Find the equation of the ellipse that has its foci at (2,1) and (2,-7) and b= 2
Answers
Foci: (2,1) and (2,-7)
\(F_1=\text{ (0+ x', 0 + y')}\)The center of the ellipse is 2, 3
\(\begin{gathered} F_1=\text{ (0+ 2, 1 + 3)}=>F_1(0,4) \\ F_2=(0+2,-7+3)\Rightarrow F_2(0,-4) \\ \text{Hence, c=4} \end{gathered}\)\(F_2=\text{ (0+x', 0 + y')}\)From
\(\begin{gathered} c^2=a^2-b^2 \\ a^2=c^2+b^2 \\ c=4,\text{ b=2} \\ a^2=4^2+2^2=16+4=20 \\ a^2=20 \end{gathered}\)The general equation of an ellipse with center ( x' ,y')
where, x'=2 and y' =3
\(\frac{(x-x^{\prime})^2}{b^2}+\frac{(y-y^{\prime})^2}{a^2}=1\)\(\begin{gathered} \frac{(x-2)^2}{4}+\frac{(y-3)^2}{20}=1 \\ \frac{5(x-2)^2+(y-3)^2}{20}=1 \end{gathered}\)\(\begin{gathered} 5(x-2)^2+(y-3)^2=20 \\ 5(x^2-4x+4)+(y^2-6y+9)=20 \\ 5x^2-20x+20+y^2-6y+9=20 \\ 5x^2+y^2-20x-6y+29-20=0 \\ 5x^2+y^2-20x-6y+9=0 \end{gathered}\)Hence the equation of the ellipse is
\(5x^2+y^2-20x-6y+9=0\)Related Questions
On Monday, Saffron bakes
324 pastries in the morning and some more in the
afternoon. She sells 584 pastries. At the end of the
day she has 52 pastries left. How many pastries did
she bake in the afternoon?
Answers
the number of pastries that she bake in the afternoon is equal to 312 pastries.
We are given that:
Saffron sells 584 pastries in the whole day and 52 pastries are left at the end of the day.
Now, we will use addition to find the total number of pastries that is being made in the day.
Total pastries = 584 + 52
Total pastries = 636
Now, she bake 324 pastries in the morning.
So, the number of pastries baked in the afternoon = 636 - 324
In afternoon = 312.
Therefore, we get that the number of pastries that she bake in the afternoon is equal to 312 pastries.
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Bally Manufacturing sent Intel Corporation an invoice for machinery with a $13,100 list price. Bally dated the invoice August 01 with 3/10
EOM terms. Intel receives a 40% trade discount. Intel pays the invoice on August 14. On August 10, Intel Corporation returns $100 of the machinery due to defects. What does Intel pay Bally on August 14?
Answers
The Intel pays $7,760 to Bally Manufacturing on August 14.
The first step in calculating what Intel Corporation pays Bally on August 14 is to determine the net price of the machinery after the trade discount and the return of $100 due to defects.
The trade discount of 40% is calculated as follows:
Discount = List price × Discount rate
Discount = $13,100 × 0.40 = $5,240
So the net price of the machinery after the trade discount is:
Net price = List price - Discount
Net price = $13,100 - $5,240 = $7,860
After Intel returns $100 of machinery, the cost of the machinery is further reduced to:
Net price after return = Net price - Return
Net price after return = $7,860 - $100 = $7,760
Since the payment terms are 3/10 EOM (end of month), Intel receives a discount of 3% if payment is made within 10 days. The 10-day period begins on August 1 and ends on August 10 (the payment due date). Since Intel pays the bill on August 14, payment is late and the 3% discount does not apply.
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What are inequality? When do we use inequalities?
What type of inequalities are there? Which symbols are used for each type?
Are the following expressions variable inequalities? Why?
a. 13z=27
b. x<0
c 3x+5x>11
d. y+5≤11
e. 7-1>- 32
Answers
Answer:
B,C,D, and E
Step-by-step explanation:
Inequality tells us about the relative size of two values.
Mathematics is not always about "equals", sometimes we only know that something is greater or less than.
Example: Alex and Billy have a race, and Billy wins!
What do we know?
We don't know how fast they ran, but we do know that Billy was faster than Alex:
Billy was faster than Alex
We can write that down like this:
b > a
(Where "b" means how fast Billy was, ">" means "greater than", and "a" means how fast Alex was)
Inequalities: Symbols and Vocabulary
Algebra rules / General Rules:
Isolate a positive x on the left side using algebra
Reverse the inequality sign when mult/divide by a negative
Less than: The symbol that: Looks like an L () for ess than
< ○ ) Points to the Left
● ] Caps the arrow pointing towards smaller numbers
on the number line
Points towards the smaller of two numbers (4 < 7)
> Greater than: The symbol that: Looks like the top of an R ( >
)for GReater than
> ○ ( Points to the Right
● [ Caps the arrow pointing towards larger numbers on
the number line
Open end is by the larger number (7 > 4)
Compound inequalities: usually in the form -4 < x < 4
but can also be x > -4 and x < 4
the sum of three consecutive integers is 78. what are the three Integers
Answers
Answer:
25, 26, and 27 are the three consecutive integers.
Step-by-step explanation:
Let the numbers be represented as x, x + 1 and x + 2.
We can write the equation:
\(x+(x+1)+ (x+2)=78\)
Opening the brackets and simplifying:
\(x+x+1+x+2=78\)
\(3x+3=78\)
Subtract 3 from both sides.
\(3x=75\)
Divide both sides by 3.
\(x=25\)
Since the three consecutive integers are x, x + 1 and x + 2, replace x with 25.
∴ 25, 26 and 27 are the three consecutive integers.
Answer:
25 , 26 and 27
Step-by-step explanation:
Which inequality represents the situation described below?
The distance, d, is less than 200 miles.
A. d ≥ 200
B. d > 200
C. d ≤ 200
D. d < 200
Answers
Hello!
The distance, d, is less than 200 miles.
B. d > 200
Two different students decide to compare their businesses. Scooter makes his own t-shirts,
while Karissa does computer repairs. For both models, x represents the number of sales made
each month and f(x) represents total money for each individual. The two functions below model
their respective businesses:
Scooter: f(x) = 200 + 15x
Karissa: f(x) = 80 + 35x
a. Describe what the slope and y intercept represent for both models based on the context.
Compare the two functions. What is one statement you could say about each?
b.
C.
In one month, Scooter sells 20 shirts. That same month, Karissa does 12 repairs. Who had
the better month?
Answers
a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.
How to Describe what the slope and y intercept represent for both models based on the contexta) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.
In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.
Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.
b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.
For Scooter, with x = 20 (number of shirts sold):
f(x) = 200 + 15x
f(20) = 200 + 15 * 20
f(20) = 200 + 300
f(20) = 500
For Karissa, with x = 12 (number of repairs):
f(x) = 80 + 35x
f(12) = 80 + 35 * 12
f(12) = 80 + 420
f(12) = 500
Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.
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Cliff takes out a $5,000 personal loan with 7
fixed annual interest compounded monthly to pay for his wedding. He repays the loan in 2 year.s
How much total interest does Cliff pay on his loan?
Answers
Cliff pays a total interest of approximately $679.90 on his $5,000 loan.
To calculate the total interest paid on the loan, we need to use the formula for compound interest:
\(A = P(1 + r/n)^{(nt)}\)
Where:
A is the final amount (loan amount + interest)
P is the principal (loan amount)
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:
P = $5,000
r = 7% = 0.07
n = 12 (monthly compounding)
t = 2 years
\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)
Calculating this expression:
A ≈ 5000\((1.00583)^{(24)\)
A ≈ 5000(1.13598)
A ≈ 5679.90
The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):
Total Interest = A - P
Total Interest = 5679.90 - 5000
Total Interest ≈ $679.90
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Imagine that a researcher correctly computes a correlation coefficient to quantify the relationship between two variables. In the data set that she works with, low scores on Variable X tend to be paired with low scores on Variable Y, and high scores on Variable X tend to be paired with high scores on Variable Y. Based on this data set, what type of correlation coefficient should the researcher expect to find
Answers
Answer:
Positive value of correlation Coefficient
Step-by-step explanation:
The correlation Coefficient value, R is a correlation measure which gives information about both the strength of association between two variables and also the type of association between them (negative or positive). R has a standardized value which ranges from - 1 to +1
Negative relationship between variables are depicted with negative (where one variable decreases as the other increases) R value while positive association (increase in one variable means leads to increase in the other variable) are depicted with positive R values.
Therefore, for the relationship described above, the correlation Coefficient will be positive.
Joeli bought a new helmet and elbow pads for riding her skateboard. The helmet costs $27.57. The elbow pads cost $17.78. What is the total cost of her purchases?
Answers
The total cost of Joeli's purchases is $45.35.
What is the addition?
Addition is a mathematical operation that combines two or more numbers or quantities to produce a sum. It is one of the four basic arithmetic operations, along with subtraction, multiplication, and division. In addition, the numbers being combined are called addends, and the result is called the sum. The addition operator is represented by the symbol "+".
To find the total cost of Joeli's purchases, we need to add the cost of the helmet to the cost of the elbow pads:
Total cost = helmet cost + elbow pads cost
Total cost = $27.57 + $17.78
Total cost = $45.35
Therefore, the total cost of Joeli's purchases is $45.35.
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Jessica earned $16 mowing a neighbor’s yard. She bought a craft kit for $7.37.
She used $3.75 to buy food for a food drive. She put the rest in her savings account.
How much money did Jessica put in her savings account?
Answers
Answer:
Jessica put $4.88 into her savings account.
Step-by-step explanation:
First, you'll add up how kuch she has spent.
7.37 + 3.75 = 11.12
Secondly, you'll subtract 11.12 from 16.
16 - 11.12 = 4.88
The height of a tree in feet over x years is modeled by the function f(x). Determine if each statement is True or False.
Answers
The statement is examined using the equation to find that
1. False
2. False
3. True
4. False
How to find the statement is trueThe given equation is
f(x) = 32 / ( 1 + e⁰°⁵ˣ)
Evaluating the first statement by substituting
For x = 3, f(3 ) gives 5.84
For x = 6, f( 6) gives 1.52
5.82 - 1.52 is not equal to 9 ft hence the statement is False
Evaluating the second statement by substituting
when x = 0, the function gives 16 which is against 2 ft hence False
Evaluating the third statement by substituting
For x = 1, f(1) = 12.08 this is less than 16 ft hence a decline hence this is True
fourth statement
The trees maximum height, captured should be 16 ft not 35 ft hence False
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IS THIS RIGHT? (28 points easy!!)
Answers
Step-by-step explanation:
yes, the step is correct.
a² = cx | multiply by c
ca² = c²x
I am just not sure how that simplified the equation.
what do you want to achieve ? what's the goal here ?
to solve the equation for x it would be to divide both sides by c, which gives
a²/c = x
AXYZ AMNL
X
XY =
33°
Y
LA
12
N
124°
N
8
M
Answers
Answer:
8
Step-by-step explanation:
You want to know the measure of segment XY if ∆XYZ ≅ ∆MNL and MN = 8.
Corresponding sidesSegment XY is named using the first two vertices listed in the name of ∆XYZ. That means the segment is the same length as the one named by the first two vertices listed in the name of congruent ∆MNL, segment MN.
Segment MN is given as 8 units long. Segment XY is congruent, so is also 8 units long.
XY = 8 units
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PLEASE HELP THIS IS DUE IN THE NEXT HOUR!!!!!!!!!!!!!!!!!!!!!!!!!!!!
10) The cost of 7 books are $ 210.70 with taxes included. How much does each book cost?
11) Ms. Sosa bought 17.86 gallons of gas on Monday, she had to refill back on Friday and
bought 10.3 gallons more. How many gallons did she buy in total?
12) Ms. Fernandez and Ms. Sosa rode their bicycles in the park. Ms. Fernandez rode her bike
for 7 % miles. Ms. Sosa rode for twice that distance. How many miles did Ms. Sosa ride?
13) Ms. Castillo put 42 pounds of almonds into small bags that could hold pound each.
How many of these small bags could she fill if she used all the almonds?
14) In Ms. Sosa class, 5/6 of the students are done with their homework, and 2 of those
students are girls. What fractional part of Ms. Sosa class is made of girls who finished
their homework?
15) The average dancer dances about 150 minutes a week. How many minutes could they
spend in the whole year?
Answers
11) 17.86 + 10.3 = 28.16 gallons in total
12) 14% miles
13) 42 small bags
14) 2/6 girls finished their homework
15) around 8,000 minutes
What are the odds of not rolling a three on a standard six-sided die?
Answers
Answer:
5/6
Step-by-step explanation:
Hope this is helpful
Answer:
5/6
Step-by-step explanation:
Determine the requested value below.
175
m/1 =
m22:
160°
Answers
The angles in the circle is as follows:
m∠1 = 25 degrees
m∠2 = 12.5 degrees
How to find the angles in the circle?The angle subtended by an arc of a circle at its centre is twice the angle it subtends anywhere on the circle's circumference.
The measure of an arc is the measure of its central angle. Therefore,
m∠1 = 360 - 160 - 175
m∠1 = 200 - 175
m∠1 = 25 degrees
Therefore, let's find the other angle m∠2.
m∠2 = m∠1 / 2
m∠2 = 25 / 2
m∠2 = 12.5 degrees
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What is the formula forfinding the area of a circle using its radius or diameter.
Answers
Answer:
The formula for finding the area of a circle using its radius is:
The formula for finding the area of a circle using its radius is:A = πr²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14
Step-by-step explanation:
Hope it Helps
The formula for finding the area of a circle using its radius is π * r².
The formula for finding the area of a circle using its diameter is (π/4) * d².
The formula for finding the area of a circle using its radius is:
A = π * r²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
r represents the radius of the circle.
If you have the diameter of the circle instead of the radius, you can use the following formula:
A = (π/4) * d²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
d is the diameter of the circle.
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a. Find x. The figure is not drawn to scale.
b. Is the triangle equilateral, isosceles, or scalene? Explain.
SOMEONE HELP!!!
Answers
Answer:
a. x = 15
b. scalene
Step-by-step explanation:
You want to know the value of x and the classification of the triangle whose circumscribing arcs are (8x-10)°, (6x)°, and (10x +10)°.
a. ArcsThe sum of arcs around the circle is 360°.
(8x -10)° +(6x)° +(10x +10)° = 360°
24x = 360 . . . . . . . . . . . divide by °, simplify
x = 15 . . . . . . . . . . . . divide by 24
b. TriangleThe arc measures around the circle are ...
(8x -10)° = 110°
(6x)° = 90°
(10x +10)° = 160°
Each arc is double the measure of the inscribed angle that intercepts it. The different arc measures mean the angle measures are different, so the triangle is scalene.
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A package of 8-count AA batteries costs $6.24. A package of 20-count Of batteries costs $15.80. Which statement about the unit prices is true?
A) The 20-count pack of AA batteries has a lower unit price of $0.78 per battery.
B) The 8-count pack of AA batteries has a lower unit prices of $0.78 per battery.
C) The 20-count pack of AA batteries has a lower unit price of $0.79 per battery.
D) The 8-count pack of AA batteries has a lower unit price of $0.79 per battery.
Answers
The 8-count pack of AA batteries has a lower unit prices of $0.78 per battery.
Option B is correct.
What is division?Division in mathematics is the process of breaking a number up into equal parts, and finding out how many equal parts can be made. For example, dividing 15 by 3 means splitting 15 into 3 equal groups of 5.
According to the question
Unit price of 8 AA batteries
= 6.24 ÷ 8
= 0.78
Unit price of 20 AA batteries
= 15.8 ÷ 20
= 0.79
Since, 0.78 < 0.79
Therefore, the unit price of 8 AA batteries is low.
Option B is correct.
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A trapezoid has an area given by A =1-2(b1-b2)h,where b1,is the length of one base, b2 is the length of the other
base, and h is the height. If the trapezoid has an area of 14 square units, solve for b in terms of the other variables.
Answers
The value of \(b_{1}\) is 69/4h and value of \(b_{2}\) is 43/4h if the area of trapezoid is 14 square units.
Given that area is equal to 1-2(\(b_{1} -b_{2}\))h and area is 14 square units.
We know that area of trapezoid is equal to (a+b)h/2.
We have to put the given equation equal to 14 to get our first equation.
14=1-2(\(b_{1} -b_{2}\))h
14=1-2\(b_{1}\)h+2\(b_{2}\)h
2\(b_{1}\)h-2\(b_{2}\)h=-13------------1
Now put the value of area in the formula of area of trapezoid.
14=\((b_{1} +b_{2})h/2\)
\(b_{1}\)h+\(b_{2}h\)=28-----------------2
Multiply equation 2 by 2 and then subtract 2 from 1
\(2b_{1}h -2b_{2}h -2b_{1}h-2b_{2}h\)=-13-56
-4\(b_{2}h\)=-43
\(b_{2}\)=43/4h
Put the value of \(b_{2}\) in 2 to get the value of \(b_{1}\).
\(b_{1} h+43/4h*h=28\)
\(b_{1}\)=69/4h
Hence The value of \(b_{1}\) is 69/4h and value of \(b_{2}\) is 51/4h if the area of trapezoid is 14 square units.
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Complete the inequality for this graph.
y < [?]
![Complete the inequality for this graph.y < [?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/j7jBauo8dNg82bAcqpiU8FTpwP1Nz1ck.png)
Answers
Answer: y < 2
Step-by-step explanation:
Which procedure can be used to solve the equation 540 = 12 z, and what is the solution?
Multiply both sides by 12; the solution is 6,480.
Multiply 12 z by 12; the solution is 540.
Divide both sides by 12; the solution is 45.
Divide 12 z by 12; the solution is 540.
Answers
Answer:
C) Divide both sides by 12; the solution is 45.
Step-by-step explanation:
Hope this helps got it right on Edge 2021
Answer:
The correct answer is C
Step-by-step explanation:
A concert venue has determined that they will clear a profit of $6,900 if it does not
rain on the night of a concert. If it does rain on the night of a concert, they will lose
$3,500. On the night of a concert, the chance of rain is 40%. Find the expected
profit/loss for the concert venue. You can ignore the dollar sign.
Answers
Answer:
E = .6 * 6900 + .4 * 3500 = 5540 expected profit
Right and solve multiplication equations
Answers
Answer:
45
Step-by-step explanation:
\(15 = \frac{1}{3} x \\ 15 \times 3 = x \\ x = 45\)
Answer:
45
Step-by-step explanation:
Divide both sides by 3
then it will be X=15×3
. =45
helo please show work
Answers
Answer:
Step-by-step explanation:
Solution:
We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).
The GCF of 305 and 60 is 5.
Divide both terms by 5.
305 ÷ 5 = 61
60 ÷ 5 = 12
Therefore:
305 : 60 = 61 : 12
A graph titled Calories in Strawberries. The x-axis shows the number of strawberries, numbered 1 to 9, and the y-axis shows the number of calories, numbered 3 to 27. A straight line with a positive slope begins at point (0, 0) and ends at point (6.8, 27). The graph shows the relationship between the number of strawberries eaten and the approximate number of calories consumed. Which statement is true? Each strawberry contains 4 calories. Each strawberry contains 3 calories. Twenty-four strawberries contain 6 calories. Four strawberries contain 15 calories
Answers
Answer:
the answer is edge 2020 A
Step-by-step explanation:
each strawberry contains four calories
gaming legend
Answer:
Its A
Step-by-step explanation:
got it right on Edge
At an auditorium, 3 1/2 sections are filled with people watching a play. Exactly 3/5 of the people watching the play are parents. What fraction of the sections are filled with parents?
Answers
Answer:
Fraction[Total number of sections filled filled with parents] = 2¹/₁₀ section
Step-by-step explanation:
Given:
Total number of sections filled = 3¹/₂ = 7 / 2 sections
Number of fraction parents watching play = 3/5
Find:
Fraction[Total number of sections filled filled with parents]
Computation:
Fraction[Total number of sections filled filled with parents] = Total number of sections filled x Number of fraction parents watching play
Fraction[Total number of sections filled filled with parents] = [7/2] x [3/5]
Fraction[Total number of sections filled filled with parents] = 21 / 10 sections
Fraction[Total number of sections filled filled with parents] = 2¹/₁₀ section
A company uses the graph to show how many packages each truck driver delivers .How many packages will one truck driver deliver in a 7-hour day?
Answers
The truck driver would deliver 105 packages in a 7 hours day
What is an equation?An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:
y - 15 = [(60-15)/(4-1)](x - 1)
y = 15x
For a 7 hour day (x = 7):
y = 15(7) = 105
The driver would deliver 105 packages in 7 hours
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what is
9 ÷ 1/5 = ? tell me in comments please i need this answer
Answers
Answer:
9÷1/5= 45
Step-by-step explanation:
hope it helps:)
Answer:
45
Step-by-step explanation:
9 / (1/5)
whenever you're dividing by a fraction, you can multiply by the reciprocal:
9 * (5/1)
45/1
9 / (1/5) = 45
A package of 25 fishing hooks costs $9.95 , while a package with 40 hooks costs $13.99 . Which is the better buy? Round your answer to the nearest cent if necessary.
Answers
Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.
To determine which package is the better buy, we need to compare the cost per hook for each package.
For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:
Cost per hook = $9.95 / 25 = $0.398
Rounding to the nearest cent, the cost per hook is $0.40.
For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:
Cost per hook = $13.99 / 40 = $0.3498
Rounding to the nearest cent, the cost per hook is $0.35.
Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.
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