NO LINKS! Please help me with this problem
What is the standard form of the equation of the ellipse?
Answers
Answer:
[tex]\frac{x^2}{9}+\frac{y^2}{4}=1[/tex]
Step-by-step explanation:
So an ellipse can be expressed in two different but very similar forms:
Horizontal Major Axis:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Vertical Major Axis:
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]
In both equations the length of the major axis is "2a" and the length of the minor axis is "2b"
In the equation you provided, the major axis is horizontal, and the minor axis is vertical.
So looking at the horizontal length, you can see that it's 6, and since this ellipse has a horizontal major axis, that means 2a=6, which means a=3
Looking at the vertical length, you can see that it's 4, and since the ellipse has a vertical minor axis, that means 2b=4, which means b=2
The last thing to note is that the center of an ellipse is (h, k) in the equation, and since here the center is (0, 0) it's (x-0)^2 and (y-0)^2 in the denominator which is just x^2 and y^2
So let's plug in the values into the equation:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
(h, k) = (0, 0)
a = 3
b = 2
[tex]\frac{x^2}{3^2}+\frac{y^2}{2^2}=1\\\\\frac{x^2}{9}+\frac{y^2}{4}=1[/tex]
Here we go ~
The given figure is of a horizontal ellipse with :
Length of major axis = 2a = 6so, a = 3
Length of minor axis = 2b = 4hence, b = 2
And as it's shown in the figure, the ellipse has its centre at origin, so we can write it's equation as :
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{b {}^{2} } = 1[/tex]
[ now, plug in the values ]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{ {3}^{2} } + \cfrac{ {y}^{2} }{2 {}^{2} } = 1[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{ {9}^{} } + \cfrac{ {y}^{2} }{4 {}^{} } = 1[/tex]
That's all, ask me if you have any questions ~
Related Questions
Find the range of y=7x-34/x-5
Answers
Answer:
Option A
Here you go.
Hope this help!!
Good luck!!
Horizontal asymptote
y=7x/x=7The range is
(-oo,oo)-{7}Or
R-{7}Option A
4x-9y=36 find the missing y-coordinate
Answers
The y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4
How to find the y-intercept of a function?The y-intercept of a function is the point where the value of x is zero. Given the function below;
4x-9y=36
when the value of x is zero, hence;
4(0) - 9y = 36
Simplify to have:
0 - 9y = 36
-9y = 36
Divide both sides by -9 to have:
-9y/-9 = 36/-9
y = -4
Hence the y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4
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Database A contains 40 data items and is made up with an equal number of the values of 0 and 100 and has a mean of 50. Database B also has 40 entries made up equally of the values 49 and51 and also has a mean of 50. Which database will have the smaller value for its standard deviation?
Set A: 1 2 3 23 24 25
Set B: 9 10 11 14 16 18
Answers
If we compare the given values then we can find that the database B is more likely to have smaller standard deviation.
Given that the values in database A are 0 from 100 and has mean of 50 and Database B has entries from 49 to 51 and also has mean of 50.
We are required to find the database whose standard deviation is lower.
Standard deviation measures the variation of values. It is calculated after finding mean. The square of a standard deviation is known as variance.
Database A has values from 0 to 100 and has mean of 50. Because the values are somewhat very larger than 50 and in database B has values from 49 to 51,there are more chances that the standard deviation of database B will have smaller value than from standard deviation of database A.
Hence if we compare the given values then we can find that the database B is more likely to have smaller standard deviation.
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3x^2 + 12x - 96 help please
Answers
Answer:
fully factored form = 3(x-4)(x+8)
Step-by-step explanation:
first you factor 3 out
3(x^2+4x-32)
then factor it
3(x-4)(x+8)
Answer:
3(x-4)(x+8) This is the answer :)
Step-by-step explanation:
3x^2+12x - 96
3(x^2+4x-32)
3(x^2+4x--32)
3(x^2+8x-4x-32)
3(x^2+8x-4x-32)
3(x(x+8)-4(x+8))
3(x(x+8)-4(x+8))
3(x-4)(x+8)
3(x=4)(x+8)
A large high school has 3,000 students.
During a one-week period, 75 students were
selected at random various times of the day.
Each student was asked if he or she had one
or more social media accounts. The survey
found that 3 out of 75 students did not have
any social media accounts. Estimate the
number of students in the entire school who
do not have social media accounts.
Answers
Answer:
120 students don't have social media accounts
Step-by-step explanation:
Whether the sample is representative:
Estimate: [tex]\frac{3}{75} (3000)=\frac{9000}{75} =120[/tex]
Hope this helps
Suppose the reserve requirement is changed to 4 percent. Reconstruct the balance sheet of the total banking system after all banks have fully utilized their lending capacity.
c. By how much has the money supply changed as a result of the lower reserve requirement (part b)?
$
billion
Answers
The total amount in the transaction account is
= $625.
The amount in the transaction account is
=75
What is a transaction account?
Your salary and any other payments that you get may be deposited into an account known as a transaction account, which is an account that you utilize on a day-to-day basis. When connected to a Visa card, your transaction account may also be used to pay bills, go shopping, and make other types of payments that are commonplace. Balances in transaction accounts do not accrue any interest for the account holder.
b) Now if the reserve requirement changes to 5%, we need to reconstruct the balance sheet of the total banking system.
Calculate the initial total reserve using the new reserve requirement as follows:
= 4% x500
= 0.04×500
=20
Calculate the excess reserve as follows:
=30-20
= $10
Calculate the money multiplier as follows:
=1/4%
=1/0.04
=25
Calculate the increase in transaction account as follows:
=25x $5
= $125
Hence, the total amount in the transaction account is
$500+ $125
= $625.
c)
Therefore, the amount in the transaction account is
=600-525
=75
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What shape best describes the cross-section cut perpendicular to the base of a right rectangular prism? O Parallelogram Trapezoid O Rectangle O Rhombus
Answers
The cross-section perpendicular to the base of a right rectangular prism is a rectangle.
What is a three dimensional shape?A shape or a solid that has three dimensions that is length, width and height is called a 3D shape. 3D shapes have faces, edges, and vertices. Examples are cylinder, cone, prism, pyramid.
A shape that has two dimensions is called a 2D shape. 2D shapes have breadth and length.
The cross-section perpendicular to the base of a right rectangular prism is a rectangle.
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Let r(x)=x^2 - x + 14. Find all values of a such that r(a) = 20.
Answers
Answer:
a=–2, 3
Step-by-step explanation:
r(a)=20
a²–a+14=20===> a²–a–6=0===> (a–3)(a+2)
please help i would really appreciate it pallas athena
Answers
The fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively. option D
Long division9√4.000
= 4.000/9
= 0.444
Approximately,
= 0.4
Fraction
This is a ratio of two numbers, the numerator and the denominator, usually written one above the other and separated by a horizontal bar.
Decimal
This is a number expressed in the decimal system (base 10).
Therefore, the fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively.
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please help me! in need of help due tomorrow!
Answers
Answer:
Step-by-step explanation:
(1). A = π r²
A = 4 π
Area of shaded region is [tex]\frac{4\pi *260}{360}[/tex] = [tex]\frac{26}{9} \pi[/tex] or [tex]\frac{26\pi }{9}[/tex]
(2). C = 4 π
In this case, the length of the bigger arc and the area of shaded region happen to be the same.
The length of the arc ADB is [tex]\frac{26}{9} \pi[/tex] or [tex]\frac{26\pi }{9}[/tex]
Write expressions for the length and width of a rectangle that has an area equal to 3x2-5x+2.
Answers
Answer:
x - 2, x - 3
Step-by-step explanation:
3x² - 5x + 2
x² - 5x + 6
(x - 3)(x - 2)
length = x - 2
width = x - 3
Some banks charge a fee on savings accounts that are left inactive for an extended period of time.
The equation `y=5000\left(0.98\right)^{x}` represents the value, y, of one account that was left inactive for a period of x years.
According to the equation, is the balance in this account increasing or decreasing?
Answers
Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.
How to recognize Exponential Function.Exponential Function can be used for increase rate and also for decay rate. The difference between the two are the plus and minus signs. To put it in another perspective, If Y = P(M)³
If M is less than one, that means it is decaying or decreasing. And if M is greater than one, that means it is increasing.
Given that Some banks charge a fee on savings accounts that are left inactive for an extended period of time. And the equation
y = 5000(0.98)^x represents the value, y, of one account that was left inactive for a period of x years.
According to the equation, to know if the balance in this account is increasing or decreasing, we will analyze the value 0.98.
Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.
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50% is what percent of 40%?
Answers
Answer:
125%Step-by-step explanation:
[tex] \frac{50}{100} \times 40[/tex][tex] = 125\%[/tex]Pharmacy receives an order for morphine sulfate 1/4 gr IM stat. The concentration on hand is 10mg per ml. How many ml Is needed for this dose?
Answers
The dosage needed for this in an order for morphine sulfate 1/4 gr IM stat is 1.5 ml.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
One grain = 60mg, hence:
1/4 gr = 1/4 gr * 60 mg per gr = 15 mg
Hence, for 10 mg per ml:
Dosage = 15 mg / 10 mg per ml = 1.5 ml
The dosage needed for this in an order for morphine sulfate 1/4 gr IM stat is 1.5 ml.
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Tell if each pairs of segments are congruent
Yes/No
A. AB and BC
B. AC and BD
Answers
A. No, AB and BC are not congruent
B. No, AC and BD are not congruent
Calculating length of a segmentFrom the question, we are to determine if the given pairs of segments are congruent
To do this, we will determine the length of the line segments
Consider the given number line,
AB = -2 - (-5) = -2 + 5 = 3
BC = 0 - (-2) = 0 + 2 = 2
AC = 0 - (-5) = 0 + 5 = 5
BD = 5 - (-2) = 5 + 2 = 7
Now,
A. AB and BC
AB = 3 and BC =2
∴ AB and BC are not congruent.
Thus, No
A. AC and BD
AC = 5 and BD = 7
∴ AC and BD are not congruent.
Thus, No
Hence,
A. No, AB and BC are not congruent
B. No, AC and BD are not congruent
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Asap help with this PLEASE
Answers
Answer:
124.5°
Step-by-step explanation:
Let the smallest angle be x. Then, the sum of the angles is an arithmetic sequence with first term x, common difference 7, and 8 terms.
Using the sum of an arithmetic series formula,
[tex]\frac{8}{2}(2x+(8-1)(7))=1080 \\ \\ 4(2x+49)=1080 \\ \\ 2x+49=270 \\ \\ 2x=221 \\ \\ x=110.5[/tex]
So, the third angle is 110.5+14=124.5
Find the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3.
Answers
The remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
How to determine the remainder?The function is given as:
f(x)=−2x3+x2−4x+1 is divided by x+3.
Set the divisor to 0
x + 3 = 0
Solve for x
x = -3
Calculate f(-3)
f(-3)=−2(-3)^3+(-3)^2 − 4(-3) + 1
Evaluate the expression
f(-3)= 76
Hence, the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
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He wants to earn 481$ By mowing lawns and he charge $22 for each long what is the maximum number of lungs that he needs to mow to reach his goal of $481
Answers
[tex]\stackrel{\stackrel{total~amount}{goal}}{481}~~ = ~~22(lawn)\implies \cfrac{481}{22}=lawn\implies \stackrel{rounded}{22}\approx lawn[/tex]
The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.
1.72 1.8 1.86 1.88 1.74 1.86
What is the mean height of the ocean's first high tide for the 6 days?
1.81 meters
1.83 meters
1.86 meters
1.87 meters
Answers
The required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.
Given that,
The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.
Number of days = 1 2 3 4 5 6 Total = 6
1.72 1.8 1.86 1.88 1.74 1.86
What is average?
The average of the values is the ratio of the total sum of values to the number of values.
Since the mean of the heights of the tides,
= sum of heights / number of heights observation
= (1.7 + 1.8 + 1.86 + 1.88 + 1.74 + 1.86)/6
= 10.86/6
= 1.81 meters
Thus, the required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.
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Solve.
|7x -5| = |8x -4
Answers
Answer:
9/25 or -1/11
Step-by-step explanation:
2 outcome
1; 7x-5=18x-4
2;-(7x-5)=18-4
There are 3
denominations of bills in a wallet: $1, $5, and $10.
There are 5 fewer $5-bills than $1-bills. There are half as many
$10-bills as $5-bills. If there is $115 altogether, find the number of
each type of bill in the wallet.
Answers
The number of $1, $5 and $10 are 49, 44 and 22 respectively.
How to use equation to find the number of bills?There are 3 denominations of bills in a wallet: $1, $5, and $10.
There are 5 fewer $5-bills than $1-bills.
let
x = number of $1 bills
Hence,
number of $5 bills = x - 5
There are half as many $10-bills as $5-bills.
number of $10 bills = 1 / 2 (x - 5)
Therefore,
x + x - 5 + 1 / 2 (x - 5) = 115
2x - 5 + 1 / 2 x - 5 / 2 = 115
2x + 1 / 2 x - 5 - 5 / 2 = 115
5 / 2 x - 7.5 = 115
2.5x = 115 + 7.5
x = 122.5 / 2.5
x = 49
Number of $1 bills = 49
Number of $5 bills = 49 - 5 = 44
Number of $10 bills = 1 / 2 (49 - 5) = 22
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Which is a factor of 144 - 49x²?
O 12-7x²
O 72-7x²
O 12-7x
O 72 + 7x
Answers
Answer: C: 12-7x
Step-by-step explanation:
This expression is a good example of the difference of two squares, as 144 is the square of 12, while 49x² is the square of 7x.
Any difference of two squares [tex]a^2-b^2[/tex] can be factored into the sum of their square roots times the difference of their square roots [tex](a+b)(a-b)[/tex].
Let's factor our expression.
[tex]144-49x^2=(12+7x)(12-7x)[/tex]
Out of all the options given, only [tex]12-7x[/tex] is a factor. Hence, option C is correct.
What is the LCM of the denominators? 8/ab^6, 9/ab^5
Answers
Answer:
8
Step-by-step explanation:
because all the number is over 1
Use the order of operations to evaluate (PEMDAS): -9 + 8 + (-2 x 6)
Answers
Answer:
-13
Step-by-step explanation:
-2x6 = -12
-9+8= -1
-1+-12=-13
Hope this helps
A newsletter publisher believes that over 30% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.05 level of significance, the advertiser failed to reject the null hypothesis.
Answers
The conclusion regarding the publisher's claim regarding the hypothesis is that have sufficient evidence to support the claim that the proportion is less than 30% of their readers own a Rolls Royce.
What is a null hypothesis?The null hypothesis is a statistical theory that suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.
Since we reject the null hypothesis , we have sufficient evidence to support the claim. In this case, we have sufficient evidence to support the claim that the proportion is less than 30% of their readers own a Rolls Royce.
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Complete question:
A newsletter publisher believes that less than 30% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 level of significance, the advertiser decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?
Andrea needs to replace a glass windowpane that is 18 inches wide and 36 inches long. The glass manufacturer charges by the square inch. What measurement does Andrea need to calculate to find the cost of a new pane?
Answers
Answer:
The area of windowpane is answer.
Answer:
The area of the window pane
Step-by-step explanation:
The area of an object is the width x length of said object.
Ex: A 4 x 4 sized square has an area of 16 ( 4 x 4 = 4 by 4)
P.S. The area of Andrea´s windowpane is 648.
Lets find the digit in blank space of thr following numbers so hat the number formed is divisible by 11.
a.27.......3
Answers
11 * 253 = 2783
What is the first term of the product of ( 4x 2 − x ) ( 6x 3 − x 4 + 3x ) when it is written in standard form?
Answers
Answer:x2−7x−8=0
Tap to view steps...
Step-by-step explanation:
7/3 4/2 as improper fraction
Answers
Answer:
If the question asked mixed fraction:
7/3 = 2 1/3
4/2 = 2
Step-by-step explanation:
I converted it to mixed fraction because it is already improper fraction.
ASAP HELPPP PLEASE ANSWER CORRECT QUESTION!! GIVING OUT BRAINLY Stars!!!
Silas is researching the cost of a specific souvenir he wants to buy on his international trip.
Use the table to answer the question.
Country Currency Name Exchange Rate Per US Dollar Average Cost of Souvenir: Britain pound 0.83 British pounds 17. British pounds Egypt pound 18 Egyptian pounds 288 Egyptian pounds
Determine which country the souvenir would be less expensive in in US dollars. Show your work. (10 points)
Answers
Using proportions, it is found that due to the smaller division of the exchange rate by the cost, the souvenir would be less expensive in Egypt.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The souvenir would be less expensive in the country in which the division of the exchange rate by the cost is smaller.
In Britain, the cost is of 17, with an exchange rate of 0.83, hence the cost in US dollars is:
c = 17/0.83 = $20.48.
In Egypt, the cost is of 288, with an exchange rate of 18, hence the cost in US dollars is:
c = 288/18 = $16.
16 < 20.48, hence the souvenir would be less expensive in Egypt.
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