For the expression:
(9x^2 + 4y^2 -12xy) / (4y^2 - 9x^2)
Find the domain
Find the domain of the simplified expression
The domain of an expression is the set of input values the expression can take
The domain of the expression is [tex]y \ne 1.5x[/tex]The domain of the simplified expression is [tex]y \ne -1.5x[/tex](a) The domain of the expression
The expression is given as:
[tex]\frac{(9x^2 + 4y^2 - 12xy)}{(4y^2 - 9x^2)}[/tex]
Set the denominator to 0, to determine the domain
[tex](4y^2 - 9x^2) = 0[/tex]
Remove brackets
[tex]4y^2 - 9x^2 = 0[/tex]
Add 9x^2 to both sides
[tex]4y^2 = 9x^2[/tex]
Divide both sides by 4
[tex]y^2 = 2.25x^2[/tex]
Take positive square roots of both sides
[tex]y = 1.5x[/tex]
Hence, the domain of the expression is [tex]y \ne 1.5x[/tex]
(b) The domain of the simplified expression
The expression is given as:
[tex]\frac{(9x^2 + 4y^2 - 12xy)}{(4y^2 - 9x^2)}[/tex]
Rewrite as:
[tex]\frac{(9x^2 + 4y^2 - 12xy)}{(4y^2 - 9x^2)} = \frac{(9x^2 - 12xy+ 4y^2 )}{((2y)^2 - (3x)^2)}[/tex]
Expand the numerator
[tex]\frac{(9x^2 + 4y^2 - 12xy)}{(4y^2 - 9x^2)} = \frac{(9x^2 - 6xy - 6xy+ 4y^2 )}{((2y)^2 - (3x)^2)}[/tex]
Factorize the numerator
[tex]\frac{(9x^2 + 4y^2 - 12xy)}{(4y^2 - 9x^2)} = \frac{3x(3x - 2y) - 2y(3x- 2y )}{((2y)^2 - (3x)^2)}[/tex]
Factor out 3x - 2y
[tex]\frac{(9x^2 + 4y^2 - 12xy)}{(4y^2 - 9x^2)} = \frac{(3x - 2y)(3x- 2y )}{((2y)^2 - (3x)^2)}[/tex]
Express the denominator as a difference of two squares
[tex]\frac{(9x^2 + 4y^2 - 12xy)}{(4y^2 - 9x^2)} = \frac{(3x - 2y)(3x- 2y )}{(2y - 3x)(2y + 3x))}[/tex]
Rewrite as:
[tex]\frac{(9x^2 + 4y^2 - 12xy)}{(4y^2 - 9x^2)} = \frac{-(2y - 3x)(3x- 2y )}{(2y - 3x)(2y + 3x))}[/tex]
Cancel out the common term
[tex]\frac{(9x^2 + 4y^2 - 12xy)}{(4y^2 - 9x^2)} = \frac{-(3x- 2y )}{(2y + 3x)}[/tex]
Set the denominator to 0, to determine the domain
[tex]2y + 3x= 0[/tex]
Subtract 3x from both sides
[tex]2y= -3x[/tex]
Divide both sides by 2
[tex]y= -1.5x[/tex]
Hence, the domain of the simplified expression is [tex]y \ne -1.5x[/tex]
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Explanation:
Domain: y does not equal 1.5x and y does not equal -1.5x
Simplifies domain: y does not equal -1.5x
The scientific study of population is known as
Answer:
Demographics help us understand the size, status, and behavior of populations. ... The field of science interested in collecting and analyzing these numbers is termed population demographics, also known as demography. Broadly defined, demography is the study of the characteristics of populations.
Explanation:
Give three examples of cow practices or beliefs that would be considered different from popular beliefs. What is the reasoning for these beliefs/practices.
The examples of cow practices that were different from popular beliefs include:
1. Cow meat was prohibited as good for Hindus.2. Cow was a god in Hindi and was worshipped.3. Cows are treated by Hindus as part of their family.It should be noted that in Hinduism, cow wasn't eaten as food as it was considered a symbol of life and shouldn't be killed.
Verses of the Rigveda considered the cow to be a goddesses that was identified with Aditi himself. Indian families have at least a diary cow that they treat as the member of their family.
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a triangle has angles that measure (x+40), (3x +20), and (10x-20) respectively. which of the following terms best describes this triangle?
Answer:
Isoceles
Explanation:
Had it on my test
The term that best describes the given triangle is known as Isosceles. Thus, the correct option for this question is C.
What do you mean by Isosceles triangle?An Isosceles triangle may be defined as a type of triangle in which two sides have the same length. With respect to the length of the sides, the angles opposite to the two sides correspond to each other and are also always equal.
According to the question,
The angles of a triangle are determined by the following concept:
x+40 + 3x+20 + 10x-20 = 180.
14x + 40 = 180.
14x = 180 - 40 = 140, x = 10.
Now, the angles are 50, 50, and 80.
Two angles are equal which means two sides are definitely equal.
Therefore, an isosceles is a term that best describes the given triangle. Thus, the correct option for this question is C.
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when the moon appears to completely cover the sun, the moon must be at which phase?
Answer: New moon
Explanation: New moon because the moon is in-between the sun and the earth so there is no light to be reflected back to earth if there is no light in that side.
Look at the series: 2, 1, (1/2), (1/4), ... What number should come next?
Answer:
1/8, 1/16, 1/32, 1/64
Explanation:
Each number is getting divided by 2
3 pros and 3 cons why jenny should or should not do a paleio diet
Which of the following is not an implication of large U.S. trade deficits?
U.S. productivity is falling.
O
Deficits cause the U.S. dollar to depreciate.
O
The nation must consume within its production possibilities curve.
O
All of these are implications of large trade deficits.
Answer:
All of these are implications of large trade deficits.
Deficits lead the US dollar to weaken, productivity to plummet, and the nation must spend within its production possibilities curve, all of which are consequences of big US trade deficits. Option D is correct.
What is the trade deficits?A trade deficit, also known as a negative balance of trade, occurs when a country spends more money than it earns in international commerce with the rest of the world.
U.S. productivity is falling, The nation must consume within its production possibilities curve. Deficits weaken the US dollar, reduce productivity, and force the country to spend inside its production possibilities curve, all of which are effects of large US trade deficits.
When a country purchases more than it sells, it has a trade imbalance. In other terms, a trade imbalance occurs when a country buys more than it exports.
Therefore, option D is correct.
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The equation 3x + 2 = 29 is modeled below.
What causes weather?
1.The spin of the planet
2.Uneven heating of the earth from the sun
3.The hydrologic cycle
4.Climate change
Answer:
2. Uneven heating of the earth from the sun
Explanation:
Weather on Earth is caused by heat from the sun and movement of the air. All weather happens in the lower layer of Earth's atmosphere, which is a layer of gases surrounding Earth. The sun's heat warms the air in this layer to different temperature levels in different places.
How is a roller coaster similar to flying
The nuclear family into which a person is born or adopted.
-family
-nuclear family
-family of orientation
-family of procreation
-extended family
-kinship
Answer:
Family
Explanation:
Family is defined as a group of people related by blood or adoption. so it doesn't matters whether born or adopted it is still a family.
On a test where the scores are normally distributed, approximately what percentage of the scores are within two
standard deviations of the mean?
O 20%
O 33%
O 50%
O 68%
0 95%
Country Z is both a producer and an importer of green tea. If country Z imposes a tariff on imports of green tea, which of the following will occur in the domestic market of green tea?
Which of the following rocks is likely to exfoliate?
Shale
Slate
Igneous
All of the above
Answer:
All of them
Explanation:
They all have a good chance of breaking up after being weathered
Which injury would most likely result in the separation of muscle and bone that were once connected?
a torn tendon
a blocked trachea
a ruptured spleen
a broken blood vessel
Answer:
A
Explanation:
:)
In the 1920s which united states action furthered the goal of international peace
Distribution chart:
A-claim: All S are P
E-claim: No S are P
I-claim: Some S are P
O-claim: Some S are not P
Evaluate the following categorical syllogisms:
1. "All A are B. All A are C. Therefore, all B are C."
2. "All B are C. No C are D. Therefore, no B are D."
3."Some A are not B. Some B are C. Therefore, some C are not A."
4."All framistans are veeblefetzers. Some veeblefetzers are carbostats. Some framistans are carbostats."
Answer:
Please help me i need to finish this and i can't find the answer
Question # 1
Multiple Choice
A holistic approach to health care involves _____.
treating all of the current illnesses
treating all of the current illnesses
creating special care plans
creating special care plans
looking at all the patient’s problems
looking at all the patient’s problems
focusing on the general wellness of patients
focusing on the general wellness of patients
Question # 2
Multiple Choice
Geriatric means _____.
relating to the ill
relating to the ill
pertaining to the elderly
pertaining to the elderly
long-term care
long-term care
individuals with multiple illnesses
Approximately how much time did it take for the human population to initially double? (to go from 250 million to 500 million).
Answer:
300 years
Explanation:
thats what i that is i think sorry if i'm wrong this is my first question
40 PTS!!!!!!
Tori has been a personal secretary for the Governor for the past three years. During this time, Tori has observed what he considers to be insincerity on the part of the Governor with regards to interest in social causes. It seems to Tori that the Governor is more interested in spending the federal government’s money than actually helping people. Tori reasons, "I think the public would be interested in this hypocrisy. I will contact a publisher to find out how much I might be paid for the story. They may even put me on television. This could be a big win for me!" Which philosophy best depicts Tori's reasoning:
Egoism
Act Utility
Rule Utility
Kantian Ethics
Don’t have a question
Answer:
don't have an answer :):):):):)
Answer:
but thanks for the pts
......
I need help anyone!!!
I have a dress rehearsal tomorrow and i need a suit like outfit what do i do (in middle school)
Answer:ask your mum for pounds and by one in the store here in englind mate
Explanation: JK just want the points
Try using a dress shirt, like a button up shirt and if you have like a blazer, or a nice other jacket coat type of thing put those together with some jeans and your golden my friend. :D
how is a strong democracy sustained
Profit equals the total amount of money made minus expenses. prices. revenue. supply.
Answer:
expenses
Explanation:
The equation for profit is revenue-expenses
not prices: remember these as price tags on the bread you get at supermarkets
not revenue: revenue is the total amount of money made
not supply: completely unrelated to price
Profit equals the total amount of money made minus expenses.
What is Profit?This is the gain or profit realized from a transaction. It can be calculated by using the formula below:
Profit = Revenue - Expenses.
The profit is important as it helps business owners in the fixing of prices of goods and services so as to ensure that gain is maximized and continuous running of the company.
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Question 8 of 10
You are paid a wage based on the number of hours you work multiplied by the
per hour.
A. rate
B. times
c. speed
D. number
SUBMIT
On December 31, 2018, Country Living Sales has 10-year Bonds Payable of $89,000 and Discount on Bonds Payable of $2350. How will this be shown on the December 31, 2018 Balance Sheet?
Answer:
87,650
Explanation:
It would look like this because you subtract,
What does the simile mean between a roller coaster can feel like flying
Answer:
Knowing that a simile is a comparison between two things/ideas using the words "like" or "as"--->
A roller coaster can feel like flying because similar to how you would imagine flying to feel like (almost free-falling, liberated, vulnerable, yet invigorating, etc.), a roller coaster enables you to feel the same way, you are high up in the air racing at fast speeds and looping in some way that somehow defies the laws of physics ✨ yes fun stuff
Essentially, roller coasters can feel like flying because flying and roller coasters give the same feelings of excitement and also being high up in the air, since being on the ground won't take ya anywhere.
What percentage of students were noted as having different values from their parents?
a. 1%
c. 56%
b. 15%
d. 99%
Please select the best answer from the choices provided
Α
B
C
D
Jimin is trying to convince himself that it's ok to cheat on a test. Jimin is thinking things like, “This class is too hard. The teacher wants me to cheat! And the whole course is a waste of time. I shouldn't have to take it." Why is Jimin telling himself things like that?
Group of answer choices
Because Jimin is struggling with a self-fulfilling prophecy
Because Jimin has developed disorganized attachment with his teacher, Mr. Suga
Because Jimin is experiencing the actor-observer effect
Because Jimin is feeling cognitive dissonance
Answer:
Because Jimin is struggling with self-fullfilling prophecy
Answer:
because jimin has more works to do like interviews and stuff coz he's a member of bts (just kidding)
So it's actually because Jimin is struggling with a self-fulfilling prophecy
It would be "Because Jimin has developed disorganized attachment with his teacher, Mr. Suga" because Mr. Suga is extremely good even if he looks cold hearted (which he isn't)
LOL what is this....a whole bts story
Scales can represent
a. A range of information
b. A range of resources
c. Proportional measurement
d. All of the above
Please select the best answer from the choices provided
Α
B
C
D
Answer:
I would suggest c for the answer
Answer:
D
Explanation:
