Write an Equation for the ellipse. The center is (1, -3).

Write An Equation For The Ellipse. The Center Is (1, -3).

Answers

Answer 1

The standard form of the equation of the ellipse is (x - 1)² / 16 + (y + 3) / 9 = 1.

How to define the standard form of the equation of an ellipse

In this problem we find the representation of an ellipse on Cartesian plane, whose center is at (h, k) = (1, - 3), whose major semiaxis length is 4 units and whose minor semiaxis length is 3 units. The standard form of the equation of the ellipse is described below:

(x - h)² / a² + (y - k)² / b² = 1

Where:

(h, k) - Coordinates of the center.a - Length of the major semiaxis.b - Length of the minor semiaxis.

If we know that (h, k) = (1, - 3), a = 4 and b = 3, then the standard form of the equation of the ellipse is:

(x - 1)² / 16 + (y + 3) / 9 = 1

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Related Questions

There are 8 blue marbles, 6 red marbles, 2 green marbles and 4 black marbles in a box.
What is the probability that the marble is not green?

Answers

The probability that the marble choose is not green is 9/10

What is probability?

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1.

Probability is expressed as;

probability = sample space/total outcome

total number of marble = 8+6+2+4 = 20marbles

Probability that it is green = 2/20 = 1/10

therefore probability that Is not green = 1-1/10

= 10-1)/10

= 9/10

therefore the probability that a marble chosen is not green is 9/10.

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A student is solving the equation shown.
√x+1+2√x-1=0
For the first step in solving the equation, the student subtracts the second term from both sides of the equation.
For the second step, the student squares both sides of the equation.
What is the result of the second step?

Answers

Answer:

C) x + 1 = 4(x - 1)

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

Given equation to solve:

[tex]\sqrt{x+1} +2\sqrt{x-1} =0[/tex]

The result of the first step:

[tex]\sqrt{x+1} =-2\sqrt{x-1}[/tex]

The second step:

[tex](\sqrt{x+1})^2 =(-2\sqrt{x-1} )^2[/tex]

And its result is:

x + 1 = 4(x - 1)

The matching choice is C.

find the value of x in the cube

Answers

Answer:

3√3 ft or 5.20 ft

Step-by-step explanation:

The main diagonal of any cube can be found by multiplying the length of one side by the square root of 3. Where “x” is the cube side.

x = L × √3

x = 3 × √3

x = 3 × 1.7

x = 5.20 ft

Find the sum of the arithmetic sequence: 7+11+15+19+...+83+87.

Answers

The sum of the arithmetic sequence is 987

What is arithmetic sequence?

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.

For example, the sequence, 2,4,6,8,10... is an arithmetic sequence.

The sum of an arithmetic sequence is given as;

Sn=n/2[2a+(n−1)d]. Where d is the common difference and a is the first term.

the last term is 87

therefore;

87= 7+(n-1) 4

87= 7+4n-4

91-7 = 4n

84 = 4n

n = 84/4

n = 21

therefore 87 is the 21st term

Sn=n/2[2a+(n−1)d]

= 21/2(2×7+(21-1)4

= 21/2 ( 14+80)

= 21×94/2

= 987

therefore the sum of the arithmetic sequence is 987

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Given: rectangle MNPQ ~ rectangle RSTU

- find the perimeter of rectangle RSTU
- find the area of rectangle RSTU

Answers

The perimeter of rectangle RSTU is 21 cm.

The area of the rectangle RSTU is 27 cm².

How to find the perimeter and area of a rectangle?

A rectangle is a quadrilateral that has opposite side equal to each other and opposite side parallel to each other.

Therefore, let's find the perimeter of the rectangle RSTU and the area of RSTU.

Hence,

Let's find the width of the rectangle MNPQ

14 = 2(4 + w)

14 = 8 + 2w

14 - 8 = 2w

2w = 6

w = 6 / 2

w = 3 cm

Therefore, using similar ratio,

4 / 6 = 3 / RU

cross multiply

4RU = 18

RU = 18 / 4

RU = 4.5 cm

Therefore,

Perimeter of the rectangle RSTU = 2(6 + 4.5)

Perimeter of the rectangle RSTU = 2(10.5)

Perimeter of the rectangle RSTU =21 cm

Area of the rectangle RSTU = 4.5 × 6

Area of the rectangle RSTU = 27 cm²

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1. Find the zeros of the quadratic function by graphing. Round to the nearest tenth if necessary.
f(x) = -2x² + 3x + 1
A 0.8,2.1) is a zero of the quadratic function because it is the peak of the parabola.
B (0,1) is a zero of the quadratic because it is where the parabola crosses the y-axis.
C (-0,3,0) and (1.8,0) are zeros of the quadratic function because it is where the parabola crosses the x-axis.
D (0.8,2.1) and (0,1) are zeros of the quadratic function because it is where the parabola crosses the x-axis.

Answers

The correct answer is C: (-0.3,0) and (1.8,0) are zeros of the quadratic function because they are the points where the parabola intersects the x-axis.

The right response is C: (- 0.3,0) and (1.8,0) are zeros of as far as possible since they are the places where the parabola meets the x-turn.

plot the y-get at (0,1),

x = - b/2a

To find the x-heading of the vertex, which is x = 3/4. Substitute this worth into the capacity to find the y-course of the vertex, which is

f(3/4) = 1/8.

Plot the vertex at (3/4, 1/8).

Then, utilize this data to plot the remainder of the parabola. The zeros are the places where the parabola crosses the x-focus, which are close (- 0.3,0) and (1.8,0) obviously following changing in accordance with the closest 10th.

To track down the zeros of the quadratic capacity by illustrating, one ought to at first plot the y-get at (0,1) and a brief time frame later utilize the vertex condition to track down the headings of the vertex. Following plotting the vertex, the remainder of the parabola can be drawn. The zeros of the capacity are the x-gets, which can be found by finding the places where the parabola combines the x-turn. For this current situation, the zeros are close (- 0.3, 0) and (1.8, 0) resulting to adjusting to the closest 10th.

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Ina Crespo rowed 16 miles down the Habashabee River in 2 ​hours, but the return trip took her 4 hours. Find the rate Ina rows in still water and the rate of the current. Let x represent the rate Ina can row in still water and let y represent the rate of the current. I need help asap

Answers

Answer:ina can row 6mph in still water and 2 mph in current

Step-by-step explanation:

A laptop computer is purchased for $4700. Each year, it’s value is 80% of its value the year before. After how many years will the laptop computer be worth $1000 or less?

Answers

Answer:

Step 1:

Let x = number of years

Let y = Value of the laptop after x years

Step 2:

Write an equation that expresses the value of the laptop after x years y = 0.8((4700)x)

Step 3:

Set the equation equal to 1000 and solve for x

1000 = 0.8((4700)x)

1 = 0.8(4700)x

1/0.8 = 4700x

1.25 = 4700x

x = (1.25/4700)

Answer: The laptop will be worth $1000 or less after 0.0026608 years.

Answer:

1 year

Step-by-step explanation:

4700 x .8= 3760

4700 - 3760 = 940$

In 1 year the laptop will be $940

NEED HELP FOR MATH HW! I need some help number 3 WITHOUT the use of a t1-83

Answers

Step-by-step explanation:

Here is a graph from Desmos....you should be able to see where the function is > 0

​Lisa an experienced shipping​ clerk, can fill a certain order in 9 hours. Felipe a new​ clerk, needs 11 hours to do the same job. Working​ together, how long will it take them to fill the​ order?
The solution is ___Hours

Answers

It will take Lisa and Felipe approximately 4.95 hours to fill the order by working together.

To solve this problem, we can use the formula:

1/T = 1/T₁ + 1/T₂

where T is the time taken to complete the job when both Lisa and Felipe work together, T₁ is the time taken by Lisa to complete the job, and T₂ is the time taken by Felipe to complete the job.

Substituting the given values into the formula, we get:

1/T = 1/9 + 1/11

Simplifying the right-hand side of the equation, we get:

1/T = (11 + 9)/(9 x 11)

1/T = 20/99

Multiplying both sides by 99, we get:

T = 99/20

Therefore, working together, Lisa and Felipe can complete the job in 4.95 hours, or approximately 4 hours and 57 minutes.

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Solve the quadratic equation 2x2 – x = 15 using the quadratic formula.

Answers

Answer:

x = 3, -5/2

Step-by-step explanation:

First, you move the 15 onto the left of the equation by subtracting it from both sides.

Second, you plug your info into the quadratic equation.  (1 +- sqrt(1+4*15*2))/4

A quality expert can test 18 units in 32 minutes. If there are 400 units to be tested, about how long will it take to test them?

Answers

It will take about 711.12 minutes or approximately 11.85 hours to test all 400 units.

To find out how long it will take to test 400 units, we need to use the information given in the problem. We know that the quality expert can test 18 units in 32 minutes. We can use this information to find out how long it will take to test one unit.

First, we need to find out how many units can be tested in one minute:

18 units / 32 minutes = 0.5625 units per minute

This means that the quality expert can test 0.5625 units per minute. To find out how long it will take to test one unit, we can divide 1 by 0.5625:

1 / 0.5625 = 1.7778 minutes per unit

So it takes about 1.7778 minutes to test one unit. To find out how long it will take to test 400 units, we can multiply this value by 400:

1.7778 minutes per unit * 400 units = 711.12 minutes

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Please I want the answer!

Answers

The subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2

Writing the subtraction expressions to calculate the lengths

From the question, we have the following parameters that can be used in our computation:

O = (3, 2)

A = (-7, 5)

B = (-7, 2)

The distance between (or length of) the coordinates is calculated as

Length = √[(x2 - x1)² + (y2 - y1)²]

Using the above as a guide, we have the following:

OB = √[(3 -- 7)² + (2 - 2)²]

OB = √[(3 -- 7)² + 0²]

OB = √[(3 -- 7)²]

OB = 3 -- 7

AB = √[(-7 -- 7)² + (5 - 2)²]

AB = √[0² + (5 - 2)²]

AB = √[(5 - 2)²]

AB = 5 - 2

Hence, the subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2

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n/4.4 =7 Pls Help nowwwwwwwwwwwwwwwwwwwww

Answers

Answer:

n=7

Step-by-step explanation:

[tex] \frac{n}{4} \times 4 = 7 \\ \frac{4n}{4} = 7 \\ 4 \times \frac{4n}{4} = 7 \times 4 \\ 4n = 28 \\ \frac{4n}{4} = \frac{28}{4} \\ n = 7 [/tex]

Enter the value of n so that the expression (-2y+5)+(-5y-3) is equivalent to (ny+2)

Answers

Answer:n=-7

Step-by-step explanation: (-2y+5)+(-5y-3)=-7y+2 so our answer is -7.

I can’t seem to figure this question out

Answers

The total surface area of the pyramid is:260 ft²

What is the total surface area of the Pyramid?

The area of a triangle is expressed as:

A = ¹/₂bh

where:

b denotes the base of the triangle

h denotes the height of the triangle

Area of rectangle is:

A = l * w

where:

l denotes the length of the rectangle

w denotes the width of the rectangle

Thus, the total surface area of the given pyramid is:

Total Surface Area =  4(¹/₂(10 * 12)) + (10 * 10)

Total Surface Area  = 240 + 20

Total Surface Area  = 260 ft²

Therefore, we can conclude that is the calculation of the total surface area of the composite figure.

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17. The Amethyst Woodstar species of
hummingbird beats its wings about
80 times per second. If there are
60 seconds in a minute, about how
many times does the Amethyst
Woodstar beat its wings in
9 minutes?
A 12,600
B 37,800
C50,400
D 43,200

Answers

Answer: D

Step-by-step explanation: 60x9=540 and 540x80=43,200

Matthew is working two summer jobs, making $9 per hour babysitting and making $13 per hour landscaping. In a given week, he can work a maximum of 16 total hours and must earn at least $180. If Matthew worked 3 hours babysitting, determine the maximum number of whole hours landscaping that he can work and still meet his requirements. If there are no possible solutions, submit an empty answer.

Answers

Answer:

Step-by-step explanation:

3 hours of babysitting = $27

if he needs $180 per week he needs to work at least 12 hours in landscaping.

12 hours of Landscaping = $156

156 + 27 = 183

It cuts down about an hour of work.

If I misunderstood something, please let me know. Have a good day :)

A side of the triangle below has been extended to form an exterior angle of 125°. Find the value of

Answers

From the given triangle, x has a value of 35°.

As a result, one of the triangle's sides has been stretched to create an exterior angle of 125° outside angle.

Which angles are adjacent?

Angles that are always located near one another, sharing a similar vertex and common side but not overlapping, are said to be adjacent angles.

According to the above figure, the tringle's exterior angle is 125°, and y is an adjacent angle to that.

Now, 125°+ y =180°

y = 180°-125°

y = 55°

As a result, the supplied triangle's value for y is 55°.

The sum of the triangle law,

55°+ 90° + x  = 180°

x = 35°

Therefore the value of x = 35°

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What is the equation of the line passing through the point (-3,-4) and parallel to the x-axis?

Answers

The equation of the line passing through the point (-3,-4) and parallel to the x-axis is y = -4.

What is the equation of the line passing through the point (-3,-4) and parallel to the x-axis?

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept

Given that; the line passing through the point (-3,-4) and parallel to the x-axis.

A line that is parallel to the x-axis has a slope of 0, because the y-coordinate of any point on the line does not change as the x-coordinate varies.

Hence;

The equation of the line passing through the point (-3,-4) and parallel to the x-axis can be written in the form y = b, where b is a constant.

To determine the value of b, we substitute the coordinates of the given point (-3,-4) into the equation y = b:

-4 = b

Note that: y = b, where b is a constant.

y = -4

Therefore, the equation of the line y = -4.

Option C) y = -4 is the correct answer.

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Please help with trigonometry

Answers

14.4 is the value of x in triangle .

What is known as a triangle?

Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. 180 degrees is the sum of the triangle's three angles.  

                                Triangular shapes have three vertices, three angles, and three sides. 180 degrees is the sum of a triangle's three interior angles. The length of a triangle's two longest sides added together exceeds the length of its third side.

17² = 9² + X²

289 = 81 + x²

289 - 81 = x²

208 = x²

 x = √208

     = 14.4

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Un elevador de taller mecánico tiene pistones de entrada y salida de 5 cm y de 60 cm de radio respectivamente. Con este dispositivo se mantiene levantado un auto de 2000 kg. ¿Cuál es la fuerza aplicada al pistón de entrada?

Answers

The force applied to the input piston is  136.25 N.

How to find the force applied to the intake piston?

This problem can be solved using the principle of hydraulic systems, which states that pressure in a confined fluid is transmitted equally in all directions.

Thus, we can equate  the pressure on the input piston to the pressure on the output piston, and solve for the force on the input piston. That is:

P₁ = P₂

F₁/A₁ = F₂/A₂    (Pressure = Force/Area)

F₂ = 2000 * 9.81 = 19620 N   (F = mg)

A₁ = π * r₁² = π * 5² = 25π cm²

A₂  = π * r₂ ² = π * 60² = 3600π cm²

F₁ = F₂/A₂ * A₁

F₁ = (19620/3600π) * 25π

F₁ = 136.25 N

Therefore, the force applied to the input piston is  136.25 N.

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Question in English

A machine shop lift has input and output pistons of 5 cm and 60 cm radius respectively. With this device, a 2000 kg car is kept lifted. What is the force applied to the intake piston?

x + 5 < 7

x + 5 -? ? 7-?


x ??

<----—------————————--->
-5 - 4 - 3 - 2 - 1 0 1 2 3 4 5

Graph the solution after you get your answer

Answers

The inequality can be solved to get x < 2, the graph is on the image at the end.

How to solve and graph the inequality?

Here we have the inequality.

x + 5 < 7

To solve this, we need to isolate the variable, subtracting 5 in both sides we will get.

x < 7 - 5

x < 2

The graph of this inequality will be a number line with an open circle at x = 2, and an arrow that extends to the left side (because x is smaller than 2)

Then we will get the graph that you can see in the image at the end.

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A ferris wheel is 40 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).

Answers

The height of the person on the ferris wheel can be modeled by the equation:

h = 20sin(π/4*t) + 21

where h is the height in meters above the ground, t is the time in minutes, and 21 meters is added to account for the height of the platform.

Fully factorise x ² + 18x​

Answers

Answer: To factorize x² + 18x, we can first find the greatest common factor (GCF) of the two terms, which is x:

x(x + 18)

This is the fully factorized form of x² + 18x.

Given that X is a normal random variable with a mean of 40 and a standard deviation of 8 what is P (34

Answers

The probability is given as follows:

P(34 < X < 46) = 0.5468 = 54.68%.

How to obtain probabilities using the normal distribution?

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 40, \sigma = 8[/tex]

The probability is the p-value of Z when X = 46 subtracted by the p-value of Z when X = 34, hence:

Z = (46 - 40)/8

Z = 0.75

Z = 0.75 has a p-value of 0.7734.

Z = (34 - 40)/8

Z = -0.75

Z = -0.75 has a p-value of 0.2266.

Hence:

0.7734 - 0.2266 = 0.5468 = 54.68%.

Missing Information

The probability is:

P(34 < X < 46).

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Who can help mee??

Answers

The answer is $119
You need to multiply the 2 numbers that they give you and divide by 100 (for example: 4700 X 8 and divide by 100)

well, let's find out how much she made on each week

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 4700}}{\left( \cfrac{8}{100} \right)4700}\implies 376\qquad \textit{ first week} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{9\% of 5500}}{\left( \cfrac{9}{100} \right)5500}\implies 495\qquad \textit{ second week}\hspace{8em}\underset{ \textit{more on the 2nd week} }{\stackrel{ 495~~ - ~~376 }{\text{\LARGE 119}}}[/tex]

Which of the following points represents a striking deviation in the box plot above?
A.
P
B.
R
C.
S
D.
Q

Answers

Answer:

  A.  P

Step-by-step explanation:

You want to identify the point that represents a striking deviation in the given box plot.

IQR

The interquartile range for this box plot is the difference between the upper and lower quartiles:

  29 -26 = 3

Outlier

The "fence" that is 1.5 times the IQR below the lower quartile is ...

  26 -3·1.5 = 21.5

Point P lies beyond this fence, so is considered an outlier in the data set.

Point P represents a striking deviation, choice A.

<95141404393>

m ∠ � = ( � + 21 ) ∘ ∠A=(x+21) ∘ and m ∠ � = ( 4 � − 30 ) ∘ ∠B=(4x−30) ∘ , then find the measure of ∠ � ∠B.

Answers

The measure of angle B is given as follows:

m < B = 49.2º.

What are complementary angles?

Two angles are said to be complementary angles when the sum of their measures is of 90º.

The measures are given as follows:

m < A = (x + 21)ºm < B = (4x - 30)º.

As the angles are complementary, the value of x is obtained as follows:

x + 21 + 4x - 30 = 90

5x - 9 = 90

5x = 99

x = 19.8.

Hence the measure of angle B is obtained as follows:

m < B = 4 x 19.8 - 30

m < B = 49.2º.

Missing Information

The measures are given as follows:

m < A = (x + 21)ºm < B = (4x - 30)º.

The angles are complementary, and it asks for the measure of angle B.

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Lines MN and GH are parallel. If m
S is 38°, then what is m
Y?

Answers

The calculated measure of the angle Y is 38°


Calculating the measure of the angle Y

From the question, we have the following parameters that can be used in our computation:

Lines MN and GH are parallel. Angle S = 38°

The angle S and angle Y are corresponding angles

This means that the angles are congruent

So, we have

Y = S

Substitute the known values in the above equation, so, we have the following representation

Y = 38°

Hence, the measure of the angle Y is 38°

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Complete question

Lines MN and GH are parallel. If mS is 38°, then what is mY?

See attachment for figure

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