The equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
How to determine the ellipse equation?The given parameters are:
Foci: (-4, 0) and (4, 0)Length of major axis = 14The above means that:
c = 4 and
The semi-major axis, a = 7 i.e 14/2
Calculate b using
[tex]b = \sqrt{c^2 + a^2[/tex]
So, we have:
[tex]b = \sqrt{4^2 + 7^2[/tex]
[tex]b = \sqrt{65[/tex]
Square both sides
[tex]b^2 = 65[/tex]
The standard form of the ellipse is represented as:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
This gives
[tex]\frac{x^2}{7^2} + \frac{y^2}{65} = 1[/tex]
Evaluate
[tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
Hence, the equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
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A depth finder shows that the water in a certain place is 620 feet deep.The difference between d,
the actual depth of the water, and the reading is |d-620] and must be less than or equal to 0.05d. Find the minimum and maximum values of d, to the nearest tenth of a foot.
Answer:
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⣤⣶⣿⡿⠛⠁⠀⣾⣿⡿⠿⠿⠟⠟⠻⢛⠛⠛⠉⠉⠂⠁⠀⠀⠰⢡⠙⡬⢳⡱⢯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⢻⣿⣧⡄⠀⠀
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8.Gracie Lou sold 15x + 4xy in inventory at her Dance Store on Saturday. Mariella
sold -15x + 3x - 2xy on Sunday. What is their combined inventory for the weekend?
Here we are given that Gracie sold 15x + 4xy in her inventory and Mariella sold -15x +3x -2xy on weekends. We need to find combined inventory.
For that simplify add both the expressions as ,
15x + 4xy + (-15x) + 3x - 2xy
15x + 4xy - 15x + 3x - 2xy
Group like terms ,
(15x + 3x - 15x ) + (4xy - 2xy)
simplify,
3x + 2xy [ required answer]
And we are done!
I need to know functions
An algorithm that converts one number into a different one is called a function.
What are the essentials of functions? A function is an algorithm that transforms one number into another.What the function receives as input is referred to as the independent variable or function's argument.The output of the function is referred to as dependent variables. Functions come in 4 different categories:the return values and arguments of functions.There are arguments and a value returned by this function:arguments-based functions without return values.functions that have both return values and no arguments.the absence of return values and arguments in functions.Chapter 1: Operation Function theory is not particularly difficult, yet students struggle because its fundamentals are unclear.Chapter 1 of Mathematics 2: Function .The human mind developed Function Theory to increase one's capacity for thought.To learn more about functions refer
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Which of the following equations represent the graph that is shown on the coordinate plane below?
Answer:
the coordinate plane has a big example
Step-by-step explanation:
In a survey, a group of students were asked to name their favorite type of game. There were 5 students who chose “other” types of games.
The percentage of students who chose " other " types of games, from the group of students was 25 %
How to find the percentage ?The percentage of students who chose " other " types of games can be found by the formula:
= Number of students who chose " other " types of games / Total number of students x 100 %
Number of students who chose " other " types of games = 5 students
Total number of students = 20 students
The percentage is:
= 5 / 20 x 100 %
= 0. 25 x 100%
= 25 %
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The full question is:
In a survey, a group of 20 students were asked to name their favorite type of game. There were 5 students who chose “other” types of games. What is the percentage of those students who chose " other "?
PLEASE I NEED HELP PLS THANK U SM MATH
In the given circle graph, central angle of people like to travel by boat is 72°.
What is circle graph?Circle graphs also known as pie charts are one of the most commonly used graphs to represent data using the attributes of circles, spheres, and angular data to represent real-world information. It is used to visualize information and data.
Given that, A travel magazine surveyed 500 of its adult readers about their favorite ways to travel.
The circle graph below shows that 125 people like to travel by train, 275 people like to travel by airplane, and 100 people like to travel by boat.
In a circle graph, the whole circle which subtends a 360-degree angle at the center is broken into different.
Central angle of people like to travel by train:
125/500 ×360°
= 90°
Central angle of people like to travel by airplane:
275/500 ×360°
= 198°
Central angle of people like to travel by boat:
100/500 ×360°
= 72°
Therefore, in the given circle graph, central angle of people like to travel by boat is 72°.
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evaluate function expressions
A geometric sequence begins with −4, 20, −100, 405, … Which option below represents the formula for the sequence? f(n) = −5(−4)n−1 f(n) = −4(−5)n−1 f(n) = −5(−4)n f(n) = −4(−5)n
The equation that represents the formula for the sequence is f(n) = −4(−5)^n−1
What is geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
The ratio of any term to the one that precedes it should be the same for all terms. If they are all the same, then r, the common difference, is that value
The nth term of a geometric sequence is given as
a(n) = ar^n -1
where a is the first term which is -4
r is the common ratio = 20/-4 = -5
Therefore f(n) = -4(-5)^n -1
Therefore the expression that represents the formula of the sequence is f(n) = -4(-5)^n - 1
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WHAT IS THE NUMBER BOND FOR 540 + 280 NUMBER BOND
541 + 279 = 820 is the number bond for the expression 540 + 280.
What is number bond?A number bond is a simple addition sum that has become so familiar to a child that they can recognise it and complete it almost immediately, with recall as automatic as that of an entry from a multiplication table in multiplication. Number bonds are used in the teaching of mathematics at the primary school level.
When given the other two numbers, a child who "knows" this number bond should be able to instantly fill in any one of these three numbers if it were missing, without having to "work it out." Number bonds are frequently taught in sets whose sums are common round numbers like 10 or 20.
We can find the number bond by simply adding 1 to first term and subtracting 1 from 2nd term.
540 + 280 = 820
(540 + 1) + (280 -1) = 820
541 + 279 = 820
Thus, 541 + 279 = 820 is the number bond for 540 + 280.
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Part B
Select the correct inequality symbol to complete the inequality.
d
Choose...
16
The complete inequality is d ≥ 3.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
We have the number line graph.
Let d be nay number in the real line.
And in the number line,
the line have the closed circle at 3 and increasing to the right to 3.
That means, the inequality,
d ≥ 3.
Therefore, the inequality is d ≥ 3.
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The complete question is given in the attached image.
How do i solve 6/8 divided by 9/8?
.En el piso de una sala cuadrada
hay un total de 49 mosaicos grandes,
todos del mismo tamaño
Cuantos mosaicos ,colocado uno
a continuación del otro, completan la
longitud de una cuadrícula
de los lados
de la sala?
The number of mosaics tiles in each side of the square floor is 7 tiles.
What is a square ?Since a square has four equal sides and four equal angles, it is a regular quadrilateral. It may alternatively be explained as a rectangle with two neighboring sides that are of equal length.
A square can have many different characteristics. The following list includes some of a square's key characteristics.
A quadrilateral having four sides and four vertices is called a square.The square's four sides are equal to one another.A square's diagonals are parpendicular to one another.Each vertex of a square has a 90° internal angle.360° is the total of all interior angles.A square's diagonals are 90 degrees apart from one another.The diagonals are all the same length.A square is also referred to as a parallelogram since its sides are parallel.In a square, the diagonals are longer than the sides.The square is divided into two similar triangles by the diagonals.The total number of mosaic tiles = 49
Let the lenght of each side of the floor be x
Therefore,
x² = 49
⇒ x = 7
The number of mosaics tiles in each side of the floor is 7 tiles.
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a) Write 5.1 x 10¹ as an ordinary number.
b) Work out the value of (1.7 x 10¹) × (8.5 × 10-²)
Give your answer in standard form.
On solving the provided question we can say that ordinary number the answer is 1.495 x 10^0
What is an ordinary number?An ordinary number, also known as a standard form number or a decimal number, is a number that is written in the familiar base-10 format, with a whole number part and a fractional part separated by a decimal point.
A) 5.1 x 10¹ as an ordinary number is 51.
B) To work out the value of (1.7 x 10¹) × (8.5 x 10-²), we first need to multiply the two numbers:
(1.7 x 10¹) × (8.5 x 10-²) = 1.7 x 8.5 x 10¹ x 10-² = 14.95 x 10-1
To express the answer in standard form, we need to move the decimal point to the left so that there is only one non-zero digit to the left of it. 14.95 x 10-1 is 1.495 x 10^0. So the answer is 1.495 x 10^0
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560/17 participate in a football tournament if each team plays against every other team ones, how many matches will be played tota
According to the information, it can be inferred that the total matches that would be played in total are 160,461.
What is a mathematical combination?A combination is a term to refer to an arrangement of elements in no particular order. For example:
When we put together a sandwich with salami, ham and turkey. The order in which the deli meats are placed does not matter as long as they are in a sandwich. There is only one way to stack the meat on the sandwich when the order doesn't matter.
How to calculate how many matches will be played in total?To calculate how many matches will be played in total we have to perform the following procedure:
[tex]= ^{567} C_{2} \\= \frac{(567)!}{2!565!} \\= \frac{567 * 566 * (565)!}{2 * (565)!} \\= 567 * 283\\= 160,461\\\\[/tex]
As we can see after the combination, the number of games that would be played in this tournament would be 160,461.
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Jewelers emphasize that the price of a diamond is
determined by cut, carat weight, color and clarity.
Draw a line that passes through the points
(0.35,1629) and (0.12,334.50).
Use your line to predict the price of a 0.17-carat
diamond.
C
Price
Check
X
Question 2
Price (U.S. $)
1500
1000
500-
T
√
On solving the provided question, we can say that the provided coordinates are(0.35 , 1629) and (0.12 , 334.50) the equation of line that can be formed it [tex]334.50x = 1629y - 0.47 = 0[/tex]
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
the provided coordinates are
(0.35 , 1629) and (0.12 , 334.50)
the equation of line that can be formed it
y1--y = m (x - x1)
1629y - 0.35 = 1(334.50x - 0.12)
334.50x = 1629y - 0.47 = 0
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Graph the linear inequality y < 3x using slope-intercept form.
Given inequality:
y < 3xTo graph it first, consider line:
y = 3xFind two points on the line.
x = 0 ⇒ y = 3*0 = 0, so the point is (0, 0)x = 1 ⇒ y = 3*1 = 3, the point is (1, 3)Now, plot the two points.
Next, draw a dashed line trough the two points. Dashed line because the line is not included into solution set, due to '<' sign.
The last step, shade the area below (to the right) the line. Below the line because 'y <' means 'y-values less than' which appears below the line.
Answer:
See attachment.
Step-by-step explanation:
Given linear inequality:
[tex]y < 3x[/tex]
When graphing inequalities, temporarily replace the inequality sign for the equals sign:
[tex]\implies y=3x[/tex]
Find two points on the line by substituting two values of x into the equation:
[tex]x=0 \implies y=3(0)=0 \implies (0, 0)[/tex]
[tex]x=1 \implies y=3(1)=3 \implies (1,3)[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Therefore, to graph the given linear inequality:
Plot points (0, 0) and (1, 3).Draw a dashed straight line through the points.Shade under the dashed line.Three cups of soup and two sides of rice cost $15.85. Six cups of soup and four
sides of rice cost $31.70. Find the cost of 1 cup of soup and 1 side of rice.
The cost of 1 cup of soup is, $5.28 and 1 side of rice is $7.92.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Three cups of soup and two sides of rice cost $15.85.
And, Six cups of soup and four sides of rice cost $31.70.
Let cost of 1 cup of soup = x
And, The cost of 1 side of rice = y
Here, Three cups of soup and two sides of rice cost $15.85.
Hence, We can formulate;
⇒ 3x + 2y = 15.85 .. (i)
And, Six cups of soup and four sides of rice cost $31.70.
Hence, We can formulate;
⇒ 6x + 4y = 31.70 .. (ii)
By equation (i) and (ii);
⇒ x = $5.28
⇒ y = $7.92
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Daniel takes out a 40-year $150,000 loan from his bank in 2020. The
quadratic equation that approximates the year/loan balance relationship is
y = -120x^2 - 2500x + 80,000, where x is the number of years and y is the
balance. In what year, will his loan balance be $21,480?
So on solving the provided question we can say that - the equation will be y = -120x^2 - 2500x + 80,000; x = 0 so, y = 80000
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
y = -120x^2 - 2500x + 80,000
x = 0
so, y = 80000
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On the unit circle, how many radians would the point (-1,0) pass if rotated counterclockwise until it first reaches (root3/2,-1/2)?
The radians that the point (-1,0) would pass if rotated counterclockwise until it first reaches (√3/2,-1/2) is 2π/3.
How do we get the radians?When a point on the unit circle is rotated counterclockwise, it traces out an angle in radians. To find the number of radians that the point (-1,0) would pass if rotated counterclockwise until it first reaches (√3/2,-1/2), we can use the fact that the point (-1,0) corresponds to an angle of π radians on the unit circle, and the point (√3/2,-1/2) corresponds to an angle of 5π/3 radians on the unit circle.
To find the number of radians passed, we need to subtract the initial angle (π) from the final angle (5π/3), so (5π/3 - π) = 2π/3 radians.
Therefore, the point (-1,0) will pass 2π/3 radians when it is rotated counterclockwise until it first reaches (√3/2,-1/2)
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I HAVE AN HOUR TO DO THIS HELP
Answer:
Step-by-step explanation:
Your first answer is correct. Good job
Your second answer is correct. good job
Your last answer is correct. good work
3. Higher Order Thinking Kim makes a bar
graph to record votes for the choice of a
class pet. Each grid line represents 4 votes.
Fish got 8 votes. The bar for hamster is
3 grid lines higher than the bar for fish.
How many votes did hamster get?
Therefore , the solution to the given problem of unitary method comes out to be Hamster got 20 votes.
What does unitary method mean?The unit method is a way of problem-solving where you first calculate the amount of a single item, then multiple that value to get the answer. Simply expression, a single system value is extracted from a specified multiple using the unit method. For illustration, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and inverse are equivalent. (Linear Algebra, Mathematical Interpretation, Mathematics of Matrix or Operators).
Here,
4 votes are represented by each grid line. then, four votes per grid.
Fish received 8 votes.
There are three more grids for hamsters than for fish.
votes per grid times the number of grids
So,
the number of fish grids is 4.
2 grids are needed for fish.
There are 3 more grids for hamsters than for fish. As a result, 2 + 3 = 5 grids for the hamster.
Grids times votes per grid divide the total number of ballots.
As a result, there are 20 votes or hamsters (5 x 4).
Hamster has 20 votes as a result.
Therefore , the solution to the given problem of unitary method comes out to be Hamster got 20 votes.
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jonah is playing a game with his frind rita.there using a spiner below for there game.If jonah spins the spinner twice ,which of these reprensents the possible outcomes of his spin
It all depends on how the spinner is set up, what symbols or numbers it contains and how it is marked.
What is symbol?Symbols are an important part of human communication. They are used to convey a specific meaning, feeling, or idea. Symbols can be visual, such as an object or gesture, or verbal, such as a word or phrase. Symbols are used to represent a concept or idea, often in a way that is easier or more efficient than using words.
The possible outcomes of Jonah's spin could be any of the following:
1. Two of the same numbers, e.g. both 7s or both 11s.
2. Two different numbers, e.g. 8 and 4.
3. One number and a symbol, e.g. 5 and the star.
4. Two symbols, e.g. the heart and the diamond.
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A woodpecker can live 27 years, a swallow 3 times less, and a crow lives 45 years longer than a swallow. How many years can a crow live?
Answer:
54 years
Step-by-step explanation:
If we want to know how to solve for the number of years a crow can live, we can use this equation:
(27 ÷ 3) + 45 =?
We can first solve for 27 divided by 3.
(27 ÷ 3) + 45 =?
9 + 45 =?
Now solve for 9 plus 45:
9 + 45 = 54
Therefore, if a woodpecker can live 27 years, a swallow 3 times less, and a crow 45 years longer than the swallow, we can say that a crow can live for 54 years.
There are 16 ounces in 1 pound, so the expression z/16, where z represents the number of ounces, can be used to find the number of pounds for any given number of ounces. How many pounds are in 40 ounces?
Answer:
40 ounces is equal to 2.5 pounds------------------------
Use the given expression z/16, substitute z with 40 and calculate:
z/16 = 40/16 = 2.5 poundsA contractor purchases 5 dozen pairs of padded work gloves for $70.40. She incorrectly calculates the unit price as $13.44 per pair for the expense report. What is the correct unit price? What is the error?
The unit price of the gloves is $ 1.173.
Finding the Unit price of the gloves:To find the Unit price of the gloves find 1 dozen gloves by dividing the total price by the number of dozens. From that find the unit price by dividing a dozen gloves price by 12 as 1 dozen = 12.
Here we have
A contractor purchases 5 dozen pairs of padded work gloves for $70.40.
She incorrectly calculates the unit price as $13.44 per pair for the expense report.
Cost of 1 dozen pairs of padded work gloves = $70.40/5
Cost of 1 dozen pairs of padded work gloves = $ 14.08
Here 1 dozen = 12 gloves
Let 'x' be the Unit price
=> 60x = 70.40
=> x = 70.40/60
=> x = 1.173
Therefore,
The unit price of the pair of gloves is $ 1.173.
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When performing a hypothesis test on two dependent samples, the variable of interest is
Choose one answer.
a. the data that is the same in both samples.
b. all of the combined data.
c. the absolute value of the differences that exist between the matched-pair data.
d. the differences that exist between the matched-pair data.
When performing a hypothesis test on two dependent samples, the variable of interest is
d. the differences that exist between the matched-pair data.
In a hypothesis test on dependent samples, the variable of interest is the difference between the two samples. The test compares the means of the two samples and checks whether the difference is significant or not. The sample data are matched-pair, meaning that each data point in one sample corresponds to a specific data point in the other sample.
The variable of interest is the difference between the two matched data points, this difference is also known as the dependent variable.
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HELP PLEASE DUE IN 10 MINUTES 20 POINTS
A. AC=0.8, mLA'= 53°
B. AC = 1, mLA' = 37°
C. A'C'= 1, mLA = 7.4°
D. AC = 25, mLA' = 37°
After dilatation, the length of AC will be 20. The angle A’ will then be measured at 37°.
What exactly is dilation?Dilation is the process of expanding the size of something without changing its shape. The size of the item can be increased or decreased depending on the scale factor.
We have done so.
AABC is dilated by a factor of four to provide AA’B’C’.
The triangle A’B’C’ is formed by diluting the triangle ABC by a factor of four.
Then the length of AC after dilatation. We now have
A’C’ = scale factor multiplied by AC
A’C’ = 4 x 5
A’C’ = 20
The angle A’ will then be measured.
Dilation has no influence on the angle.
∠A = ∠A’ = 37°
As a result, the proper selection.
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Myra blended 24 oz of orange sherbet when making 5/8 of smoothie. How many ounces of orange sherbet are needed for one batch?
Answer: To find out how many ounces of orange sherbet are needed for one batch of smoothie, you can use the proportion of orange sherbet to the total amount of smoothie.
24 oz of orange sherbet / 5/8 of smoothie = x oz of orange sherbet / 1 batch of smoothie
To solve for x, you can cross-multiply and simplify:
(24 oz of orange sherbet) * (1 batch of smoothie) = (5/8 of smoothie) * x oz of orange sherbet
24 * 1 = 5/8 * x
24 = 5/8 * x
By multiplying both sides by 8/5,
x = 24 * 8/5
x = 38.4 oz
So, 38.4 ounces of orange sherbet are needed for one batch of smoothie.
Step-by-step explanation:
Evaluate The Following Integral If R [0, 1] X [0, 1]. 3yexy DA
Evaluated the Following Integral If R [0, 1] X [0, 1]. 3y xy DA is [tex]\frac{3}{24}[/tex].
What is integral ?
An integral is a mathematical concept that represents the area under a curve, or the accumulation of a quantity over a given interval. Integrals are a fundamental concept in calculus, which is the branch of mathematics that deals with the study of rates of change and accumulation. In other words, an integral can be thought of as the sum of an infinite number of infinitesimal "slices" of the quantity being measured, over a given interval. Integrals can be used to solve a wide variety of problems.
The integral is evaluated as follows,
∫[0,1]∫[0,1] 3yxy dydx
= 3∫[0,1] yxy dxdy
= 3 * (1/4) * ∫[0,1] x dxdy
= 3 * (1/4) * (1/2) * x^2 dy
= 3 * (1/4) * (1/2) * (1/3) = 3/24
Hence , Evaluated the Following Integral If R [0, 1] X [0, 1]. 3y xy DA is [tex]\frac{3}{24}[/tex].
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Find the value of x and m