Write the equation of the ellipse with its center at the origin. the height of the ellipse is 12 units and the width is 14 units.

Answers

Answer 1
Sketch the ellipse as shown in the figure below.

The general form of the equation of an ellipse centered at (h,k), with semi -major axis of a and semi - minor axis of b is
[tex] \frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} =1[/tex]

Because the width is 14, therefore a = 7.
Because the height is 12, therefore b = 6.
Because the ellipse is centered at the origin, h=0, and k=0.

Answer:
[tex] \frac{x^{2}}{49} + \frac{y^{2}}{36} =1[/tex]
Write The Equation Of The Ellipse With Its Center At The Origin. The Height Of The Ellipse Is 12 Units

Related Questions

Mx = Nx - Pt isolate x

Answers

Mx = Nx - Pt

To isolate 'x', we have to group all terms that have 'x' together 
We have Mx on the left-hand side of the equation and Nx on the right.
Moving Nx to the left-hand side of the equation, we have:

Mx - Nx = Pt

From here we factorize 'x'

x (M - N) = Pt

Then we divide both sides by (M-N)

[tex]x= \frac{M-N}{Pt} [/tex]

Identify the reflection of the figure with vertices

Answers

reflection across the x-axis:
the x coordinate will stay the same but y coordinate will change sign 

for example ( 2, -4)  will reflect to 2 , 4)

Check out option B

An extension ladder leans agintst a biulding, making a 75 degree angle of elevation with the ground. The base of the ladder is 8 ft from the base of the building.

To the nearest tenth of a foot, how long is the ladder?

Answers

For this problem, you're going to need to use trig. More specifically, you need to use the tangent function:

tan (value) = opposite/adjacent

tan 75 = opposite/8 (Here, the opposite side is the length of the ladder)

8 * tan 75 = opposite

29.8564065 = opposite

So, the ladder is 29.9 feet.

The ladder is 29.9 feet long.

For solving this problem we have to use trigonometric ratio  

We need to use the tangent function:

What is the ratio of tangent function?

[tex]tan (\theta) = opposite/adjacent[/tex]

[tex]tan 75 = opposite/8[/tex]

multiply both side by 8 so we will get,

Here, the opposite side is the length of the ladder and angle [tex]\theta =75^0[/tex]

Therefore by using the tan ratio we have,

[tex]8 * tan 75 = opposite[/tex]

[tex]29.8564065 = opposite[/tex]

Therefore, the ladder is 29.9 feet.

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Four times the difference of a number and seven is 12

Answers

4(x-7)=12=


4x-28=12 

add 28 to both sides

4x=40

x =40/4 = 10

x = 10

Simplify this problem please

Answers

First work out the parenthesis:

9x⁴y⁴ / 3y²

Then get rid of the denominator using 9/3=3 and y⁴/y² = y²

3x⁴y² is the simplest form.

10(2y+2)−y=2(8y−8)

y= ???

Answers

Y = -12
- distribute the 10 into (2y+2)
- distribute 2 into (8y-8)
You will have 20y +20 - y = 16y - 16
- bring the 20 to the other side to get
20y - y = 16y - 36
- subtract y from 2y to get 19y = 16y -36
- bring 16y to the other side to get 3y = -36
- divide 3 from both sides to single out y.
Your final answer is y = -12
10(2y+2)−y=2(8y−8) 
20y + 20 - y = 16y - 16
19y - 16y = -16 - 20
3y = -36
y = -36/3
y = -12

What price do farmers get for the peach crops? in the third week of June, a random sample of 40 farming regions gave a sample mean of $6.88 per basket. assume that the standard deviation is known to be $1.92 per basket. find a 90% confidence interval for the population mean price per basket that farmers in this region get for their peach crop.

Answers

Given:
n = 40, sample size
xb = $6.88, sample mean
σ = $1.92, population standard deviation

At 90% confidence interval, the expected range is 
[tex](xb - 1.645 \frac{ \sigma }{ \sqrt{n}} ,\, xb + 1.645 \frac{ \sigma }{ \sqrt{n} } )[/tex]
= [ 6.88 - 1.645*(1.92/√40), 6.88 + 1.645*(1.92/√40)]
= (6.38, 7.38)

Answer:
The 90% confidence interval is ($6.38, $7.38)

NEED HELP PLEASE!!!!
The diameter of a hydrogen atom is about 5×10^-15 meter. Suppose 8.4×10^8 hydrogen atoms were arranged side by side in a straight line. Multiply these numbers to find the length of this line of atoms. What is the length in scientific notation?

Select one:

a. 4.2×10^−2 meter
b. 0.042 meter
c. 42×10^−3 meter
d. 4.2×10^−3meter

Answers

Answer:

I'm a few years late, lol, but um the answer is 42 x [tex]10^{-3}[/tex] meters

For all the people who still need the answer.

Step-by-step explanation:

5 x [tex]10^{-11}[/tex] and 8.4 x [tex]10^{8}[/tex]

5 x 8.4 = 42  (multiply like terms)

[tex]10^{-11}[/tex] + [tex]10^{8}[/tex] = [tex]10^{-3}[/tex]  (add the exponents)

42 x [tex]10^{-3}[/tex]

The length in scientific notation is [tex]42\times10^{-7[/tex] meter.

What is scientific notation?

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as [tex]1.56\times10^7[/tex].

Given that, the diameter of a hydrogen atom is about [tex]5\times10^{-15}[/tex] meter. Suppose 8.4×10⁸ hydrogen atoms were arranged side by side in a straight line.

Now, multiply the numbers

[tex]5\times10^{-15}[/tex]×8.4×10⁸

= [tex]42\times10^{-7[/tex] meter

Therefore, the length in scientific notation is [tex]42\times10^{-7[/tex] meter.

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Which expression is equivalent to complex fraction 3/x-1-4/2-2/x-1

Answers

The answer on e2020 is B

The standard formula for the volume of a cylinder is V = πr2h. If the cylinder is scaled proportionally by a factor of k, its volume becomes V' = V × k3. Use your algebra skills to derive the steps that lead from V = πr2h to V' = V × k3 for a scaled cylinder. Show your work.

Answers

So, r' (the new r) becomes kr, and h'=h*k,

so V' = pi * (r')^2*h' = pi * (r*k)^2*(h*k) = pi*r^2*h*k^3 = V * k^3

Convinced?

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

so

[tex]k=r'/r[/tex]  and [tex]k=h'/h[/tex]

The volume of the original cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

If the cylinder is scaled proportionally by a factor of k

then

the new radius is ------> [tex]r'=kr[/tex]

the new height is ------> [tex]h'=kh[/tex]

The volume of the scaled cylinder is equal to

[tex]V'=\pi r'^{2}h'[/tex]

substitute the values

[tex]V'=\pi (kr)^{2}(kh)[/tex]

[tex]V'=(k^{3})\pi r^{2}h[/tex]

Remember that

[tex]V=\pi r^{2}h[/tex]

so

substitute

[tex]V'=V(k^{3})[/tex]

The volume of the scaled cylinder is equal to the scale factor elevated to the cube multiplied by the volume of the original cylinder

What shape will stay the same no matter how many degrees it is rotated?

Answers

a circle is round, so no matter how many degrees it is rotated it will remain the same

For the graph y= 1 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explain your answer with two or more sentences

Answers

It is a horizontal line on 1

Answer:

Parallel: [tex]m = 0[/tex] (Horizontal), Perpendicular: [tex]m = -\frac{1}{0}[/tex] (Vertical)

Step-by-step explanation:

The equation y = 1 is an horizontal straight line ([tex]y = 0\cdot x + 1[/tex]). The slope of a line parallel to it is [tex]m = 0[/tex]. The slope of line perpendicular to it is [tex]m = -\frac{1}{0}[/tex], since slope is represented by tangent function, which is undefined at [tex]\theta = \pm 0.5\pi[/tex].

F r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to ?

Answers

 (r/s)(6) = r(6) / s(6) 
= (3*6 - 1) / (2*6 + 1) 
= 17/13

geometry help! this is my 2nd to last question

Answers

A square since all sides are equal and the angles aren't acute so it can't be a rhombus
Hi.
Your answer would be d. square. Rhombus have actute angles, squares have right angles. It's clearly not a rectangle (as the sides are all the same) so it has to be square.

I hope I helped and if you need more you could always ask me :)

-Dawn

one number is 10 times another number. their difference is 72. what are the two numbers?

Answers

lets 2 numbers are x and y
x = 10y
x - y = 72

substitute x = 10y into x - y = 72

10y - y = 72
9y = 72
 y = 8

x = 10y = 80

answer
2 numbers are 8 and 80

The two numbers are 80 and 8.

What is linear equation in two variables?

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e. a and b respectively, are not equal to zero.

What is substitution method ?

The substitution method can be defined as a way to solve a linear system algebraically. This method works by substituting one y-value with the other.

Let the two numbers be x and y.

According to the question.

x = 10y

And,

x - 10y = 72

Now, We have a linear equation in two variables. So, for finding the values of x and y we solve the above two equations by substitution method.

Substitute the value of x = 10y in x - y = 72

[tex]\implies 10y -y = 72 \\\implies 9y = 72\\\implies y = \frac{72}{9} \\\implies y = 8[/tex]

Therefore,

x = 10 × 8 = 80

Hence, the two numbers are 80 and 8.

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True or False
The geometric mean of 8 and 2 is 4.

Answers

TRUE IVE GOT IT WRONG  ON MY ASSIGNMENT.

Answer:

True

Step-by-step explanation:

To find the geometric men you have to cross multiply the two given numbers and then find x squared for those numbers. So to find x squared you have to find the square root of the product from the two multiplied numbers.

8/x = x/2

8*2 = 16 = x squared

x= square root of 16 which equals 4

what is the circumference of a circle with a radius of 39

Answers

The circumference would be 78 pi.

The formula for finding circumference is C = 2[tex] \pi [/tex]r

[tex]C = 2 \pi r C = 2 \pi 39 C = 78 \pi [/tex]


A collection of quarters and nickels contains at least 42 coins and is worth at most $8.00. If the collection contains 25 quarters, how many nickels can be in the collection?

Answers

The total number of nickels that can be collected is 17 and this can be determined by forming the inequality.

Given :

A collection of quarters and nickels contains at least 42 coins and is worth at most $8.00.

The inequality can be formed in order to determine the total number of nickels that can be collected.

Let the total number of quarters be 'x' and the total number of nickels be 'y'. Then the inequality that represents the total number of quarters and nickels contained in the collection is at least 42 is given by:

x + y [tex]\geq[/tex] 42  --- (1)

The inequality that represents that the worth of the coins is at most $8 is given by:

0.25x + 0.5y [tex]\leq[/tex] 8   --- (2)

Now, according to the given data there are a total of 25 quarters in the collection, so, the number of nickels contained in the collection is:

x + y [tex]\geq[/tex] 42

25 + y [tex]\geq[/tex] 42

y [tex]\geq[/tex] 17

So, the total number of nickels that can be collected is 17.

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Final answer:

The collection can contain up to 35 nickels, given that it already includes 25 quarters and the total value does not exceed $8.00.

Explanation:

To determine how many nickels can be in the collection, we must first calculate the total value of the 25 quarters. Since each quarter is worth 25 cents, we multiply 25 quarters by 25 cents to get 625 cents, which is $6.25. The maximum value of the entire collection is $8.00. Thus, we subtract $6.25 from $8.00 to find the remaining value that can be occupied by nickels, which is $1.75. Each nickel is worth 5 cents, so we divide $1.75 by 0.05 (5 cents) to find the maximum number of nickels. $1.75 divided by 0.05 equals 35. Therefore, the collection can contain up to 35 nickels.

Which situation involves descriptive statistics?
A) The food cans have a mean shelf life of 14 months.
B) The study estimates that 10% of the fish died as a result of the drought.
C) According to a poll, about 12% of our customers have returned at least one item. D) The sample indicates that the mean weight of all the boxes is 3.3 kg.

Answers

the answer:
The descriptive Statistics are used to introduce quantitative depictions in a sensible shape. In an examination contemplate we may have several number of measures. Or, then again we may quantify countless on any measure. Clear measurements with descriptive statistics help us to simplify a lot of information sensible manner.
so the answers are 
A) The food cans have a mean shelf life of 14 months. 
D) The sample indicates that the mean weight of all the boxes is 3.3 kg.

Answer:

The correct answer is:


A) The food cans have a mean shelf life of 14 months.


Just took this quiz and this was the correct answer.

Step-by-step explanation:


The mean is defined as the

Answers

It is defined as the average of the data.
average of the set of numbers. In order to find the mean, add up all the numbers, and divide the sum of all the numbers by the number of numbers there are.
hope this helps:)

Please help solve -2|5y-1|=-10

Answers

Alright, so we can start by dividing -2 from both sides, getting |5y-1|=20. Then, since 5y-1 is in an absolute value, 5y-1 is either 20 or -20.
In 5y-1=20, we can add one to both sides, getting 5y=21 and y=21/5. In
5y-1=-20, we can add one again, getting 5y=-19 and y=-19/5.

If you have any more equations, make sure to plug both numbers in to check, but otherwise y has two answers , which are -19/5 and 21/5.

In the triangle below, what ratio represents cot θ?

Answers

tanα=9/12

cotα=1/tanα

cotα=12/9

cotα=4/3
We know that the tangent of an angle in a right triangle is the opposite divided by the adjacent. This is the cotangent, so we reciprocate that to get that the cotangent is the adjacent divided by the opposite!
Plugging in, we get that the cotangent of the indicated angle is [tex]$\frac{12}{9}=\frac{4}{3}$[/tex].

You can solve equations by graphing. Explain how to find the solutions by a given graph.

Answers

For solve equation by graphing, it need to come equation at the form, that it's simple to build a graph for left part of equation, and another graph for right part. The intersection of thats two graphs is the solution.



Solve the linear equation:
3.4 + 2(9.7 – 4.8x) = 61.2

Answers

3.4 + 2(9.7 – 4.8x) = 61.2 ,   x = -4

steps:
subtract 3.4 from both sides
simplify 
divide both sides by 2
subtract 9.7 from both sides
simplify again
divide both sides by -4.8
simplify once more 


To which graph does the point (2, 4) belong?

y ≥ x + 3
y ≥ −x + 8
y ≥ 4x − 5
y ≥ −2x + 9

Answers

(2,4) belongs to the graph y is greater than or equal to 4x - 5

Answer:

Option (3) is correct.

(2,4) belongs to y ≥ 4x - 5

Step-by-step explanation:

Given : the point (2,4)

We have to find the equation of graph to which the point (2,4) belongs.

We will substitute the point in the  each given equation and for which the point satisfies will contain the point.

For 1) y ≥ x + 3

Put x = 2 and y = 4

⇒ 4 ≥ 2 + 3

⇒  4 ≥ 5 (false)

For 2) y ≥ -x + 8

Put x = 2 and y = 4

⇒  4 ≥ -2 + 8

⇒  4 ≥ 6 (false)

For 3) y ≥ 4x - 5

Put x = 2 and y = 4

⇒  4 ≥ 4(2) - 5 = 8 - 5

⇒  4 ≥ 3 (true)

For 4) y ≥ -2x + 9

Put x = 2 and y = 4

⇒  4 ≥ -4 + 9

⇒  4 ≥ 5 (false)

Since, the point (2,4) satisfies only inequality y ≥ 4x - 5.

Thus, (2,4) belongs to y ≥ 4x - 5

(6u3 + 7u2 + 2) + (3u3 – 8u + 4)

Answers

Remove the parentheses and bring like terms together:-

=  6u3 + 3u3 + 7u2 - 8u + 2 + 4    Simplifying like terms :-

= 9u3 + 7u2 - 8u + 6
(6u3 + 7u2 + 2) + (3u3 – 8u + 4)
=6u³+3u³+7u²-8u+4+2
ANSWER:9u³+7u²-8u+6 

The graph below shows the value of Edna's profits f(t), in dollars, after t months:

graph of quadratic function f of t having x intercepts at 6, 0 and 18, 0, vertex at 12, negative 36, and passes through point 21, 41.25

What is the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month?

a. Three dollars per month

b. Nine dollars per month

c. 13.75 dollars per month

d. 41.25 dollars per month

Answers

The easiest way to find the average rate of change is with the formula:
( y 2 - y 1 ) / ( x 2 - x 1 )
We have to find the average rate of change from the 18th month to the 21st month. So: y2 = 41.25, y 1 = 0,  x 2 = 21, x 1 = 18;
( 41.25 - 0 ) / ( 21 - 18 ) = 41.25 / 3 = 13.75
Answer:
c. 13.75 dollars per month.

Answer:

C) 13.75 dollars per month

Step-by-step explanation:

i took the test and got it right

All of the following are equivalent except _____.

x - (-2)
-2 + x
x - 2
x + (-2)

Answers

All are equivalent except the first one.

A.

Its correct i got 100% on a test

Which one of the numbers in the series is wrong, and should be replaced? 2 - 4 - 8 - 16 - 20 - 22 - 44 - 46?

Answers

Final answer:

The number series 2 - 4 - 8 - 16 - 20 - 22 - 44 - 46 has a pattern whereby each number doubles the previous number. However, 20 does not follow this pattern, and the correct number should be 32 (being double of 16). Therefore, 20 is the incorrect number in this series.

Explanation:

This question is a query regarding a number series, specifically asking for us to identify any number that does not fit the pattern of the series. The series given is: 2 - 4 - 8 - 16 - 20 - 22 - 44 - 46. By examining the series closely, we can observe a clear pattern: each number is doubling the previous number. So, after 2 we have 4 (2x2), then 8 (4x2), then 16 (8x2) and so forth.

However, at the fifth place, we have the number 20, which doesn't follow this pattern. If we were to follow the established pattern, the fifth number should be 32 (16x2), not 20. Therefore, the incorrect number in this series is 20, and the correct series should be 2 - 4 - 8 - 16 - 32 - 22 - 44 - 46.

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The incorrect number in the series is 20, and it should be replaced with 32. The accurate sequence is 2, 4, 8, 16, 32, 64, 128, 256.

Let's examine the sequence: 2 - 4 - 8 - 16 - 20 - 22 - 44 - 46.
At a glance, it appears each number is double its preceding number, except for a couple of deviations.

If we look at the pattern,

2 x 2 = 44 x 2 = 88 x 2 = 1616 x 2 = 32

Here, we expect 32 instead of 20.
Therefore, 20 is the incorrect number in the series. When we continue correctly:

32 x 2 = 6464 x 2 = 128

The correct sequence would be,
2 - 4 - 8 - 16 - 32 - 64 - 128 - 256.

So, the number that should be replaced is 20, and it should be 32.

Prove abcd is a parallelogram

Answers

AD and BC slant while AB and DC are parallel

Since both pairs of opposite sides of quadrilateral ABCD are parallel and equal, by definition, ABCD is a parallelogram.

Given that in quadrilateral ABCD, side AD is equal to side BC (AD = BC) and side AD is parallel to side BC (AD || BC), we can use these properties to prove that ABCD is a parallelogram.

Here is a step-by-step proof:

1. Definition of a parallelogram: A quadrilateral is a parallelogram if both pairs of opposite sides are parallel.

2. Given: AD = BC (opposite sides are equal) and AD || BC (opposite sides are parallel).

3. To Prove: AB || CD and AB = CD (the other pair of opposite sides are also parallel and equal).

4. Proof:

   - Since AD = BC and AD || BC, we have one pair of opposite sides that are equal and parallel.

   - In a quadrilateral, if one pair of opposite sides is equal and parallel, the quadrilateral is a parallelogram (This is a theorem in Euclidean geometry).

   - Therefore, AB must be parallel to CD (AB || CD) because the opposite sides of a parallelogram are parallel by definition.

   - Also, in a parallelogram, opposite sides are equal (another property of parallelograms), so we can conclude that AB = CD.

5. **Conclusion**: Since both pairs of opposite sides of quadrilateral ABCD are parallel and equal, by definition, ABCD is a parallelogram.

This logical sequence uses the properties of parallelograms and the given information to prove that ABCD must be a parallelogram.

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