Identify the type of conic section that has the equation 16x^2 + 4y^2 = 16 and identify its domain and range.

Answers

Answer 1

16x²+ 4y² = 16 is an equation of ellipse, domain of the equation is all real numbers and the range is -2 ≤ y ≤ 2.

What is Conic Section?

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane.

The given equation is 16x²+ 4y² = 16.

Divide both sides by 16.

x²/1 + y²/4 = 1

This is the equation of an ellipse.

It is an ellipse centered at the origin, with semi-major axis length of 2 and semi-minor axis length of 1.

Since the x² term is not negative, the domain is all real numbers.

The range of the ellipse is the range of y-values that make the equation true.

Since the y² term is not negative, the range is all real numbers as well. However, since the ellipse is centered at the origin, the range is bounded by -2 and 2, which are the y-coordinates of the endpoints of the major axis. Therefore, the range is -2 ≤ y ≤ 2.

Hence, 16x²+ 4y² = 16 is an equation of ellipse, domain of the equation is all real numbers and the range is -2 ≤ y ≤ 2.

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Answer 2

Answer:

ellipse; Domain: {-1≤y≤1}; Range: {-2≤y≤2}

Step-by-step explanation:

Graph the equation. An ellipse has two lines of symmetry, the x-axis, and the y-axis. The domain is the set of all real numbers with x, written as -a ≤ x ≤ a. The range is the set of all real numbers with y, written as -b ≤ y ≤ b.

Identify The Type Of Conic Section That Has The Equation 16x^2 + 4y^2 = 16 And Identify Its Domain And

Related Questions

Find the measure of the angle given

Answers

Step-by-step explanation:

This is a cyclic quadrilateral, so angles E and P are supplementary.

Since angle P is 100 degrees, angle E is 180-100=80 degrees.

Which ones are correct?

Answers

Answer:

2 only

Step-by-step explanation:

This answer assumes that we can assume that lines which look straight are straight.
Straight angles are also known as 180 degree angles, and if a straight angle is cut in half, then the two parts must add up to 180 degrees. In the first picture, we see that 90-x and 90+x are the angle measurements.
(90-x)+(90+x)=90+90+x-x=180 degrees
the second one has angles 97 and 83, which add up to 180 degrees
the third one has angles which add up to more than 180 degrees, so any answer containing the third one as being correct is wrong.
The answer should be 1 and 2, but, that isn't an answer. Looking back at 1, it can be seen that if x is a negative number, or if x was a number greater than 180 degrees, then the picture would not work, so 1 is invalid. this leaves only 2, so 2 only.

Is this just a fancy way of saying to graph the point (2,-6) or am I supposed to graph a line?​

Answers

Answer:

I do know what that is saying it's saying the rise of the line is going to be -6 and the run is going to be 2.

Step-by-step explanation:

Your supposed to graph a line I don't exactly remember how to do it but yeah you're supposed to graph the line.

PLS HELP!!!!For each sequence determine whether appears to be a ARITHMETIC or GEOMATRIC or neither ( pictures attached)

Answers

Answer:

The first one is geometric. The second one is gemetric. The last one is arithmetic.

Step-by-step explanation:

Prove the identity.
(1 - sin’x) cscx = cosx cotx
=
Note that each Statement must be based on
the right of the Rule.
rules:
algebra, reciprocal, quotient, pythagorean, odd/even

Answers

[tex]\textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\\ [1-sin^2(x)]csc(x)~~ = ~~cos(x)cot(x) \\\\[-0.35em] ~\dotfill\\\\\ [1-sin^2(x)]csc(x)\implies cos^2(x)csc(x)\implies cos^2(x)\cdot \cfrac{1}{sin(x)} \\\\\\ cos(x)\cdot \cfrac{cos(x)}{sin(x)}\implies cos(x)cot(x)[/tex]

Find the area of a circle with a radius of 21 inches. Use 22/7 for pi .

Answers

Answer:

okay so the area is 1386inches2

Step-by-step explanation:

[tex]area \: of \: a \: circle = \pi {r}^{2} \\ = \frac{22}{7} \times {21}^{2} \\ = \frac{22}{7} \times 441 \\ = 1386 {inches}^{2} [/tex]

The length of a rectangle is eight more than triple the width. If the perimeter is 168 inches, find the dimensions.

Answers

Answer:

P= 2(3W + 7) + 2(W) = 110.

                         P= 6W + 14 + 2W = 110.

                           = 8W + 14 = 110.

                           = 8W = 110 - 14 = 96

                                 W = 96/8 = 12- inches.

Now solve for (L) by L = 3W + 7 = 3(12) + 7 = 36 + 7 = 43- inches

7=43 inches if this help.can u mark me brainliest

The width of the rectangle is 12 inches and the length is 43 inches.

What is the perimeter?

The perimeter is defined as the sum of all the sides of the figure. It is given that the length of a rectangle is eight more than triple the width and the perimeter is 168 inches.

The length and the width are calculated as:-

P= 2(3W + 7) + 2(W) = 110.

6W + 14 + 2W = 110.

8W + 14 = 110.

8W = 110 - 14 = 96

W = 96/8 = 12 inches.

Now solve for (L) by

L = 3W + 7 = 3(12) + 7

L = 36 + 7 = 43 inches

Hence, the width is 12 inches and the length is 43 inches.

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How many different possible outcomes are there if you flip five coins?

Answers

Answer:

There are 10 different outcomes of flipping a coin five times.

Step-by-step explanation:

there are two sides on a coin. 2 x 5 = 10

Hope that helps!

Answer:

2

Step-by-step explanation:

it heads or tales a coin is two-sided no matter what kind unless you are talking about all together then it would be 10

choose the imensions that represen this rectlangl



answer

length:2/5
width: 3/6

length:2/4
width:3/4

length:2/3
width:3/5

length:2/3
width:3/4

Answers

Answer:B

Step-by-step explanation:I hope it help

PLEASE SOLVE THIS I NEED IT I GOTTA GO TO SCHOOL AT MONDAY I NEED IT ​ILL GIVE BRAINLIES

Answers

Answer:

In order to make a triangle, the sum of 2 sides must be greater than the third side

in number one 2+3=5 so no you can't make a triangle

you can do it likewise ...

What is the scale factor???

Answers

Answer:

I believe your answer is 2 because that is the difference in the width of the cars.

Farm A has 120 sheep. of the sheep have lambs. Some of the sheep have 1 lamb and some of the sheep
have 2 lambs. The ratio of the sheep who have 1 lamb to the sheep who have 2 lambs is 3:5.


(a) What fraction of the sheep who have lambs on farm A have 2 lambs?

Answers

Answer:

75/120 = 15/24 = 5/8

Step-by-step explanation:

3 + 5 = 8 There are 8 parts

120 / 8 = 15

15 X 5 = 75

There are 75 sheeps with 2 lambs

The total number of sheep having 2 lambs in farm A is [tex]0.625[/tex].

To find the fraction of the sheep who have lambs on farm A have 2 lambs, we need to have the total number of sheep having 2 lambs in farm A.

How to determine the fraction of sheep?

According to the question, the ratio of the sheep having 1 lamb and 2 lambs is [tex]3:5[/tex] and the total number of sheep is 120.

So, the total number of sheep having 2 lambs in farm A is calculated as-

[tex]L_2=\dfrac{5}{3+5}\times 120\\=5\times 15\\=75[/tex]

Now, the fraction of the total number of sheep having 2 lambs in farm A is-

[tex]F=\dfrac{75}{120}\\=0.625[/tex]

Thus, the total number of sheep having 2 lambs in farm A is [tex]0.625[/tex].

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A triangular prism is 15 yards long and has a triangular face with a base of 12.9 yards and a height of 10.3 yards. what is the volume of the triangular prism?

Answers

Answer:

Step-by-step explanation:

Area of the base = 1/2 * B * h

B: 12.9

h = 10.3

Area of the face = 1/2 * 12.9 * 10.3

Area of the face = 66.435

Volume = Triangle * height

Triangle = 66.435  yd^2

Height = 15 yd

Volume = 66.435 * 15

volume = 996.525

I think this should be rounded to one decimal place: 996.5

Can someone solve this for me please.

Answers

Answer:

y= .5x+2

Step-by-step explanation:

Slope= 2/4 (rise over run) = .5

B/ y intercept = 2

y=.5x+2

Can y’all help me on this graph work asap pls

Answers

Just divide one of number of tickets by which ever of the ticket prices that goes on a line, like for example $24 divided by 3 equals $8 a ticket

Tyrell and Marianne start at the same point. Tyrell walks 2.5 miles north in a straight path. Marianne walks 6.0 miles east in a straight path. How many miles apart are they at the end of their walks rounded to the nearest hundredth mile?

Answers

Answer: 6.5 is the answer.

Step-by-step explanation:

Garrett is cutting square patches from old sports jerseys. Each
patch has an area of 1 ft?. He wants to put some of the
patches together to make square quilts.

Which areas listed below are possible areas of the square
quilts Garrett can make? What side length will each of
those square quilts have? Show your work.

Answers

The areas listed that are possible areas of the square quilts Garrett can make will be 0.25, 0.81, etc.

How to calculate the area?

Your information is incomplete as your didn't give the areas listed. Therefore, an overview will be given.

It should be noted that the area of a square is simply gotten by multiplying the side by itself. For example, if a side is 4cm, the area will be 4 × 4 = 16cm².

In this case, we are told that each patch has an area of 1 ft. Therefore, the square of the area gotten should not be more than 1 feet. Possible values include:

0.5 × 0.5 = 0.25

0.9 × 0.9 = 0.81

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Garrett is cutting square patches from old sports jerseys. Each

patch has an area of 1 ft?. He wants to put some of the

patches together to make square quilts.

Which areas listed below are possible areas of the square

quilts Garrett can make? What side length will each of

those square quilts have? Show your work.

Suppose that a family wants to start a college fund for their child. if they can get a rate of 5.2%, compounded monthly, and want the fund to have a value of $55,500 after 20 years, how much should they deposit monthly? assume an ordinary annuity and round to the nearest cent. a. $131.93 b. $2,662.49 c. $1,643.30 d. $3,446.64 please select the best answer from the choices provided a b c d

Answers

Answer:

a. $131.93

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

edge

omg please help its due by 12 am! the sum of 2 numbers is 69. the larger number is 3 less than twice the smaller number .find the numbers. show your work!

Answers

Answer:

The smaller number is 24

The larger number is 45

Step-by-step explanation:

smaller number  = x

Larger: 2x - 3

Smaller + larger = 69

x + 2x - 3 = 69                        Combine left

3x - 3 = 69                              add 3 to both sides

3x - 3+3 = 69+ 3                     Combine

3x = 72                                    Divide by 3

3x/3 = 72/3                        

x = 24

Larger number = 2*24 - 3

Larger number = 45

Sasha is mailing a photo box that has the dimensions shown in a rectangular box that is 12.5 inches long, 4.2 inches wide, and 12.5 inches tall. If one bag of packing material holds 75 cubic inches of material, how many bags does Sasha need to buy to fill the space around the photo box?

Answers

The number of bags that Sasha would need to fill the space around the photo box is 9 bags.

How many bags would be needed?

The first step is to determine the volume of the photo box. The photo box has the shape of a cuboid. A cuboid is a three-dimensional object. It has six sides and six vertices.

Volume = length x width x height

12.5 x 4.2 x 12.5 = 656.25

Bags needed - 656.25 / 75 = 9

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Solve for x and round to nearest tenth <3

Answers

it might be 45! best of luck:)

2,5,8,...
Find the 41st term.

Answers

Answer:

Step-by-step explanation:

hello :

this is  the arithmetic -sequence because : 8-5=5-5=3 (comon dif)

An =A1+(n-1)r   calculate......... (A1=2   and  r=3   and  n=41) continu...

Answer:

122

Step-by-step explanation:

If you help I’ll give brainlist thing pleaseeee

Answers

Answer:

a. y = 10

b. x = 5 - (5y/2)

c. y = 6x - 11

Step-by-step explanation:

a.

2(y - 3) = 4

2y - 6 = 4

2y = 10

y = 5

b.

2x + 5y = 10

2x = 10 - 5y

x = 5 - (5y/2)

c.

6x + 3y = 4y + 11

6x = y + 11

y = 6x - 11

d.

I don't know this one, sorry.

Find the area of the shaded region

Answers

Answer:

Step-by-step explanation:

Remark

There are many ways you can do this. I think the simplest way is to find the area of the rectangle enclosing the winged shape and take away the area of the three unshaded triangles.

Area of enclosed rectangle

Area = L * w

L = 26    in

w =  15   in

Area = 26 * 15

Area = 390    square inches.

Find the area of the triangle on the right.

Area = 1/2 * b * h

base = 26 inches

height = 15 - 6 = 9

This is a little tricky. What you need to do to get the height of the triangle is realize that it is made from a line that goes from the base of the triangle to its peak. This line is perpendicular to the base. The line you just drew is 15 inches tall, same as the width of the enclosing rectangle.

Substitute values into the formula

Area = 1/2 * 26 * 9

Area = 117 square inches.

Find the area of the top and bottom triangles.

These 2 triangles are the same sort of thing only the base requres a bit of manipulation

height = 15 inches

base = (26 - 14)/2

base = 12/2

base = 6

Again, this requires a little bit of thought. You have 2 bases making up each of the right triangles. To find the sum of both of them, you take 26 and subtract 14 from it. That's where the 12 comes from. Now you divide 2 to get the base of each of the triangles. That gives you 6.

Find the area of one of the triangles.

Area = 1/2 * b * h

Area = 1/2 * 6 * 15

Area = 45 square inches

Find the area of both triangles.

Area of triangles at the top and bottom = 2*45 = 90

Finally find the area of the shaded area.

Area = enclosed rectangle - top triangle and bottom triangle - the triangle on the right.

Area shaded area = 390 - 45 - 45 - 117 = 183

Answer: Area shaded region = 183 square inches.

Please help me con la resolución porfa

Answers

Answer:

2,591 esta bien la respuesta

I need a lot of help!
Is 54.03 + 4.04 greater than 54 + 4.4?

Answers

Answer:

54+4.4 is greater

Step-by-step explanation:

if u need explanation than please ask

Using the Rule of 72, how long would it take for Anthony to double his investment of $5,000 in a
money market account that earns 7% per year?

Answers

Answer: About 10.2857 years

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

Explanation:

For the rule of 72, we divide the number 72 over the interest rate without the percent sign. We do not convert to decimal form. Simply erase the percent sign.

For example, if the interest rate was 6%, then we estimate it would take 72/6 = 12 years for the amount to double.

In this case of a 7% interest rate, the doubling time is roughly 72/7 = 10.2857 years.

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

Extra Notes:

The starting deposit doesn't matter, so we can ignore the "5000". The interest rate must stay the same the entire time.

Can someone please help me with this (a^3-(2*b))*(a^3-(3*b)) equation​

Answers

Hope the picture will help you...

identify which of the following sequences is a geometric sequence. check all that apply. from math nation test yourself

Answers

A geometric sequence is any sequence that has a common ratio and a non-zero initial value

The sequence 2, 6, 18, 54, ..... is a geometric sequence

How to determine the geometric sequence?

A geometric sequence is represented as:

Tn = ar^(n - 1)

Where:

n represents the number of termsa represents the initial valuer represents the common ratioTn represents the current term

Assume that:

a = 2 and r = 3.

The terms of the sequence would be:

T1 = 2 * 3^0 = 2

T2 = 2 * 3^1 = 6

T3 = 2 * 3^2 = 18

T4 = 2 * 3^3 = 54

So, we have:

2, 6, 18, 54, .....

Hence, the sequence 2, 6, 18, 54, ..... is a geometric sequence

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Abby and her mom are driving on a road trip, and Abby is watching the milepost signs go by. Each hour she writes down which mile marker they pass and records her results in the table given. HoursMilepost162262 plus 50 equals 1123112 plus 50 equals 1624162 plus 50 equals 212 Question If Abby wants to write an equation to find the milepost they will pass, y, after driving for x hours, which type of equation would be ,begin emphasis, most

Answers

Considering that the mile counter increases by 50 every hour, a linear function should be empathized.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem, they start at mile 62, and the counter increases by 50 every hour, which is a fixed amount, hence a linear function should be used.

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