The equation of ellipse with foci (2, 4) and (2, -8) and co-vertices (10, -2) and (-6, -2) is ((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
What is the equation of ellipseTo find the equation of the ellipse, we first need to determine the center of the ellipse. Since the foci are on the same vertical line, the center of the ellipse is at the midpoint of the segment connecting the foci.
The midpoint of the segment connecting the foci is:
((2+2)/2, (4-8)/2) = (2, -2)
So the center of the ellipse is (2, -2).
Next, we need to determine the lengths of the semi-major and semi-minor axes. The semi-major axis is half the distance between the co-vertices, which is:
a = (10 - (-6))/2 = 8
The semi-minor axis is half the distance between the foci, which is:
c = (4 - (-8))/2 = 6
Now we can use the standard form of the equation of an ellipse centered at (h,k):
((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1
where a is the length of the semi-major axis and b is the length of the semi-minor axis.
Plugging in the values we have:
((x - 2)^2 / 8^2) + ((y + 2)^2 / 6^2) = 1
Simplifying and rearranging:
((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
So the equation of the ellipse is:
((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
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sk A pond in the shape of a right-angled triangle is shown below. Calculate the perimeter of the pond. Give your answer in metres to 1 d.p. 2.42 m.
The perimeter of the pond from the calculation is 5.42 meter
How to solve for the perimeter of the pondWe would first have to find the sides using the angle that we have here
b / 2.42 = sin 74
cross multiply
2.42 x sin 74 = 2.33 meters
h / 2.42 = cos 74
2.42 x cos 74 = 0.67 meters
Given that the sides of the triangle are 2.33 , 2.42 and 0.67 meters
The perimeter would be solved by 2.33 + 2.42 + 0.67
= 5.42 meters
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Which sets of numbers do 3/5 belong to
Answer:
Rational numbers, Real Numbers, Fractions, and Percentages.
Consider the following figure.
(Note that the figure is not drawn to scale.)
46°
72°
53°
L
57°
K
Order the side lengths IJ, JL, IK, JK, and LK from least to greatest.
O
The order of the side lengths of the triangles from the least to the greatest is Lk < JL < IJ < JK < IK.
How does angle opposite to a side of triangle affect its size?
If the angle facing a side of a triangle increases, then the length of the opposite side may also increase. This is because the larger the angle, the more vertical the opposite side becomes, and therefore the longer it may become.
Conversely, if the angle facing a side of a triangle decreases, then the length of the opposite side may also decrease. This is because the smaller the angle, the less vertical the opposite side becomes, and therefore the shorter it may become.
From the given diagram, the largest side of the triangle will be the side directly opposite the largest angle.
Also, the smallest side of the triangle will be the side directly opposite the smallest angle.
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What is the outcome and sample space of getting a sum of 9 when three dice are rolled
The outcome of getting a sum of 9 when three dice are rolled is that the sum of the three numbers shown on the dice must add up to 9. The sample space for this scenario can be written as S = { (1,3,5), (2,3,4), (2,4,3), (3,2,4), (3,4,2), (4,2,3), (4,3,2), (5,1,3)}
What is outcome?Outcome refers to the result of an action or event. It is the end result of the process and can be positive, negative, or a mix of both. Outcome can also refer to the impact of an event, such as the effect it has on the environment, the people affected, or the economy.
The sample space for this scenario is the set of all possible combinations of three dice that add up to 9.
Each of the elements in this set represents a combination of numbers on the dice that will add up to 9 when rolled. For example, the first element of this set (1,3,5) means that if the three dice are rolled, the numbers shown on the dice will be 1, 3, and 5, and the sum of the numbers will be 9.
When determining the sample space for the outcome of rolling three dice, the order of the numbers does not matter. Therefore, the sets (2,3,4) and (4,2,3) are equivalent, since the sum of the numbers is still 9 regardless of the order.
In conclusion, the outcome of getting a sum of 9 when three dice are rolled is that the sum of the three numbers shown on the dice must add up to 9. The sample space for this scenario is the set of all possible combinations of three dice that add up to 9.
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As the Earth revolves around the sun, it travels at a speed of approximately 18 miles per second. Convert this speed to kilometers per second. At this speed, how many kilometers will the Earth travel in 10 seconds? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Answer:
[tex]\frac{28.5km}{sec}[/tex]
In 10 seconds the earth will travel 288 km
Step-by-step explanation:
[tex]\frac{18miles}{sec}[/tex] x [tex]\frac{1.6km}{1 mile}[/tex] = [tex]\frac{28.8km}{sec}[/tex]
[tex]\frac{28.8km}{sec}[/tex] x [tex]\frac{10sec}{1}[/tex] = 288 km
Helping in the name of Jesus.
Which of these relations is a function?
➤
Video
Answer:
Step-by-step explanation:
Only the one on the bottom right is a function. It's the only one that does not have 2 of the same x value for a single y value.
What is the sum of 1h20, 2h40, 3h05?
Answer:
6h65
Step-by-step explanation:
Add up all the values:
1h+2h+3h= 6
20+40+05= 65
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The area of a square is 196 square feet. Find the length of a side.
FIND THE LENGTH IN FEET!!
What is the best estimate of 2/3, 1, 0
The estimated value of 2/3 is roughly 0.67, of 1 it is 1 and for 0 it is 0.
What does a estimate mean?
A number given to a demographic parameter that was taken from the a statistical sample. A pricing estimate for the job that needs to be done. 3. an assessment or view of the essence, character, or trait of an object or a person.
What is an illustration of an estimate?
To make computations simpler, an estimate is an approximate estimation of the real value, amount, or quantity.
For 2/3, on dividing we get the value as 0.67.
Since 1 is a number and doesn't need to be rounded or approximated, the guess is 1.
Since it is a number without a fractional component, the approximation of 0 also is 0.
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What THREE statements are correct with the variation in the random samples?
A-Samples 1, 2, and 4 best represent the data set because the data in these sets have similar results.
B-Sample 5 may not be an accurate sample for hamburgers and other because of the difference in numbers compared to other samples.
C-Samples 1, 2, and 4 best represent the data set because there are different results when comparing these samples.
D-Sample 2 may not be an accurate sample for pizza and hot dogs because of the difference in numbers compared to other samples.
E-Sample 3 may not be an accurate sample for pizza and hot dogs because of the difference in numbers compared to other samples.
A, B, and E are the consistent with the random samples on preferred school lunches by 100 students.
What is a random sample?A random sample is a subset of a larger population that is selected in such a way that each member of the population has an equal chance of being included in the sample. Random sampling is an important tool in statistics and allows researchers to make inferences about the larger population based on the characteristics of the sample.
Random sampling helps to ensure that the sample is representative of the population and that any statistical analysis done on the sample can be generalized to the larger population.
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PLEASE PLEASE PLEASE HELP ASAP!! LOTS OF POINTS
The time taken, in hours, for the bacteria to double in size, found using the given function is 26.25 hours.
What is a function?
A relation between a set of inputs and a set of allowable outputs is called a function. It has the property that every input is associated with exactly one output. A function from one set X to another allocates precisely one element of the other set Y to each element of X. Both the set X and the set Y are referred to as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.
The given function is:
[tex]y = y_0e^{(0.0264t)}[/tex]
We are asked to find the time taken for the bacteria to double.
y = a number of bacteria at present time t.
y₀ = initial number of bacteria
When y = 2y₀
The function becomes,
[tex]2y_0 = y_0e^{(0.0264t)}\\\\2 = e^{(0.0264t)}\\\\ln (2) = 0.0264t\\\\0.693 = 0.0264t\\\\t = 26.25[/tex]
Therefore the time taken, in hours, for the bacteria to double in size, found using the given function is 26.25 hours.
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Resuelva por medio de la función y = mx + b con los siguientes datos:
I. m =3 y b =7 ➔ f(x) = ¿?
Answer:
which of the following set of nos could not be the length of sides of aright angled triangles.
I have enough money to buy 4 exercise books at 120 naira each. how many pencils costing 80 naira each can I buy for the same amount
Answer:
6 pencils
Step-by-step explanation:
120*4=480, 480/80=6
Nakia is an architect designing a house with a peaked roof. She is trying to decide what the limitations are on her design. If AB is 8 feet and triangle ABC will be isosceles, describe the possible lengths for AC.
The possible calculated length of the segment AC is a length of any value that exceeds around 7.15 feet.
How to use Pythagoras Theorem?If triangle ABC is an isosceles triangle, then the length of AC must be equal to the length of BC.
Let's denote the length of AC as "x".
To find the length of the diagonal line segment referred to as BD, which represents the height of the peaked roof, we can use the Pythagorean theorem:
BD² = AB² - (AC/2)²
BD² = 8² - (x/2)²
BD² = 64 - x²/4
In order for the roof to be peaked, BD must be less than x, otherwise the roof would be flat.
Therefore, we can set up the inequality:
x√(64 - x²/4) < x
64 - x²/4 < x²
Multiplying both sides by 4 gives:
256 - x² < 4x²
5x² > 256
Dividing both sides by 5 gives:
x² > 51.2
x > √(51.2)
x > 7.15 feet
As a result, any value greater than the square root of 51.2 (approximately 7.15 feet) is a possible length for AC.
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The possible lengths for AC are any values greater than 7.15 feet.
How to use Pythagoras theorem?We are given that the triangle ABC is an isosceles triangle. This means that the length of segment AC must be equal to the length of segment BC.
Let x denote the length of AC.
With the aid of the Pythagorean theorem, the length of the diagonal line segment BD which denotes the height of the peaked roof is:
BD² = AB² - (AC/2)²
BD² = 8² - (x/2)²
BD² = 64 - x²/4
If the roof is to be peaked, then the length of segment BD must be less than x. Thus, we generate the inequality:
BD < x
√(64 - (x²/4)) < x
Square both sides to get:
64 - x²/4 < x²
256 - x² < 4x²
5x² > 256
x² > 51.2
x > √(51.2)
x > 7.15 ft
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50 hombres tienen provisiones para 20 días a razón de tres raciones diarias. Sí las
raciones se disminuyen en 1/3 y se aumentan 10 hombres ¿Cuántos días durarán
los víveres?
Answer:
Para resolver este problema, primero debemos encontrar la cantidad total de raciones que tienen los 50 hombres para 20 días a razón de tres raciones diarias:
50 hombres x 3 raciones por día x 20 días = 3000 raciones
Esto significa que tienen un total de 3000 raciones de alimentos para los 50 hombres durante 20 días.
Luego, podemos calcular la cantidad de raciones diarias después de la disminución en 1/3:
3 raciones diarias - (1/3)(3 raciones diarias) = 2 raciones diarias
Esto significa que cada hombre ahora recibe 2 raciones diarias en lugar de 3.
Después de aumentar el número de hombres en 10, tenemos un total de 60 hombres:
50 hombres + 10 hombres = 60 hombres
Podemos calcular la cantidad total de raciones diarias para los 60 hombres durante los días que durarán las provisiones:
60 hombres x 2 raciones por día = 120 raciones diarias
Finalmente, podemos calcular la cantidad de días que durarán los víveres:
3000 raciones totales / 120 raciones diarias = 25 días
Por lo tanto, los víveres durarán 25 días después de disminuir las raciones en 1/3 y aumentar el número de hombres en 10.
Step-by-step explanation:
ey-intercept of the graph of the equation y = 4 (3^X) ?
Answer: 4
See the graph attached
Hope it helps
Please answer the question in the picture, I will mark brainliest. Show all work pls!!!
The measure of angle ABC is 40 degrees.
What is inscribed angle theorem ?
The inscribed angle theorem, also known as the central angle theorem, states that an angle inscribed in a circle is half the measure of the central angle that intercepts the same arc, or in other words, the angle that connects the endpoints of the arc.
In other words, if we draw a chord of a circle and an angle with its vertex on the circumference of the circle and its sides passing through the endpoints of the chord, then the measure of the inscribed angle is half the measure of the central angle that subtends the same arc as the inscribed angle.
According to the question:
By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc it intercepts.
Since chord AB is congruent to chord CB, we can conclude that angle A is congruent to angle C, because they both intercept the same arc AC. Thus, we have:
angle BAC + angle ABC + angle ACB = 180 degrees (by the angle sum property of triangles
Substituting the measure of arc AC, we get:
angle BAC + angle ABC + 70 degrees = 180 degrees
Simplifying, we get:
angle BAC + angle ABC = 110 degrees
Since angles A and C are congruent, we have:
2 x angle BAC + angle ABC = 180 degrees
Substituting angle BAC + angle ABC = 110 degrees, we get:
2 x 110 degrees - angle ABC = 180 degrees
Solving for angle ABC, we get:
angle ABC = 40 degrees
Therefore, the measure of angle ABC is 40 degrees.
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The expression (x−2)+x+(x+3) represents the combined hours a salesperson works on Monday, Wednesday, and Friday, respectively. Which statement is true? The salesperson works 2 hours less on Monday than Wednesday and works 3 hours less on Wednesday than Friday. The salesperson works 2 hours less on Monday than Wednesday and works 3 hours less on Wednesday than Friday. The salesperson works 2 hours less on Monday than Friday and works 3 hours less on Wednesday than Friday. The salesperson works 2 hours less on Monday than Friday and works 3 hours less on Wednesday than Friday. The salesperson works 3 hours more on Monday than Wednesday and works 2 hours less on Wednesday than Friday. The salesperson works 3 hours more on Monday than Wednesday and works 2 hours less on Wednesday than Friday. The salesperson works 3 hours more on Monday than Friday and works 2 hours less on Wednesday than Friday.
The salesperson works 2 hours less on Monday than Wednesday and works 3 hours less on Wednesday than Friday
Identifying the relationship between the daysGiven that
Combined hours = x - 2 + x + x - 3
When splitted, we have
Monday = x - 2
Wednesday = x
Friday = x + 3
To determine which statement is true, we need to compare the hours worked on Monday and Wednesday, and the hours worked on Wednesday and Friday.
By comparison, Option 1 is correct
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Determine whether the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.
Pq
q
..~P
Is the argument valid or invalid?
O Valid
< Question 9 of 11 >
Invalid
Using tautology, we can conclude that the argument here is invalid.
Define Tautology?A compound statement known as a tautology is one that is true regardless of whether the individual statements inside it are true or false.
The Greek term "tautology," which means "same" and "logy," is where the word "tautology" comes from.
We need to build a truth-table and examine the truth value in the last column in order to determine whether a particular statement is a tautology.
It is a tautology if all of the values are true.
In the given case:
p is TRUE
and
q is FALSE
In this case:
p→q : is FALSE (the assumption “TRUE implies FALSE” is FALSE)
So, here:
p → (p→q) is equal to as p → FALSE
But p is TRUE so in that case it’s TRUE→ FALSE, which is in fact FALSE.
Since there a case where the expression is not true, then it’s not valid.
It’s invalid.
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Write an equation in slope intercept form given m = 2 and the point (0,-5)
Answer:
y = 2x - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = 2 and point where line crosses y- axis (0, - 5 ) , then c = - 5
y = 2x - 5 ← equation of line
3.5 cm
6 cm
3.5 cm that is my question I don’t understand it’s something. With pyramids
Based on the information provided, the volume of the pyramid would be 5308.33 cubic centimeters.
How to calculate the volume of a pyramid?The volume or the space occupied by the pyramid can be calculated using the following formula
V=(1/3)Ah
In this formula, A is the area of the base and h is the height.
Area of the base: 6.5 x 3.5 = 22.75 squared centimeters.
Now, let's calculate the volume:
V = (1/3)*22.75 x 700 cm = 5308.33 cm^3 (Cubic centimeters)
Here 1 meter = 100 cm, then 7 m = 700 cm
Note: This question is incomplete; here is the missing information:
The base of a pyramid is 6.5 cm by 3.5cm and its height is 7m. What is its volume?
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15. What is the name of an account managed by a third party who makes
payments according to a set of instructions, often used for insurance and tax
payments for a mortgage?
5. Jennifer bought 14.75 gallons of gasoline for her car at a cost of $2.95 a gallon. Which is closest to the amount she paid for the gasoline? Responses
A. less than $35.00
B. between $35.00 and $40.00
C. between $40.00 and $45.00
D. more than $45.00
the factor of 70
the common factor of 70
[tex]the factor of 70[/tex]
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
What is a factor?
A factor is a number that completely divides another number. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product because the product is divisible by them.
Multiplication and division are the two techniques for determining factors. Rules of divisibility can also be applied.
The given number is 70.
70 is completely divisible is 1.
70 is completely divisible is 2.
70 is completely divisible is 5.
70 is completely divisible is 7.
70 is completely divisible is 10.
70 is completely divisible is 14.
70 is completely divisible is 35.
70 is completely divisible is 70.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
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Which system of equations can you use to find the roots of the equation? x3 – 10x = x2 – 6 y = x3 – x2 + 10x + 6 y = 0 y = x3 – x2 + 10x y = 6 y = x3 – 10x y = x2 – 6.
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths. , ,
Answer:
429
Step-by-step explanation:
How many cups of water will you need for 8
cups of flour?
Answer:
Step-by-step explanation:
2 cups of water.
PLEASE HELP ASAP!!! THANK YOU
Answer:
360 in^2
Step-by-step explanation:
Area of bottom rectangle : A = 7.5 x 17 = 127.5
Area of front rectangle: A = 6 x 17 = 102
Area of back rectangle: A = 4.5 x 17 = 76.5
Area of 2 triangles: 2(4.5 x 6) = 54
Total surface area = 127.5 + 102 + 76.5 + 54 = 360 in^2
find (-21 ) + (13 ) + 20
Answer:
the correct answer is 12
Answer:
12
Step-by-step explanation:
54000 rounded to the nearest ten
54,000 rounded to the nearest ten is 54,000 because the zeros after the 4 are insignificant
What is approximation?Rounding off in math is the process of approximating a number to a certain degree of accuracy. This involves changing the value of a number to one that is simpler or easier to work with, while still maintaining an acceptable level of accuracy.
For example, rounding off 3.75 to the nearest whole number would give you 4, while rounding off 3.75 to the nearest tenth would give you 3.8.
Rounding off 54000 to the nearest ten is still 54000 because the zeros after the 4 are insignificant
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The graph of an exponential function is shown in the figure below.
The horizontal asymptote is shown as a dashed line.
Find the domain and the range.
Write your answers as inequalities, using x or y as appropriate.
Or, you may instead click on "Empty set" or "All reals" as the answer.
The range of this function is: (0, 2].
Which examples of exponential functions are there?f(x) = bx, where b is a positive integer between 0 and 1, denotes an exponential function. Like in every exponential expression, B and x are referred to as the base and exponent, respectively. An excellent illustration of an exponential function is bacterial proliferation. Some microorganisms reproduce every hour.
As all real numbers are the domain of an exponential function, the following is the domain of this function:
(-∞, ∞)
We must examine the function's behaviour as x gets closer to positive and negative infinity in order to determine the range. The function approaches the horizontal asymptote at y = 2 as x increases to positive infinity. The function gets close to 0, but never quite achieves it as x increases to negative infinity. The scope of this function is as follows:
(0, 2].
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