Find the center, vertices, and foci of the ellipse with equationx^2/144+y^2/2525 = 1

Answers

Answer 1

x^2/144+y^2/25=1

The largest denominator is a^2 and the smallest denominator is b^2, then:
a^2=144→sqrt(a^2)=sqrt(144)→a=12
b^2=25→sqrt(b^2)=sqrt(25)→b=5

The equation is of the form:
x^2/a^2+y^2/b^2=1
This is an ellipse with center C=(h,k) at the Origin → C=(0,0) and major axis on the x-axis and minor axis on the y-axis.

The vertices have coordinates:
V'=(-a,0) and V=(a,0)
Replacing a=12
V'=(-12,0) and V=(12,0)

The foci have coordinates:
F'=(-c,0) and F=(c,0)

c^2=a^2-b^2
c^2=144-25
c^2=119
sqrt(c^2)=sqrt(119)
c=sqrt(119)

Then the coordinates of the foci are:
F'=(-sqrt(119),0) and F=(sqrt(119),0)

Answers:
Centrer: C=(0,0)
Vertices: V'=(-12,0) and V=(12,0)
Foci: F'=(-sqrt(119),0) and V=(sqrt(119),0)

Related Questions

The foci of the hyperbola are ( 13 , 0) and (− 13 , 0), and the asymptotes are y = 12 x and y = − 12 x. find an equation of the conic section with the given properties. use x and y as the variables in your answer.

Answers

y=k+- a/b(x-h)

y=-+12x

12=a/b

a=12b

c²=a²+b²

(13,0) and (-13,0)

13²=(12b)²+b²

169=145b²

b= 13/12

169=a²+169/145

a²= 24336/145

x²/a²-y²/b²=1

145x²/24336 + 145y²/169=1

The equation of the conic section is [tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

The foci of the hyperbola are given as: (13,0) and (-13,0)

The asymptote is given as [tex]y =\pm 12x[/tex]

Divide both sides of [tex]y =\pm 12x[/tex] by x.

[tex]\frac yx = \pm 12[/tex]

Where y/x = a/b.

So, we have:

[tex]\frac ab = \pm 12[/tex]

Make a the subject

[tex]a = \pm 12b[/tex]

Recall that

[tex]c\²=a\²+b\²[/tex]

Where:

[tex]c = \pm13[/tex]

[tex]c\²=a\²+b\²[/tex] becomes

[tex](\pm 13)^2 = (\pm 12b)^2 +b^2[/tex]

[tex]169 = 144b^2 +b^2[/tex]

Evaluate like terms

[tex]169 = 145b^2[/tex]

Make b^2 the subject

[tex]b^2 = \frac{169}{145}[/tex]

Recall that [tex]a = \pm 12b[/tex]

Square both sides

[tex]a^2 = 144b^2[/tex]

Substitute [tex]b^2 = \frac{169}{145}[/tex]

[tex]a^2 = 144 \times \frac{169}{145}[/tex]

[tex]a^2 = \frac{24336}{145}[/tex]

The equation of the conic section is represented as:

[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

Substitute known values

[tex]\frac{x^2}{24336/145} - \frac{y^2}{169/145} = 1[/tex]

Rewrite as:

[tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

Hence, the equation of the conic section is [tex]\frac{145x\²}{24336} - \frac{145y\²}{169}=1[/tex]

Answers

(base 13) (height 5)

(base 5) (height 13)

Area of parallelogram = base × height

Base = 13
Height = 5

Or:

Base = 5
Height = 13

Hope this helped☺☺

A standard dartboard has a diameter of 18 in. What is its area to the nearest square inch?

Answers

The meaning of the area is the measurement of a surface in this case a circle, which can be find by using the formula [tex]A= \pi r^{2} [/tex], where r is equal to the radius of the circle.

In this exercise is given that the diameter of a standard cardboard is 18 inches or a radius of 9 inches and it is asked to find its area. Therefore, to find the area of the circle you should substitute the value of the radius into the previous mention formula.

[tex]A= \pi r^{2}[/tex]
[tex]A= \pi (9 in)^{2} [/tex]
[tex]A= \pi (81 in^{2})[/tex]
[tex]A=254.47 in^{2} [/tex]

The area of the standard dartboard is 254.47 square inches or 254 square inches.

solve the system using substitution method
3x+y=6
2x-4y=10

Answers

[tex]\left\{\begin{array}{ccc}3x+y=6&|-3x\\2x-4y=10\end{array}\right\\\\\left\{\begin{array}{ccc}y=6-3x\\2x-4y=10\end{array}\right\\\\substitute\ y=6-3x\ to\ the\ second\ equation\\\\2x-4(6-3x)=10\\\\2x-4\cdot6-4\cdot(-3x)=10\\\\2x-24+12x=10\\\\14x-24=10\ \ \ |+24\\\\14x=34\ \ \ \ |:14\\\\x=\dfrac{34}{14}\to x=\dfrac{17}{7}\\\\substitute\ the\ value\ of\ x\ to\ first\ equation\\\\y=6-3\cdot\dfrac{17}{7}=6-\dfrac{51}{7}=\dfrac{42}{7}-\dfrac{51}{7}=-\dfrac{9}{7}[/tex]

[tex]\boxed{\left\{\begin{array}{ccc}x=\dfrac{17}{7}\\\\y=-\dfrac{9}{7}\end{array}\right}[/tex]

[tex]\begin{cases}&3x + y = 6 \\&2x - 4y = 10\end{cases}[/tex]

Multiply 4 to the first equation:
[tex]\begin{cases}&12x + 4y = 24 \\&2x - 4y = 10\end{cases}[/tex]

ADD Equation 1 to Equation 2 and find x:
[tex]\begin{aligned}&14x =34 \\&x= 34/14 \\& x = 17/7\end{aligned} [/tex]

Substitute x = 17/7 and find y:
[tex]\begin{aligned}&3x + y = 6 \\&3 (17/7) + y = 6 \\& 51/7 + y = 6 \\&y = -9/7\end{aligned} [/tex]

Answer: x = 17/7, y = -9/7

hello can you please help me posted picture of question

Answers

1/25, since there are 25 square in total and there is only one center square.

your answer would be 1/25 since there are 25 squares in all. The 1 as a denominator would come from the probability.

hello can you please help me posted picture of question

Answers

Total number of people = 10

Number of women = 6

Probability of selecting 1st women = 6/10
Probability of selecting 2nd women = 5/9
Probability of selecting 3rd women = 4/8

Probability that are 3 selected candidates are women = 6/10 x 5/9 x 4/8 = 1/6

So, the correct answer is option A

If the volume is 56 1/4 cubic feet and the length is 7 1/2ft and the width is 3 3/4ft what is the height?

Answers

The height is 2. Multiply 7.5 by 3.75 and you should get 28.125. Divide 56.25 by 28.125 and you will get 2. If you want to check, multiply 2 by 7.5 by 3.75 and you will get 56.25.

dr. Trekcir has $875 to invest. he invests some of it in account#1 paying 8% annual interest and the rest of it in account#2 paying 4% annual interest. After 1 year total interest is $49.00. find hou much is invested in each account

Answers

Here's what the equation would look like (I'm using the variable n for the investments):
0.08n + 0.04(875-n) = 49
Multiply both sides by 100:
8n + 3500 - 4n = 4900
Simplify:
4n+3500=4900
Isolate n:
4n = 1400
n = 350
8% invested: 350
4% invested: 525

Can someone help with this math question

Answers

This is a problem of region. As shown in the figure, we have straight lines. We know that the equation for non-vertical lines is often given in the slope-intercept form by:
[tex]y=mx+b[/tex]

being m the slope of the line and b the y-intercept of it.

On the other hand, if x = 0 then y = b.

We will order the equations above without inequalities like this:

[tex]y=-x-6[/tex]

So, the G and J are straight lines with negative slope. We need to find the one that matches the inequality. Taking a point, for example (0, 0), we will analyze Figure J, so in the inequality:

[tex]0+0\ \textless \ -6[/tex]

This is false, so this statement doesn't match the Figure J. Therefore, the answer is G.

If the radius of a cone is doubled and the height is tripled, what happens to the volume?

Answers

This is the answer . Have a nice day

Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 4

Answers

Final answer:

Given the lengths of the major and minor axes of an ellipse, one can derive the standard form equation of the ellipse. In this example, the lengths were 16 and 4, yielding a standard form equation of x²/4 + y²/64 = 1.

Explanation:

The subject of this question is about finding the standard form equation for an ellipse given the lengths of the major and minor axes. To find the equation of the ellipse, we need to identify the semi-major axis (a) which is half the length of the major axis, and the semi-minor axis (b), which is half the length of the minor axis.

In this case, the lengths of the major and minor axes are 16 and 4 respectively, which gives us a semi-major axis of 8 and a semi-minor axis of 2. The standard form equation of an ellipse with a vertical major axis is given by:

(x-h)²/b² + (y-k)²/a² = 1

Where (h, k) is the center of the ellipse. In this case, since the center of the ellipse is at the origin (0,0), the equation becomes:

x²/4 + y²/64 = 1

Learn more about Ellipse Equation here:

https://brainly.com/question/33868440

#SPJ12

if an object is propelled upward from a height of s feet at an initial velocity of v feet per second h=-16t^2+96t+8 after how many seconds is the height 116 feet?

Answers

654 is the answer for this question

Someone please help.

Answers

In the given geometric series, each next term is obtained by multiplying the previous term by a fixed number known as common ratio.

In this case the common ratio is -3.

As,

- 3.49 x -3 = 10.47
10.47 x - 3 = -31.41
and so on...

So, the next number of the series will be:

94.23 x - 3= -282.69

Thus, the answer to this question is - 282.69

What is the value of x in the equation –6 + x = –2?
8
4
–4
–8

Answers

the answer is 4.... -6+4=-2

a cube with side length s has a volume of 216 cubic centimeters. the equation s^3 = 216 shows the volume of a cube. what is the side length of the cube in centimeters

Answers

I would say 44 is the answer

s³ = 216 ⇒ s = ∛( 216 )

So you just need to take cubic root of 216.

Since 6³ = 216, then ∛( 216 ) = 6

So the side length of the cube would be 6 cm.

Hope this helps.

write an expression that represents the difference between t and 8

Answers

An expression could be x= t-8

Hello there, and thank you for posting your question here on brainly.

Short answer: t - 8

Why?

When we are finding the difference between two numbers, we are subtracting. So, the difference between t and 8 would be t - 8.

Hope this helped you! ♥

Iris is building a model of the Washington Monument. Her model measures 15 in. tall and is 1.5 in. wide at the base. The actual width measurement at the base of the Washington Monument is about 55 ft. About how tall is the Washington Monument?

Answers

Using how tall it is over how wide
=>tall/wide
The model 15in/1.5in
The actual x/55ft

Convert everything into the same units so 55ft to inches
There are 12in in 1ft
55ft * 12in/1ft
The ft cross out leaving in
55*12in= 660 in

So
15in/1.5in = x/660in
Now solve for x my multiplying both side by 660in
660in *15in/1.5in=x
x= 6600in tall

Answer: 550

Step-by-step explanation:Solve the proportion: 15 in./1.5 in. = h/55 ft. The value of h is 550 ft. The Washington Monument is about 550 ft tall.

N a class, 20% of the students are male and 80% female. among male students, 40% wears eyeglasses; among female students, 30% wear eye glasses. if we select a student from the class at random, what is the probability that the student wears eyeglasses

Answers

[tex]|\Omega|=100\%=1\\ |A|=40\%\cdot20\%+30\%\cdot80\%=0.4\cdot0.2+0.3\cdot0.8=0.08+0.24=0.32\\\\ P(A)=\dfrac{0.32}{1}=0.32=32\%[/tex]

Ted researched the price of airline tickets and discovered a correlation between the price of a ticket and the number of miles traveled. After recording his data on a scatter plot, he determined the equation for the line of best fit is y = 300 + 0.45x. What does 0.45 represent in the equation? A) the lowest ticket price B) the number of miles traveled C) the expected change in the price of multiple tickets Eliminate D) the expected change in price of the ticket for each mile traveled

Answers

D) the expected change in price of the ticket for each mile traveled
Because it is a coloration between the two

A die is continuously rolled until the total sum of all rolls exceeds 375. what is the probability that at least 90 rolls are necessary?

Answers

Final answer:

To find the probability of at least 90 rolls being necessary for the total sum of all rolls to exceed 375, we need to consider the probabilities associated with each roll.

Explanation:

To find the probability of at least 90 rolls being necessary for the total sum of all rolls to exceed 375, we need to consider the probabilities associated with each roll.

The maximum possible sum from a single roll of a six-sided die is 6, so after 90 rolls, the maximum possible sum is 90 * 6 = 540. If the total sum exceeds 375, it means that at least one roll resulted in a value greater than 2.

To calculate the probability, we need to find the complement of the event that the total sum is less than or equal to 375, which is the event of the total sum being greater than 375. Let's assume that the probability of rolling a value greater than 2 is p. The probability of at least 90 rolls being necessary is 1 - (1 - p)^90.

Q9 Q3.) Solve the matrix equation 4X + 5A = B

Answers

Hi there!

See pictures below for the answer! My handwriting isn't that good. Let me know if you can't read it :)

The perimeter of the base of a regular quadrilateral prism is 60 cm, the area of a lateral face is 105 cm2. Find: the volume of the prism

Answers

Since the base is a regular quadrilateral, each of its 4 sides must have length
s = P/4
s = (60 cm)/4 = 15 cm

The area of one lateral face is the product of side length and height.
A = s×h
105 cm² = (15 cm)×h
Then the height of the prism is
h = (105 cm²)/(15 cm) = 7 cm

The area of the base is then
B = s²
B = (15 cm)² = 225 cm²

The volume of the prism is the product of its base area and height.
V = Bh
V = (225 cm²)×(7 cm) = 1575 cm³

The volume is 1575 cm³.

What percent of the scores were between 71 and 96

Answers

Any more info? Please?

Suppose you have an isosceles triangle, and each of the equal sides has a length of 1 foot. suppose the angle formed by those two sides is 45^\circ. then the area of the triangle is

Answers

The triangle has a 45-deg angle.
The base angles are congruent and measure 67.5 deg.
The congruent sides measure 1 ft.
Use law of sines to find the length of the base.

[tex] \dfrac{\sin 67.5^\circ}{1~ft} = \dfrac{\sin 45^\circ}{b} [/tex]

[tex] b = \dfrac{\sin 45^\circ}{\sin 67.5^\circ}~ft [/tex]

[tex] b = 0.765~ft [/tex]

Draw a height from the vertex of the 45-deg angle to the base.
Half of the base is 0.765 ft/2 = 0.383 ft

We can find the height of the triangle using the small triangles.

0.383^2 + h^2 = 1^2

h = 0.9239 ft

A = bh/2 = 0.765 * 0.9239/2 ft^2

A = 0.354 ft^2

Final answer:

The area of a given isosceles triangle with sides of 1 foot in length and a 45-degree angle between these sides is 0.5 square feet.

Explanation:

The area of an isosceles triangle can be calculated using the formula 1/2 base times height. But since we know that the triangle is isosceles and the angle between the equal sides is 45 degrees, this forms a 45-45-90 degree triangle which is a special kind of triangle. In a 45-45-90 degree triangle, the lengths of the sides are in the ratio 1:1:√2. Therefore, the length of the base (which also serves as the height in this case) will be the same length as the equal sides, 1 foot. Substituting these into the formula for area, we get Area = 1/2 * 1 ft * 1 ft = 0.5 square feet.

Learn more about Triangle Area

https://brainly.in/question/789756

#SPJ3

what is the solution to the equation 3sqrt(5x-4)=3sqrt(7x+8)

Answers

x = -6

However this is an extraneous solution since it would make the number under the sqrt a negative number.

Answer:

The answer is: 'no solution'

Step-by-step explanation:

The given equation is: [tex]3\sqrt{5x-4}=3\sqrt{7x+8}[/tex]

Dividing both sides of the equation by 3, we will get.....

[tex]\sqrt{5x-4}=\sqrt{7x+8}[/tex]

Taking square on both sides.....

[tex](\sqrt{5x-4})^2=(\sqrt{7x+8})^2\\ \\ 5x-4=7x+8\\ \\ 5x-7x=8+4\\ \\ -2x=12\\ \\ x=\frac{12}{-2}=-6[/tex]

Plugging this [tex]x=-6[/tex] back to the given equation......

[tex]3\sqrt{5(-6)-4}=3\sqrt{7(-6)+8}\\ \\ 3\sqrt{-34}=3\sqrt{-34}[/tex]

As we are getting a negative number inside the square root, so the equation becomes imaginary. Thus [tex]x=-6[/tex] is a restricted value.

Hence, there is 'no solution' for this equation.

Suppose that 44% of all Americans approve of the job the President is doing. The most recent Gallup poll consisted of a random sample of 1,400 American adults.

a. What is the mean of the sampling distribution?

b. What is the standard deviation of the sampling distribution (don't forget to justify the use of the formula)?

c. Describe the normal approximation for this sampling distribution (don't forget to justify this) You can simply write as N (mean, standard deviation)

d. What is the probability that the Gallup poll will come up with a proportion within three percentage points of the true 44%

Answers

a) Mean = n × p, n is 1400 and p is 0.44, using what you know 0.44 (p)× 1400 (n) = 616

b) SD = √ (n×p×q) n 1400 p is 0.44 and q = 1-p=1-0.44=0.56

5u exponent 7 - 21u exponent 7

Simply

Answers

Assuming the given is: 5u^7 - 21u^7
Since both algebraic terms are identical (both are using u^7), we can subtract the coefficients directly, as in: 5 - 21 = -16
Therefore, 5u^7 - 21u^7 = -16u^7

2.
Find the annual percentage rate, using the annual percentage rate table.
Amount Financed: $8,900

Finance Charge: $1,030.62

Number of Payments: 24

Answers

Amount Financed: $8,900
Finance Charge: $1,030.62
Number of Payments: 24

(Finance Charge)/(Amount Financed)*100$=($1,030.62)/($8,900)*100$
(Finance Charge)/(Amount Financed)*100$=(0.1158)*100$
(Finance Charge)/(Amount Financed)*100$=$11.58

In the row of number of Payments 24, we look for:
(Finance Charge)/(Amount Financed)*100$=$11.58, and we to which annual porcentage rate it corresponds in the first row

Answer: The annual percentage rate is 10.75%

I suck at math lol. Could someone give me the answers in detail? Picture attached! Thanks

Answers

11] Volume of cylinder is given by:
Volume=πr²h
r=1.7m, h=15 m
plugging in the values in our formula we get:
V=π(1.7)²×15
V=43.35π

Answer: 43.35π m³

12]
Volume of the oblique cylinder will be:
V=πr²h
r=4 in, h=8
thus
V=π×4²×8
V=128π in²

Answer: 128π in²

A triangle has side lengths of 10 centimeters, 2 centimeters, and c centimeters.

Enter a value to complete the inequality that describes the possible values for c, the length of the third side of the triangle.

HELP ASAP I COULD GET A PRESIDENTIAL AWARD FOR THIS!!!

Answers

Answer:

Step-by-step explanation:

The possible values of the third side of the triangle can be written as, 8 < c < 12.

What is Triangle?

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given a triangle.

Side lengths of the triangle are 10 centimeters, 2 centimeters, and c centimeters.

We have to find the possible values of c.

By the triangle Inequality Theorem,

10 - 2 < c < 10 + 2

8 < c < 12

Hence the possible values of c are 9, 10 and 11.

Learn more about Triangles here :

https://brainly.com/question/30095626

#SPJ2

Other Questions

Which sentence has an infinitive that functions as a direct object? We were given clear instructions to follow. Some types of fires are hard to contain. The team of fire inspectors decided to stay. I was about to speak about fire prevention. Question 11 please solve A mutation in a dna strand is least likely to affect the cell when the mutation: In three activities, how can I change my daily habits to help the ecosystem? What is the slope of this line? Diego has a large box that is 4 feet high, 3 feet wide, and 5 feet long. Can he fit 65 smaller boxes that each have a volume of 1 cubic foot in the large box? You randomly select one card from a 52-card deck. find the probability of selecting a black seven or a red three. 1. (MC) Which of these statements is written using passive voice? (5 points) I went to the store because it was having a sale. It was said that the store had a good sale. The store was advertising a good sale. A sale at the store led me there. a truth about life that is revealed in a story in mexico " email " can substitute itself for "correo electronico" why is that ? Although intended to win national support for douglas's vision of a transcontinental railroad, the kansas-nebraska act sacrificed the antislavery provisions of the What is the surface area of a rectangular prism that has a length of 9 feet, a width of 5 feet, and a height of 7.5 feet? Life-cycle analysis is useful because energy and environmental hazards are associated with Which of the following statements is TRUE about molecules getting from the digestive tract to cells of the brain and cells of the skin? Linda needs 20 gallons of juice that has 75%fruit juice. she has a mixture that has 80% fruit juice and another mixtures that has 60% fruit juice. how much of each mixture should she use to get what she need? What is the perimeter of the rectangle? Write your answer in scientific notation. The area is 2.76 x 10 pw12 the width is 4.6 x 10 pw5pw is the power Subtract the quotient of 18 and 2 from sum of 22 and 9 how many atoms of each element are needed to create an ionic compound of strontium selenide The graph of the function f(x)=4sqrt x is shifted down by three units. What is the domain of the resulting function A ________ is a tax on the market value of oil produced in the state.a. severance taxb. selective sales taxc. general sales taxd. hidden tax