C. Surveying members of a political party by calling people listed in the telephone directory whose last names begin with the letter A. D. Surveying subscribers to a magazine by separating the list of subscribers into four age groups and choosing a sample from each group proportional to its size in the population.
Answers
Answer:
the answer is D
Step-by-step explanation:
i just did the test
Answer:
D
Step-by-step explanation:
what’s the slope of (5,9) and (8,4)
Answers
Answer: -5/3
Step-by-step explanation:
Use the slope formula: \(\frac{y_{2}-y_1 }{x_2-x_1}\)
You substitute the numbers in and subtract to get -5/3.
Suppose f and g are holomorphic in a region containing the disc |z|≤1.Suppose that f has a simple zero at z=0 and vanishes nowhere else in |z|≤1.Let fϵ(z)=f(z)+ϵg(z).Show that if ϵ is sufficiently small, then(a) fϵ(z) has a unique zero in |z|≤1, and(b) if zϵ is this zero, the mapping ϵ↦zϵ is continuous.
Answers
The statement that f has a simple zero at z=0 and vanishes nowhere else in |z|≤1 implies that the function f is non-vanishing and has a derivative that does not vanish at z=0.
From this, we can use the Implicit Function Theorem which states that if f is holomorphic in a neighborhood of a point (a,b) and f(a,b)=0 and ∂f/∂y(a,b)≠0, then there exists an open neighborhood U of a and a unique holomorphic function g:U→R such that g(a)=b and (x,g(x)) is a solution of the equation f(x,y)=0 for all x in U.
In this case, since f(z) has a simple zero at z=0 and f'(0)≠0, by the Implicit Function Theorem, there exists an open neighborhood U of 0 and a unique holomorphic function h:U→C such that h(0)=0 and f(h(ϵ))=0 for all ϵ in U. Hence, fϵ(z) has a unique zero in |z|≤1.
Also, since f and g are holomorphic in a region containing the disc |z|≤1 and ϵ is continuous, it follows that fϵ is holomorphic in the same region. Thus, by the holomorphicity of fϵ and h, the mapping ϵ↦zϵ is continuous.
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What inequality sign also means "Has a limit of"?
I will mark brainiest
Answers
Answer:
greater/less than or equal to sign
Step-by-step explanation:
Answer: ⩽
Step-by-step explanation:
This inequality symbol means "at most"
hope this helps :)
plss help me noww if you can
Answers
Answer:
i cant see the picture at all
Step-by-step explanation:
A box in the shape of a rectangular prism has a length of 358 inches in width of two 1/2 inches and a height of 4 inches. What is the volume of the box?
Answers
The volume of the box in shape of a rectangular prism is solved to be
716 inches³
What is a rectangular prism?Three-dimensional object with six faces is called a rectangular prism (two at the top and bottom and four are lateral faces).
The prism has rectangular-shaped faces on each side. As a result, there are three sets of matching faces in this picture. Rectangular prisms are sometimes known as cuboids due to their shape.
In the given problem the formula used for volume of prism is
= length * width * height
= 358 * 1/2 * 4
= 716 inches³
The prism has a volume of 716 inches³
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The volume of the rectangular prism with a length of 358 inches, width of 1/2 inches and a height of 4 inches is 716 in³.
What is the volume of the rectangular prism?The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is width, h is height and l is length.
Given that;
Length l = 358 inWidth w = 1/2 inHeight h = 4 inPlug the given values into the above formula and simplify.
V = w × h × l
V = 1/2 in × 4 in × 358 in
V = 716 in³
Therefore, the volume of the box is 716 in³.
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Bring 8/(a-x) to a denominator of x-a
Answers
Answer:
\(-\frac{8}{x-a}\)
Step-by-step explanation:
\(\frac{8}{a-x}\)
we can take common factor of -1 in the denominator
\(\frac{8}{-(-a+x)}=\frac{8}{-(x-a)}\)
and now multiply and divide by -1
\(\frac{8}{-(x-a)}\cdot \frac{-1}{-1}=\frac{-8}{x-a}=-\frac{8}{x-a}\)
HELP ASAP!!! BRAINLIEST!
Answers
Answer:
( 1/25 x^-12 y^-14 )
Step-by-step explanation:
( 5 x^6 y^7 ) ^-2
We know that ( ab) ^c = a^ c * b^c
( 5^-2 x^6^-2 y^7^-2 )
We know that a^b^c = a^(b*c)
( 5^-2 x^-12 y^-14 )
We know that a^ -b = 1/ a^b
( 1/25 x^-12 y^-14 )
A school ordered 323 new science books. If each book has 421 pages, how many total pages are there combined in the new science books?
Answers
Answer: 135983 pages
Step-by-step explanation:
1 book = 421 pages
323 books = 135983 ( 421 x 323)
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Elie built a large rectangular vegetable garden that i 9 meter long and ha an area of 72 quare meter. What i the perimeter of Elie’ vegetable garden
Answers
Answer:
The perimeter of Elie's vegetable garden is 34 meters.
Step-by-step explanation:
The formula for area is: a=w*l.
A = area
W = width
L = length
If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.
72=w*9
You can divide both sides by 9 to get the width, which is 8 meters.
To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:
2(9)+2(8)=34
The perimeter of Elie's vegetable garden is 34 meters.
what is 3 and 1/6 as an improper fraction
Answers
Answer:
Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer