HELP WILL GIVE BRAINLIEST
Which is the equation of an ellipse with directrices at y = ±2 and foci at (0, 1) and (0, −1)?
(possible answers shown in image)
Answers
Answer:
[tex]\frac{x^{2} }{1} +\frac{y^{2} }{2}=1[/tex]
Step-by-step explanation:
The directrices of an ellipse are defined by
[tex]x=(+-)\frac{a}{e}[/tex]
Where [tex]a >b[/tex], and [tex]e[/tex] is the eccentricity defined by [tex]e=\frac{c}{a}[/tex]
So, in the first choice, we have the equation
[tex]\frac{x^{2} }{4}+\frac{y^{2} }{1} =1[/tex]
Where [tex]a^{2}=4[/tex] and [tex]b^{2}=1[/tex], which means [tex]a=2[/tex] and [tex]b=1[/tex].
In an ellipse, we have the relation
[tex]c^{2}=a^{2}-b^{2}[/tex]
Replacing values, we have
[tex]c^{2} =4-1=3\\c=\sqrt{3}[/tex]
So, the eccentricity is [tex]e=\frac{\sqrt{3} }{2}[/tex] and the directrices are [tex]x=(+-)\frac{2}{\sqrt{3} }[/tex], which means the first choice is not the right answer. In other words, the right answer is the second choice, because third and fourth choices don't represent an ellipse, both fractions must be positive in that case.
Therefore, the right answer is
[tex]\frac{x^{2} }{1} +\frac{y^{2} }{2}=1[/tex]
Answer:
OPTION B IS CORRECT
Step-by-step explanation:
FOR A VERTICAL ELLIPSE a IS ALWAYS LARGER THAN b AND a is always right under y-squared in the equation.
Related Questions
5. Investment account 1 starts with a balance of $200 and doubles every year. Investment account 2 starts with $1,000 and increases by $100 each year.
a. How long does it take for each account to double?
b. How long does it take for each account to double again?
c. How does the growth in these two accounts compare? Explain your reasoning.
Help Me PLSSSSSSSSSSSSSSSS!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
a. Account 1: 1 year Account 2: 10 years
b. Account 1: 2 years Account 2: 30 years
c. The first account grows exponentially, while the second one grows at a linear rate. Therefore, over time the first account tends to surpass the second one in value.
Step-by-step explanation:
The first account can be modeled by using a compounded formula with 100% rating, since it doubles every year. The formula is shown below:
M = C*(1 + r)^t
Where M is the final amount, C is the initial amount, r is the interest rate and t is the elapsed time. If r = 1, then it doubles every year, so we have the following expression for the first account:
M = 200*(2)^t
While the second acount grows at a steady rate of $100, therefore it can be modeled by the initial amount added by the growth rate multiplied by the elapsed time as shown below:
M = 1000 + 100*t
a. The first acount take 1 year to double, since it doubles every year.
In order for the second acount to double it needs to reach M = 2000, so we have:
2000 = 1000 + 100*t
100* t = 2000 - 1000
100*t = 1000
t = 10
It will take 10 years to double.
b. The first account will double again in 1 more year, so 2 years total.
The second account will need to reach M = 4000, therefore:
4000 = 1000 + 100*t
100*t = 4000 - 1000
100*t = 3000
t = 30
It'll take 30 years total for the second account to double again.
c. Since the first account grows exponentially it grows at a faster rate in comparison to the second one that grows linearly over time. Therefore over time the first account tends to surpass the second one in value.
In this exercise we will have to use the knowledge of finance to calculate the income time in this way we can say that:
a. [tex]Account 1: 1 year \\Account 2: 10 years[/tex]
b. [tex]Account 1: 2 years\\ Account 2: 30 years[/tex]
c. The first account grows exponentially, while the second one grows at a linear rate.
Then writing the yield formula as:
[tex]M = C*(1 + r)^t[/tex]
Where:
M is the final amountC is the initial amountr is the interest ratet is the elapsed timeIf r = 1, then it doubles every year, so we have the following expression for the first account:
[tex]M = 200*(2)^tM = 1000 + 100*t[/tex]
a. In order for the second acount to double it needs to reach M = 2000, so we have:
[tex]2000 = 1000 + 100*t100* t = 2000 - 1000100*t = 1000t = 10[/tex]
b. The second account will need to reach M = 4000, therefore:
[tex]4000 = 1000 + 100*t100*t = 4000 - 1000100*t = 3000t = 30[/tex]
c. Since the first record of finances evolve exponentially it become larger at a faster rate distinguished to the second individual that evolve linearly over opportunity. Therefore over opportunity the first fees be apt to outdo something or someone the second individual fashionable advantage.
See more about finances at brainly.com/question/10024737
Given PQ | | ST
Triangle P Q R. Side P Q is 16 kilometers and side P R is 24 kilometers. Triangle S R T. Side R T is 33 kilometers.
What is the distance of Line S T?
7 km
StartFraction 128 Over 11 EndFraction km
22 km
49.5 km
Answers
The answer is C = 22km
Final answer:
To determine the distance of line ST, we use the fact that triangles PQR and SRT are similar, which allows us to set up a proportion with the given side lengths. Solving this proportion reveals that the length of ST is 22 kilometers.
Explanation:
To find the distance of line ST, we need to recognize that if lines PQ and ST are parallel (PQ | | ST) and we are given the lengths of the sides PQ and PR in triangle PQR and side RT in triangle SRT, we can infer that triangles PQR and SRT are similar by the Angle-Side-Angle (ASA) postulate since they share angle P (or R in triangle SRT) and have proportional corresponding sides.
Using the lengths PQ = 16 kilometers and PR = 24 kilometers from triangle PQR and RT = 33 kilometers from triangle SRT, we can set up a proportion to solve for the unknown length ST.
The proportion based on the similarity of triangles is:
PQ/PR = ST/RT
Substituting the given values, we get:
16/24 = ST/33
Solving for ST, we multiply both sides by 33:
ST = 33 * (16/24) = 22 kilometers.
Therefore, the distance of line ST is 22 kilometers.
What do both of these functions have in common?
f(x) = 3/2lx-7l -2
0(x) = 1.51n(x - 2) +7
O
A. They have the same horizontal translation
O
B. They have the same vertical shift
O
C. They have the same vertical stretch
O
D. They have the same end behavior
Answers
Answer:
C
Step-by-step explanation:
If a box of 100 pencils cost $4.75, what should you expect to pay for 225 pencils?
Answers
Answer:
$ 10.69
Step-by-step explanation:
225 is 2.25 times the 100 pencils. ( 225/100) So all you have to do is multiply 2.25 the price ($4.75) and you get 10.6875, money can only go to the tenth place so you round it to $10.69
Hope this helped and pls mark as brainliest!
~Luna
What two numbers multiply together to get -42 and add up to be -1?
Answers
Answer:
-7 and 6
Step-by-step explanation:
You can solve this problem by setting up a system of equations. Lets call the first number x, and the second number y. Now:
x*y=-42
x+y=-1
You can subtract y from both sides of the second equation to get x=-y-1, which you can then substitute into the first:
(-y-1)*y=-42
-y^2-y=-42
y^2+y-42=0
Solving the quadratic equation:
(y-6)(y+7)=0
y=-7 or 6
x= 6 or -7
When one of the numbers is -7, the other is 6, and when it is 6, the other is -7. Hope this helps!
Im so confused please help!
Answers
Answer:
18
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
The base length is 6 and the height is 6
A = 1/2 (6) * 6
A =18
Answer:
B. 18 units²
Step-by-step explanation:
You find the area of the triangle with the dotted lines first:
[tex]\frac{1}{2}[/tex]*b*h
[tex]\frac{1}{2}[/tex]*9*6=
27
The area of the triangle including the dotted lines is 27 units²
Now we need to find the area of the small dotted triangle using the solid line triangle as a hypotenuse.
[tex]\frac{1}{2}[/tex]*b*h
[tex]\frac{1}{2}[/tex]*3*6=
9
The area of the small dotted triangle is 9 units²
To find the area of the solid lined triangle, you need to subtract the area of the small dotted line triangle (9 units²) from the triangle with the dotted lines (27 units²) which is:
27-9=18
The solid lined triangle is 18 units²
Four times a number less 6 is 8 more than twice that number. find the number.
Answers
Answer:
Four times a number less 6 is 8 more than twice that number. find the number. Denote that number: a, we have:
a x 4 - 6 = a x 2 + 8
=> a x 2 = 6 + 8 =14
=> a = 14/2 = 7
Hope this helps!
:)
What is the quotient of 5/6÷3/4?
Answers
Answer:
20/18
Step-by-step explanation:
Answer:
1 1/3
Step-by-step explanation:
Which is the angle of elevation from Kelley to the top of the waterfall? ∠7 ∠5 ∠8 ∠6
Answers
Answer:
∠6
Step-by-step explanation:
The angle of elevation is the angle between an horizontal line and the line from the object to the observers eyes. The line from the object is above the horizontal line. The angle of elevation denotes the angle from the horizontal upward.
The first picture below is where your question emanated .The second picture describes the angle of elevation. The angle of elevation from kelley to the top of the waterfall is ∠6.
PLS HELP ME PLS I'M GOING TO FAIL THIS!!!!!
Answers
Answer:
1. 27
2. 63
3. 135
4. 28
5. First answer choice
Step-by-step explanation:
I can explain any specific problem in the comments if you'd like, but explaining all 5 would take too long. Hope this helps!
Please help! Will mark brainliest
Answers
Answer:
0 ≤ x ≤ 4
Step-by-step explanation:
we are asked to find all the values of x such that y>0.
for y>0, this means that we will only consider the portion of the graph that is above the x - axis (i.e the part of the graph above y=0)
By observation, we can see that the graph is only above the x-axis between the interval 0 ≤ x ≤ 4 (which is the answer to your question)
URGENT!!! Which is a y-intercept of the graphed function?
(-9, 0)
(-3, 0)
(0, -9)
(0, -3)
Answers
The y-intercept is where the graph goes through the y-axis (the vertical line in the center). It goes through at y=-9, so the coordinates would be (0,-9), since it is (x,y).
Answer:
The y-intercept is (0, -9)
Step-by-step explanation:
A rectangle has a perimeter of 6 feet.
Choose all the possible dimensions of the rectangle.
Answers
Which describes the correlation shown in the scatterplot?
A) there is a positive correlation in the data set
B) there is a negative correlation in the data set
C) there is no correlation in the data set
D) more points are needed to determine the correlation
Answers
There is a negative correlation in the data set, Option B is correct.
As per the question, it is to be determined which correlation is shown in the scatterplot.
What is a scatter plot?The association between two numerical variables measured for the same individuals is displayed in a scatterplot. One variable's values are displayed on the horizontal axis, and the other variable's values are displayed on the vertical axis.
Here,
In the scatter, plot the graph of the points shows a decline while moving on the positive x-axis. Thus the negative correlation is plainly going down, starting at the top left and moving down to the bottom right.
Thus, there is a negative correlation in the data set, Option B is correct.
Learn more about scatter plots here:
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Need help ASAP please
Answers
Adding a value at the end shifts the graph up that number of units.
The answer is C.
Cindy bought an item from the store. The cashier charged her $22.42 which included the original price of the item plus 7% state sales tax. What was the original price of the item? Your answer must be correct to the penny and must be stated as an amount of money
Answers
What is the diameter of a circle with circumference 57.52 m?
Answers
Answer:
18.31 meters
Step-by-step explanation:
Use the circumference formula C =2πr = dπ
C = 57.52 m = dπ
d = 57.52 m / π = 57.52 / 3.1415926= 18.308 m.
Pentagon VWXYZ is shown on the coordinate grid. A student reflected pentagon VWXYZ across the y-axis to create pentagon V'W'X'Y'Z'. Which rule describes this transformation? *
(x, y) --> (-x , y)
(x, y) --> (x , y + 8)
(x, y) --> (-y , x)
(x, y) --> (x , -y)
Answers
Answer: (x, y) —> (-x, y)
Step-by-step explanation:
This is because the translation rule for reflection across the y-axis is (x, y) —> (-x, y)
(x, y) --> (-x , y)
Step-by-step explanation:
When reflecting across the y-axis, you will want to switch the sign of the x-coordinate. If the x-coordinate is positive, you will want to switch it to negative and vice versa.
Examples:
(3,5) --> (-3,5)
(-6,-2) --> (6,-2)
~
If you are going to reflect across the x-axis, you will change the y-coordinate, so it is the opposite of reflecting across the y-axis.
What is the perimeter of the given composite figure
Answers
Answer:
The perimeter of the given composite figure is:
106 ydStep-by-step explanation:
The perimeter is defined as the sum of the sides in a figure, therefore, what you should do in this exercise is to add all the yards of the sides of the compound figure, however, you should notice that there are two sides of which They do not give you the measurement and you must identify it based on the sides that do have it, which would be:
Vertical line measurement = (19 + 4-17) yards Vertical line measurement = 6 yardsIn the previous case, the two measures on the other side that are complete are used, which are 19 yards and 4 yards respectively, then the measurement that is on our same side (17 yards) is subtracted and thus we obtain the value of the vertical line that it did not have, now that of the horizontal line:
Horizontal line measurement = (30-12-15) yards Horizontal line measurement = 3 yardsIn this case, something similar was done, the total measurement of the base was taken and the measurements of the upper zone were subtracted, with which the measurement of the remaining zone was found.
All the measures are added together:
The perimeter of the figure = 30 yd + 17 yd + 12 yd + 6 yd + 15 yd + 4 yd + 3 yd + 19 yd = 106 ydAnswer:
934
Step-by-step explanation:
Each of 4 tables at a party is set with a bowl of grapes. Each
bowl contains 5/8 of a pound of grapes. How many pounds of
grapes are there altogether? Show your work.
Answers
Answer:
2.5
Step-by-step explanation:
youll have to multiply 4 times 5/8
what is -2.25w ≥ 13.5?
Answers
Answer:
w < (line under the sign) -6
Step-by-step explanation:
Here are the numbers on a table that shows student's scores for 10 rounds of a video game.
130,150,120,170,130, 120, 160, 160, 190, 140
What is the median score?
A-125
B-145
C-147
D-150
Answers
Answer:
B-145
Step-by-step explanation:
120-190 is the spread in the middle is 145
Answer:
B- 145
Step-by-step explanation:
hoped this helped!
The length of a rectangle is 1 ft less than 3 times the width. The area is 310 ft^2. Find the dimensions of the rectangle.
Answers
Answer:
Length = 32 ft
Width = 10 1/3 ft
Step-by-step explanation:
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Roger and Evelyn decided to shoot arrows at a simple target with a large outer ring and a smaller bull's-eye. Roger went first and landed 2 arrows in the outer ring and 5 arrows in the bull's-eye, for a total of 416 points. Evelyn went second and got 2 arrows in the outer ring and 1 arrow in the bull's-eye, earning a total of 112 points. How many points is each region of the target worth?
The outer ring is worth __ points, and the bull's-eye is worth __ points.
Answers
Answer:
outer region= 18pts, bulls eye=76pts
Step-by-step explanation:
its a system of equations
Look at this check register. Calculate the current balance.
A check register has a balance of 82 dollars and 92 cents. 78 dollars and 24 cents is debited for a phone bill. 125 dollars is deposited for a pay check. 40 dollars is debited from the A T M. 56 dollars and 50 cents is debited for tennis lessons.
The current balance is $
.
Answers
Answer:
$33.18
Step-by-step explanation:
$33.18 is the answer because...
Step one first we have the money in the cash register of $82.92. Unfortunately she has to pay a phone bill of $78.24 so we subtract 82.92 and 78.24 which leaves the person with $4.68.Step two so she has $4.68 but now she gets an outstanding $125 paycheck. So we add $4.68 and $125 to get $129.68 as her new balance.Now the person's balance is $129.68 it says in the question she debited $40 from the ATM. So we subtract $129.68 and $40 to get $89.68.Step four she also had to pay $56.50 for the persons tennis lessons so we subtract $89.68 and $56.50 to get our final answer of $33.18Hope this helped :)The current balance is calculated by starting with the initial balance of $82.92 and then subtracting debits and adding credits from various transactions. After all adjustments, the current account balance is $33.18.
To calculate the current balance, we'll start with the first number under Balance and adjust it based on the recorded transactions.
Start with the initial balance: $82.92
Subtract the debit for the phone bill: $82.92 - $78.24 = $4.68
Add the deposit from the paycheck: $4.68 + $125.00 = $129.68
Subtract the ATM debit: $129.68 - $40.00 = $89.68
Finally, subtract the debit for tennis lessons: $89.68 - $56.50 = $33.18
Therefore, the current balance is $33.18.
Learn more about Calculating Balance here:
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n...
Select the best answer for the question
13. Which of the following is an example of a proper fraction?
.
O A. 4
O B.76
O c. 4/4
O D.43
eh...
Answers
Identify the correct formula for the following sequence. 2, -4, -10, -16, -22, ...
A. an = 6n - 8
B. an = -8n + 6
C. an = 8n - 6
D. an = -6n + 8
Answers
Answer:
D
Step-by-step explanation:
The terms in the sequence have a common difference d between consecutive terms, that is
d = - 4 - 2 = - 10 - ( - 4) = - 16 - (- 10) = - 22 - (- 16) = - 6
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = - 6, thus
[tex]a_{n}[/tex] = 2 - 6(n - 1) = 2 - 6n + 6 = - 6n + 8 → D
l What are the 1st 4 terms of the sequence defined by the following equation AN equals 5 × 2 in -1
Which expression has a value greater than 9.862?
Answers
Answer:
the answer is D
Step-by-step explanation:
9,862 times 2/2 = 9862 so that doesn't work
but 9,862 times 4/2 = 19724 and that is greater than 9,862.
Answer: D) 9,862 * [tex]\frac{4}{2}[/tex]
Step-by-step explanation: If a number is not greater than one, then the number will actually decrease. Let's turn [tex]\frac{4}{2}[/tex] into a decimal.
4 ÷ 2 = 2
9,862 * 2 = 19,724
I hope this helps!
What operation should you perform first when you evaluate the expression 85+(9−25×5)÷3
Answers
46.33
fdsgsdgsdgsdgdsgsdgsdg
Answer:
Follow the rules of PEMDAS, so start with whats in the ()
Step-by-step explanation:
1. Multiply 25x5
2. Then subtract 9-125=-116
3. The -116÷3
4. Add 85
5. Answer 46.33 or 139/3Hope this helps!!!GIVING BRAINLIEST BRAINLIEST!!!! Easy mathhh
Answers
Truthfully, this is tough to type over a computer but, let me see if I can guide you through doing it.
Method: Starting from the very center of the graph, move according to the coordinates, using (x, y)
- X is your horizontal axis.
- Y is your vertical axis.
Concept of Understanding Negatives and Positives:
A positive X, will mean it goes to the right.
A positive Y, will mean it goes up.
A negative X, will mean it goes to the left.
A negative Y, will mean it goes down.
Apply!
- From the center, "A (-2 , -1)" will translate to "go left two spaces, and go down by one". Plot the point.
- From the center, "B (-3 , -1)" will translate to "go left three spaces, and go down by one". Plot the point.
- From the center, "C (3 , 3)" will translate to "go right three spaces, and go up by thjree". Plot the point.
- From the center, "B (-2 , 3)" will translate to "go left two spaces, and go up by three". Plot the point.
CONNECT THE LINES! :D
Next, let's find the area of that shape!
Area = Base×Height
In this case, 4×1, because the height is 4 boxes, and it's 1 box for it's base.
Answer:
Answer is 4X1, PLEASE GIVE ME BRAINLIEST
Step-by-step explanation: