What are the lengths of the major and minor axes of the ellipse?

(x−3)212+(y+4)224=1

Drag a value to the boxes to correctly complete the table.

What Are The Lengths Of The Major And Minor Axes Of The Ellipse?(x3)212+(y+4)224=1Drag A Value To The

Answers

Answer 1

The lengths of the major and minor axis of the ellipse, [tex] \displaystyle{ \frac{ {(x - 3)}^{2} }{12} +\frac{ {(y + 4)}^{2} }{24} = 1}[/tex] are;

Length of major axis; 4•√6Length of minor axis; 4•√3

What is an ellipse in coordinate geometry?

An ellipse describes the locus of a point on a curve, such that the sum of the distance from two focal points from the points on the curve is a constant.

The given given function of the ellipse can be presented as follows;

[tex] \displaystyle{ \frac{ {(x - 3)}^{2} }{12} +\frac{ {(y + 4)}^{2} }{24} = 1}[/tex]

The above equation can be compared to the standard equation of an ellipse as follows;

[tex] \displaystyle{ \frac{ {(x - h)}^{2} }{ {b}^{2} } +\frac{ {(y - k)}^{2} }{ {a}^{2} } = 1}[/tex]

Where;

(h, k) = The coordinates of the center of the ellipse

a = The length of the semi major axis

b = The length of the semi minor axis

By comparison, we have;

(h, k) = (3, -4)

a = √(24) = 2•√6

b = √(12) = 2•√3

The length of the major axis = 2•a

The length of the minor axis = 2•b

The length of the major axis is therefore;

2•a = 2 × 2•√6 = 4•√6

The length of the minor axis is therefore;

2•b = 2 × 2•√3 = 4•√3

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Related Questions

Write the sentence as an equation.
312 equals the total of 380 and p

Answers

Answer:

P+380=312

Step-by-step explanation:

The total, meaning addtion, and equals meaning equals sign. P+380=312

Please help me. Please don’t give me a answer on the internet

Answers

Answer

A) f(w) = 80w + 30

B) w represents the number of weeks and f(w) the number of flowers that bloomed

C) 2830 flowers

Step-by-step explanation

A) To find the function f, which represents the number of flowers that bloomed, as a function of w, the number of weeks, we have to evaluate f(s) with s = s(w) = 40w, as follows:

[tex]\begin{gathered} f(s)=2s+30 \\ \text{ Substituting }s=s(w), \\ f(s(w))=2s(w)+30 \\ \text{ Substituting }s(w)=40w \\ f(s(w))=2\cdot40w+30 \\ f(w)=80w+30 \end{gathered}[/tex]

B) w represents the number of weeks and f(w) the number of flowers that bloomed, like before.

C) Substituting w = 35 weeks into f(w), we get:

[tex]\begin{gathered} f(w)=80(35)+30 \\ f(w)=2800+30 \\ f(w)=2830\text{ flowers} \end{gathered}[/tex]

The difference between 75% of a number and 20% of the same number is 378.4 what is 40% of that number?

Answers

Answer:

40% of the number is 275.2.

Step-by-step explanation:

I am going to call the number x.

75% of the number: 0.75x

20% of the same number: 0.2x

The difference between 75% of a number and 20% of the same number is 378.4:

This means that:

0.75x - 0.2x = 378.4

0.55x = 378.4

x = 378.4/0.55

x = 688

40% of the number:

0.4*688 = 275.2

40% of the number is 275.2.

what is equivalent to 0.5×0.6

Answers

Answer: 0.3

5/10 x 6/10 = 30/100 = 3/10 = 0.3

n your initial post, answer the following questions: identify the many variables that a hospital needs to consider in layout design? what are the advantages of the circular pod design over the traditional linear hallway layout at arnold palmer? what suggestions about wheeled coach layout would you make to bob collins?

Answers

The structure must be designed so that there are no risks to the health and safety of the patients, staff, and general public. The main goal of layout exists to make clear that work, materials, and information flow through a system smoothly.

What is the layout of a hospital?

Layout design generally seeks to arrange organizational units inside a building so that the space is used to its fullest potential and total distances are kept to a minimum.

The structure must be designed so that there are no risks to the health and safety of the patients, staff, and general public. It must be able to endure the pressure and environmental conditions that they might encounter.

A facility's layout and design are crucial to a company's overall operations because they may both suit the needs of employees and maximize the efficiency of the production process. The main goal of layout exists to make clear that work, materials, and information flow through a system smoothly.

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Help me and be a real g pls!!!

Answers

Answer: 1. C=43.96 in  A=153.86 in²

              2. C=56.52 in  A=254.34 in²

Step-by-step explanation:

1.

R=7 in

C=2πR

C=2*3.14*7

C=43.96 in

A=πR²

A=3.14*7²

A=3.14*7*7

A=153,86 in²

2.

R

D=18 in

⇒ R=D/2

⇒ R=18/2

⇒ R=9 in

C=2πR

C=2*3.14*9

C=56.52 in

A=πR²

A=3.14*9²

A=3.14*9*9

A=254.34 in²

Rectangles ABCD and DEFG are congruent

AB=7cm
AD=17cm

Work out the length of CE

Answers

The length of CE is 7cm

How to determine the length

To determine the length, we need to consider the properties of a rectangle, we have;

It is a quadrilateralOpposite sides are known to be parallel and congruent to each otherThe interior angles are equal to 90 degreesDiagonals bisect each other at right anglesThe two diagonals have the same lengthRectangle having side lengths of x and y has the perimeter as 2x+2y unitsA rectangle with side lengths x and y has its area as: xy sin 90 = xy square unitsA diagonal of a rectangle is said to be the diameter of its circumcircle

From the information given, we have that;

AB = 7cm

AD = 17cm

Then, line CE = line AB

But line AB = 7cm

CE = 7cm

Hence, the length is 7cm

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PLS HELP ALL THIS IS DUE TOMORROW AND I HAVE NO TIME ! ( the red box is the stuff I need answers for )

Answers

Answer:

The answers are all below.

Step-by-step explanation:

7. Yes

Plug 10 in for t

10-3 ≥ 2

7 ≥ 2

8. No

Plug 1 in for w

6(1) < -2

6 < -2 (Nope)

9. Yes

Plug 5 in for p

5 + 1.6 ≤ 4

6.6 ≤ 4

10. Yes

Plug 0 in for d

[tex]\frac{1}{2}[/tex](0) > -3

0 > -3

11.

1(------------------>k

12.

n<------------------]2.5

13.

In order to try out for one of the parts in a play at the local theater, you must be at most 12 years old. Write an inequality that represents this situation.

x≤12

x<-----------------]12

14. Yes

Plug 2 in for h

3(2) - 7 < 2

Simplify

6 - 7 < 2

-1 < 2

15. No

Plug -12 in for q

-12 + 8 ≥ [tex]\frac{-12}{4}[/tex]

Simplify

-4 ≥ -3 (Nope)

16.

    a. Yes

    Plug 0 in for x

    -2(0) < 10

    and

    -6 < -2(0)

    Simplify

    0 < 10

    and

    -6 < 0

    b. No

    Plug 4 in for x

    -2(4) < 10

    and

    -6 <  -2(4)

    Simplify

    -8 < 10

    -6 < -8 (Nope)

    c. -1

    Plug -1 in for x

    -2(-1) < 10

    and

     -6 < -2(-1)

    Simplify

    2 < 10

    and

    -6 < 2

   

   

thought provoking the postulates and theorems in this book represent euclidean geometry. in spherical geometry, all points are points on the surface of a sphere. a line is a circle on the sphere whose diameter is equal to the diameter of the sphere. explain how many right angles are formed by two perpendicular lines in spherical geometry.

Answers

Inequality involving the sum of the angles of a triangle i.e,

[tex]\alpha +\beta +y > \pi[/tex]

The area of a spherical triangle ABC with angles a, B, Y are

AABC = ([tex]\alpha[/tex] + [tex]\beta[/tex]+ Y- [tex]\pi[/tex] ) [tex]R^{2}[/tex]

The AA'B'C' = AABC (by sss) as we discuss move.

We just need to demonstrate that IACI = IAC' and C'L IBCI = 1BC '1 will proceed similarly.

since AC & ATC resulted in the same.

the middle.

We now have external proof that the surface and their mon- are real. As of (ABCA) and LA'B'C) cover. A overlapping sphere with appropriate angles for each letter of the alphabet Las offered my first figure of $ segments that are completely separate from one another, so we may write -

( AABC A ) + ( A A'B'C' )A + ( An -x ) + ( Ax-B ) + ( An-V ) = [tex]4\pi R^{2}[/tex]

2 ( A ABC A ) =[tex]4\pi R^{2}[/tex] - 2 ( [tex]\pi -\alpha[/tex] ) [tex]R^{2}[/tex]- 2 ( [tex]\pi -\beta[/tex])[tex]R^{2}[/tex]-2([tex]\pi -Y[/tex])[tex]R^{2}[/tex]

AABCA = [tex](\alpha +\beta +Y-\pi )R^{2}[/tex]

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a ball was dropped from the empire state building observatory. the height of the ball in feet is described by the function f(x)=1048-16x^2 where x is time in seconds

Find the time when the ball hits the ground. round your answer to the nearest tenth

Answers

The time when the ball hits the ground is 8. 09 seconds

What is a function?

A function can be defined as an expression, theorem, law, or rule that elaborates, explains or holds true for the relationship between two variables.

These variables are namely;

The dependent variablesThe independent variables

From the information given, we have that;

f(x) = 1048 - 16x²

Where;

f(x) is The height of the ball in feetx is the time in seconds

To determine the time, we have;

collect like terms

- 16x² = - 1048

Divide both sides by the coefficient of x²

-16x²/-16 = -1048/-16

x² = 65.5

Find the square root of both sides, we have;

x = √65.5

x = 8. 09 seconds

Hence, the value is  8. 09 seconds

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someone include steps if you can

Answers

Using the concept of the equation, it can be concluded that Levi answered the first question wrong and the last two correctly. Thus,

No

Yes

Yes

How to check whether the value of x satisfies the equation?

To check the value of x satisfies the equation, put the value of x and if it matches the resultant, it is correct.

Now solving the first part, x/4=20;x=5

So, putting x=5 in the equation 5/4=1.25 is not matching with the resultant ie. 20.

Therefore, this is the incorrect value of x.

Now solving the second part, 1.5x-8=7;x=10

So, putting x=10 in equation 1.5*10-8= 15-8=7

It matches with the resultant.

Therefore, this is the correct value of x.

Now solving the third part, 4x+6=58; x=13

So, putting x=13 in equation 4(13)+6= 52+6=58

It matches with the resultant.

Therefore, this is the correct value of x.

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PLS HELP ME< WILL APPRICIATE

Answers

Answer:

<F=74

Step-by-step explanation:

No explanation just asked my teacher

Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,6) and perpendicular to 3 x + 7y = 1.a) The equation of the line in slope-intercept form is   enter your response here

Answers

The equation

[tex]3x+7y=1[/tex][tex]7y=-3x+1[/tex][tex]y=\frac{-3x}{7}+\frac{1}{7}[/tex]

has slope -3/7.

The product of perpendicular lines must be -1, so the slope of the new equation must be:

[tex]m\cdot-\frac{3}{7}=-1[/tex][tex]m=\frac{-1\cdot7}{-3}=\frac{7}{3}[/tex]

The line with that slope and that passes throught (1,6) is:

[tex](y-6)=m(x-1)[/tex][tex](y-6)=\frac{7}{3}(x-1)[/tex][tex]y-6=\frac{7}{3}x-\frac{7}{3}[/tex][tex]y=\frac{7}{3}x-\frac{7}{3}+6[/tex][tex]y=\frac{7}{3}x-\frac{7}{3}+\frac{18}{3}[/tex][tex]y=\frac{7}{3}x+\frac{11}{3}[/tex]

The following graph shows both equations:

[tex]y=\frac{7}{3}x+\frac{11}{3}[/tex][tex]3\cdot y=(\frac{7}{3}x+\frac{11}{3})\cdot3[/tex][tex]3y=7x+11[/tex][tex]-7x+3y=11[/tex]

Janice is cutting ribbon to decorate a present. She has 7/8 foot of ribbon. She needs to make pieces that are 3/8 foot each. How many 3/8-foot pieces will she get from the 7/8-foot ribbon?

Enter the correct answer in the box.

Answers

Based on the length of the ribbon, and the length of the pieces Janice needs to make, the number of 3/8 foot pieces she can make would be

How to find the number of pieces?

To find the number of pieces that Janice can get from the 7/8 foot ribbon, you need to divide this length by the length of each piece of ribbon.

The length of each of these pieces is 3/8 so the number of pieces of ribbon that Janice can get from the 7/8 foot ribbon is:

= 7 / 8 ÷ 3 / 8

= 7 / 8 x 8 / 3

= 56 / 24

= 2.33 ribbons

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Janice can make 2 pieces of ribbon from 7/8 feet of ribbon each measuring 3/8 feet.

What is a fraction?

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Janice is cutting the ribbon to decorate a present. She has 7/8 feet of ribbon.

She needs to make pieces that are 3/8 feet each.

To obtain the no. of pieces we have to divide the total length of the ribbon by the length of each piece.

∴ (7/8)/(3/8).

= (7/8)×(8/3).

= 7/3 pieces.

But he can only make 2 pieces as pieces must be in integers.

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Find the equivalent expression using the
same bases.
(71.81)4.

Answers

        Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

A similar expression can be found in what way?

          X-terms and constants should be combined with any other like terms on either side of the equation. Put the terms in the same order, with the x-term usually coming before the constants. The two phrases are equal if and only if each of their terms is the same.

        Consequently, (f + g)(4) is equal to f(4) + g(4)

         If two systems of equations have the same solution, they are equivalent (s).

Simplify

(71 . 81) 4 = 287.24

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What is the equation of the line that passes through the point (-3,1) and has a slope of -3?

Answers

Answer:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Since line has a slope of -3, equation is y = -3x + c.

Substitute (-3,1) into the equation to find c.

1 = -3(-3) + c

c = -8

Hence, equation of line is y = -3x - 8.

Please help! i would be able to learn the answer if i took some time but pls just help me so i don't have to. simplify: 4 1/5 + 3 2/3 + 1 1/6. a: 8 11/30. b: 7 13/15. c: 9 1/30. or d: 9 1/5

Answers

The value of expression 4 1/5 + 3 2/3 + 1 1/6  is 9 1/30

Given that,

to  simplify: 4 1/5 + 3 2/3 + 1 1/6

Mixed fraction definition?

It is a type of fraction, and those that have both a fraction and a whole number are considered to be it.

How to convert Improper fraction to a mixed fraction?

Divide the fraction's numerator by its denominator, or 15/7, in step one.

Second Step: Since 2 is an integer, the answer's integer component will be a mixed fraction.

Step 3: The original denominator of seven will be used as the denominator.

Step 4: The incorrect fraction 15/7 is now a mixed fraction with the value 2 (1/7)

To simplify ,

4 1/5 + 3 2/3 = 7 13/15

7 13/15 + 1 1/6 = 9 1/30

Therefore the correct answer is 9 1/30

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arie is driving from the usa into canada. she notices that all of the canadian speed limit signs are in kilometers per hour; her odometer only displays miles per hour. how many kilometers per hour is she driving when the odometer reads 19 miles per hour?

Answers

The answer is 30.571 because 1 mile = 1.609 km. So if you multiply 1.609 to 19 it will be 30.571 km.

4
Ryan is installing new flooring in his house. Ryan can install 144 square feet of flooring in
3 hours. How much new flooring can Ryan install in 21 hours?
OA. 1,008 square feet
OB. 252 square feet
OC. 3,024 square feet
OD. 3,049 square feet

Answers

A. It’s a because 3 can go into 21 7 times and then all you have to do is times 7 to 144 which 1,008.

5(23)=5(20)+ what property is being used help please i have till monday

Answers

The property used here is the distributive property of the multiplication.

What property is being used?

Here we have the expression:

5*23 = 5*20 + 5*3

This is the distributive property of the multiplication, it says that:

A*(B + C) = A*B + A*C

Now, the original expression can be rewritten as:

5*23 = 5*(20 + 3)

And now we apply the above property to get:

5*23 = 5*(20 + 3) = 5*20 + 5*3

5*23 = 5*20 + 5*3

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Evaluate. 34+(12+14)2⋅2 Enter your answer as a mixed number in simplest form by filling in the boxes. $$

Answers

The result of 34+(12+14)2.2 in the mixed fraction is  [tex]91\frac{1}{5}[/tex]

The expression is

34+(12+14)2.2

The mixed fraction is defined as the fraction that consist of one whole number part and a simple fraction part. simple fraction is the fraction that consist of numerator and denominator as whole numbers. The top term of  the simple fraction is called numerator and bottom term of the simple fraction is called denominator.

The expression is

=34+(12+14)2.2

First do the arithmetic operation in the bracket

= 34 + 26×2.2

Do the Multiplication

= 34+57.2

= 91.2

Convert the decimal form to simple fraction

91.2 = 456/5

Convert the simple fraction to the mixed fraction

456/5 = [tex]91\frac{1}{5}[/tex]

Hence, The result of 34+(12+14)2.2 in the mixed fraction is  [tex]91\frac{1}{5}[/tex]

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A grain tank on a farm is composed of a storage portion in the shape of a cylinder anda cone-shaped dispensing area at the bottom. The bottom cone portion has a slantheight of 5.5 feet. The entire exposed surface of the tank is to be painted. What is theapproximate amount of surface area that will receive the painting?8.4 ft12 ft5.5 ft

Answers

To fidn the surface area of the grain tank you need to find the area of:

Cylinder (without one of the bases as there are just one base exposed), use the next formula:

[tex]A_1=\pi\cdot r^2+h(2\pi r)[/tex]

You have for the given cylinder:

h=12ft

r: as the diameter is 8.4ft the radius is 8.4tf/2=4.2ft

[tex]\begin{gathered} A_1=\pi(4.2ft)^2+12ft(2\pi(\text{4}.2ft)) \\ =17.64\pi ft^2+100.8\pi ft^2 \\ =118.44\pi ft^2 \end{gathered}[/tex]

Cone (without the base as the base is not exposed), use the next formula:

[tex]A_2=\pi\cdot r\cdot s[/tex]

You have for the given cone:

r= 4.2ft

s= 5.5ft

[tex]\begin{gathered} A_2=\pi(4.2ft)(5.5ft) \\ =23.1\pi ft^2 \end{gathered}[/tex]

The entire exposed surface of the tank is:

[tex]\begin{gathered} A_T=118.44\pi ft^2+23.1\pi ft^2 \\ \\ =141.54\pi ft^2 \\ \\ \approx444.66ft^2 \end{gathered}[/tex]

The approximate amount of surface area that will receive the painting is 444.66 squared feets

please see attached question
correct answer will get brainliest​

Answers

Answer:

Step-by-step explanation:

[tex]\frac{y}{\sqrt{x} }[/tex] - [tex]\frac{\sqrt{x} }{x}[/tex] = [tex]\frac{y\sqrt{x} }{\sqrt{x} \sqrt{x} }[/tex] - [tex]\frac{\sqrt{x} }{x}[/tex] = [tex]\frac{y\sqrt{x} }{x}[/tex] - [tex]\frac{\sqrt{x} }{x}[/tex] = [tex]\frac{y\sqrt{x} -\sqrt{x} }{x}[/tex]    

Express the equation y=x^2+8x+25 in the form y=a(x-h)^2+ka. y=a(x-h)^2+kb. y=(x+4)^2+9c. y=(x-4)^2-9d.y=(x-4)^2+9

Answers

ANSWER :

The answer is B. y = (x + 4)^2 + 9

EXPLANATION :

From the problem, we have :

[tex]y=x^2+8x+25[/tex]

Group the terms in which the constant term and the terms with variables are separated.

[tex]y=(x^2+8x)+(25)[/tex]

add and subtract a variable m to the parenthesis to maintain equivalency.

[tex]y=(x^2+8x+m)+(25-m)[/tex]

Calculate the value of m using b^2/4a^2 with a = 1 and b = 8

[tex]m=\frac{b^2}{4a^2}=\frac{8^2}{4(1^2)}=16[/tex]

Then :

[tex]\begin{gathered} y=(x^2+8x+16)+(25-16) \\ y=(x^2+8x+16)+(9) \end{gathered}[/tex]

The first parenthesis will be a perfect square trinomial.

Factor and simplify :

[tex]\begin{gathered} y=(x^2+8x+16)+9 \\ y=(x+4)^2+9 \end{gathered}[/tex]

Given g(x)=−23(x−4)2+3, g ( x ) = − 2 3 ( x − 4 ) 2 + 3 , what is the value of g(–5)? *Type in your answer. g(–5) =

Answers

The output value of g( -5 ) in the function g( x ) = −23( x - 4 )2 + 3 is 417.

What is the output value of g(-5) in the given function?

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

g( x ) = −23( x - 4 )2 + 3g( -5 ) = ?

To find the g( - 5 ), replace all the occurrence of x with -5 in the function and simplify.

g( x ) = −23( x - 4 )2 + 3

g( -5 ) = −23( -5 - 4 )2 + 3

g( -5 ) = −23( -9 )2 + 3

g( -5 ) = −23( -9 × 2) + 3

g( -5 ) = −23( -18) + 3

g( -5 ) = ( -23 × -18) + 3

g( -5 ) = ( 414 ) + 3

g( -5 ) = 414 + 3

g( -5 ) = 417

Therefore, the output value of g( -5 ) is 417.

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Estimate 71.47 + 54.357 by first rounding each number to the nearest whole number.

Answers

Answer:

125

Step-by-step explanation:

71.47 rounded to the nearest whole number would be 71.

54.357 rounded to the nearest whole number would be 54.

Now, when we add 71 and 54, we get:

71+54=

125

The total would be 125

Multiply. Write your answer as a fraction in simplest form.
8/15(−2/3)=

Answers

Answer:

8/15(-2/3)

we simply multiply them

-8*2/15*3

as we know that+*-=-

-16/30

so simply divided by 2 because it whole decide them 16/2and30/2

-8/15

we have a large dataset and we plot its density curve, which is a smooth curve representing the relative frequency distribution (aka probability distribution). let's call this probability distribution curve p1. we then construct a new dataset by calculating the standard scores of the original dataset. for this standardized dataset, we plot a new density curve. let's call this probability distribution curve p2. which is true?

Answers

The required correct answer is,

The area under P2 is 1, the area under P1 depends on the standard deviation of the dataset

i.e., Option d. is correct.

What is density curve ?

A density curve is a curve that illustrates the general shape of a data distribution. It is always above the x-axis; the area beneath it is always equal to one whole; the area beneath shows the percentage of all observations that fall in a given range. It is statistically easier to deal with a smooth curve than a histogram.

The bell-shaped density curve, which symbolizes the normal distribution, is the most well-known.

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Ingrid is buying her
grandmother a new
coffeemaker for
her birthday. If the
tax rate is 8.5%, how
much tax will she
pay on a coffee-
maker with a sales
price of $48.90?
085,

Answers

The total price of that Ingrid has to pay is $52.90.

How to find percentage?

From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.

Sales price = $48.90

Amount needed to be paid = 8.5% of $48.90 + $48.90

= 4.15 + $48.90

= $52.90

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For his science project, Spencer needs to photocopy his 21-page
presentation. There are 37 students in his class, and he will need copies for
each person, including his teacher. Each photocopy is $0.12.
How much will Spencer spend at the copy center?
A $77.70
B $93.24
C $95.76
D $100.3

Answers

Answer: $95.76

Explantion: Spencer spend $95.76 dollars at the copy center.

Then your done

The answer is $93.24

This is right⬆️
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