Hcf of two expressions is (x + 1) and lcm is (x^3+ x^2 – x – 1). if one expression is (x^2 - 1), then what is the second expression?
Answers
After solving by formula the second expression is y = \((x^2 + 1)\).
We know that the product of the HCF and LCM of two numbers is equal to the product of the numbers themselves. In this case, we can apply the same principle to expressions:
HCF * LCM = (x + 1) * \((x^3+ x^2 - x - 1)\)
the first number is \(x^{2} -1\\\) and let the second number is y
Therefore, we can set up the equation:
(x + 1) * \((x^3+ x^2 - x - 1)\) = \(x^{2} -1\\\) * y
\(x^4 + x^3 + x^2 - x^3 - x^2 + x - x - 1 = x^2 - 1 * y\)
Simplifying:
\(x^4 - 1 = (x^2 - 1) * y\)
Now, we can divide both sides by \((x^2 - 1)\):
\((x^4 - 1) / (x^2 - 1) = y\)
Notice that \((x^2 - 1)\)can be factored as (x + 1)(x - 1). Therefore, we can simplify further:
\((x^4 - 1) / ((x + 1)(x - 1)) = y\)
The expression \((x^4 - 1)\) can be factored using the difference of squares:
\((x^4 - 1) = (x^2 + 1)(x^2 - 1)\)
\([(x^2 + 1)(x^2 - 1)] / ((x + 1)(x - 1)) = y\)
Now, we can cancel out the common factor \((x^2 - 1)\) from the numerator and denominator:
\(y =(x^2 + 1)\)
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Related Questions
What is the measure of ZL?
Enter your answer in the box. Round only your final answer to
the nearest hundredth.
m/L=
18 in.
М'
60 in.
N
Answers
Angle L's in the triangle LMN is,
⇒ L = 72.54°
We have to given that;
A triangle LMN is shown in figure.
And, The sides are,
Since, We know that;
A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.
Since, We know that;
⇒ sin L = Opposite / Hypotenuse
And, cos L = Base / Hypotenuse
Two rays after combined into an angle have a single terminal. And, latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms.
Now, We can use trigonometry formula to find the value of angle l we get;
⇒ sin L = Opposite / Hypotenuse
⇒ sin L = LM / LN
⇒ sin L = 18/60
Taking arc sin both side, we get;
⇒ L = 72.54°
Therefore, The value of measure of angle L is triangle LMN is,
⇒ L = 72.54°
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What is the domain of the function
Answers
Hope this will help you have a nice day
What is the cos A?Will give 15 points.
Answers
Answer:
Step-by-step explanation:
cos A = \(\frac{\sqrt{8} }{3}\)
The three sides of a triangular fence have lengths 4x + 5, y − 7, and 3x − 2. What is the total perimeter?
A) 7x + y + 10 feet
B) 7x + y − 4 feet
C) 7x + y feet
D) 4x + y − 4 feet
Answers
The correct option is (b) i.e. the total perimeter of the fence is 7x + y − 4 feet.
What is Perimeter?
Perimeter is the total length of the boundary or outer edge of a two-dimensional shape, such as a polygon, circle, or ellipse. It is the sum of the lengths of all the sides or arcs that make up the shape. For example, the perimeter of a square is the sum of the lengths of all its sides, while the perimeter of a circle is the circumference, which is the distance around the circle. The perimeter is often measured in units such as centimeters, meters, or feet, depending on the context of the problem.
Given : sides of the fence
s₁ = 4x + 5
s₂ = y − 7
s₃ = 3x − 2
We know that, perimeter of a triangle is sum of all three sides.
So, Perimeter of the fence = s₁+ s₂+ s₃
= 4x + 5 + y − 7 + 3x − 2
= 7x + y - 4 ft.
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12a-12b+12c please help to simplify
Answers
Answer:
12(a+b+c)
Step-by-step explanation:
how to verify:
Distribute 12 and you'll get the original expression
I hope my answer was helpful!
- 2.7f + 0.9f - 16-6=
Answers
I think( -1.8f -22 )
-2.7f + 0.9f
|
|
-1.8f.
then -16-6
|
|
-22
2. A(n) is NOT an example of an agreement. (1 point)
O lease
O month-to-month
O annual
O fine print
Answers
An Annual is not an example of an agreement.
Jazel time to check your progress. So far you have completed 816 miles which is 47% of the trail. Can you find about how many miles for the total trip?
Answers
Answer:
1,736.17miles
Step-by-step explanation:
Let the total trip be x miles
If 47% of the total trip is 816, then;
47% of x = 816
0.47x = 816
Divide both sides by 0.47
x = 816/0.47
x = 1,736.17miles
Hence the total miles for the trip is 1,736.17miles
A bag with 12 marbles has 5 red marbles, 3 yellow marbles, and 4blue marbles. A marble is chosen from the bag at random. What is the probability that it is red? Write your answer as a fraction in simplest form.
Answers
Answer:
5/12 is already in simplest form
Step-by-step explanation:
12m = 5r + 3y + 4b
red is chosen = 5r / 12 = 5/12
Step-by-step explanation:
the answer is 5/12. It's quite simple
Mr. Hooper has a tree in his front yard that grows every year. If the tree was 3 feet tall when he planted it 6 years ago , what is the current height of the tree in terms of f?
A. 3f + 6 feet
B. 6f + 3 feet
C. 3f + 18 feet
D. 6f + 18 feet
Answers
The height of the tree after 6 years can be expressed as "3 feet + 6f feet."
The correct answer is A. 3f + 6 feet.
To determine the current height of the tree in terms of "f,"
let's analyze the given information.
We know that the tree was initially 3 feet tall when it was planted 6 years ago.
Since the tree grows every year, we can assume that its growth rate is consistent.
Let's denote the current height of the tree as "h" (in feet).
After 6 years, the tree has grown by a certain amount, which we'll represent as "6f" (6 years multiplied by the growth rate "f").
Therefore, the height of the tree after 6 years can be expressed as "3 feet + 6f feet."
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For Serenity's lemonade recipe, 4 lemons are required to make 5 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade?
Answers
For Serenity's lemonade recipe, the lemons being used per cup of lemonade is 0.8
What is ratio?Ratio is a comparison of two quantities that are expressed in relation to each other. Ratios are typically expressed in the form of a fraction, with the numerator representing one quantity and the denominator representing the other quantity.
According to question:To find the rate at which lemons are being used in lemons per cup of lemonade, we need to calculate the ratio of lemons used to cups of lemonade.
According to the recipe, 4 lemons are required to make 5 cups of lemonade. So the rate of lemons used is:
4 lemons / 5 cups = 0.8 lemons per cup of lemonade
This means that for every cup of lemonade, 0.8 lemons are used.
Alternatively, we can also express this rate as a fraction, which gives us:
0.8 lemons / 1 cup of lemonade
Either way, the rate of lemons used is 0.8 lemons per cup of lemonade.
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Grade 5 math. ! 30 points !
During the month of june, jessica volunteers at a library every 6 days and at a veterinarians office every 10 days. jessica’s first visit to the library was on June 6 and her first visit to the veterinarian office was on June 1th.
What day in June will jessica volunteer at both locations?
Anwser Options
june 6
june 10
june 18
june 20
june 24
june 30
Answers
The day in June, Jessica volunteered at both locations if she volunteers at the library every 6 days and at a veterinarian's office every 10 days is June 30, so option F is correct.
What is LCM?The abbreviation LCM stands for "Least Common Multiple." The smallest multiple that two or more numbers share is known as the least common multiple.
For instance: The LCM of 2 and 3 is 6.
Given:
Jessica volunteers library every 6 days,
Jessica's veterinarian's office, every 10 days,
So for her visit to both, the place takes the LCM of 6 and 10,
LCM of 6 and 10 = 30,
Hence, on the 30th day, she visits both places so if she starts volunteering from the 1st of June then she will visit both places on the 30th of June.
Therefore, The day in June, Jessica volunteered at both the location if she volunteers at a library every 6 days and at a veterinarian's office every 10 days. Jessica’s first visit to the library was on June 6 and her first visit to the veterinarian's office was on June, 1st is June 30.
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Answer:June 30th
Step-by-step explanation:
So Jessica volunteers every 6 days and 10 days at different places.From June 6th and June 1st you see which one is good for both of them and then June 30th is the answer.
Solve the inequality 2x ≥ 6
Answers
Answer:
I think the answer would be x = 3, 4, 5, 6 (Anything greater than 3)
The answer is: x ≥ 3
Step-by-step explanation:
I think this is the answer because:
1) Since the sign ≥ means equal to or less than, x has to equal 3 or greater.
2) This is because if x = 3 then, 2 x 3 equals to 6. 6 and 6 are equal. If x = 4 then, 2 x 4 would equal 8. 8 is greater than 6.
3) Since 2x has to be something equal to or greater than 6, x has to equal 3 or something greater than 3.
Hope this helps!
The solution of the inequality 2x ≥ 6 is greater than or equal to three.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The inequality is given as,
2x ≥ 6
Simplify the inequality, then the value of x will be
x ≥ 6/2
x ≥ 3
Thus, the value of the variable x is greater than or equal to three.
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Which of the following is an example of a census?
a) Survey parents whose children attend a local elementary school by randomly selecting 50 parents from the school’s records.
b) The U.S. Population Census
c) Poll students at a college by including a pop-up window in the online registration form. Students have to answer the survey questions before they can register. Try to catch the remaining students at the admissions window when they register in person. d) Weigh every child at an elementary school for a study of physical fitness at the school.
Answers
Answer:
B
Step-by-step explanation:
because its something thats important and needs to be done
The U.S. Population Census is an example of a census
Census means the procedure of counting, calculating and recording the number and information about the members of the nation's.
Generally, population census are conducted every 10 years although some nations conduct their's every 5 years.
The primary objective of population census is to know the total size of the population of a country.
Population census also enable the government to appropriate resources fairly based on the number of people in a geographical area.
In conclusion, the U.S. population census is the only example of census.
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Help me !!!
Please I really need it
Answers
Answer:
i don't know
Step-by-step explanation:
If a=8 and b=5 and x=4 and y=6m -2 what is the value of m ?
Answers
Answer:
m = 2
Step-by-step explanation:
Given:
x = 4
y = 6m - 2
a = 8
b = 5
Required:
Value of m
SOLUTION:
x and y are segments of a chord divided when it intersects another chord that also has segments a and b.
According to the Intersecting chords theorem, \( a*b = x*y \)
Thus:
\( 8*5 = 4*(6m - 2) \)
Solve for m
\( 40 = 24m - 8 \)
\( 40 + 8 = 24m - 8 + 8 \)
\( 48 = 24m \)
\( \frac{48}{24} = \frac{24m}{24} \)
\( 2 = m \)
The value of m = 2
prove that there exist only five regular polyhedron
Answers
To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.
Proving there exist Five Regular PolyhedronThe five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.
The five regular polyhedra are:
1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.
2. Cube: It has six square faces, and three squares meet at each vertex.
3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.
4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.
5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.
To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:
"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".
For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:
V - E + F = 2
=> kV/2 - kE/2 + F = 2
=> k(V/2 - E/2) + F = 2
Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:
k(V/2 - (nF)/2) + F = 2
=> (kV - knF + 2F)/2 = 2
=> kV - knF + 2F = 4
Now, we need to consider the conditions for a valid polyhedron:
1. The number of faces (F), edges (E), and vertices (V) must be positive integers.
2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.
Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:
(n, k) pairs:
(3, 3) - Tetrahedron
(4, 3) - Cube
(3, 4) - Octahedron
(5, 3) - Dodecahedron
(3, 5) - Icosahedron
Therefore, there exist only five regular polyhedra.
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Jenny bought scrapbooking supplies for $156.50. She paid $10.17 in sales tax. What was the sales tax rate on the supplies? If necessary, round your answer to the nearest tenth.
Answers
Answer:
6.5%
Step-by-step explanation:
sales price x sales tax rate = sales tax
156.50 x sales tax rate = 10.17
sales tax rate = 10.17/156.50
sales tax rate = .065 or 6.5%
Which term of the sequence 1/4;-1;-21/4;...is equal to -131/2
Answers
11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).
Step-by-step explanation:
the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the
How are the expressions that you wrote in problem 6 similar? How are they different?
Answers
What is the area of this irregular shape 28in 7in 20in 30in 25in
Answers
Answer:
\(b1=1b2=1h=7b1=1b2=6h=2b1=6b2=9h=2\)
During a middle school lacrosse game, every spectator placed his or her ticket stub into one of several containers. After the
game, the coach chose twenty people to march in the victory parade. What is the sample in this situation?
Choose the correct answer below.
O The lacrosse game spectators
The ticket stubs
O The coach
O The twenty people to march in the victory parade
Answers
The sample in this situation is 'The twenty people to march in the victory parade'
What is sample?The sample size is a term we use to represent the amount or the quantity we have taken from the whole to do some researches.
Given that, during a middle school lacrosse game, every spectator placed his or her ticket stub into one of several containers. After the game, the coach chose twenty people to march in the victory parade. We need to identify the sample in this situation,
A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population.
A sample should represent the population as a whole and not reflect any bias toward a specific attribute.
Since, the coach chose 20 people to March in the sportsmanship parade, the sample in this situation, The 20 people to March in the sportsmanship parade is the sample.
Hence, the sample in this situation is 'The twenty people to march in the victory parade'
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At the airport, d airplanes flew away, and b were still there. How many more airplanes stayed at the airport than flew away?
Answers
Answer:
b-d
Step-by-step explanation:
At the airport, d airplanes flew away, and b were still there.
Number of airplanes which flew away =d Number of airplanes which stayed at the airport =bWe are required to determine how many more airplanes stayed at the airport than flew away.
To do this, we subtract the number of airplanes which flew away from the number which stayed.
Therefore:
Number of more airplanes which stayed than flew away
=Number of airplanes which stayed-Number of airplanes which flew away
= b-d
Select the correct answer. Four figures. Figure 1 shows a right triangle A C B with a line D E parallel to base B C. Figures 2, 3, and 4 shows a triangle A B C with a line D E parallel to base B C. In which figure is ? A. figure 1 B. figure 2 C. figure 3 D. figure 4
Answers
Answer: going to take a wild guess and say figure 2 or figure 4 is correct but I'm going with figure 2
Step-by-step explanation:
Answer: Figure 4
Step-by-step explanation:
I got it right on Edmentum
On which number line are -9 and its opposite shown?
Answers
Answer:
Step-by-step explanation:
The answer is c.
this is because the sections on the line are counting by 3 and 3 away from -12 is -9. it's opposite is shown on the right of this line as shown to the right.
It snowed 3 inches on Monday and 0.5 inches on Tuesday. How much did it snow on Monday and Tuesday combined?
Answers
Answer: It snowed 3.5 inches on Monday and Tuesday combined.
Step-by-step explanation: 3 + 0.5 = 3.5 inches of snow
Hope this helped!
I Need Help Please This Will Only Take 1min…
Answers
The (C) solution of the equation is the value of the variable that causes an equation to be a true statement.
What are equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others.So, the Root or solution of the equation is the value of the variable that turns an equation into a true statement.
An equation that compares two mathematical expressions is a sentence or mathematical statement.The value of the variable that makes the equation true or satisfies it is referred to as the equation's root or solution.For instance,
"x + 2 = 0"The equation's solution in this case is x = - 2.
x² - 1 = 0Here, the equation's roots or solutions are x = 1 and -1.
Therefore, the (C) solution of the equation is the value of the variable that causes an equation to be a true statement.
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The complete question is given below:
The value of the variable which makes an equation a true statement is called the ________ of the equation.
A. Coefficient
B. Equation
C. Solution
D. Algebraic expression
E. Constant
F. Variable
Simplify: 9^0. I’m a bit confused so can somebody please help me? (:
Answers
Answer:
the answer is 1 because the power of any no. 0 is always 1
How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads? Which of the following represents a function
Answers
Answer: The required number of heads = 30
Step-by-step explanation:
Given, Total tosses = 50
The theoretical probability of getting head = \(\dfrac{1}{2}\)
As per given,
Experimental probability = Theoretical probability + 20% of Theoretical probability
= \(\dfrac{1}{2}+\dfrac{20}{100}\times\dfrac{1}{2}\)
= \(\dfrac{1}{2}+\dfrac{1}{10}=0.5+0.1=0.6\)
Required number of heads = (Experimental probability) x (Total tosses )
= 0.6 x 50
= 30
Hence, the required number of heads = 30
A relation is said to be a function if each input value corresponds to a unique output value.For example: {(1,2), (3,4), (2,3), (4,1))}
Answer:
35 is the Answer
7. The Taylor Rule states that the central bank should set the short-term nominal interest rate (i)
based on the inflation gap [the difference between inflation (3.14) and desired inflation (3.14*)] and the
output gap (the percentage difference between real GDP (Y) and potential GDP (Y*) An
example of a Taylor Rule would be the formula
i - 3.14 = 1.5 +0.5(3.14-3.14*) +0.5 (Y-Y*/Y*)
The term on the left-hand side is the real interest rate. Consider the following table
Inflation rate (3.14), %
Target inflation rate (3.14*), %
Output gap, %
Real interest rate
Nominal interest rate
Base Scenario Scenario B Scenario C
4.0
20
2.0
20
0.0
20
20
20
00
a. Fill in the real and nominal interest rates chosen by the policy maker in the base scenano
b. How does scenario B differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move the inflation rate toward its target?
c. How does scenario C differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move output toward the potential level?
d. Suppose a new chair of the central bank is appointed and she switches to a new policy rule of
the form given in the next equation. Recalculate the real and nominal interest rates for the
three scenarios. What has been the effect of the change in weights?
i-3.14=1.5 +0.75(3.14-3.14*) +0.25(Y-Y*/Y*)
Answers
The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%
a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.
b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).
Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).
Now, let's calculate the real interest rate.
Real interest rate in base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)
= 19.22%.
The real interest rate has moved in the direction to move inflation rate towards its target.
c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.
Inflation gap is 0% in both the scenarios
Inflation rate is 3.14% and in scenario C, inflation rate is 2%.
Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)
= 20.15%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.
The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.
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