Find the standard form of the equation of the ellipse with the given characteristics. Center: (1, 2); vertex: (−7, 2); minor axis of length 12

Answers

Answer 1

Answer:

(x-1)²/64 + (y-2)²/144 = 1

Step-by-step explanation:

The standard equation of an ellipse is expressed as (x-h)²/a² + (y-k)²/b² = 1

Where the coordinate (h,k) is the centre of the ellipse.

a is the the difference of the x coordinates of the centre and the vertex.

b is the minor axis.

Given the centre to be (1,2), on comparing with the coordinate (h,k),

h = 1 and k = 2

The difference of the x coordinates of the centre and the vertex = -7-1 = -8

The minor axis as given in the equation is b = 12

Substituting the given parameters into the equation of an ellipse above we will have;

(x-1)²/(-8)² + (y-2)²/12² = 1

(x-1)²/64 + (y-2)²/144 = 1

The final equation gives the required standard form of the equation of the ellipse.


Related Questions

circle the digit is in the tens place

219,358,675​

Answers

Answer:

219,358,675

the tens digit is the second digit before decimal point (from right to left)

219,358,675

Hope this helps!! :)

Answer:

Hey!

The 7 in *...675*  is in the tens place!!

Step-by-step explanation:

Tens place??

AkA THE SECOND PLACE IN FROM RIGHT

▶hOPE IT HELPED!!◀

Find the midpoint of CD when
C (-2, -1) and D (4, 3).

Answers

Answer: (1, 1)

Step-by-step explanation:

Midpoint formula: [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]

(x1, x2)=(-2, 4)

(y1, y2)=(-1, 3)

-----------------------------------------

 [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]

=[tex](\frac{-2+4}{2} ,\frac{-1+3}{2} )[/tex]

=[tex](\frac{2}{2} ,\frac{2}{2} )[/tex]

=[tex](1, 1)[/tex]

Hope this helps!! :)

Please let me know if you have any question or need further explanation

If you count 14 beats in 6 seconds, what is your approximate rate?​

Answers

Answer:

About 2.3 beats per second

Step-by-step explanation:

14 / 6 is approximately 2.3.

Answer: About 2.33  beats per second

Step-by-step explanation:

Divide the number of beats by the seconds and find the approximation rate.

Two hoses are filling a pool the first hose fills at a rate of x gallons per minute the second hose fills at a rate of 15 gallons per minute less than the first hose.

Answers

The correct answer would be B!

I’m a constant function. There are two possible ways to write me; one way being slope-intercept form and the other being constant form
(I don’t really understand what this question is asking)

Answers

Answer:

constant function has the same output no matter what are the inputs and it is written in the form : y=b where b is a constant  that does not change. the slope of this function always equal to zero.

slope intercept form : y=mx+b ( where m=0)

constant form : y=b ( y equal a constant that does not change)

Principal: $1500.
Annual interest rate: 72%.
What is the interest after
6 months?

Answers

I’m assuming you mean 7.2% for the annual interest rate and not 72%. If the annual interest rate is 7.2% then the interest after 6 months is $54.

To solve this problem, you us the equation A=P(1+rt)

A stands for the amount of money accumulated after t years
P stands for principal
r stands for annual interest rate
t stands for time (in years)

Next you need to plug it into your formula which should look like this...
A=1500(1+(0.072*0.5))

When you plug in your annual interest rate, you have to move your decimal place 2 places to the left. That is why 7.2% is 0.072 in the formula above.

The reason that I plugged in 0.5 for the time instead of 6 months is because the time in this formula is calculated in years. For example, if the question told you the time was 12 months, 12 months is one year, so you would plug in a 1 for t. Since your question asked for 6 months, 6 months is equal to half a year or 0.5 of a year. That is why t is 0.5 in the formula.

Now that you have your problem, the next step is to solve. I will show you what that looks like down below.

A=1500(1+(0.072*0.5))
A=1500(1+(0.036))
A=1500(1.036)
A=1554

From this problem, we just solved for how much money is in this account after 6 months which is $1554. But we’re not done yet, we are looking for how much interest was earned after 6 months.

To find this, all you have to do is subtract the amount earned after 6 months ($1554) by the principal amount ($1500) using this formula (the I stands for Interest).

A-P=I
1554-1500= 54

The interest earned after 6 months is $54.
(If the annual interest rate is 72% and not 7.2%, you can still use the formulas and my lesson to solve it yourself)

3x-30 =1.5 plz help me

Answers

Answer:

x = 10.5

Step-by-step explanation:

3x - 30 = 1.5

3x = 31.5

x = 10.5

Lee spent $29 to purchase a combination of drinks, sandwiches, and chips for himself and his friends. A drink costs $1.50, a sandwich costs $5, and chips cost $1.25. Identify the linear equation that represents this situation.

Answers

Answer:

1.5d+5s+1.25c=29

Step-by-step explanation:

let d be the number of drinks, s be the number of sandwich, and c be the number of chips Lee purchased.

1.5×d and 5×s and 1.25×c must total 29, or

1.5d+5s+1.25c=29.

A 2000 kilogram sports car accelerates at a ratr of 30 meters per second squared. The velocity of the car is v=at where a is acceleration in meters per second squaref and t is tome in seconds. The kinetic energy of the car is KE = 1/2 mv^2

Answers

Answer:

KE = 900,000t²

Step-by-step explanation:

The formula for calculating the kinetic energy of a body is expressed as KE = 1/2mv² where;

m is the mass of the sport car = 2000kg

v is the velocity of the car

Since v = at

v = 30t

Substituting the given values into the KE formula;

KE  1/2 * 2000 * (30t)²

KE = 1000*900t²

KE = 900,000t² Joules where t is the time measured in seconds

Answer:

KE = 900,000t²

Step-by-step explanation:

Answer is D if you use edgenuity, answers do not mix

Please help me please

Answers

Answer:

y = 4  (Answer C)

Step-by-step explanation:

We want to find side y.  The sine function relates the 30 degree angle, the hypotenuse 8 and the opposite side y:

                                          y

sin 30 degrees = 1/2 = -----------

                                           8

so y = 4  (Answer C)

Determine the rate of change for 3/2x -5/4y = 15

Answers

Answer:

-6/5

Step-by-step explanation:

3/2x - 5/4y = 15

-5/4y = -3/2x + 15

multiply each side by (-4/5)

(-4/5)(-5/4y) = (-4/5)(-3/2x + 15)

y = -6/5x - 12

rate of change: -6/5

49 divided by 7 get a decimal answer

Answers

Answer:

7.0?

Step-by-step explanation:

49/7 would be 7, If the question was 7/49 the answer would be 0.14285714285 (a decimal)

Simplify: (3n2 +9+5n4 – 3n)+(-9n* - 7 -5n?)

Answers

Answer:

3n^2+9+5n^4+55n

Step-by-step explanation:

Steps

$\left(3n^2+9+5n^4-3n\right)+\left(-9n\left(-7\right)-5n\right)$

$\mathrm{Remove\:parentheses}:\quad\left(a\right)=a,\:-\left(-a\right)=a$

$=3n^2+9+5n^4-3n+9n\cdot\:7-5n$

$\mathrm{Add\:similar\:elements:}\:-3n-5n=-8n$

$=3n^2+9+5n^4-8n+9\cdot\:7n$

$\mathrm{Multiply\:the\:numbers:}\:9\cdot\:7=63$

$=3n^2+9+5n^4-8n+63n$

$\mathrm{Add\:similar\:elements:}\:-8n+63n=55n$

$=3n^2+9+5n^4+55n$

Each school day, Aidon wolks 11 blocks to school after school, he wolks 4 blocks to the library
and 12 blocks home. How many blocks does Aidon wolk in a week? *
e

Answers

Answer:

189

Step-by-step explanation:

Aidon walked 11 blocks to begin with than he walks 4 blocks to the library and 12 blocks home. This mean we add 11+4+12=27 and a week has 7 days which means we need to multiply that by 7 which gives us the product of 189.

Also, i double checked

Solve the equation 6x + 2x - 5= 19 x=? Simplify your answer

Answers

Answer:

x = 3

Step-by-step explanation:

6x + 2x - 5= 19  

8X -5 = 19

8x = 24

x = 3

A research company wants to test the claim that a new multi vitamin helps improve short term memory state the objective of the experiment suggest a population determine the experimental and control groups and describe a simple procedure

Answers

Answer:

To test the effects of the multi-vitamin, we must test it on people with short-term memory loss. So the population should be people with short-term memory loss. The independent variable is the multi-vitamin and the dependent variable is the short term memory state of the people being tested. A control group can consist of people with short-term memory loss NOT being treated by the multi-vitamin.

If you would like more help on math or other subjects for FREE, check out growthinyouth.org.

How can i write all the names that apply √36 NEED IT ASAP

Answers

Answer:

square of 36 is 6

or maybe 6²

I NEED HELP Are the two functions inverses? f ( x ) = − 8 x + 5 g ( x ) = − 1 8 x + 5 8 Group of answer choices Yes No

Answers

Answer: No

Step-by-step explanation:

To know if the functions are inverses of each other, it is easiest to just find the inverse of one of the functions. To find the inverse, you want to replace y with x and x with y and solve for y.

y=-8x+5                                  [switch x with y and y with x]

x=-8y+5                                  [subtract both sides by 5]

x-5=-8y                                   [divide both sides by -8]

y=(x-5)/-8

f⁻¹(x)=(x-5)/-8

Since we know that the inverse doesn't match g(x), we know that these functions are not inverses of each other.

Please HELP ASAPPPP uts not -3!!!

Answers

Here you go hopes this helps

Answer:

x= 11

Step-by-step explanation:

(7x -1)° + (9x +5)°= 180° (adj. ∠s on a str. line)

7x -1 +9x +5= 180

16x +4= 180 (simplify)

16x= 180 -4 (-4 on both sides)

16x= 176 (simplify)

x= 176 ÷16

x= 11

The sum of the angles on a straight line is 180°

on a piece of paper, graph y<-3/4x+2. Then determine which answer choice matches the graph you drew.

Answers

Answer:

  D.  Graph D

Step-by-step explanation:

The  "y <" tells you two things: (1) shading will be below the line, where y-values are less than those on the line, and (2) the line will be dashed, because the "equal to" case is not included.

Only one graph has a dashed line with shading below: Graph D.

Helpp me out pls!!!!!!!!!

Answers

Answer:

a. Maurice walked farther.

b. 0.62 m

Step-by-step explanation:

Maurice

4.1 × 1.8 = 7.38 miles

Junnie

2.5 × 3.2 = 8 miles

This shows that Junnie walked more than Maurice.

8 - 7.38 = 0.62

Junnie walked 0.62 m more than Maurice

1/2(-2x - 12) > 7(3 - 4x)

The solution is____​

Answers

Answer:

x > 1

interval (1,∞)

Step-by-step explanation:

1/2(-2x - 12) > 7(3 - 4x)

-x - 6 > 21 - 28x

-x + 28x > 21 + 6

27 x > 27

x > 27 / 27

x > 1

interval (1,∞)

-x - 6 > 21 - 28x     if x = 2

-2 - 6 > 21 -28(2)

-8 > 21 - 56

- 8 > - 35

please quickly answer. i cant be waiting for 20 mins.

Answers

Answer:

C ( -2,4)

Step-by-step explanation:

In quadrant II, the x values are negative and the y values are positive

( -, +)

(-2,4) is the only point that meets this

Answer:

[tex]\huge \boxed{\mathrm{\bold{C.}} \ ( -2,4)}[/tex]

Step-by-step explanation:

The x values are negative and the y values are positive in quadrant II.

The point (-2, 4) is in quadrant II.

17 POINTS!!!! List the elements in the set described. {x|x is a natural number between 9 and 17} (Use a comma to separate answers as needed. use ascending order.)

Answers

Answer:

10, 11, 12, 13, 14, 15, 16

Step-by-step explanation:

The natural numbers are 1, 2, 3, 4, ...

The natural numbers between 9 and 17 are 10, 11, 12, 13, 14, 15, 16.

Answer: 10, 11, 12, 13, 14, 15, 16

please help// geometry question.... “the distance from” is cut off from the picture

Answers

Answer:332

Step-by-step explanation:

View Lab
Which of the following functions is most likely to have the smallest value for y if x is large? (Assume k is positive.)
a direct variation function with a small value fork
a direct variation function with a large value fork
an inverse variation function with a small value fork
an inverse variation function with a large value fork
Nexi
Subm
Save and Exit
Mark this and retum

Answers

Answer:

  an inverse variation function with a small value for k

Step-by-step explanation:

The attached graph shows the cases described. The function with the smallest function value for large x is ...

  an inverse variation function with a small value for k

___

On the graph, it is the green curve. The inverse variation functions both continue to decrease for large x, but the function with the smaller k value has a smaller function value.

Answer:an inverse variation function with a small value for k

Step-by-step explanation:Because i took the test

Write 6.93 repeating a mixed number in simplest form.
6.93 =?

Answers

Answer:

[tex]6\frac{93}{100} = \frac{693}{100}[/tex]

Step-by-step explanation:

Turn 6.93 into a fraction: [tex]6\frac{93}{100}[/tex]  To turn into a mixed number, first multiply 6 and 100, then add 93. Put 693 over 100: [tex]\frac{693}{100}[/tex]  

I hope this helps!

Answer:  [tex]6 \frac{31}{33}[/tex]

This is a mixed number where the whole part is 6, and the fractional part is 31/33.

=============================================

Explanation:

The 93 repeats forever, so we can say

x = 6.939393...

100x = 693.939393....

Subtracting the left hand sides leads to 100x-x = 99x

Subtracting the right hand sides leads to 693.939393.... - 6.939393... = 687

Notice how the decimal terms cancel out when we subtract.

We're left with 99x = 687 which solves to x = 687/99

This reduces to 229/33 when you divide both parts by 3.

The last step is to convert to a mixed number

The answer will be in the form [tex]6 \frac{x}{33}[/tex] where 6 is the whole part and x/33 is the fractional part. We know the whole part is 6 from the 6 in the original number given.

229/33 = 6.939393... helps confirm we're on the right track so far

this is another way of saying 229/33 = 6 remainder x, where x is the unknown remainder and the numerator we're after for the fraction x/33.

To get the remainder, we just compute 229-6*33 to get 31

This means 31/33 = 0.93939393...

and that [tex]6 \frac{31}{33} = 6.\overline{93} = 6.93939393...[/tex]

Simplify 3√-1000 and 3√g6h30

Answers

Answer:

[tex] \sqrt[ ]{1000} [/tex]

Step-by-step explanation:

[tex]3 \sqrt{ - 1000} = 3 \sqrt{1000i {}^{2} } \\ = 3 \times 10i \\ = 30i \\ (in \: complex \: form \: i {}^{2} = - 1)[/tex]

Answer:

1st one = -10

2nd one = g2h10

Step-by-step explanation:

Edge2020!!

u= ab/k, for a
Solve form A

Answers

Answer:

a = uk/b

Step-by-step explanation:

u = ab/k

uk = ab

a = uk/b

Write a ratio for the following description: Kaleel made three times as many baskets as John during basketball practice. Type your answer in the format: 3:4 with no spaces.

Answers

Answer:

3:1

Step-by-step explanation:

hey there,

< We know Kaleel made 3x as many baskets as John.

We're going to make our ratio Kaleel:John.

The answer would be 3:1 because every time John makes 1 basket, Kaleel makes 3 baskets. If John made 2, then Kaleel would make 6, etc...

Sorry, I can't explain this very well! >

Hope this helped. Feel free to ask anything else.

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