An ellipse is a curved shape characterized by two foci and a major axis, with every point on the ellipse being at a constant sum of distances from the foci. The eccentricity, which is the ratio of the distance between the foci to the length of the major axis, determines the 'roundness' of the ellipse. The ellipse can be constructed using the gardener's method to showcase this constant sum property.
Explanation:An ellipse is a specific type of curve that is noticeably different from a circle in that it is elongated; it has two distinct foci instead of a single central point and a major axis that defines its longest diameter. The foci are two fixed points located within the ellipse such that the sum of the distances from any point on the ellipse to the two foci is constant. This consistent sum of distances is what gives an ellipse its characteristic shape. This property is often demonstrated by the 'gardener's method' of creating an ellipse by anchoring a string to two fixed points (the foci) and tracing a path with a marker keeping the string taut.
The eccentricity of an ellipse, which determines its 'roundness,' is the ratio of the distance between the two foci to the length of the major axis. If the foci are close together relative to the major axis, the ellipse will appear more circular; if they are further apart, the ellipse will be more stretched out. The major axis (2a) cuts the ellipse into two equal halves, and each half is referred to as the semimajor axis (a).
A crucial aspect of drawing an ellipse involves identifying the length of the major axis and the location of the two foci. Because these elements are so fundamental, an ellipse can be readily illustrated by the use of string and a couple of tacks representing the foci.
5/8 0.67 1.2 3/5 Greatest to least
please help the temperature in degrees fahrenheit can be estimated by counting the number of times a cricket chirps in one minute write an algebraic expression for the following written expression
the number of chirps divided by 4 added to 37
We have been given that the temperature in degrees Fahrenheit can be estimated by counting the number of times a cricket chirps in one minute.
Let us start with assuming the number of chirps as x.
We are supposed to write an algebraic expression for the number of chirps divided by 4 added to 37.
Let us first write an algebraic expression for number of chirps divided by 4. The algebraic expression for this will be [tex]\frac{x}{4}[/tex].
Let us now write an algebraic expression for number of chirps divided by 4 added to 37. The algebraic expression for this will be [tex]\frac{x}{4}+37[/tex].
Therefore, the required algebraic expression is [tex]\frac{x}{4}+37[/tex].
In the box, complete the first 4 steps for graphing the quadratic function given. (Use ^ on the keyboard to indicate an exponent.) Then print a sheet of graph paper and graph the quadratic function to turn in to your teacher. Be sure to label the axes and vertex.
y = -x2 - 4x - 3
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Answer:
This was my answer, hopefully it helps!
To graph the quadratic function y = -x^2 - 4x - 3, find the vertex, plot additional points, and connect them with a curve.
Explanation:To graph the quadratic function y = -x2 - 4x - 3, follow these steps:
Identify the coefficients and constant term: a = -1, b = -4, c = -3.Find the x-coordinate of the vertex using the formula x = -b/(2a):x = -(-4)/(2*(-1)) = -4/(-2) = 2Substitute the x-coordinate of the vertex into the equation to find the y-coordinate:y = -(2)2 - 4(2) - 3 = -4 - 8 - 3 = -15Plot the vertex at (2, -15) on the graph paper.Use the symmetry of the parabola to plot two additional points, equidistant from the vertex:If we move 1 unit to the right of the vertex (x = 3), we find y = -(3)2 - 4(3) - 3 = -9 - 12 - 3 = -24.If we move 1 unit to the left of the vertex (x = 1), we find y = -(1)2 - 4(1) - 3 = -1 - 4 - 3 = -8.Connect the three points with a smooth curve to complete the graph.Label x-axis, y-axis, the vertex, and any other relevant points or lines.The volume of a cube is 8 cubic units. What is the length of each edge? Explain how u know.
a jar contains blue, red, yellow, and green marbles. p(blue) = 1/4. what type of probability isillustrated and why
Which of these is an example of a random sample?
A.
The manager of a baseball team asks his team members about their views on the previous game they played.
B.
For a survey on air travel, 100 people are chosen randomly from five different airports.
C.
Five players from a basketball team are chosen for a game.
D.
Three members of a band are chosen for a concert.
Answer:
b
Step-by-step explanation:
the others are incorrect because they talk about group so its not random.
Solve. 5x+10+7x=-3+13+7x+12
how would I set up and solve this problem?
3/4 + 5/7 reduce to lowest term
need an answer as soon as possible.
asking for a friend.
Use the sequence: 1, –2, 4, –8, . . .
a. Find the common ratio in the sequence.
b. Write a rule for the sequence.
c. Find the next three terms
Plsssssssss help i willmark brainliest
How much interest is earned in four years on a deposit of 10,000 if it is allowed to accumulate in an account paying 7% interest compounded annually
Please help (puppy eyes)
How to Factor out the coefficient of the variable 3n-24
Emanuel was charged $32\$32$32dollar sign, 32 for a 1429 km14\dfrac29 \text{ km}1492 km14, start fraction, 2, divided by, 9, end fraction, space, k, m taxi ride. What was the cost per kilometer?
We are required to find the cost per kilometer of Emmanuel.
The cost per kilometre is $2.25 OR $2 and 25cents.According to the question, the total cost of the journey = $32
The total distance covered during the journey =
14 2/9 km
Therefore, the cost per kilometre can be evaluated mathematically as follows;
Cost per kilometer = cost of the journey ÷ Distance of the journey
= 32 ÷ 14 2/9
By converting 14 2/9 to an improper fraction; we have;
= 32 ÷ 128 / 9= 32 × 9/128= (32×9) / 128= 288 / 128= 2 32/128= 2.25 dollar per kilometerTherefore, the cost per kilometer is $2.25
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Write a word problem that can be described by the division expression 9 1/3÷2 3/4 . Use complete sentences in your answer. im very bad with word problems
The word problem involves dividing 9 1/3 loaves of bread into servings of 2 3/4 each to find out the total number of servings.
Explanation:Lisa baked 9 1/3 large loaves of bread for a community event. She wants to split each loaf into servings that are 2 3/4 each. How many total servings can Lisa make? This problem can be solved by dividing 9 1/3 by 2 3/4, with the result representing the total number of servings.
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The tires on your bicycle have a radius of 8 inches. How many rotations does each tire make when you travel 700 feet? Round your answer to the nearest whole number.
Two lines, C and D, are represented by the equations given below: Line C: y = x + 14 Line D: y = 3x + 2 Which of the following shows the solution to the system of equations and explains why?
Answer:
(6, 20), because both lines pass through this point
Step-by-step explanation:
We see that both equations are equal to y. This means we can set the two equations equal to each other:
x+14 = 3x+2
Subtract x from each side:
x+14-x = 3x+2-x
14 = 2x+2
Subtract 2 from each side:
14-2 = 2x+2-2
12 = 2x
Divide both sides by 2:
12/2 = 2x/2
6 = x
Substitute this into the first equation:
y = x+14
y = 6+14
y = 20
This makes the solution (6, 20).
The solution for the given system of equations are (6, 20).
What is a linear system of equations?A system of linear equations is a set of two or more equations involving two or more variables. All of the equations must be considered at once in order to find the solution, which is any pair of values that makes each equation true independently.
The given system of linear equations are y=x+14 -----(i) and y=3x+2 -----(ii).
From equation (i) and (ii), we get
x+14=3x+2
3x-x=14-2
2x=12
x=6
Substitute x=6 equation (i), we get
y=20
Therefore, the solution for the given system of equations are (6, 20).
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One of the tallest living trees today is the Mendocino Tree found at Montgomery Woods State Park, California. Its height is about 11,200 centimeters. What is this height in scientific notation?
A. 0.112*10'-4cm
B. 1.12*10'4cm
C. 11.2*10'4cm
D. 1.12*10'-4cm
plz help me i need help
i will make brainiest
1.12 × 104
(scientific notation)
= 1.12e4
(scientific e notation)
11.2 × 103
(engineering notation)
(thousand; prefix kilo- (k))
11200
(real number)
B. 1.12*10'4cm should be the correct answer.
The height of the tree which is 11,200 centimeters is written as 1.12*10'4cm in scientific notation. The conversion involves placing the decimal point after the first digit and then counting the number of places moved, which forms the power of 10.
Explanation:The question is asking you to express the height of a tree, which is 11,200 centimeters, in scientific notation. Scientific notation is a way of writing very large or very small numbers into a format that is easier to read and understand. It is formatted as a number between 1 and 10 multiplied by 10 raised to a certain power.
To convert 11,200 into scientific notation, we first place the decimal point after the first digit, which results in 1.12. Secondly, we count the number of places moved. In this case, we moved the decimal point 4 places to the left. Therefore, 11,200 cm is equal to 1.12 × 10^4 cm. So, the correct answer is B. 1.12*10'4cm.
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Write about a real-world situation that can be represented by the equation y=4x.
what is the simplest form of this expression -x(7x+2)+x^2
What does the phrase “took to It like a duck takes to water” mean in this sentence?
When the young woman started learning how to play the saxophone she “took to It like a duck takes to water”
A) she practiced often
B) she found It natural
C) she played for others
D) she improved gradually
The phrase means the young woman found it natural and quickly developed a liking for learning how to play the saxophone.
Explanation:The phrase "took to it like a duck takes to water" means that the young woman found it natural and took a liking to learning how to play the saxophone effortlessly and quickly. It implies that she had a natural talent and aptitude for playing the instrument. This expression is often used to describe someone who picks up a new skill or activity easily and enthusiastically.
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A board game that normally costs $30 is on sale for 25 percent off. What is the sale price for the game?
find the value of x.
Each side of ΔABC is 75 units in length. Point D is the foot of the altitude drawn from side A to side BC. Point E is the midpoint of segment AD. What is the length of BE
Figure a’b’c’d’f is a dilation or figure abcdf by a scale factor of 1/2. The dilation is centered at (-4,-1)
Which statement is true?
I'm deeply sorry for my inconvenience. Hopefully this is my last question. Will someone help?
(I forgot how to do taxes and discounts)
choose the equation that is the standard form of
5y=3-2x
5y-3=-2x 2x+5y=3
2x+5y-3=0
hint the standard form of a linear equation is Ax+By=C
john surveyed a random sample of 10 students in 7th grade seven of them they would vote for tammy as class president if there are 230 students in 7th grade what is the best estimate of the students who would vote for tammy
Find a irrational number between 7.7 and 7.9 explain why it’s irrational