Answer:
The best example of a defined benefits plan is: "a set amount an employee will receive at retirement".
In a defined benefits plan, the employer promises to pay employees a specific, predetermined amount of money upon retirement. This amount is typically based on factors such as the employee's salary and years of service. The employer is responsible for contributing to and managing the retirement fund, and the employee receives a guaranteed amount of money upon retirement, regardless of how the fund performs.
The other options listed are not examples of defined benefits plans. The wages and benefits an employee receives at a job are part of their compensation package and may include retirement benefits, but they do not guarantee a specific amount of money at retirement. The amount of pay an employee receives each hour is their hourly wage and is not related to retirement benefits. The money an employer puts into a retirement fund for each employee may be part of a defined benefits plan, but it is not a complete plan in and of itself.
fP=\ (x, y) : y = 3x-1, x ≤ 4, xe N}, find P * P State the elements of the following relations: (b) y = 4x (d) x + y >= 20 (a)y = x (c) x + y
The elements of the given relations in the set P = {(x, y) : y = 3x - 1, x ≤ 4, x ∈ N} are: (a) y = x: {(1, 1), (2, 2), (3, 3), (4, 4)}
(b) y = 4x: {(1, 4), (2, 8), (3, 12), (4, 16)}
(c) x + y: {(1, 3), (2, 7), (3, 11), (4, 15)}
(d) x + y ≥ 20: {(3, 8), (4, 11)}
To find the elements of the given relations in the set P = {(x, y) : y = 3x - 1, x ≤ 4, x ∈ N}, we substitute the x-values from the set P into the corresponding equations.
(a) y = x:
In this relation, the y-values will be the same as the x-values.
Substituting the x-values from the set P into the equation, we get:
(1, 2), (2, 5), (3, 8), (4, 11)
So, the elements of the relation y = x in the set P are:
{(1, 1), (2, 2), (3, 3), (4, 4)}
(b) y = 4x:
Substituting the x-values from the set P into the equation, we get:
(1, 4), (2, 8), (3, 12), (4, 16)
So, the elements of the relation y = 4x in the set P are:
{(1, 4), (2, 8), (3, 12), (4, 16)}
(c) x + y:
Substituting the x-values from the set P into the equation, we get:
(1, 2), (2, 5), (3, 8), (4, 11)
So, the elements of the relation x + y in the set P are:
{(1, 3), (2, 7), (3, 11), (4, 15)}
(d) x + y ≥ 20:
Substituting the x-values from the set P into the inequality, we get:
(1, 2), (2, 5), (3, 8), (4, 11)
So, the elements of the relation x + y ≥ 20 in the set P are:
{(3, 8), (4, 11)}
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a box contains two white socks, two blue socks, and two red socks. two socks are drawn at random. find the probability they are a match (the same color).
The probability of drawing a matching pair of socks is 1/5 or 0.2.
Calculating Probability:The basic principle of probability, states that the probability of an event happening is the number of ways the event can occur divided by the total number of possible outcomes.
In this problem, we first calculated the number of ways to draw a matching pair of socks for each of the three possible colors.
We then added these probabilities together to get the total probability of drawing a matching pair of socks.
Here we have
A box contains two white socks, two blue socks, and two red socks.
To find the probability of drawing a matching pair of socks, consider the different cases of matching pairs of socks that can be drawn.
Case 1: Matching white socks
The probability of drawing one white sock = 2/6
After drawing one white sock,
Remains 5 socks and of which 1 is white
The probability of drawing 2nd white sock = 1/5
Hence, probability of selecting 2 white socks = (2/6) × (1/5) = 1/15
Similarly, we can calculate probabilities for Red and Blue socks
Case 2: Matching blue socks
The probability of drawing two blue socks is (2/6) × (1/5) = 1/15
Case 3: Matching red socks
The probability of drawing two red socks is (2/6) × (1/5) = 1/15.
Therefore, the total probability of drawing a matching pair of socks is the sum of the probabilities of each of these cases:
P(matching pair) = P(white) + P(blue) + P(red)
= 1/15 + 1/15 + 1/15 = 3/15 = 1/5
Therefore,
The probability of drawing a matching pair of socks is 1/5 or 0.2.
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On what interval is the function positive?
f(x) = 2(6)^(x+1) -3
Enter your answer, in interval notation. Round any necessary values to the nearest tenth.
The function f(x) is positive on the interval (-0.744, infinity).
In interval notation: (−0.744, ∞).
What is a function?A function is a relationship between inputs in which each input corresponds to exactly one output.
When [tex]f(x) = 2(6)^{X+1} -3[/tex] is greater than zero, it is positive.
[tex]2(6)^{(x+1) } - 3 > 02(6)^{(x+1)} > 3(6)^{ (x+1) } > 3/2[/tex]
Now taking logs on both sides gives
[tex]log(6)^{ (x+1) } > log3/2[/tex]
(x+1) * log6 > log3/2
(x+1) > [tex]\frac{log3/2}{log6}[/tex]
(x+1) > [tex]\frac{0.17609}{ 0.77815}[/tex]
(x +1) > 0.2265
x > 0.2265 - 1
x > -0.7735
Thus, the function f(x) is positive on the interval (-0.744, infinity).
In interval notation: (−0.744, ∞).
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solve this and I will give u brainlst.
Answer:
20
Step-by-step explanation:
1
At the beginning of the passage, what is Makayla getting ready to do?
A
open Christmas presents
(в
go trick-or-treating on Halloween
go on an Easter egg hunt
eat Thanksgiving dinner
2 Throughout the story, Makayla remembers information Mrs. Narula taught in
class. What does this information describe?
a) The passage is a piece of written text that provides information about Makayla's experience during an Easter egg hunt. (option c)
(b) It also highlights how knowledge gained in the classroom can be applied to everyday life.
At the beginning of the passage, Makayla is getting ready to go on an Easter egg hunt. This is evident from the line "Makayla was getting ready for the Easter egg hunt at the park." Easter egg hunts are a popular tradition in many parts of the world, where children search for hidden eggs that are often filled with candy or small toys.
Hence the correct option is (c).
Throughout the story, Makayla remembers information that Mrs. Narula taught in class. Mrs. Narula is Makayla's science teacher, and the information she taught in class is about the process of photosynthesis. Photosynthesis is the process by which plants convert sunlight, water, and carbon dioxide into oxygen and sugar.
Makayla remembers this information as she observes the trees and plants in the park during the Easter egg hunt. She notes that the plants are producing oxygen through photosynthesis and that this process is essential for the survival of all living beings.
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A chemist wishes to make a 10% acid solution. she has a 4% acid solution and a solution that is 28% acid. how many liters of each should she use if she needs 5 liters of the 10% solution?
The chemist should use 3.75 liters of the 4% acid solution and 1.25 liters of the 28% acid solution to make 5 liters of a 10% acid solution.
Let's denote the volume of the 4% acid solution as x and the volume of the 28% acid solution as y, both in liters.
To make a 10% acid solution, we need to mix the two solutions in such a way that the resulting mixture has a total volume of 5 liters, and the concentration of acid in the mixture is 10%.
Since we want 5 liters of the final mixture, we can write the following equation based on the conservation of volume:
x + y = 5
The total amount of acid in the final mixture should be 10% of the total volume of the mixture, so we can write the following equation:
0.04x + 0.28y = 0.1(5)
On simplifying:
0.04x + 0.28y = 0.5
From the first equation:
y = 5 - x
Substituting into second equation:
0.04x + 0.28(5 - x) = 0.5
Simplifying and solving for x:
0.04x + 1.4 - 0.28x = 0.5
-0.24x = -0.9
x = 3.75
Using first equation,
x + y = 5
3.75 + y = 5
y = 1.25
Therefore, she needs to use 3.75 liters of the 4% acid solution and 1.25 liters of the 28% acid solution to make 5 liters of a 10% acid solution.
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What is the value of -1/6 + 2/3(9- 3/4) - 1/2
The value of the given expression is 31/6.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
We can simplify the given expression using the order of operations (PEMDAS):
First, we evaluate the expression inside the parentheses:
9 - 3/4 = 35/4
Next, we simplify the multiplication by 2/3:
2/3 * 35/4 = 35/6
Now we substitute the above values in the expression and simplify:
-1/6 + 35/6 - 1/2 = (-1 + 35 - 3)/6
= 31/6
Therefore, the value of the given expression is 31/6.
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a randomly selected sample of 100 students was drawn from a population with an average grade point average (gpa) of 3.2 and a standard deviation of 0.2. the standard deviation of the sampling distribution of the sample mean is
The standard deviation of the sampling distribution of the sample mean is 0.02.
The standard deviation of the sampling distribution of the sample mean can be calculated using the formula:
σ/√n
Where σ is the population standard deviation and n is the sample size.
In this case, the population standard deviation (σ) is 0.2 and the sample size (n) is 100. Substituting these values in the formula gives:
0.2/√100
Simplifying, we get:
0.2/10 = 0.02
This means that if we were to take multiple random samples of size 100 from the population, the mean of each sample would vary around the population mean of 3.2, with a standard deviation of 0.02.
This is because the standard deviation of the sampling distribution represents the amount of variation in sample means around the population mean.
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Together, Xavier Yolando, and Zachary have $4. 44 if each person has the amount, how much money does each person have what us the correct answer
The amount that each of Xavier Yolando, and Zachary has is $1.48
How much does each person have?We know that what we need to do is to convert the problem to an equation. The first step is always to be able to form the equation from the sentence that we have been given and we must have to look out for the key words in the problem.
We are told that each of them; Xavier Yolando, and Zachary have the same amount thus;
3x = 4.44
x = 4.44/3
x = $1.48
Thus they would all have a sum of $1.48
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3) Which experience uses social and professional connections to learn more about jobs from others?
Question 3 options:
informational interview
job shadowing
internship
networking
Networking is the experience that uses social and professional connections to learn more about jobs from others. So, correct option is D.
It involves building and maintaining relationships with individuals who can offer information, advice, or support related to one's career goals. Networking can be done in various settings such as professional organizations, conferences, social events, and online platforms.
It can also involve exchanging information, sharing experiences, and providing referrals or recommendations. By networking, individuals can learn about job opportunities, industry trends, and insights into different career paths.
Additionally, networking can lead to mentorship and collaboration, which can help individuals develop their skills and expand their professional network further. Networking is an essential aspect of career development, as it can help individuals gain exposure and access to new opportunities that can lead to career advancement.
So, correct option is D.
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Solve 12x<96 . Graph the solution.
Answer:
x<8
Step-by-step explanation:
...................
0.4x+2.9=1.5 solve for x
Answer:
x= -3.5
Step-by-step explanation:
0.4x+2.9= 1.5
-2.9. -2.9
(0.4/0.4)x= -1.4/0.4
x= -3.5
By solving the given equation 0.4x + 2.9 = 1.5, the value of x is -3.5
In the given equation, we have one variable of 'x' with a constant value of 0.4 and two non-variable values of 2.9 and 1.5.
To solve the given equation, we have to transfer the non-variable values to either the L.H.S (Left Hand Side) or R.H.S (Right Hand Side) of the equation. After transferring the non-variable values, we will solve it by dividing it by the constant value of the given variable as shown below:
0.4x + 2.9 = 1.5
0.4x = 1.5 - 2.9
0.4x = -1.4
x = [tex]\frac{-1.4}{0.4}[/tex]
x = -3.5
By solving the above equation, we can conclude that the value of x in equation 0.4x + 2.9 = 1.5 is -3.5
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How many more bytes of information are in a gigabyte than a megabyte?
Answer:
999,000,000 bytes
Step-by-step explanation:
if you subtract the total of the gigabytes from the total of the megabytes you get this answer.
Ken ran from one corner of a field to the opposite corner, a distance of 85 meters. Then he ran along its length, a distance of 77 meters. How wide is the field?
Answer:
24 meters
Step-by-step explanation:
We can use Pythagoras' theorem to solve this problem. Let's call the width of the field "w". We know that Ken ran from one corner of the field to the opposite corner, a distance of 85 meters. This distance is equal to the hypotenuse of a right triangle whose legs are the length and width of the field. We also know that Ken ran along its length, a distance of 77 meters. This length is one of the legs of the right triangle.
Using Pythagoras' theorem, we can write:
w^2 + 77^2 = 85^2
Simplifying this equation gives:
w^2 = 85^2 - 77^2
w^2 = 576
Taking the square root of both sides gives:
w = sqrt(576)
w = 24
Therefore, the width of the field is 24 meters 1.
I hope this helps!
Pls Help with this question.
Step-by-step explanation:
16x²-1 = (4x-1)(4x+1)
4x²-9 = (2x+3)(2x-3)
16x²-4 = 4(2x+1)(2x-1)
4x²-1 = (2x+1)(2x-1)
16x²+1 = (4x+i)(4x-i)
I went hiking over the weekend. I hiked 1 3/4 miles when I came to a fork
in the trail. I went to the right. I hiked another 2 1/2 miles until I reached
the overlook. How far did I hike to get there?
O 4 1/4
O 4 1/2
O 4 1/3
O 4 1/5
Over the weekend, I went hiking. I had hiked 1 3/4 miles when I came to a trail fork. I turned to the right. I continued hiking for another 2 1/2 km till I arrived at the lookout. I hiked for A) 4 1/4 miles to get there.
In this question, we have been given that the person first hikes for 1 3/4 miles and then for 2 1/2 miles, so we will first convert them into mixed fractions and we will add the fractions.
Total miles hiked to get there = 1 3/4 miles + 2 1/2 miles
= 7 / 4 miles + 5/2 miles
= (7 + 10) / 2 miles
= 17 / 2 miles
= 4 1/4 miles
If the denominators of two fractions are the same (such fractions are said to be similar fractions), they can be added directly. If the denominators are different (such fractions are known as unlike fractions), we must change the denominators and then add the fractions.
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Please help!! I’m so behind
To find the area of a specific parallelogram, we need to know the length of its base and the height.
What is the area of the parallelogram?To find the area of a parallelogram, we multiply the base of the parallelogram by its height, where the height is the perpendicular distance between the base and its opposite side. So, the formula for the area of a parallelogram is:
Area = base x height
where the base and height are both expressed in the same units.
We know that the area of the parallelogram can be given as bh or absinα
Thus we have for each of the parallelograms shown;
1) 6 * 4 = 24 ft^2
2) 9 * 5 = 45 yd^2
3) 8 * 10 sin 45 = 56.6 cm^2
4) 5 * 11 sin 60 = 47.6 m^2
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surface area of the triangular prism 5ft 5ft 4ft 6ft 18ft
The surface area of the triangular prism is 312 ft².
How to calculate the surface area of a prism?In order to calculate the surface area of a prism, we twice the perimeter of base of the prism to twice the area of the base of the prism
To calculate the surface area of the triangular prism in the question, we use the formula below
Formula:
S.A = bh+H(a+b+c).................. Equation 1Where:
S.A = Surface area of the triangular prismb = Base of the triangleh = Height of the trianglea,c = The other two sides of the triangleFrom the question,
Given:
b = 6 fth = 4 fta = c = 5 ftH = 18 ftSubstitute these values into equation 1
S.A = (6×4)+18(5+5+6)S.A = 24+228S.A = 312 ft²Hence, the surface area is 312 ft².
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whats the answer for this math problem
The solution to the equation -2/(x - 8) = (x - 1)/(x + 2) is x = 3 after checking for extraneous solutions.
To solve the equation
-2/(x - 8) = (x - 1)/(x + 2)
We can start by cross-multiplying to eliminate the fractions
-2(x + 2) = (x - 1)(x - 8)
Simplifying both sides, we get
-2x - 4 = x² - 9x + 8
Bringing all the terms to one side, we get
x² - 7x + 12 = 0
Now we can factor the quadratic equation to get
(x - 3)(x - 4) = 0
So the solutions are x = 3 and x = 4. However, we need to check for any extraneous solutions that may have been introduced by the original equation.
Plugging in x = 3 to the original equation, we get
-2/(3 - 8) = (3 - 1)/(3 + 2)
Which simplifies to
2/5 = 2/5
Therefore, x = 3 is a valid solution.
Plugging in x = 4 to the original equation, we get
-2/(4 - 8) = (4 - 1)/(4 + 2)
Which simplifies to
1/2 = 3/6
Therefore, x = 4 is not a valid solution.
So the only solution to the equation is x = 3.
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7z + 7> - 2z -4 solve the following for inequality for z simplest form
Answer:
z > - [tex]\frac{11}{9}[/tex]
Step-by-step explanation:
7z + 7 > - 2z - 4
9z + 7 > - 4
9z > -11
z > - [tex]\frac{11}{9}[/tex]
Answer: Just turn it into an equation! Replace the > with a =.
Step-by-step explanation:
Subtract 7 from both sides (bc you’re doing the opposite of +7) So 7z +7-7 cancels out so you just have 7z. 7z = -2z -4 -7, so 7z = -2z -11
Add 2z to both sides (bc your doing the opposite again) to get 9z = -11
Divide both sides by the number of the of the term with both a number and variable, in this case 9z, the number is 9. So 9z/9= -11/9 so simplified, z= -11/9
Final answer = -11/9
Hope this helps :D
what is ordinary least squares (ols) method? in order for the ols method to produce best linear unbiased estimators (blue), what assumptions must be satisfied?
Ordinary Least Squares (OLS) is a method used to estimate the parameters of a linear regression model.
In OLS, the objective is to find the line that best fits the observed data by minimizing the sum of squared residuals between the predicted values of the dependent variable and the actual values.
To produce the Best Linear Unbiased Estimators (BLUE) in OLS, the following assumptions must be satisfied:
Linearity: The relationship between the dependent variable and the independent variables must be linear.
Independence: The observations must be independent of each other.
Homoscedasticity: The variance of the residuals should be constant across all levels of the independent variables.
Normality: The residuals should be normally distributed.
No multicollinearity: The independent variables should not be highly correlated with each other.
If these assumptions are met, then OLS produces the BLUE, which means that the estimated coefficients are the best unbiased estimates of the true population parameters, and they have the smallest variance among all unbiased linear estimators.
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Select the figure that shows a division into composite parts. Then find the area of the figure. Each square represents 1 square unit. Round to the nearest tenth, if necessary. The area of the composite figure is sq. units.
The total area is given as 30 sq units.
What is Area of a Composite Figure?A composite figure is a two-dimensional shape that is made up of two or more simpler shapes, such as squares, rectangles, triangles, circles, or trapezoids. The area of a composite figure is the total amount of space that is enclosed within its boundaries.
To find the area of a composite figure, you need to first identify all of the individual shapes that make up the figure. Then, you can find the area of each shape using the appropriate formula. Finally, you add up the areas of all the shapes to get the total area of the composite figure.
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how many times as many robberies were there actually in year 5 compared to year 3? round your answer to 2 decimal places.
The answer to 2 decimal places, we only need to keep two numbers after the decimal point. In this case, there are no numbers after the decimal point, so the answer is simply 5.00.
To find the answer, we need to know the number of robberies in year 3 and year 5. Let's say there were 100 robberies in year 3 and 500 robberies in year 5.
To compare the two numbers, we can divide the number of robberies in year 5 by the number of robberies in year 3:
500/100 = 5
This means that there were 5 times as many robberies in year 5 compared to year 3.
To round the answer to 2 decimal places, we only need to keep two numbers after the decimal point. In this case, there are no numbers after the decimal point, so the answer is simply 5.00.
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10% of a number is X. What is 100%? Assume X > 0
100% of the number is 100 times X.
What is percentage?A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
If 10% of a number is X,
0.1 * number = X
number = X / 0.1
number = 10 * X
As a result, if X represents 10% of a number, the whole number is 10 times X. To get 100% of the answer, simply multiply X by 10 again:
100% of the number = 10 * X * 10 = 100 * X
So, 100% of the number is 100 times X.
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Is it just asking me a congruence theorem, does it want me to say what’s congruent to what, or does it just want the angles and or sides?
You are being asked to provide the minimum amount of information necessary to build a triangle that is congruence to the triangle shown in the image. All that is needed are the sides and angles.
What are the congruent triangle's five rules?
If two triangles satisfy all conditions for congruence, then they are congruent. They are right angle-hypotenuse-side (RHS), side-side-side (SSS), angle-side-angle (ASA), and angle-angle-side (AAS).
In order to form a triangle , two sides must be long and there must be an angle between them. A triangle's angle total is 180 degrees, and an acute angle is one with a measure of fewer than 90 degrees, among other triangle-related properties.
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Hence , the least amount of additional information that Andre needs to construct a triangle congruent to the given triangle is either the length of one side or the lengths of two angles other than angle LKJ.
What are the condition of congruent triangle?If two triangles satisfy all conditions for congruence, then they are congruent. They are right angle-hypotenuse-side (RHS), side-side-side (SSS), angle-side-angle (ASA), and angle-angle-side (AAS).
How to construct congruent triangle?To construct a triangle congruent to the given triangle, Andre needs to know the length of at least one side or the length of two angles other than angle LKJ.
If Andre knows the length of one side, say LJ, he can construct a line segment of the same length, say MN, and then construct two angles at each end of the line segment congruent to angles LJK and LKJ. The triangle formed by the three line segments LJ, JK, and KM will be congruent to the given triangle.
If Andre knows the lengths of two angles other than angle LKJ, he can use the Law of Sines or Law of Cosines to find the lengths of two sides, and then proceed as described above.
Therefore, the least amount of additional information that Andre needs to construct a triangle congruent to the given triangle is either the length of one side or the lengths of two angles other than angle LKJ.
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Use the order of operations to evaluate the expression 8 + 18 ÷ 3 – 7 pls need help asap
Answer:
Step-by-step explanation:
Evaluate the expression
Divide 18 by 3 = 6
Then add the 6 to the 8
then subtract 7 from 14
answer=7
There are 31 students in a class. Each student was asked how many pets he has at home. The table below summarizes the data.
Based on the data, estimate the probability that a randomly selected student from this class has four or more pets at home. Round your answer to the nearest two decimal places.
The probability that a randomly selected student from this class has four or more pets at home is 4/31 ≈ 0.13 when rounded to the nearest two decimal places.
Explain probability
Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, with 0 indicating no chance and 1 indicating certainty. Probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes. It is used in many fields, including mathematics, statistics, science, and engineering.
According to the given information
Based on the data provided, there are a total of 4 students who have four or more pets at home
(0 with 4 pets + 1 with 5 pets + 2 with 6 pets + 1 with 7 pets).
Since there are a total of 31 students in the class, the probability that a randomly selected student from this class has four or more pets at home is 4/31 ≈ 0.13 when rounded to the nearest two decimal places.
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Point Q is the center of a circle passing through points A, B, C
The center will be on the line segment CA because, as we already know, a circle's diameter is a chord that passes through its center.
Therefore, the answers are CA and diameter.
How do we calculate?we have that in the question, a circle with center 'O' is passing through three A, B and C, where ∠B is a right angle.
In the circumscribed circle, we have the converse of the Thales' theorem, which states that -
if A, B, and C are distinct points on a circle where angle ∠ABC is a right-angle, then the line AC will be a diameter of the circle.
The given information is drawn in the attached figure.
Applying the converse of Thales' Theorem, we have AC will be a diameter of the circle.
As the longest side (hypotenuse) of a right-angled triangle is the opposite side of the right-angle, CA is the longest side of ABC.
The longest side of the triangle equals the diameter of the circle because CA is likewise a diameter of the circle.
Thus, the center will lie on the line segment CA and the longest side of the triangle is equal to the diameter of the circle.
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#complete question:
Point O is the center of a circle passing through points A, B, and C. ∠B is a right angle.
The center of the circumscribed circle lies on line segment, (options: AB,BC, or CA) and the longest side of the triangle is equal to the (options: radius, diameter, or circumference) of the circle.
From the cyclic quadrilateral, If ∠ADC=120° and AB is a diameter, then ∠BAC=30°
Correct option is A
Solving the cyclic quadrilateralGiven that: ∠ADC=120
∠ACB=90° (Diameter of the circle subtends an angle of 90°)
Consider cyclic quadrilateral ABCD:
∠ADC+∠ABC=180° (sum of opposite angles of a cyclic quadrilateral is 180°)
Thus, ∠ABC=180°−120°=60°
In △ABC:
∠BAC=180°−∠ACB−∠ABC .....(Sum of three angles of a triangle is 180°)
∠BAC=180°−90°−60°=30°
Answer: ∠BAC=30°
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Point Q is the centre of a circle passing through the points A, B, C and D taken in order. If ∠ADC=120° and AB is a diameter, then ∠BAC=
A 30°
B 40°
C 45°
D50°
Shapes A and B are similar.
a) Calculate the scale factor from shape A to shape B.
b) Find the value of r.
Give each answer as an integer or as a fraction in its simplest form.
5 cm
11 cm
A
20 cm
3 cm
7'cm
B
12 cm
Not drawn accurately
Answer:
a) The scale factor from A to B is 3/5 since (3/5)(5) = 3.
b) r = (3/5)(11) = 33/5 = 6 3/5
2a. complete the table for values for the equation y=3x+4 X0 1 2 Y b. Plot the coordinates from the table. Join them with a straight line. Extend your straight line to y=-2 d. Write three pairs of negative x- and y-coordinates that lie on the line y = 3x + 4. 4 5x
Y = 3(-3) + 4 = -5 when x is equal to 3. Hence, the final set of negative x- and y-coordinates is (-3, -5).
what is coordinates ?A set of numbers known as coordinates describes a point or object's location in a given space or coordinate system. When representing a spot's location in a plane or three-dimensional space, coordinates are frequently expressed as x or triples in mathematics. Depending also on system being utilised, several values can be used to represent coordinates, although often, integers or real numbers are used to express them.
given
We can substitute negative values for x and solve for y to obtain three pairs of negative x and y coordinates that lie on the line y = 3x + 4.
With x = 1, y = 3(-1), plus 4, equals 1. Hence, one set of negative x and y coordinates is (-1, 1).
Y = 3(-2) + 4 = -2 when x is equal to 2. In light of this, another set of negative x- and y-coordinates is (-2, -2).
Y = 3(-3) + 4 = -5 when x is equal to 3. Hence, the final set of negative x- and y-coordinates is (-3, -5).
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