Answer:
I think that it is n<3
Step-by-step explanation:
Q.6. The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes
through the points (-3, 1) and (2,-2) is
(A) 5x2 + 3y =32 (B) 3r? + 5y = 32 (C) 5x° - 3y2 = 32 (D) 3x* + 5y? + 32 = 0
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 = 32(-8,6); slope = 1/4
Turn into y intercept equation !
Re write the statement 19+7 divided by 2-5 by including one pair of brackets to make the total equal to 8
Answer:
The solution is given below:
Step-by-step explanation:
The computation is shown below:
= 19 + 7 divided by 2 - 5
= (19 + 7) ÷ (2) - 5
= 26 ÷ 2 - 5
= 13 - 5
= 8
Hence, after solving this the value would be 8
Therefore it is equal to the 8
Hence, the given statement is true
The sum of two numbers is 25. Twice the first number minus the second is 6. Find the numbers.
Answer:
Step-by-step explanation:
x + y = 25
2x - y = 6 Solve for y in this the second equation. Add y to both sides
2x = 6 + y The ys on the left cancel. Subtract 6 from both sides.
2x - 6 = y
Put this value of y into the first equation
x + y = 25
x + 2x - 6 = 25 Combine on the left
3x - 6 = 25 Add 6 to both sides.
3x = 25 + 6 Combine the right
3x = 31 Divide by 3
x = 31 / 3
x = 10.333333
x + y = 25
10.33333 + y = 25 Subtract 10.33333
y = 25 - 10.333333
y = 14.666666
x + y = 25
10.33333 + 14.66666
25 approximately.
2x - y = 6
2*10.33333 - 14.66666
20.66666 - 14.66666
6
You should note that those numbers are repeating decimals
2x - 6 = y
Ajar contains 100 coins. If it is very unlikely that you will randomly choose a quarter out of the jar, how many quarters
could be in the jar?
10
85
50
35
Translate the phrase into an algebraic expression. The quotient of y and 4
Answer:
y/4
Step-by-step explanation:
What is the exact volume of the cylinder
Answer:
Volume = πr2h
= π×52×9
= 225π
= 706.85 inches3
Step-by-step explanation:
Ben is playing a card game. The numbers of the cards in his hand are 2, 3, 4, 4, 5, 7, 9, and 10. Ben may only play one card at a time.
What is the probability the next card Ben plays will be an odd number?
A. 3/4
B. 1/2
C. 3/8
D. 1/4
If a factory can make 28 candles in 2 hours how many can make in 1 hour
Answer: 14 candles in 1 hour
Step-by-step explanation: To find how many candles they can make in 1 hour, simply divide 28 by 2.
28/2 = 14 candles in 1 hour.
What is Santon’s goal?
Anno one came answer that without numbers
Step-by-step explanation:
Answer:
Although Stanton remained committed to efforts to gain property rights for married women and ending slavery, the women's suffrage movement increasingly became her top priority. Stanton met Susan B
Step-by-step explanation:
Find the equation of the exponential function represented by the table below
Answer:
[tex]y=4^x[/tex]
Step-by-step explanation:
[tex]y=4^x[/tex]
For x=0
[tex]y=4^{0}=1[/tex]
For x=1
[tex]y=4^1=4[/tex]
For x=2
[tex]y=4^2=16[/tex]
Answer:
Step-by-step explanation:
-2 - 14 + 147
What is the value
The population in England goes up by 1/5 every year. If the population was £20mil in 2008 what would be the population in 2010?
Answer:
1/5 = 20%
20.000.000 x 20% =4.000.000 / year
from 2008 to 2010 is : 2 years
So the population in 2010 is : 20.000.000 + ( 4.000.000 x 2 ) = 28.000.000 population
Step-by-step explanation:
HELPPPP iLL GIVE YOU BRAINLIEST
Miguel wants to determine how long it takes him to run a mile on any given day. If he collects his running times for 14
days, he can determine the time it usually takes him to run a mile by
A. calculating the sum of all of the running times
B. subtracting the longest time from the shortest time
C. adding the values together and dividing by 14
D. adding the longest time to the shortest time and dividing by 2
Answer:
it would be D
Step-by-step explanation:
and I say this because i did this before.
Answer:
C
Step-by-step explanation:
It's basically finding the average or mean of the problem, so he would add up all his times and divide by 14 because that's the total "amounts" he has. Hope this helped!
Evaluate each expression for the given value of each variable.
SHOW YOUR WORK!
10y + x², x is 6 y is 4
Answer:
76
Step-by-step explanation:
10 * 4 + 6 ^ 2 = 40 + 36 = 76
If someone could help with these questiones
Find the perimeter of the image below: (4 points)
a. 37 units
b. 38 units
c. 39 units
d. 40 units
Answer:
The correct answer is 39 units.
Parameter is the sum of the lengths of all sides of a polygon. The sides of the polygon are PT, TS, SR, RQ, and QP. To get the length of a side, we use the distance formula:
d =
Each vertex in the polygon has its corresponding points:
P (-2,11)
T (8, 7)
S (1, 7)
R (2, 0)
Q (-4,5)
So to get the length of side PT, we use the distance formula and the vertices of side PT:
P = (-2, 11)
T = (8, 7)
The length of PT is
The same procedure is done for the other 4 sides and the following are the answers:
TS =
SR =
RQ =
QP =
And by adding all the sides, you get the perimeter:
By rounding off, the answer is 39 units.
Step-by-step explanation:
Yesterday, a movie theater sold 278 bags of popcom. A large bag of popcorn costs $3. A small bag of popcom costs $1. In all, the more theater made shes from
popcorn sales. Write and solve a system of equations to find how many bags of each size of popcom were sold.
Answer:
They sold 175 small popcorns and 103 Large popcorns
Step-by-step explanation:
The equation is
L + S = 278 this means the total large and small popcorn that they sold is 278
3L+1S= 484 The owner of the question told me the total profit is 484
When we solve we can turn the first equation into L=-S+278
we substitute L=-S+278 into 3L+1S=484 we get -3S+ 834+ S= 484
-3S+834+1S=484
-2S+ 834= 484
-2S=- 350
2s= 350
s= 175
We know that they sold 175 small popcorns now. Now we Substitute 175 into L+ S= 278 and get L+ 175=278
L+175=278
L= 103
They sold 175 small popcorns and 103 Large popcorns
Please help, will give brainlist
Answer:
[tex]x^{2}-2+\frac{20}{x+7}[/tex]
Step-by-step explanation:
x + 7) x³ + 7x²- 2x + 6 ( x²- 2
x³ + 7x²
-2x + 6
-2x - 14
+20
Therefore, we can write the expression in the remainder quotient form as,
[tex]x^{2}-2+\frac{20}{x+7}[/tex]
Someone please help?
Answer:
42°
Step-by-step explanation:
its 42° because its smaller than 48° and that's the only option smaller lol
Answer:
42 degrees
Step-by-step explanation:
The angle forms a right angle, which in total would be 90 degrees.
48 + 42 would be the only option because it is the only one that adds up to 90 degrees.
Which statement best describes what happened when h is changed from 4 to - 2.
The line CD passes through the points C (2.-1) and D (1, 1). Which of the
following represents the equation of the line in Point-Slope Form?*
Answer:
The equation of the line in Point-Slope Form will be:
[tex]y + 1 = -2(x - 2)[/tex]
Also, check the attached graph below.
Step-by-step explanation:
Given the points
C(2, -1)D(1, 1)Determining the slope between the points C (2.-1) and D (1, 1).
(x₁, y₁) = (2, -1) (x₂, y₂) = (1, 1)Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [1 - (-1)] / [1 - 2]
= [1+1] / [-1]
= [2] / [-1]
= -2
Thus, the slope of the line = m = -2
The point-slope form of the line equation is defined as
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
m is the slope of the line(x₁, y₁) is the pointIn our case:
(x₁, y₁) = (2, -1)m = -2substituting the values m = -2 and the point (x₁, y₁) = (2, -1) in the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - (-1) = -2 (x - 2)[/tex]
[tex]y + 1 = -2(x - 2)[/tex]
Therefore, the equation of the line in Point-Slope Form will be:
[tex]y + 1 = -2(x - 2)[/tex]
Also, check the attached graph below.
Show how to rewrite 1/5 with the denominator 10
The denominator is the bottom number.
To change the 5 to 10, you would multiply 5 by 2: 5 x 2 = 10
Because you multiplied the 5 by 2, you also need to multiply the numerator ( top number) by the same amount.
1 x 2 = 2
So 1/5 = 2/10
The answer is 2/10
A store marks up its notebook computers by 22%. What price does the store charge
its customers for a $600 notebook computer?
4. Ms. Beltran buys songs from a music website. She buys 20 songs for $12.
a. What is the price per song?
Answer:$1.67
Step-by-step explanation:
Divide 20 and 12 to get 1.6666666 round the number and you get 1.67
Michelle wants to make a long-term investment. She wants to triple an initial investment of
$2,000. If she invests at a simple interest rate of 12% per year, approximately how long will it
take her principal to triple?
Answer:
It will take approximately 17 years
Step-by-step explanation:
Let the initial investment be x
The investment plus the principal yields 3x
The interest is thus 3x-x = 2x
Formula for simple interest is;
I = PRT/100
R is rate = 12%
T is time = ?
x =$2,000 which is the principal
2x = x * 12 * T/100
2 = 12t/100
12t = 200
t = 200/12
t = 16.67 which is approximately 17 years
Is 5 a factor of 6w + 30?
yes
no
HELP PLSS HELP
Answer:
yes
Step-by-step explanation:
A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36° E. There is a 10mi/h cross wind blowing due east. What is the balloon's actual speed and direction? Round angles to the nearest degree and other values to the nearest tenth.
Answer:
The actual speed = 27.12 mi/h
Direction = 36.5° in NE(north of east)
Step-by-step explanation:
As given , A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36° E.
⇒θ = 36°
Let v₀ be the constant speed, then v₀ = 20
Let vₓ be the speed in East direction
[tex]v_{y}[/tex] be the speed in North direction
So,
vₓ = v₀ sin(θ) = 20 sin(36°) + 10 ( As given, There is a 10mi/h cross wind blowing due east.)
⇒vₓ = 20(0.588) + 10 = 11.76 + 10 = 21.76 mi/h
and [tex]v_{y}[/tex] = v₀ cos(θ) = 20 cos(36°) = 20(0.809) = 16.18 mi/h
Now,
the actual speed = √(vₓ)² + ([tex]v_{y}[/tex])²
= √(21.76)² + (16.18)²
= √473.498 + 261.792
= √735.29 = 27.12
⇒The actual speed = 27.12 mi/h
Now,
Direction = θ = [tex]tan^{-1}(\frac{v_{y} }{v_{x} } ) = tan^{-1}(\frac{16.18 }{21.76 } ) = tan^{-1}(0.74) = 36.5[/tex]
⇒ Direction = 36.5° in NE(north of east)
Answer:
27.1 mi / h; N 53° E
Step-by-step explanation
1/1
3. Maria's dinner bill is $13.53 after tax. If she wants to leave a 15% tip.
what will the total cost of the dinner be?
Answer:
$15.56
Step-by-step explanation:
So start by doing a 10% tip, because you just move the decimal place over by 1, so $1.35, and then divide that by 2 to get 5% which is .68, and add them to get 2.03. You can get the same answer by multiplying 0.15 to 13.53. 13.53 + 2.03 is 15.56. Hope this helped and have an awesome day!
20 % of the m&ms are red. There were 40 m&ms in the bag . How many red m&ms are there?
Answer:
8 Red M&M's
Step-by-step explanation:
40 M&M's × 0·20 = 8 red M&M's in the bag
Hope this helps, plz mark brainliest!
answer 8 red m&ms are there
Step-by-step explanation:
20/100*40
100/20=5
40/5=8
answer is 8red m&ms are there