Answers
The area of the preimage is 400units²
What is dilation?Dilation is a transformation, which is used to resize a given object. We can use dilation to either make the objects larger or smaller.
A scale factor shows the relationship between the old shape and new shape.
The scale factor is expressed as ;
scale factor = dimension of the new length / dimension of old length
scale factor = 3/2 = 1.5
old length = x
therefore 1.5 = 30/x
1.5x = 30
divide both sides by 1.5
x = 30/1.5 = 20units
therefore the area of the preimage = l²
= 20²
= 400units²
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Related Questions
Do you pay less at Payless? Mary Ann and Abigail were shopping for prom shoes and wondered
how the prices at Payless compared to the prices
at Famous Footwear. At each store, they randomly
selected 30 pairs of shoes and recorded the price of
each pair. The table shows summary statistics for
the two samples of shoes. 28
Store
Mean
SD
Famous Footwear
$45. 66
$16. 54
Payless
$21. 39 $7. 47
Do these data provide convincing evidence at the
0. 05 significance level that shoes cost less
, on
average, at Payless than at Famous Footwear?
a =
Answers
To test whether shoes cost less on average at Payless than at Famous Footwear, we can conduct a two-sample t-test for the difference in means.
The null hypothesis is that there is no difference in the mean prices between the two stores, and the alternative hypothesis is that the mean price at Payless is less than the mean price at Famous Footwear.
We can calculate the t-statistic using the formula:
t = [tex](x1 - x2 - 0) / sqrt(s1^2/n1 + s2^2/n2)[/tex]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Substituting the values given in the table, we get:
t =[tex](21.39 - 45.66 - 0) / sqrt((7.47^2/30) + (16.54^2/30))[/tex] = -10.78
The degrees of freedom for this test is (30-1) + (30-1) = 58.
Using a t-table or calculator, we find the p-value to be very small, much less than 0.05.
Therefore, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 significance level that shoes cost less on average at Payless than at Famous Footwear.
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Dilate the figure by the scale factor. Then enter
the new coordinates.
(-1. 4)
A
K = 3
SB
(3,2)
1962,-2)
A’ ([?], []).
B'(]], [])
C), D
Answers
Dilating the figure by a scale factor of 3, the new coordinates are:
A' (-3, 12)
B' (9, 6)
C' (5886, -6)
D (unknown)
To dilate a figure by a scale factor, we need to multiply the coordinates of each point by the scale factor. Given the scale factor K = 3, we can dilate the figure using the formula:
New x-coordinate = K * original x-coordinate
New y-coordinate = K * original y-coordinate
Let's apply this to the given coordinates:
(-1, 4)
New x-coordinate = 3 * (-1) = -3
New y-coordinate = 3 * 4 = 12
A' (-3, 12)
(3, 2)
New x-coordinate = 3 * 3 = 9
New y-coordinate = 3 * 2 = 6
B' (9, 6)
(1962, -2)
New x-coordinate = 3 * 1962 = 5886
New y-coordinate = 3 * (-2) = -6
C' (5886, -6)
Dilating the figure by a scale factor of 3, the new coordinates are:
A' (-3, 12)
B' (9, 6)
C' (5886, -6)
D (unknown)
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Define a useful quantity for our expectation about the amount of a time an
in-control process will remain ostensibly in-control, the average run length (ARL), to be the number of samples that will be observed, on average, before a point falls outside control limits. If p is the probability that any given point falls outside the control limits, then:
ARL = 1/p
(Estimating the true ARL may be useful for detecting an out-of-control process, but not
necessarily doing so quickly.) A process is Gaussian with mean 8 and standard deviation 2. The process is monitored by taking samples of size 4 at regular intervals. The process is declared to be out of control if a point plots outside the 3σ control limits on an X-chart. If the process mean shifts to 9, what is the average number of samples that will be drawn before the shift is detected on an X-chart?
Answers
Answer:
First, we need to calculate the control limits for the X-chart. Since the sample size is 4, the standard deviation of the sample mean is:
σ/√n = 2/√4 = 1
The 3σ control limits for the X-chart are:
Upper Control Limit (UCL) = 8 + 3(1) = 11
Lower Control Limit (LCL) = 8 - 3(1) = 5
Next, we need to find the probability that a point falls outside the control limits when the process mean shifts to 9. This can be calculated using the Gaussian distribution:
P(X < 5 or X > 11) = P(Z < (5-9)/2) + P(Z > (11-9)/2) = 0.00135 + 0.00135 = 0.0027
where Z is the standard normal distribution.
Therefore, the average run length (ARL) is:
ARL = 1/p = 1/0.0027 = 370.37
So on average, it will take 370.37 samples before the process mean shift is detected on an X-chart.
Bilquis is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 29 meters from the building. The angle of elevation from her eyes to the roof (point A) is 17°, and the angle of elevation from her eyes to the top of the antenna (point B) is 31º. If her eyes are 1. 51 meters from the ground, find the heigh[of the antenna (the distance from point A to point B). Round your answer to the nearest meter if necessary.
Answers
The height of the antenna is approximately 17 meters.
To solve for the height of the antenna, we need to use trigonometry. Let's call the height of the antenna "h".
First, we need to find the distance from point A to point B. We can use the angle of elevation from her eyes to the roof (17°) and the horizontal distance from the building (29m) to find the height of the building.
tan(17°) = height of building / 29m
height of building = 29m * tan(17°)
height of building = 8.20m
Now we can use the height of the building and the angle of elevation from her eyes to the top of the antenna (31°) to find the distance from point A to point B.
tan(31°) = h / 29m + 8.20m
h = (29m + 8.20m) * tan(31°)
h = 15.51m
Finally, we need to add the height of Bilquis' eyes to the height of the antenna to find the total height.
total height = h + 1.51m
total height = 17.02m
Therefore, the height of the antenna is approximately 17 meters.
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Can someone please help me ASAP? It’s due tomorrow.
Answers
Answer: m*n
Step-by-step explanation:
Already Know The Vertex but need help on the opens and axis of symmetry
Answers
Answer: x = -3
Step-by-step explanation:
Hope this helps.
HELPPPPP FAST PLEASEEEE
Answers
Answer:
AEC is similar to BDC in terms of the type of triangle
That's all I can really say
I hope this helps :)
The circle at each end of the court that surrounds the free throw line is the same size as the jump ball circle. (In other words, they have the same radius. ) What is the area of the rectangle (called the lane) whose length is 19 feet and whose width is the free throw line?
Answers
So the area of the rectangle (or lane) whose length is 19 feet and whose width is the free throw line, together with the two circles at each end of the court that surround the free throw line, is approximately 450.39 square feet.
What is the length of the rectangle and how many free throw line square feet?Since the circle at each end of the court that surrounds the free throw line is the same size as the jump ball circle, they both have the same radius. Let's call this radius "r".
The diameter of the circle is equal to the width of the lane, which is the same as the width of the free throw line. Therefore, the diameter of the circle is also 12 feet (the width of the free throw line is always 12 feet).
We know that the area of a circle is given by the formula A = πr^2, so the area of each circle is πr^2.
The rectangle (or lane) has a length of 19 feet and a width of 12 feet. Therefore, its area is simply the product of its length and width, which is:
A = 19 feet * 12 feet
A = 228 square feet
Since there are two circles, the total area of the circles is 2πr^2.
We know that the diameter of the circle is equal to the width of the lane, which is 12 feet. Therefore, the radius is half of the diameter, or:
r = 12 feet / 2
r = 6 feet
Now we can calculate the area of the circles:
A = 2πr^2
A = 2π(6 feet)^2
A = 72π square feet
Therefore, the total area of the rectangle and circles (or lane and circles) is:
A_total = A_rectangle + A_circles
A_total = 228 square feet + 72π square feet
A_total ≈ 450.39 square feet
So the area of the rectangle (or lane) whose length is 19 feet and whose width is the free throw line, together with the two circles at each end of the court that surround the free throw line, is approximately 450.39 square feet.
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Determine whether the series 2 + cos(n) n 71.1 is convergent or divergent using the Comparison Test. ow
Answers
To use the Comparison Test, we need to find a series that we know is either always greater than or always less than our given series
. Since cosine values oscillate between -1 and 1, we know that 2 + cos(n) is always greater than or equal to 1. Therefore, we can compare our given series to the series 1/n, which we know is a p-series with p = 1 and is divergent.
Using the Comparison Test, we can say that since 1/n is divergent and 1/n ≤ 2 + cos(n) for all n ≥ 71.1, then the series 2 + cos(n) n 71.1 must also be divergent. Therefore, the series 2 + cos(n) n 71.1 is divergent.
Hi! To determine whether the series Σ(2 + cos(n)), where n ranges from 1 to infinity, is convergent or divergent using the Comparison Test, we need to compare it with another series whose convergence behavior is known.
Consider the series Σ(2), which is a constant series where every term is 2. This series diverges, as its partial sums keep increasing without bound. Since cos(n) is bounded between -1 and 1, we know that for every n, 1 ≤ (2 + cos(n)) ≤ 3.
Now, using the Comparison Test, we can compare Σ(2 + cos(n)) with Σ(2). Since Σ(2) is divergent and 2 + cos(n) is always greater than or equal to 2, we can conclude that the series Σ(2 + cos(n)) is also divergent.
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A ramp at a dog park is made of three sections. The incline and decline pieces are the same length, 13√37 inches. The center is 10√41 inches long. What is the total length of the ramp? Give your answer as a radical expression.
Answers
The total length of the ramp is 222.18 inches
How to find the total length?Let's denote the length of the incline and decline pieces by x, and use the given information to form an equation in terms of x:
Length of incline + length of decline = 2(13√37) inches
= 26√37 inches
The total length of the ramp is the sum of the lengths of all three sections:
Total length = Length of incline + Length of center + Length of decline
Total length = 26√37 inches + 10√41 inches
Total length = 222.18 inches
Therefore, the total length of the ramp is 222.18 inches
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V=-x2+14x -24 I need to find the range domain and graph?
Answers
For domain, that’s going to be the distance on your x-axis, which in this case should be something like:
Domain : (-infinity sign, infinity sign)
That’s because the line is continuous, therefore eventually running into all numbers on the x-axis.
Range: (-infinity, 25]
That’s because the highest number the line touches on the y-axis is 25, and continuously goes downwards.
Make sure to put the parenthesis on the infinity signs, and a bracket around 25!
Richard lends to Martin P154,600. 00 under the condition that simple interest will be charged at 8. 5% per annum and the debt is payable after months. How much will Martin have to pay Richard after 36 months ?
Answers
We know that after 36 months, Martin will have to pay Richard P193,969.
Hi! Based on your question, Richard lends P154,600 to Martin at an 8.5% simple interest rate per annum, and the debt is payable after 36 months. To find out how much Martin will have to pay Richard after 36 months, we'll first calculate the interest.
Simple Interest = Principal × Rate × Time
Interest = P154,600 × 8.5% × (36 months / 12 months per year)
Interest = P154,600 × 0.085 × 3
Interest = P39,369
Now, add the interest to the principal to find the total amount Martin needs to pay Richard:
Total Amount = Principal + Interest
Total Amount = P154,600 + P39,369
Total Amount = P193,969
After 36 months, Martin will have to pay Richard P193,969.
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< Question 7 Σ Next Use partial fraction decomposition to evaluate the integral: (198r2 + 9r – 50 dr 99r2 - 26r - 8
Answers
The value of integral of (198r² + 9r – 50 dr is (16/27)ln|11r + 2| - (2/3)ln|9r - 4| + C
Now, we can write the integrand as a sum of two fractions:
(198r² + 9r - 50) / (11r + 2)(9r - 4) = A/(11r + 2) + B/(9r - 4)
To find A and B, we need to solve for them using the method of equating coefficients:
198r² + 9r - 50 = A(9r - 4) + B(11r + 2)
Setting r = 4/9 and r = -2/11, we get two equations:
198(4/9)² + 9(4/9) - 50 = A(9(4/9) - 4) + B(11(4/9) + 2)
198(-2/11)² + 9(-2/11) - 50 = A(9(-2/11) - 4) + B(11(-2/11) + 2)
Solving these equations gives A = 16/27 and B = -2/3.
So, the integral can be written as:
∫(198r² + 9r - 50) / (11r + 2)(9r - 4) dr = ∫16/27(11r + 2)^-1 dr - ∫2/3(9r - 4)^-1 dr
Integrating each term gives:
(16/27)ln|11r + 2| - (2/3)ln|9r - 4| + C
where C is the constant of integration.
In summary, using partial fraction decomposition, we can express the given integral as a sum of two simpler integrals, which can be evaluated using the natural logarithm function.
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The number of coyotes found in certain state counties is decreasing at a rate of 4. 5% per year. A wildlife biologist recently counted 100 coyotes in one tri-county area. The biologist uses a function to model the population over time and then uses this model to predict the coyote population. Which function model did the biologist correctly use to predict when the population would be fewer than 50 in this tri-county area?
Answers
The biologist predicts that the population would be fewer than 50 in approximately 30 years from the initial count.
The biologist likely used the exponential decay function to model the coyote population over time. This function takes the form:
P(t) = P0 * (1 - r)^t
Where:
P(t) is the population at time t,
P0 is the initial population (100 coyotes),
r is the rate of decrease (0.045 or 4.5%),
t is the time in years.
To predict when the population would be fewer than 50, the biologist would solve the equation:
50 = 100 * (1 - 0.045)^t
t = 30
This equation can be used to find the value of t, which represents the number of years it takes for the population to decrease to fewer than 50 coyotes in the tri-county area, which is 30 years.
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Pythagorean theorem help quickly please
Answers
Answer:
In an isosceles right triangle, the length of the diagonal is √2 times the length of a leg.
c = 6√2 in. = 8.5 in.
A tray of lasagna comes out of the oven at 200°F and is placed on a table
where the surrounding room temperature is 70°F. The temperature T (in °F) of
the lasagna is given by the function (0) -e(486753-1) +70, 0 s t, where tis time
(in hours) after taking the lasagna out of the oven. What is the rate of change
in the temperature of the lasagna exactly 2 hours after taking it out of the
oven?
Answers
Rate of change in the temperature of lasagna given by function T(t) = 70 + (200 - 70) × [tex]e^{(-0.0001t)}[/tex] exactly 2 hours after taking it out of oven is -0.013 °F/hour.
Surrounding room temperature is equal to 70°F
Temperature at which lasagna comes out of the oven = 200°F
The temperature T (in °F) of the lasagna at time t (in hours) after taking it out of the oven is equal to,
T(t) = 70 + (200 - 70) × [tex]e^{(-0.0001t)}[/tex]
To find the rate of change in the temperature of the lasagna exactly 2 hours after taking it out of the oven,
Find the derivative of the temperature function with respect to time t.
T'(t) = -0.013[tex]e^{(-0.0001t)}[/tex]
Substituting t = 2 into this expression gives:
T'(2) = -0.013[tex]e^{(-0.0001\times 2)}[/tex]
= -0.013[tex]e^{-0.0002}[/tex]
= -0.013 × 0.99980
= -0.0129974
= -0.013
Therefore, the rate of change in the temperature of the lasagna exactly 2 hours after taking it out of the oven is approximately -0.013 °F/hour.
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The given question is incomplete, I answer the question in general according to my knowledge:
A tray of lasagna comes out of the oven at 200°F and is placed on a table where the surrounding room temperature is 70°F. The temperature T (in °F) of the lasagna is given by the function T(t) = 70 + (200 - 70) × [tex]e^{(-0.0001t)}[/tex] where t is time(in hours) after taking the lasagna out of the oven. What is the rate of change in the temperature of the lasagna exactly 2 hours after taking it out of the oven?
Gianna keeps track of the number of people inside a music hall to attend a concert by looking at the number of scanned tickets. She plotted the data on the graph below, where x = 0 x=0 represents the time at 6 p.m., then drew a line of best fit. What does the point ( 1 , 92 ) (1,92) represent?
Answers
Note that the point ( 1 , 92 ) (1,92) represents the estimated number of people in the hall at 7pm.
How is this so?This is based on the given graph.
Note tha the horizontal axis = x = 0
which corresponds to 6pm
the vertical is the number of scanned tickets.
Also, the pont (1, 92) is the line of best fit so that means that at 7pm which is a n hour after 6pm, there were about 92 persons still in the hall.
Hence we are correct to state that the point ( 1 , 92 ) (1,92) represents the estimated number of people in the hall at 7pm.
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Full Question:
See attached image/graph
Find the absolute maximum and absolute minimum values off on the given interval. f(x) = 3x^4 – 4x^3-12x^2 + 1, {-2, 3] absolute minimum value
absolute maximum value
Answers
The absolute maximum value of f(x) on the interval [-2,3] is 201 and occurs at x = -2, and the absolute minimum value of f(x) on the interval [-2,3] is -79 and occurs at x = 2.
To find the absolute maximum and absolute minimum values of f(x) on the interval [-2,3], we need to first find the critical points of the function and evaluate the function at these points as well as at the endpoints of the interval.
To find the critical points, we need to find where the derivative of the function equals zero or does not exist. Taking the derivative of f(x), we get:
f'(x) = 12x^3 - 12x^2 - 24x
Setting this equal to zero and factoring out 12x, we get:
12x(x^2 - x - 2) = 0
Using the quadratic formula to solve for x^2 - x - 2 = 0, we get:
x = -1, 0, 2
These are our critical points.
Now we evaluate f(x) at the critical points and the endpoints of the interval:
f(-2) = 201
f(-1) = 6
f(0) = 1
f(2) = -79
f(3) = 16
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Determine the equation of the line that passes through the point ( 3,-1/2) and is perpendicular to the line y =-2x+3
Answers
The equation for the line that passes through the point ( 3,-1/2) and is perpendicular to the line y =-2x+3 is:
y = (1/2)*x - 2
How to find the equation of the line?Remember that two linear equations are perpendicular if the product between the slopes is -1, here we want a line perpendicular to:
y =-2x+3
Then if the slope of our line is a, we must have that:
a*-2 = -1
a = 1/2
Then our line is something like:
y = (1/2)x + b
Now we also want our line to pass through (3, -1/2), then:
-1/2 = (1/2)*3 + b
-1/2 = 3/2 + b
-1/2 - 3/2 = b
-2 = b
The linear equation is:
y = (1/2)*x - 2
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1. Direct or indirect characterization? "Nina was so annoyed at her little brother for bothering her. " Direct Indirect 2. Direct or indirect characterization? "Tim's room was a mountain of dirty clothes and used dishes that had been piled up for weeks. " Direct Indirect 3. An author can show indirect characterization through a character's thoughts, feelings, actions, and the setting of the story. Their effect on others. The rising action. Do all 3
Answers
An author can show indirect characterization through a character's thoughts, feelings, actions, and the setting of the story, as well as through their effect on others and their role in the rising action of the plot.
All of these elements can provide insights into a character's personality, motivations, and values, without the author explicitly stating them.
By carefully observing the character's interactions with others, their reactions to events, and the situations in which they find themselves, readers can draw conclusions about who the character is and what drives them.
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When the mortgage is completely paid off for Mark and Lynne’s house, it will be 3 times as old as it is now. If they have 12 years left on the mortgage, how old is the house right now?
Answers
The house is currently 6 years old.
It is mentioned that when the mortgage is completely paid off for Mark and Lynne's house, it will be 3 times as old as it is now. They have 12 years left on the mortgage.
Let's denote the current age of the house as x. When the mortgage is paid off, the house will be x + 12 years old (since they have 12 years left on the mortgage). At that point, the house will be 3 times its current age, so we can write the equation:
x + 12 = 3x
Now we can solve for x:
12 = 2x
x = 6
So, the house is currently 6 years old.
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Which linear equation represents a relation that is NOT a function? y = 3x +6 y = 9 −4y + 5x = 20 x = 7
Answers
Answer:
x = 7 is not a function--it is a vertical line.
The scatter plot shows the number of miles per gallon (MPG) for trucks with different weights. Select all the associations shown by the scatter plot.
positive association
negative association
linear association
nonlinear association
no association
Answers
The associations rhat are shown by the graph are
negative associationlinear associationHow does a graph show negative association linear associationA graph depicting a negative linear association appears as points on the chart are concomitantly placed around a straight line that confidently descends from left to right. In simpler terms, there is a notable inverse correlation between the x and y variables, which can be best comprehended with the help of an illustration.
For instance, if one were to consider a dataset representing the age of an automobile (x) and its fuel efficiency in miles per gallon (y), a graph displaying a rigorous negative linear association implies that with an increase in the age of the car, its energy proficiency has an inclination to decrease.
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Ross Times, the student newspaper of Ross College, printed a "What do you think?" column feature asking: "Do you think that the college is doing enough to provide student parking?" Anyone could mail in a response or use the paper's Web site to respond. In all, 126 answers were received.
This is an example of:
(a) a voluntary response sample.
(b) a multistage sample.
(c) a simple random sample.
(d) a convenience sample.
(e) the placebo effect
Answers
The answer is (d) a convenience sample.
This is because the sample is not randomly selected from the population of all students at Ross College. Instead, it relies on individuals who are willing and available to respond to the question through the methods provided by the newspaper.
Therefore, the sample is more likely to be composed of individuals who feel strongly about the issue of student parking or who have had particularly positive or negative experiences with it, rather than being representative of the entire population of Ross College students.
In conclusion, the Ross Times student newspaper's feature column asking for opinions on the provision of student parking at Ross College represents a convenience sample of responses, and may not be representative of the entire population of Ross College students.
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X varies jointly as y and z.
Write an equation that express each relationship. Then solve the equation for y.
Answers
An equation that express each relationship for the joint variation is X = kyz. Solving for y will give the equation y = X/(kz)
What is joint variationJoint variation is a mathematical concept that describes the relationship between two or more variables.
If X varies jointly as y and z, we can express this relationship mathematically using the formula:
X = k × y × z
X = kyz
where k is a constant of proportionality.
We can solve for y by dividing both sides by kz follows:
X/kz = kyz/kz
X/(kz) = y
Therefore, the equation that express each relationship for the joint variation is X = kyz. And the equation solved for y is y = X/(kz).
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please can someone help i really need help thank you
Answers
The equation of the function h(x) from the transformation is h(x) = f(x + 1)
Describing the transformation of f(x) to h(x).From the question, we have the following parameters that can be used in our computation:
The functions f(x), g(x) and h(x)
In the graph, we can see that
The graph of f(x) is the parent functionThe graph of h(x) is a shift of 1 unit leftHorizontal Shift = 1 unit left
This is represented as
h(x) = f(x + 1)
This means that the transformation of f(x) to h(x) is f(x) is shifted left 1 unit to h(x).
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In the number 217 361. 05 which digit is in the hundreds place?
Answers
Answer:3
Step-by-step explanation: We see that 217361.05 =217000+361.05 so our answer is 3
Which unique sequence of rigid motions maps quadrilateral abcd to quadrilateral efgh?
s
а
ib
4
d
ll2_3 4 5 6
e
f
h
g
a a reflection over the x-axis followed by a translation of (,y) → (, y - 4).
b. a reflection over the y-axis followed by a translation of (1,y) → (, y-6).
c a translation of (+,y) → (2, y - 3) followed by a reflection over the y-axis.
a translation of (cv) (1-6, y) followed by a reflection over the x-axis.
d.
Answers
The correct answer is option B, a reflection over the y-axis followed by a translation of (1,y) → (1, y-6).
To solve this problem, we need to find the sequence of rigid motions (i.e., transformations that preserve distance and angle) that maps quadrilateral ABCD to quadrilateral EFGH.
First, we need to identify the corresponding vertices of the two quadrilaterals. Let's assume that vertex A maps to vertex E, vertex B maps to vertex F, vertex C maps to vertex G, and vertex D maps to vertex H.
Now, we can apply different transformations to map each vertex of quadrilateral ABCD to the corresponding vertex of quadrilateral EFGH. We can try each option provided and check if it maps all the vertices correctly.
Option A involves a reflection over the x-axis, followed by a translation of (0,y) → (0, y - 4). This transformation does not map vertex A to vertex E correctly.
Option B involves a reflection over the y-axis, followed by a translation of (1,y) → (1, y - 6). This transformation maps vertex A to vertex E, vertex B to vertex F, vertex C to vertex G, and vertex D to vertex H, which is the correct mapping.
Option C involves a translation of (+,y) → (2, y - 3) followed by a reflection over the y-axis. This transformation does not map vertex A to vertex E correctly.
Option D involves a translation of (1-6, y) followed by a reflection over the x-axis. This transformation does not map vertex A to vertex E correctly.
Therefore, the unique sequence of rigid motions that maps quadrilateral ABCD to quadrilateral EFGH is a reflection over the y-axis followed by a translation of (1,y) → (1, y-6), which is option B.
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Explain how the arc BX, central angle BCX, and inscribed BNX are connected. what are the relationships between them?
Answers
Answer:
[tex]\overset{\frown}{BX}=\angle BCX=2\angle BNX[/tex]
Step-by-step explanation:
A chord is a straight line joining two points on the circle.
Therefore, the chords in the given diagram are BN and XN.
An inscribed angle is the angle formed (vertex) when two chords meet at one point on a circle.
Therefore, the inscribed angle in the given diagram is BNX.
An intercepted arc is the arc that is between the endpoints of the chords that form the inscribed angle.
Therefore, the intercepted arc in the given diagram is BX.
The radius is a straight line joining the center to a point on the circle.
Therefore, the radii in the given diagram are CB and CX.
The central angle of a circle is the angle formed at its center by two radii.
Therefore, the central angle in the given diagram is BCX.
[tex]\hrulefill[/tex]
The measure of the central angle of a circle is equal to the measure of the corresponding intercepted arc. Therefore:
[tex]\angle BCX=\overset{\frown}{BX}[/tex]
According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore:
[tex]\angle BNX=\dfrac{1}{2}\overset{\frown}{BX}[/tex]
So the relationship between the arc BX, the central angle BCX and the inscribed angle BNX is that both the arc and central angle are equal to twice the inscribed angle:
[tex]\overset{\frown}{BX}=\angle BCX=2\angle BNX[/tex]
Find the sum of all the integers between 100 and 400 that are multiples of 6.
Answers
Answer:
The sum of all numbers divisible by 6 between 100 and 400 is 12450.
Step-by-step explanation:
I think this is correct.
If it isn't, I'm sorry.
