The best method to compare the lengths of two line segments is by using a ruler and divider.
The most precise way to measure a line segment is by penetrating the two needles of a divider at its ends, then set it next to a ruler without moving the divider's arms once they have been fastened at the ends of the line segment.
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places.
The difference between a line and a line segment is that a line has no endpoints and can go on forever in any direction.
Thus, The best method to compare the lengths of two line segments is by using a ruler and divider.
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For questions 19-27, use the ellipse defined by the following equation: 2(x+4)^2+3(y-1)^2=24.
19. write the equation of the ellipse in standard form.
20. What are the coordinates of the center?
21. What is the length of the major axis?
22. What is the length of the minor axis?
23. What is the sum of the focal radii?
24.What are the coordinates of the foci?
25. What are the coordinates of the vertices?
26. Find the eccentricity of the ellipse.
27. Draw a sketch of the ellipse.
PLEASE SHOW WORK!!
Answer:
[tex]\textsf{19.} \quad \dfrac{(x+4)^2}{12}+\dfrac{(y-1)^2}{8}=1[/tex]
[tex]\textsf{20.} \quad \textsf{Center}: \;\;(-4, 1)[/tex]
[tex]\textsf{21.} \quad \textsf{Major axis}:\;\;4\sqrt{3}[/tex]
[tex]\textsf{22.} \quad \textsf{Minor axis}:\;\;4\sqrt{2}[/tex]
[tex]\textsf{23.} \quad \textsf{Sum of the focal radii}:\;\;4 \sqrt{3}[/tex]
[tex]\textsf{24.} \quad \textsf{Foci}:\;\;(-6, 1)\;\; \textsf{and}\;\;(-2,1)[/tex]
[tex]\begin{aligned}\textsf{25.} \quad &\textsf{Vertices}:\;\;(-4-2\sqrt{3}, 1) \;\; \textsf{and}\;\; (-4+2\sqrt{3}, 1)\\ &\textsf{Co-vertices}:\;\;(-4, 1-2\sqrt{2}) \;\; \textsf{and}\;\; (-4, 1+2\sqrt{2})\end{aligned}[/tex]
[tex]\textsf{26.} \quad \textsf{Eccentricity}\;\;\dfrac{\sqrt{3}}{3}[/tex]
27. See attachment.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{General equation of an ellipse}\\\\$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$\\\end{minipage}}[/tex]
Given equation:
[tex]2(x+4)^2+3(y-1)^2=24[/tex]
To write the equation of the ellipse in standard form, divide both sides by 24 so that the right side of the equation is equal to one:
[tex]\implies \dfrac{2(x+4)^2}{24}+\dfrac{3(y-1)^2}{24}=\dfrac{24}{24}[/tex]
[tex]\implies \dfrac{(x+4)^2}{12}+\dfrac{(y-1)^2}{8}=1[/tex]
Therefore:
[tex]h = -4[/tex][tex]k = 1[/tex][tex]a^2 = 12 \implies a=2\sqrt{3}[/tex][tex]b^2 = 8 \implies b=2 \sqrt{2}[/tex]The center of the ellipse is (h, k).
Therefore, the coordinates of the center are (-4, 1).
As a > b, the ellipse is horizontal, so 2a is the major axis and 2b is the minor axis. Therefore:
Major axis = 2 × 2√3 = 4√3Minor axis = 2 × 2√2 = 4√2The focal radius is the distance from a point on the ellipse to a focus.
The sum of the focal radii is equal to the length of the major axis.
Therefore, the sum of the focal radii is 4√3.
As a > b, the coordinates of the foci are (h±c, k).
As c² = a² - b², first find the value of c:
[tex]\implies c^2=12-8[/tex]
[tex]\implies c=\sqrt{4}=2[/tex]
Therefore, the coordinates of the foci are:
(-4+2, 1) = (-2, 1)(-4-2, 1) = (-6, 1)As a > b, the coordinates of the vertices are (h±a, k):
(-4-2√3, 1) and (-4+2√3, 1)and the coordinates of the co-vertices are (h, k±b):
(-4, 1-2√2) and (-4, 1+2√2)The eccentricity of the ellipse is:
[tex]\implies e=\dfrac{c}{a}=\dfrac{2}{2\sqrt{3}}=\dfrac{\sqrt{3}}{3}[/tex]
What is the height in feet geometry
The height of the zip line is 203 feet.
What are trigonometric functions?Trigonometric functions are required when the value of an unknown side or internal angle of a right triangle are to be determined. Some of the basic functions are: sine, cosine, tangent etc.
Tangent of an angle is the ration of the opposite side to the angle and the adjacent side.
Tan θ = opposite/ adjacent
To determine the height of the zip line required in the question, we have;
let the height be represented by h,
Tan θ = opposite/ adjacent
Tan 10 = h/ 1150
h = Tan 10 * 1150
= 0.1763*1150
= 202.745
h = 202.8 feet
The height of the zip line is 203 feet.
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Determine p(not orange) if the spinner is spun once. 25% 12.5% 87.5% 37.5%
Answer: 87.5%
Step-by-step explanation:
I hope this helps!
A coach needs to decide who will kick the field goal during a football game. He wants to choose the player with the best chance of making a field goal. He has the following statistics for his top four players. Player Field Goal Kick Statistics Brian made 7 out of 12 penalty kicks. Darius made 15 out of 23 penalty kicks. Fong made 12 out of 20 penalty kicks. Mike made 19 out of 32 penalty kicks.
The coach should choose Darius because he has highest probability of 65.21% of scoring a penalty kick
What is statistics?Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.
The top four players have the following statistics partaining to penalty kick
Brian Who made 7 out of 12
Darius who made 15 out of 23
Fong who made 12 out of 20 and Mike who made 19 out of 32
To get the best we have to put them on percentage.
% to score of Brian = 7/12 ×100 = 58.33%
% to score for Darius = 15/23 ×100 =
65.21%
% to score for Fong = 12/20× 100 = 60%
% to score for Mike = 19/32× 100 = 59.4%
Therefore out of the four top players Darius has higher probability to score. He is the best among them. Therefore the coach should choose Darius.
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Determine the scale factor.
Pre-Image: (-5, 3), (-2, 3), (-2, 1), (-5, 1)
Image: (-10, 6), (-4, 6), (-4, 2), (-10, 2)
The required scale factor with respect to the pre-image and image is equal to 2.
What is scale factor?In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures, which can be used to either vertically or horizontally enlarge or reduce a function representing their size.
In Mathematics, the scale factor of any geometric figure can be calculated by using this mathematical expression:
Scale factor = Dimension of image/Dimension of pre-image
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor = -10/-5 = -4/-2
Scale factor = 2.
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The ratio of the sides of two similar regular octagons is 3:11. If the measure of each side of the larger octagon is 33 cm, then the measure of each side of the smaller octagon is Ci. , Enter a number answer only
The measure of each side of the smaller octagon is 9cm. Therefore, Enter 9
How find the measure of each side of the smaller octagon?
Given that:
The ratio of the sides of two similar regular octagons is 3:11.
The measure of each side of the larger octagon is 33
The measure of each side of the smaller octagon is Ci
we can write that:
smaller octagon : larger octagon = 3 : 11
smaller octagon / larger octagon = 3 / 11
smaller octagon / 33 = 3 / 11
smaller octagon = (3 × 33)/11 = 99/11 = 9 cm
Thus, Ci = 9 cm
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what is the slope of (-4,-9) and (4,-9)
Answer: m (slope) = 0
Step-by-step explanation:
The slope can be found through the equation (y2-y1)/(x2-x1)
(-4, -9) and (4, -9) can be: (x1, y1) and (x2, y2)
We can plug the variables into the formula above:
(-9-(-9))/(4-(-4) = 0/8
The slope is 0.
Answer: slope=0
Step-by-step explanation:
usually slopes are found by taking
change in y
-----------------
change in x
but in all horizontal lines (matching y values, -9 in this case) the line has no slope as it doesn't go up or down.
Consider. F (x) = log2 x
Graph g(x) =log2(x-3) on the graph
The graph of g(x) = [tex]-log_{2}(x - 3)[/tex] is in graph attached.
What are Logarithmic Functions?The logarithmic function is a crucial tool for mathematical computations. Scottish mathematician, physicist, and astronomer John Napier made the first formal study of logarithms in the 16th century. Numerous astronomical and scientific calculations requiring large numbers can use it. The exponential function is thought of as the inverse of the logarithmic function because of their close relationship.
Given
F(x) = log₂ x
and graph of equation is given in question,
to plot the graph of g(x) = -log₂(x - 3)
The shape of graph will be same as log₂x but in different quadrant because of negative sign.
The point of function g(x) = -log₂(x - 3)
x = 4, g(x) = 0
x = 19, g(x) = -4
and graph will be parallel to y axis at x = 3,
Hence the graph is in image.
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At the beginning of a study, 24 fish are caught, tagged and released back into a large pond containing fish. A few days later, 19 fish are caught from the pond and three of them have tags. How many total fish would you expect to be living in the pond
There are 152 fish would you expect to be living in the pond if At the beginning of a study, 24 fish are caught.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
At the beginning of a study, 24 fish are caught, tagged and released back into a large pond containing fish.
The answer would be 152.
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Use the models to complete the statement. The first model has 1 shaded square and 5 unshaded squares. The second model has 2 shaded squares and 4 unshaded squares.
The fraction is 1/6 is less than 2/6.
Less than is the answer
How to use the models to complete the statement?A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.
From the image, the fraction to the left is 1/6 and the fraction to the right is 2/6.
You can think of 1/6 as having a pizza divided into 6 equal portions and you are to pick 1 out of the 6 whereas in the case of 2/6 you are to pick 2 out of the 6. You will notice that you have less pizza in 1/6 than 2/6.
Thus, 1/6 is less than 2/6
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If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 8 cm. (Round your answer to three decimal places.)
The surface area of a snowball decreases at a rate of 6 cm²/min. Its diameter decreases at rate of 0.119 cm/minute
The surface area of a ball is given by:
A = 4πr²
= πd²
Where:
A = surface area
r = radius of the ball
d = diameter of the ball
When the surface area decreases, so does the diameter.
To find the rate of change, take the derivative with respect to time (t)
A = πd²
dA/dt = 2πd dd/dt
Substitute dA/dt = 6 cm²/min, d = 8 cm:
6 = 2π x 8 dd/dt
dd/dt = 0.119 cm/minute
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Determine whether each function is even, odd, or neither.
Answer:
We can decide algebraically if a function is even, odd or neither by replacing x by -x and computing f(-x). If f(-x) = f(x), the function is even. If f(-x) = -f(x), the function is odd.
Step-by-step explanation:
Classify the following Graphs as "(1) Function" or "(2) Not a Function"
HELPPP!!!!
1.
Function
2.
Not a function
The relations in this problem are classified as functions or not as follows:
1. Not a function.
2. Function.
3. Not a function.
4. Function.
5. Function.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output.
Hence, a graph will represent a function if, and only if, it contains no vertically aligned points, that is, if there isn't a vertical line that will cross the graph of the relation in more than one point.
Then the graphs that are not functions in this problem are given as follows:
Graph 1, as there are points inside the pentagon, such as x = 2, for which the vertical line would cross the pentagon twice.Graph 3, as there are two dots for x = 1, which are y = -2 and y = 3.More can be learned about relations and functions at https://brainly.com/question/29701528
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Could you please give me an explanation for this question?
Thanks!
268 divided n = 0.268
find the value of n
Answer: 1000
Step-by-step explanation:
268 / n = 0.268
(268 / n) x n = 0.268 x n
268 = 0.268n
268 / 0.268 = 0.268n / 0.268
1000 = n
________ are measures that marketers can use to watch the performance of their marketing efforts.
Answer:
Step-by-step explanation:
alfreda made a container shaped like a triangular prism, as shown in the diagram what is the volume of the volume of the container in cubics inches?
Four packages are delivered to four houses, one to each house. If these packages are randomly delivered, what is the probability that exactly two of them are delivered to the correct houses
The probability that exactly two of them are delivered to the correct houses as calculated from the data is 4/24 = 1/ 6.
The total number of ways to deliver four packages can be found out by taking the factorial of 4 , i.e., the permutation of 4.
4 × 3 × 2 × 1 = 4!
= 4P4
= 24
A permutation is a referred to as a specific arrangement of items. The set members and elements are arranged in a sequence in a permutation. For example, the permutation of set A=1,6 is 2, as in 1,6,1. There are no alternative ways to arrange the items in set A.
In permutation, the elements must be arranged in a particular sequence, whereas in combination, the order of the elements is irrelevant.
To calculate the permutation we calculate it's factorial.
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Please help me I have a learning disability and need help with this.
Define a variable and write the phrase as an algebraic expression.
six feet less than the width
What is the phrase as an algebraic expression?
Group of answer choices
w+6
6-w
6w
w-6
Answer: Six feet less than the width.
Step-by-step explanation: The algebraic expression for the given statement is. Detailed description: As we are given information.
Consider this quotient (x^3-8x+6) / (x^2-2x+1)
The expression in the form of q(x) + r(x) / b(x) is
(x + 2) + (-13x + 4) / (x² + 2x + 1).
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(x³ - 8x + 6) ÷ (x² + 2x + 1)
Using the long division.
x² + 2x + 1 ) x³ - 8x + 6 ( x + 2
x³ + 2x² + x
(-) (-) (-)
2x² - 9x + 6
2x² + 4x + 2
(-) (-) (-)
-13x + 4
Quotient = x + 2
Remainder = -13x + 4
Thus,
Quotient + Remainder / Divisor
= (x + 2) + (-13x + 4) / (x² + 2x + 1).
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Sharon is ordering tickets for an upcoming basketball game for herself and her friends.
The ticket website shows the following table of ticket options.
The slope intercept form for the cost of tickets can be written as C = 26t + 16.50.
How to write the equation of a straight line in slope-intercept form?A straight line can be written in the slope-intercept form as, y = mx + c.
In order to obtain the slope, the ratio of the difference of the coordinates are taken and c is the y-intercept which can be found by substituting x = 0 in the equation.
As per the question, the number of tickets are represented as t and cost as C.
The slope from the table can be found as,
⇒ (68.50 - 42.50) ÷ (2 - 1) = 26
Plug m = 26 in y = mx + c to get,
y = 26x + c
Plug y = 42.50 and x = 1 to get,
⇒ 42.50 = 26 × 1 + c
⇒ c = 16.50
Then, the equation can be written in terms of C and t as,
C = 26t + 16.50
where c = 16.50
Hence, the equation to represent the total cost is given as C = 26t + 16.50.
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The approximate solution to the given equation after three iterations of successive approximations is when x is about.
The approximate solution to the given equation after three iterations of successive approximations is when x is about -37/16.
In the given question, we have to find in which value of x, the approximate solution to the given equation after three iterations of successive approximations.
The given function is
2/(x+4) = 3^x + 1
As we know that,
The technique known as the iteration method uses the beginning value to generate a number of subsequent approximations of the equation's solution.
Now subtract 3^x + 1 on both side, the function is
f(x) = -3^x - 1 + 2/(x+4)
Now differentiating the function f(x) with respect to x
f'(x) = -3^xIn3 - 2/(x+4)^2
Here, for this function
x 0, -1, -2, -3
x -1.5, -0.667, -0.111, 0.963
As we can see on the table that,
f(-3) = 0.963>0
f(-2) = -0.111<0
So the root of the function lies between -3 and -2.
So x(0) = -3+(-2)/2
x(0) = -3-2/2
x(0) = -5/2
x(0) = -2.5
This value is more near to the value -37/16 from the given option.
So, the approximate solution to the given equation after three iterations of successive approximations is when x is about -37/16.
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The complete question is given below:
After three iterations of successive approximations, the approximate solution to the given equation is when x is about 1.702
The given equation is x^3-x-1=0. To solve it using successive approximations, we need to start with an initial guess for the solution. Let us assume x0=1 as the initial guess. We can now calculate the successive approximations using the formula xn+1=xn-f(xn)/f'(xn).
In this case, f(x)=x3-x-1 and f'(x)=3x2-1.
For x0 = 1, x1 = x0 - f(x0)/f'(x0) = 1 - (1-1-1)/(3*12-1) = 2.
For x1 = 2, x2 = x1 - f(x1)/f'(x1) = 2 - (8-2-1)/(3*22-1) = 1.732
For x2 = 1.732, x3 = x2 - f(x2)/f'(x2) = 1.732 - (5.829-1.732-1)/(3*1.7322-1) = 1.702.
Therefore, after three iterations of successive approximations, the approximate solution to the given equation is when x is about 1.702.
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-10[tex]-10\sqrt{x} 11-11\sqrt{x} 11\\[/tex]
The radical would to become -10 -21√x11.
What are like radicals?We define the term like radicals as the kind of radicals that have the same kind of values inside the radical sign. This implies that they have similar values in the square root sign. When this is the case, we can be able to handle the radical as an algebraic expression and then simplify it accordingly.
In this case, we would have that;
-10 -10√x11 - 11√x11
-10 -21√x11
This is now the simplified form of the expression that has been shown here.
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For 30 points (messed up on the last question)
Answer:
4
Step-by-step explanation:
Take any point other than (0,0) that is on the line and put it in the form 7/x and that will give you your constant of proportionality.
For example the point graphed is (1,4) 1 is the x value and 4 is the y value.
4/1 = 4
Answer: 4
Step-by-step explanation:
The constant of proportionality is the slope of a line that goes through the origin.
The slope/constant of proportionality is how much the Y increases every time the X increases by 1. Since your graph has the point (1, 4) labeled, the Y goes up 4 units for every 1 unit the X increases by.
Triangle Inequalities
The inequality that represents the third side of the given triangle is 3 < x <19.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, The side length of the triangle are 8, 11, and x.
From the General property of the triangle
The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is more than the length of the 1/3 side. In the same way, the difference between the various 2 sides of a triangle is a great deal much less than the length of the 3rd side.
Since the sum of two sides should be greater than the third
x < 8 + 11
=> x < 19
Since the difference between the two sides of a triangle is less than the length of the third side.
=> x > 11 - 8
=> x > 3
therefore, The inequality that represents the third side of the given triangle is 3 < x <19.
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please help ∠a is opposite
∠a is opposite to BC. Option D is correct.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The given triangle is ABC
In the given triangle AB, BC and AC are the edges or sides.
A, B and C are the vertices of triangles.
∠a, ∠b and ∠c are the angles.
In the given triangle we need to find what is opposite to the ∠a
∠a is opposite to the BC
Hence, ∠a is opposite to BC. Option D is correct.
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Given the points A (1, -0.5) and B (-9, 7), find the coordinates of the point P on the directed line segment that partitions in the ratio 1:4 Write your answer as an ordered pair (a, b).
The coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 : 4 is the ordered pair (-1, 1).
How to determine the coordinates of point P?In this exercise, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 to 4.
Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(1(-9) + 4(1))/(1 + 4)], [(1(7) + 4(-0.5))/(1 + 4)]
P(x, y) = [(-9 + 4)/(5)], [(7 - 2)/5]
P(x, y) = [-5/5], [(5)/(5)]
P(x, y) = [-1, 1]
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the point p(2 -1) lies on the curve y=1/(1-x)
Yes, the point (2,-1) lies on the curve y=1/(1-x) as when x=2, y=1/(1-2)=1/(-1)=-1, which is equal to -1.
y=1/(1-x)
y=1/(1-2)
y=1/(-1)
y=-1
Yes, the point (2,-1) lies on the curve y=1/(1-x). To prove this, we can substitute the x-coordinate of the point (2) into the equation. When x=2, the equation becomes y=1/(1-2). Simplifying this equation, we get y=1/(-1) which is equal to -1. Thus, y=-1, which is the same as the y-coordinate of the point (-1). This means that the point (2,-1) does indeed lie on the curve y=1/(1-x). This can be further verified by plotting the point (2,-1) on a graph and seeing that it is indeed located on the curve y=1/(1-x).
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Work out the area of a square with base,
b
= 13cm.
The diagram is not drawn to scale.
given base of square =13cm
all sides of squares is equal so
area of square is a^2 =13cm*13cm =169cm^2
Answer:
[tex] 196 \: {cm}^{2} [/tex]
Explanation:
As the area of a square is
[tex]l {}^{2} [/tex]
Where l is the length. As we know that all rhe sides of a square are equal in length therefore, each side of the square has a length of 13 cm.
Now,
[tex] {l}^{2} [/tex]
[tex] {13}^{2} [/tex]
Which is equal to
[tex]169 \: cm {}^{2} [/tex]
In ΔKLM, the measure of ∠M=90°, LK = 73, ML = 55, and KM = 48. What is the value of the sine of ∠L to the nearest hundredth?
Answer is : Cos L = 55/73.
