The equation be x²(x + y)³ - 2xy²(x + y)² then the factorization be x(x + y)²(x - y)(x + 2y).
What is meant by factorization?In mathematics, the term "factorization" or "factoring" refers to the splitting apart or "factoring" of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together yield the original number, matrix, etc.
Factoring is a useful skill in real life. Examples of typical uses include splitting something into equal portions, exchanging money, comparing costs, understanding time, and performing calculations while traveling.
Let the equation be x²(x + y)³ - 2xy²(x + y)²
Factor out common term [tex]$x(x+y)^2= x(x+y)^2\left(x(x+y)-2 y^2\right)$[/tex]
[tex]$=x(x+y)^2\left(x(x+y)-2 y^2\right)$$[/tex]
Expand [tex]$x(x+y)-2 y^2= x^2+x y-2 y^2$[/tex]
simplifying the above equation, we get
[tex]$=x(x+y)^2\left(x^2+x y-2 y^2\right)$$[/tex]
Factor [tex]$x^2+x y-2 y^2=(x-y)(x+2 y)$[/tex]
= x(x + y)²(x - y)(x + 2y)
Therefore, the factorization be x(x + y)²(x - y)(x + 2y).
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pls help meeeeeee with this problem
Answer:
9
Step-by-step explanation:
this is the explanation 6×3=18 18÷2=9
7. Noah edits the school newspaper. He is planning to print a photograph of a
flyer for the upcoming school play. The original flyer has an area of 576
square inches. The picture Noah prints will be a dilation of the flyer using a
scale factor of What will be the area of the picture of the flyer in the
newspaper? (Lesson 5-4)
On solving the provided question, we can say that the area of the picture of the flyer in the newspaper is = 36 square inches.
What is area?The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.
he original flyer has an area of = 576 square inches.
The Picture Noah prints will be a dilation of the flyer using a scale factor of 1/4.
Scale factor k=1/4
So the area of the picture of the flyer in the newspaper is
A = 576 X k^2
A = 576*1/4*1/4
A = 36 sq in.
the area of the picture of the flyer in the newspaper is = 36 square inches.
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The population of the Vatican is 10-4 million and the population of India is 10³ million. How many times more is the population of India than the Vatican? Leave your answer in the form a^b. times more
Answer:
10²
Step-by-step explanation:
assume you typed 10.4 million
so 10³/10.4 ≈ 10²
PLEASEE HELPPP LOOK AT IMAGE
Answer:
y = 3(2)^x
Step-by-step explanation:
If we look at the x and y values, we see that the xs' increase by 1 each time, while the ys' double (12*2 = 24, 24 *2 = 48 etc.).
Because the value doubles each time, we know that this is an exponential equation, and the base (b) is 2.
The general form (as shown) is y = a(b)^x, where a is the initial value (y-intercept or value of y when x = 0) and b is the base.
We can find a by plugging in one x and y coordinate and 2.
For example, we can use (1, 6) to solve for a:
[tex]y=a(b)^x\\6=a(2)^1\\6=a(2)\\3=a[/tex]
If 6 Gardner's can now the grass of a soccer field in 2 hours how many gardeners can mow the same field in 3 hours
The same field can be mowed in 3 hours by 2 gardeners.
A soccer field may be mowed by 6 gardeners in 2 hours, meaning each one works at a rate of 1/6 of the field per hour.
We must ascertain the rate at which the field can be mowed in 3 hours, which is 1/3 of the field every hour, in order to establish the number of gardeners required to mow the same field in that amount of time.
We divide this rate by the rate of each gardener, which is 1/6 of the field each hour, to determine the required number of gardeners, resulting in the equation 1/3 / 1/6 = 2.
Hence, 2 gardeners can mow the same field in 3 hours.
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WILL GIVE brainliest
Answer:
Step-by-step explanation:
Distribute.
4xb and 4x-0.17b
C. 4b - 0.68b
Cheko and Sharko started running at the same time and starting point in a circular stadium. Cheko took 7 minutes to complete a round while Sharko took 6 minutes to complete a round. They started at 9.00 a.m. What time will they meet at the starting point again?
Time is 9:42 a.m. when they meet will at the starting point again.
We have, Cheko and Sharko started running at the same time and starting point. The shape of ground or stadium is circular. Time taken by Cheko to complete the one round of stadium
= 7 minutes
Time taken by Sharko to complete the one round of stadium = 6 minutes.
At 9.00 a.m, both are start running together. We have to calculate time they will meet at the starting point again. So, they will starting together after LCM ( 7, 6) minutes. LCM stands for least common multiple of 7 and 6. The factors of 7 and 6 are the following, 7 = 1×7
=> 6 = 2× 3 × 1
So, LCM (6,7 ) = 2×3×7×1 = 42 minutes
Thus, the again starting time = 9:00 a.m. + 42 minutes = 9: 42 a.m.
Hence, the required time is 9: 42 a.m.
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which number completes the sequence
Answer:
6
Step-by-step explanation:
The number completes the sequence is 6
the cost of living increased by 2% one year. the next year it increased by 3%. work out the total percentage increase over these two years
Answer:
5.06%
Step-by-step explanation:
x = cost of living....then increase it 2 %
1.02 x = new cost of living now increase this 3 %
(1.03) 1.02x = 1.0506x which equates to 5.06% increase in 2 years
a sequence can be defined by an = an-1 + an-2 where a0 = 0 and a1 = 1. What are the first 6 terms of the sequence?
The first six terms of the sequence are 1, 1, 2, 3, 5 and 8. The solution has been obtained by using arithmetic progression.
What is arithmetic progression?
In an arithmetic progression (AP) sequence of numbers, there is always the same amount of difference between any two subsequent integers. Arithmetic Sequence is another name for it.
We are given a sequence as a[tex]_{n}[/tex] = a[tex]_{n-1}[/tex] + a[tex]_{n-2}[/tex] where a₀ = 0 and a₁ = 1.
So, the first term is a₁ = 1
The second term is
a₂ = a₂₋₁ + a₂₋₂
a₂ = a₁ + a₀
a₂ = 1
The third term is
a₃ = a₃₋₁ + a₃₋₂
a₃ = a₂ + a₁
a₃ = 1 + 1
a₃ = 2
The fourth term is
a₄ = a₄₋₁ + a₄₋₂
a₄ = a₃ + a₂
a₄ = 2 + 1
a₄ = 3
The fifth term is
a₅ = a₅₋₁ + a₅₋₂
a₅ = a₄ + a₃
a₅ = 3 + 2
a₅ = 5
The sixth term is
a₆ = a₆₋₁ + a₆₋₂
a₆ = a₅ + a₄
a₆ = 5 + 3
a₆ = 8
Hence, the first six terms of the sequence are 1, 1, 2, 3, 5 and 8.
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2y8x = 20
y = [?]x +
Mark also has a 1:40 model Phantom II plane.The real Phantom II has a wingspan of 465”. What’s the wing span of the model in inches.
“=inches
The wing span of the 1:40 model Phantom II is 18.31 inches.
What is unit conversion?
A unit conversion is a conversion with different units of measurements of same quantity. It is a process with multiple steps that involves multiplication or division by particular factor.
Wingspan of real Phantom II =465''(in millimeter)
1 inch = 2.54 cm⇒25.4 mm.
465''=[tex]\frac{465}{25.4}[/tex]
= 18.31 inches.
Hence, wingspan of the model 1:40 model Phantom II in inches is 18.31.
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Mark bought s sheets of stickers. There are 9 stickers on each sheet. Write an expression that
shows how many stickers Mark bought.
The expression to find the total number of stickers bought by Mark is x = 9s.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The number of sheets of stickers Mark bought is denoted by the variable = s.
The number of stickers on each sheet is = 9
Let the total number of stickers be x.
Use the arithmetic operation of multiplication.
Then the expression will be -
Total number of stickers = Number of sheets of stickers × Number of stickers on each sheet
Substitute the values into equation -
x = s × 9
x = 9s
Therefore, the expression is obtained as x = 9s
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Identify the like terms in the expression:
-12x +15y -17x +16y
what is the slope of the line shown below? (-2,5) (3,-5)
Answer: -2
Step-by-step explanation: use the slope formula.
HELP PLS AND FAST!!!
Answer:
The correct equation you're looking for is the first choice: [tex]\frac{240 miles}{5 hours}[/tex] = 48 miles per hour.
Step-by-step explanation:
The formula to show the relationship between rate, time, and distance is [tex]rt=d[/tex], where [tex]r[/tex] represents the rate of change, [tex]t[/tex] represents time, and [tex]d[/tex] represents the total distance. Since you are given the distance and time, and are looking for the rate of change, then you need to divide the total distance traveled by the time it took to travel that distance, so the correct equation is [tex]\frac{240miles}{5hours}[/tex] = 48 miles per hour.
Have a great day! Feel free to let me know if you have any more questions :)
An automat machine make good pieces with a probability 0,96. Wich are the chances that the two piece is wrong?
The given information states that the machine produces good pieces with a probability of 0.96, which means that there is a 0.04 probability of getting a bad piece.
To calculate the probability of getting two bad pieces in a row, we multiply the probabilities of each individual bad piece:
0.04 * 0.04 = 0.0016
So the chances of getting two bad pieces are 0.0016, or 0.16%. This means that out of 100 tries, you would expect to get two bad pieces in a row 0.16 times.
It's vital to remember that independent events, like obtaining two terrible pieces, have probabilities that are determined by multiplying the individual possibilities.
This is based on the idea of the multiplication rule of probability, which states that the likelihood of two unrelated events occurring simultaneously is the sum of the probabilities of each event occurring separately.
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Doris and Miguel are saving money weekly but at different rates. Doris
and Miguel both write and graph equations to represent their savings. In
both equations y represents the amount in savings account after x
number of weeks. When the equations are graphed, the lines intersect at
the point (6,114). Which statement best explains the point of
intersection?
Miguel will have $114 more than Doris after 6 weeks.
Doris will have $114 more than Miguel after 6 weeks.
Doris and Miguel will have the same amount after 6 weeks.
Doris and Miguel will have the same amount after 114 weeks.
Answer:
Doris and Miguel will have the same amount after 6 weeks.
Step-by-step explanation:
if 6 is the amount of weeks and 114 is the savings, then the point that the lines will cross at represents 114 dollars after 6 weeks. this means that after six weeks, both doris and miguel will have 114 dollars.
A salesman sold 75 percent of his first shipment of 800 units. How many of his next shipment of 600 units must he sell in order to have sold 80 percent of all of the units?
He must sell 520 units from the second shipment in order to have sold 80 percent of all of the unit.
This is mathematical equations.
The salesman sold 75% of 800 units, so he sold 0.75 * 800 = 600 units from the first shipment.
The salesman wants to sell 80% of all the units, which is a total of 0.80 * (800 + 600) = 0.80 * 1400 = 1120 units.
To find out how many units he must sell from the second shipment, we subtract the number of units he has already sold from the number of units he wants to sell:
1120 units - 600 units = 520 units.
Therefore, the salesman must sell 520 units from the second shipment in order to have sold 80% of all the units.
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15 more than twice a number is 37. Wht is the number
A number which is 15 more than twice a number is 37 is 11.
Let the number be N.
Let's set up the equation.
A number is 15 more than twice a number is 37,
2N + 15 = 37
Let's subtract 15 from both sides.
2N = 22
Divide both sides by 2, and you get
N = 11
So the number which is 15 more than twice a number is 37 is 11.
A number system is a means of representing numbers. It is a method of representing numbers in a set of numbers consistently by using digits or other symbols. Each number receives a unique representation as well as information about the arithmetic and algebraic structure of the numbers. Addition, subtraction, multiplication, and division are just a few of the mathematical operations we may carry out using it.
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PLEASE HURRY! You encounter the following statement and explanation when reviewing a report at your finance job: (14^0/14^3)^1/3=14^-2/3 They are equivalent because (14/14^3)^1/3=(14^-2)^1/3
You notice this statement and explanation in the report are wrong. explain why it is wrong and give the correct answer.
The expressions are not equal and the explanation is wrong because the index forms have different exponential values.
The correct answer is 14^-1/3
How to determine the correct optionEquivalent expressions are known as expressions that are the same solution but differ in the mode of their arrangement.
From the information given, we have the index forms;
(14^0/14^3)^1/3=14^-2/3
It is important to note that exponents with zero equals 1.
Then, we have that;
1/14^1/3 = 14 ^-2/3
Take the inverse of the exponent
14^-1/3 is not equal to 14^-2/3
Hence, the correct answer is 14^-1/3
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complete the equivalent fractions
please help
brainly i have 19 mins left
Answer:
4) 175
5) 2
6) 72
7) 48
8) 45
9) 5
10) 18
11) 3
12) 10
13) 30
14) 12
15) 1
16) 2
17) 2
18) 8
Step-by-step explanation:
The easiest way to do this is to cross-multiply.
Ans:
Q4. 175
Q5. 2
Q6. 72
Q7. 48
Q8. 45
Q9. 5
Q10. 18
Q11. 3
Q12. 10
Q13. 30
Q14. 12
Q15. 1
Q16. 2
Q17. 2
Q18. 8
a large Ghirardelli bar is 30cm long and 12cm wide. a smaller Ghirardelli bar is 10cm long. If the bars are similar, what is the width of the smaller Ghirardelli's bar?
Answer:
Step-by-step explanation:
if the bars are similar, they are proportional.
make a proportion: length = 30 = 10
width 12 x
cross multiply: 12 times 10 = 120
divide by the number that ids left - 120 ÷ 30 = 4 cm
The width of the smaller bar is 4 cm.
which expression is equivalent to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a
The equivalent expression of 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a is 136/120a + 107/120b.
One common way to simplify an expression is to use the unitary method, which involves finding a common denominator and then canceling out like terms.
In this case, we'll use the unitary method to find an equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a.
To start, we'll find a common denominator for all the terms in the expression.
The least common multiple of 5, 3, 8, 6, and 5 is 120. Now, we can convert all the fractions to have a denominator of 120.
Next, we'll simplify each term by dividing the numerator and denominator by their greatest common factor.
96/120a can be simplified to 8/10a by dividing both the numerator and denominator by 8. 80/120b can be simplified to 2/3b by dividing both the numerator and denominator by 40. And so on.
Finally, we'll rearrange the terms and simplify them using the unitary method. We'll start by canceling out like terms, which have the same variable and the same sign.
So, 8/10a and 96/120a are both positive and have the variable a, so we can simplify them to 104/120a.
Similarly, we can simplify 2/3b and 105/120b to 107/120b. We'll then add up all the positive terms and subtract all the negative terms.
The final equivalent expression is
=> 104/120a + 107/120b + 15/120 - 90/120
=> (104 + 107 + 15 - 90)/120a + (107/120)b
=> 136/120a + 107/120b.
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Find the solution to the linear system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3:
The solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:
[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]
[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]
Let x(t) and y(t) be the solution of the linear system of differential equations:
[tex]$\frac{dx}{dt} = ax + by$[/tex]
[tex]$\frac{dy}{dt} = cx + dy$[/tex]
with initial conditions x(0)=5 and y(0)=3.
The general solution of the system of differential equations can be written as:
[tex]$x(t) = e^{at} (X0 \cos(bt) + Y0 \sin(bt))$[/tex]
[tex]$y(t) = e^{ct} (X0 \sin(bt) - Y0 \cos(bt))$[/tex]
where X0 = 5 and Y0 = 3.
Therefore, the solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:
[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]
[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]
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HELP ME PLEASE!!! 15 POINTS
In the diagram, KG, JF, AE and AH intersect at point A. Use this diagram for problems 1-3.
1. Describe the relevant angle relationships in the diagram.
2. Write and solve an equation to find the value of x.
3. What are the measures of ZJAH and ZGAH?
The relevant angle relationship in the diagram is that the total angle of line JKEF = the total angle on line JHGF.
The value of X = 20
The measures of ZJAH and ZGAH = 60° and 100° respectively.
How to solve the equation used to fine the missing value of X?To find the value of X, the angle of the straight line = 180°
Therefore, 3x+5x+X = 180
180 = 9x
X = 180/9
X = 20
Therefore the measures of <JAH = 3 × 20 = 60°
the measure of <GAH = 5×20 = 100°
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pls help, geometry !!!!!! NEED HELP ASAP
Step-by-step explanation:
what is the question ?
without an actual question I can only "daydream" things about this information.
EB is the diameter, FB is therefore the radius.
since FB = 3 units, EB = 2×FB = 2×3 = 6 units.
the arc angle AB = 120°.
if you need to express the angle in radians, remember :
360° (the full circle) = 2pi
120° = 360/3 = 2pi/3
the arc angle AE is the supplementary angle to AB (both together have 180° or 2pi/2 = pi).
180 = AB + AE = 120 + AE
AE = 180 - 120 = 60°
60° = 360/6 = 2pi/6 = pi/3
the arc angle BC = 45°.
45° = 360/8 = 2pi/8 = pi/4
the arc angle CD = 30°
30° = 360/12 = 2pi/12 = pi/6
the arc angle ED is the supplementary angle to BC and CD.
180 = ED + BC + CD = ED + 45 + 30 = ED + 75
ED = 180 - 75 = 105°
105° = pi - pi/4 - pi/6 = 12pi/12 - 3pi/12 - 2pi/12 = 7pi/12
the sum of
AB + BC + CD = 2pi/3 + pi/4 + pi/6 =
= 4×2pi/12 + 3pi/12 + 2pi/12 =
= 8pi/12 + 3pi/12 + 2pi/12 = 13pi/12
so, nothing fits to any of your answers.
again, I am not sure what problem you need to solve here.
maybe you can build your answer out of the various pieces I gave you here.
Marcus bought a plant that originally cost $40. All plants were discounted 35%. What did Marcus pay for the plant after the discount
50 POINTS. PLS REFER TO PICTURE
The correct answer is:
Function f is translated to the right 7 units.
Function f is translated down 4 units
A man and a woman receive a monthly salary of gh3725 and gh2962 respectively. Find their total income after 3 and half years
Answer:
gh280,854
Step-by-step explanation:
You want the total income after 3 and half years of a man and a woman who receive a monthly salary of gh3725 and gh2962 respectively.
TotalYou can add up the income from each of the months for each of them, or you can use multiplication to simplify the problem.
The total income each month is ...
gh3725 +gh2962 = gh6687
The total received in 42 months is ...
42 × gh6687 = gh280,854
Their total income after 3 1/2 years is gh280,854.
__
Additional comment
There are 12 months in a year, so ...
3×12 +1/2×12 = 36 +6 = 42
months in 3 1/2 years.