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 = 32what is the other endpoint of a segment with one endpoint at(-3, 8) and the midpoint at (7, 1)?
Answer: The other point is (17, -6).
Step-by-step explanation:
Midpoint (x,y) of the line segment joining (a,b) and (c,d) is given by :-
[tex](x,y) =(\dfrac{a+c}{2}, \dfrac{b+d}{2})[/tex]
Here, we need to find the other endpoint of a segment with one endpoint at(-3, 8) and the midpoint at (7, 1).
Let other point be (a,b), then
[tex](7,1)=(\dfrac{-3+a}{2},\dfrac{8+b}{2})\\\\\Rightarrow\ \dfrac{-3+a}{2}=7\ \text{ and }\dfrac{8+b}{2}=1\\\\\Rightarrow\ -3+a = 7\times2 \text{ and } 8+b=1\times2\\\\\Rightarrow\ -3+a=14\text{ and }8+b=2\\\\\Rightarrow\ a=14+3, \ \ \ b= 2-8\\\\\Rightarrow\ a=17, b= -6[/tex]
hence, the other point is (17, -6).
Which number would make this number sentence true? (3 + 2) x ? = 5 x 8
Answer:
8
Step-by-step explanation:
3+2=5
5 x 8 = 5 x 8
Answer:
8
Step-by-step explanation:
2 numbers are in perenticies so do them first 3+2 = 5 Then wait dont do nothing with that do 5x8 to get what to need to get 5 x? to witch is
40 so 8 would be the correct answer
Can the sides of a triangle have lengths 3, 7, and 15?
Please help. I don't understand this.
Answer:
radius=6
Step-by-step explanation:
arc ACB=6xPi
Pi=3.14159
arc ACB=18.85 (rounded to 2 places)
ACB is a half circle so a full circle would be 18.85x2 or 37.7
circumference (whole circle)=2 x Pi x radius
37.7=2 x 3.14159 x radius
radius= 37.7/(2 x 3.14159)
radius=6
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
8x – 6y = 54
look at screenshot and answer question
Answer:
32x +20
Step-by-step explanation:
Answer:
32x+20
Step-by-step explanation:
If you use distributive property you would multiply each number by 4. 4 times 8x is 32x and 4 times 5 is 20, and when you put those together you get 32x+20!
I hope this helps, and have a great day!
is this a domain or range?
please help :(
Step-by-step explanation:
it's a function.
the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
the domain is (1,3,7,8)
the range is (2,4,6,9)
can i plz get some help
Olivia wants to know the proportion of students at her school who use a
certain social media app. She interviews a random sample of students at
her school. She finds that 30% of the students in the sample use the app.
What conclusion can she draw from the sample?
А
It is likely that about 30% of the students at her school use the app.
B Exactly 30% of the students at her school use the app.
Every random sample would find that 30% of the students use
the app
It is likely that 30% of the students at her school were selected for
the sample.
Answer:
A
Step-by-step explanation:
Random sampling is a sampling method where each sample has an equal chance of being chosen. The random sample chosen is meant to be an unbiased representation of the population.
If 30% of the sample uses the app, it means that 30% of the population are likely to use the app
What is the decimal form of 45/129
Answer:
0.348837
Step-by-step explanation:
How many ounces are equal to 7 pounds?
Answer: 112 ounces
Answer:
Why did you7 ask a question then anwser it yourself
Step-by-step explanation:
Which statement best describes what happens when k is changed from 2 to – 3
5 6 costs $150 to rent a party room at Pizza-n-Games, plus $6 per person for pizza and $5 per person for game ckets. The expression shown gives the total cost for n people. 150+60+5n Evaluate the expression to find the cost for a party of 15 people, A $161 B. $165 C. $315 Click to add speaker note
Answer:
315
Step-by-step explanation:
Pls Help Step by step look at picture
Answer:
-6(x-y)
Step-by-step explanation:
Combine the same terms together
; (-3x+2x-5x) + (y+7y-2y)
Use parentheses to make thinking easier.
Combine ; -6x + 6y
Factoring polynomials ; -6(x-y)
hope it helps ☺️
pls anwer fast is due in 5min
Answer:
Taking my points
Step-by-step explanation:
You spammed my own question
If the triangles are similar, find the value of x.
Answer:
x=25Step-by-step explanation:
the triangles are similar
so as we know
when two triangles are similar the rotio of triangles is equalnow let's solve it
to understand the solving stepsyou need to know aboutequation with fractionPEMDASaccording to the question
[tex] \frac{24}{30 } = \frac{x + 7}{2x - 10} [/tex]
[tex] \frac{4}{5} = \frac{x + 7}{2x - 10} [/tex]
[tex]4(2x - 10) = 5(x + 7) \: (cross \: multiplication)[/tex]
[tex]8x - 40 = 5x + 35[/tex]
[tex]8x - 5x = 35 + 40[/tex]
[tex]3x = 75[/tex]
[tex]x = 25[/tex]
Pleasse Helppp Asapppp.
Answer:
77 degrees
Step-by-step explanation:
supplementary angles add up to 180 degrees
subtract 103 from 180 to get 77 degrees
Does anyone know this if you could help me I would appreciate it
Answer:
C, B
Step-by-step explanation:
Basically to find the slope you take the rise over run. How many squares does the line go up, over how many does it go left or right. As you can see in the diagram, it goes up 2 squares and goes left 1 square, giving the slope 2/1, which is 2.
The slope of a horizontal line is straight, which means it goes up 0, so automatically your answer is zero, because dividing anything by 0 is 0.
Please help!20 POINTS BRAINLIEST
Answer: The answer is 0.20
Step-by-step explanation: To find a scale factor all you need to do is find the ratio of a side on the scaled shape to its corresponding side on the original figure. We know the bottom of the scaled figure is 0.5 and the same side on the original rectangle was 2.5 so we can just divide like so...
0.5/2.5 = 0.2 which is our correct answer. I hope this has been of use to you :) If you have any other questions please do not hesitate to ask!
What is the slope of the line y=8?
Answer:
undefined or 0
Step-by-step explanation:
Answer:
The answer is 0 because undefined is straight up or vertical
How many kilometers are there in 4 miles?
Hint: 1 mi ≈ 1.6 km
Round your answer to the nearest tenth.
Need correct answer only PLS
Which option identifies the sectors of the economy involved in the following scenario?
Joe owns a family farm in central Illinois. He goes to the bank for a loan for a new combine.
agriculture and services
services and industry
agribusiness and industry
agriculture and industry
Answer:
Step-by-step explanation:
A and c
Answer:
a
Step-by-step explanation:
Hope this helps:)
1/10( x + 130) = -2(3-X)
I need help
Answer:
x = 10
Step-by-step explanation:
1/10(x + 130) = -2(3 - x)
x + 130 = -20(3-x)
x + 130 = -60 + 20x
x - 20x = -60 - 130
-19x = -190
x = 10
Mai bought gas for her car.
Gas cost $2.95 per gallon
Mai bought 8.2 gallons
What was the total cost for Mai's gas?
Express the answer as dollars.cents.
Only 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, . , -, and / are allowed in your answer.
Answers that are mixed numbers must be entered as an improper fraction or decimal.
brianna caught 4 fish . gabi caught 8 times as many fish as brianna. which expression shows how many fish gabi caught
Answer:
multiplication
Step-by-step explanation:
brianna=4
gabi=8 x brianna
4 to 7 equals 21 to what
Answer:
Step-by-step explanation:
I dunno wether addition or multiplication, if it's multiplication, it would be 36.75 if it's addition, then it's 24
3. A computer is priced at $65,000 plus value added tax at 15%. What amount does the computer actually cost the customer?
Answer:
$74,750
Step-by-step explanation:
Given that,
The cost of a computer = $65,000 + value added tax at 15%
We need to find the amount the computer actually cost the customer.
Total cost = Cost of computer + VAT at 15%
[tex]=65000+65000\times \dfrac{15}{100}\\\\=\$74,750[/tex]
So, the computer actually cost the customer is $74,750.
Kimberly has a job to tile a room 14 x 12 ft with 1 ft square tiles. How many tiles Does he need?
A model rocket was launched from a podium 5 meters above are
an initial velocity of 98 m/s. The function that models height in me
with respect to time (in seconds) is h(t) = 5 + 987-4.9t2
meters above ground at
meters)
Answer:
See solution belowStep-by-step explanation:
Find the complete question below;
Given the height modeled by the function;
h(t) = 5 + 98t-4.9t²
when t = 0
h(0) = 5 + 98(0)-4.9(0)²
h(0) = 5
when t = 5
h(5) = 5 + 98(5)-4.9(5)²
h(5) = 5 + 490 - 122.5
h(5) = 372.5
when t = 10
h(10) = 5 + 98(10)-4.9(10)²
h(10) = 5 + 980 - 490
h(10) = 495
when t = 15
h(15) = 5 + 98(15)-4.9(15)²
h(15) = 5 + 1470 - 1,102.5
h(15) = 372.5
when t = 20
h(10) = 5 + 98(20)-4.9(20)²
h(10) = 5 + 1960 - 4.9(400)
h(10) = 1965- 1960
h(10) = 5
Find the graph attached
What is the value of y