Identify the type of conic section that has the equation 16x^2 + 4y^2 = 16 and identify its domain and range.
Answers
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:
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.
Related Questions
What is the scale factor???
Answers
Answer:
I believe your answer is 2 because that is the difference in the width of the cars.
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
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
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:
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.
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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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]
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
Solve for x and round to nearest tenth <3
Answers
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.
Please help me con la resolución porfa
Answers
Answer:
2,591 esta bien la respuesta
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
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.
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
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.
Can someone please help me with this (a^3-(2*b))*(a^3-(3*b)) equation
Answers
Hope the picture will help you...
Can y’all help me on this graph work asap pls
Answers
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.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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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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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]
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 ...
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
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:
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
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.
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 termAssume 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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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:
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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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.