Equation of the ellipse = 3x² + 5y² = 32
Step-by-step explanation:Given:The centre of the ellipse is at the origin and the X axis is the major axisIt passes through the points (-3, 1) and (2, -2)To Find:The equation of the ellipseSolution:The equation of an ellipse is given by,
[tex]\sf \dfrac{x^2}{a^2} +\dfrac{y^2}{b^2} =1[/tex]
Given that the ellipse passes through the point (-3, 1)
Hence,
[tex]\sf \dfrac{(-3)^2}{a^2} +\dfrac{1^2}{b^2} =1[/tex]
Cross multiplying we get,
9b² + a² = 1 ²× a²b²a²b² = 9b² + a²Multiply by 4 on both sides,
4a²b² = 36b² + 4a²------(1)Also by given the ellipse passes through the point (2, -2)
Substituting this,
[tex]\sf \dfrac{2^2}{a^2} +\dfrac{(-2)^2}{b^2} =1[/tex]
Cross multiply,
4b² + 4a² = 1 × a²b²a²b² = 4b² + 4a²-------(2)Subtracting equations 2 and 1,
3a²b² = 32b²3a² = 32a² = 32/3----(3)Substituting in 2,
32/3 × b² = 4b² + 4 × 32/332/3 b² = 4b² + 128/332/3 b² = (12b² + 128)/332b² = 12b² + 12820b² = 128b² = 128/20 = 32/5Substituting the values in the equation for ellipse,
[tex]\sf \dfrac{x^2}{32/3} +\dfrac{y^2}{32/5} =1[/tex]
[tex]\sf \dfrac{3x^2}{32} +\dfrac{5y^2}{32} =1[/tex]
Multiplying whole equation by 32 we get,
3x² + 5y² = 32
Hence equation of the ellipse is 3x² + 5y² = 32answer choices
A. -4
B. 5.8
C.4
D.8
Answer:
the answer is C (4)
I really need this quick plz
Answer:
C=8
Step-by-step explanation:
−0.2x=1.6
Help a brother out
Answer:
I getcha
Step-by-step explanation:
-8
I hope this is correct
KAMAKURA KAMAKUARA YASS QUEEN ✨Anywaysss.. help me, I know this but I’m too lazy to do it, DKSKSK
Answer:
a= 6 7/8
Step-by-step explanation:
Which of the following statements is false?
8<8
2>8
2<8
2<8
Answer:
8<8 and 2>8 are both false
Answer:
B
Step-by-step explanation:
Pls help!
Find the Area of the following composite figure. (Round to one
decimal place if necessary)
Answer:
A=132in^2
Step-by-step explanation:
A=1/2(a+b)h
A= 1/2(6+16)12
A= 1/2(22)(12)
A= (11)(12)
A= 132
Write and solve a proportion to answer the question.
42 is what percent of 80?
42
р
100
80
p= %
Answer:
the ans. is 52.5 percent
There are only red beads and green beads in a bag.
The ratio of the number of red beads to the number of green beads is 5 : 9
(a) What fraction of the beads are red?
There is a total of 84 beads in the bag.
(b) How many of the beads are green?
Susie is going to put some more beads in the bag.
There will still be only red beads and green beads in the bag.
Susie wants to have twice as many green beads as red beads in the bag.
(c) What beads should she put in the bag?
You must explain your answer
Answer:
(a) 5/14
(b) 54 beads
(c) 6 green beads
Step-by-step explanation:
(a) Find the total number of units for red and green beads.
5 + 9 = 14
Since red beads is 5, it is 5/14.
(b) Find the units for red and green beads altogether.
5 + 9 = 14
14 units = 84 beads
Find one unit.
1 unit = 84 ÷ 14 = 6 beads
Since green beads have 9 units, find how many beads there are in 9 units.
9 units = 6 x 9 = 54 beads
(c) As there are 54 green beads and Susie wants to have twice as much green beads as red beads, she have to find how many red beads there are first.
Since red beads have 5 units, find how many beads there are in 5 units.
5 units = 6 x 5 = 30 beads
After that, since she wants twice, she have to find x2 of 30 beads which are red.
30 x 2 = 60
After that, find the remaining amount of green beads needing to make x2 of 30.
60 - 54 = 6 beads (green)
Part(a),
5/14 of the beads are red.
Part(b),
There are 54 green beads in the bag.
Part(c),
Add 18 red beads and 36 green beads to the bag to get the desired ratio.
How to get the solution?(a) There are five times as many red beads as green beads, or a 5:9 ratio. Therefore, there are 9 green beads in the bag for every 5 red beads. Therefore, the fraction of the beads that are red can be expressed as:
5/(5+9) = 5/14
So, 5/14 of the beads are red.
(b) The bag contains 84 beads, and the proportion of red to green beads is 5:9. Let G equal the number of green beads and R equals the number of red beads. Next, we have:
R/G = 5/9
And we also know that:
R + G = 84
We can use the first equation to express R in terms of G:
R = (5/9)G
This results from substituting this into the second equation:
(5/9)G + G = 84
Simplifying:
(14/9)G = 84
G = (9/14) * 84 = 54
So there are 54 green beads in the bag.
(c) Let's assume that the bag currently contains G-green beads and R red beads. So that there are twice as many green beads as red beads, we wish to add a few more beads.
G = 2R
We also know that the total number of beads in the bag should be:
R + G + X = 84
Where X is the required number of beads. G = 2R is substituted into this equation to produce:
R + 2R + X = 84
3R + X = 84
Finding R and X numbers that meet both this equation and the prerequisite that G = 2R is necessary. One potential answer is:
R = 18, X = 30
This gives:
G = 2R = 36
And:
R + G + X = 18 + 36 + 30 = 84
Hence, to get the correct ratio, we can add 18 red beads and 36 green beads to the bag. There might be other workable alternatives as well, though.
To know more about an expression follow
https://brainly.com/question/13590692
#SPJ2
PLEASE ANSWER ASAP !!!!! WILL GIVE BRAINLIEST
Answer:
*answers*
Step-by-step explanation:
u just answer it
Answer:
1
Step-by-step explanation:
2cos(2x)=6sinx+1
Simplify
Answer:
x=0.15197212 +2 pie n, 9.27280583 + 2 pie n for any integer n.
NEED THE ANSWER NOWWWWW!!!!!!!!!!!
Graph the following features: Slope = -3 Y-intercept = 4
Answer:
Step-by-step explanation:
Use Desmos. Y-intercept is 4 so start from there (place a point on (0,4)). From the y-intercept use the slope. -3 technically means three down and one to the right.
y-intercept form --> y= -3x + 4
13 of snow fell in 9 hours. Write the number of inches per hour?
Answer:
1.44
Step-by-step explanation:
All you have to do is divide 13 by 9 and get 1.44, that is how much snow fell in 1 hour
pls mark brainliest
4, 6, 2, 6, 9, 3, 5
Mode ??
Median ?? Mean??
explanation ;)
MEAN - add all the numbers = 4+6+2+6+9+3+5 =42
then you count have many numbers you got 7
after that you divided 7/42 = 6 that the mean or something call average:)
MEDIA - to find out was the meaning is you first make in order like youngest to oldest 2, 3, 4, 5, 6, 6, 9 and circle what numbers is on the middle that is 5.
listen if there even amounts of numbers you just circle the two numbers in the middle then add does two numbers and divide dy 2 ONLY IF IS EVEN
MODE- look for the two numbers they are the same 6
and that's the mode
6,5,6
I need help Finding the perimeter of a towel that measures 2 feet by 34 foot
Answer:
72 feet
Step-by-step explanation:
multiply 34 by 2 (because there is 2 sides), and multiply 2 by 2 (because there is 2 sides), and you'll get 68 and 4. add them together, and you'll get 72.
a triangle has side length of 10 inches, 24 inches, and 26 inches. Is the triangle a right triangle
Answer:
yes!
Step-by-step explanation:
one side is longer than the other then the 10 inch line is used to connect them!
(hope this helps)
convert 0.11 to a percentage
NEED TO BE ANSWERED ASAP
I will award them the brainliest
Answer:
11%
Step-by-step explanation:
0.11*100=11%
necause 1%=1/100
HELP ASAP!!!!!!!!!!!!
Answer:
It would be the second one, angle A would equal angle F
Step-by-step explanation:
They are both in the same position. A is the first one in the sequence ABC and F is the first one in the sequence FED
*giggling*
❤️✨
Why’s it saying it’s too short?
Answer:
-15(7/20) = -307/20 = -15.35, which is less than -15.
Step-by-step explanation:
Aight
Answer:
>
Step-by-step explanation:
-15(7/20) = -307/20 = -15.35, which is less than -15.
- 8/3x -3 + 1/3x -1 =5
Answer:
3 6/7.
Step-by-step explanation:
Answer:
-3 6/7
Step-by-step explanation:
rewrite with 'like' terms next to each other:
-8/3x + 1/3x + (-3) + (-1) = 5
-7/3x + (-4) = 5
-7/3x = 9
multiply each side by -3/7
x = -27 /7 or -3 6/7
*inhale* AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
Answer:
ANSWER IS CAUSE ONES A NEG AND ONES A POSITIVE HAPPY TO HELP
Step-by-step explanation:
does anybody know this ?
Answer:
37 degrees
Step-by-step explanation:
First, solve for the angle beside 152 degrees. Subtract 180 to 152 and you get 28 degrees. Next, we add 28 degrees to 115 degrees, which is 143 degrees. After, we subtract 143 from 180 (since the total angle of a triangle is 180) and we arrive at 37 degrees.
The employees van assemble 1,576 cell phones in 8 hours.
If these employees continue to work at the same rate,how many cell phones will they assemble in 53hours?
A - 12,608
B - 10,441
C - 83,528
D - 70,920
Answer:
10,441
Step-by-step explanation:
1576/8=197
197x8=10,441
What is the best prediction of the amount of money earned when the lemonade stand has been open for 9 hours
Answer: $50
Step-by-step explanation: Draw a line through the apparent center of the scattered dots. See where that line intersects 9 in the time scale (x-axis numbers) and the dollars earned scale (y-axis numbers)
It could be 50 or 55, but since there are a few more dots below the apparent midline, it may be best to use the lower estimate.
NEED HELPP CORRECTT ANSWERS AND WILL GIVE THANKS AND MARK BRAINLIST ONLY FOR CORRECT ANSWER
4,20
i think that the answer
Which equation represents the slope-intercept form of the line below?
y-intercept = (0,3)
slope = 4
O A. y = 3x + 4
O B. y = 3x - 4
O C. y = 4x-3
D. y = 4x + 3
help asap
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 4 and c = 3, then
y = 4x + 3 → D
Answer:
b
Step-by-step explanation:
PLEASE HELP!!! THIS IS MY LAST QUESTION!! PLEASE(show work)
Answer:
sign = negative, degree = 5Step-by-step explanation:
The graph has negative leading coefficient as
x → ∞, y → - ∞It is of the odd degree, and the degree is most probably 5
Please help......
Please....
All sweaters at a store are on sale at the same percent discount. A sweater that is regularly priced at $32.00 is on sale for $25.60. What is the sale price of a sweater regularly priced at $28.00?
Answer:
$22.40
Step-by-step explanation:
32 - 25.60 = 6.40
6.40/32 = 0.2
0.2 X 100 = 20%
100 - 20 = 80
28/100 X 80 = 22.40
Justin can replace three windows in an 8 hour day. How many hours will he need to replace 20 windows on a house
2.16 ÷ 4 hurry its a timed test thank you!
Answer:
0.54
Step-by-step explanation:
2.16/14 = 0.54