The equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1) is (x - 1)^2 + (y - 1)^2 = 13.
The endpoints are (2, -5) and (-3,1).
The standard form equation for a circle is known as
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where (a, b) are the center's coordinates and (r) is the radius.
Taking into account the stated endpoints of the diameter. The center will then be at the midpoint, and the radius will be the distance between the center and either of the two endpoints.
Calculating the midpoint is as follows:
[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]
where, [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points.
Now putting the values
[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{-2+4}{2}, \frac{3-1}{2}\right)[/tex]
[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{2}{2}, \frac{2}{2}\right)[/tex]
[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(2, 1)[/tex]
Now we determine the equation of circle.
The center (2, 1) and the terminal are the two points (-2, 3).
r = [tex]\sqrt{(-2-1)^2+(3-1)^2}[/tex]
r =[tex]\sqrt{(-3)^2+(2)^2}[/tex]
r = [tex]\sqrt{9+4}[/tex]
r = √13
Now we can write the equation of circle as:
(x - 1)^2 + (y - 1)^2 = (√13)^2
(x - 1)^2 + (y - 1)^2 = 13
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The complete question is:
Find the equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1).
Write the standard equation for the circle.
A total of 362 adults and children are at a theatre. There are 140 more adults than children. If x represents the number of adults and y represents the number of children, which system of equations could be used to find the number of adults and the number of children in the theatre?
A system of equations that could be used to find the number of adults and the number of children in the theatre is:
x + y = 362
y = x + 140
How to write the required system of linear equations?In order to write a system of linear equations to describe this situation, we would assign variables to the number of adults and number of cats respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of adults.Let the variable y represent the number of children.Since the total number of adults and children at this theatre is 362, a linear equation which represents this situation is given by;
x + y = 362
Additionally, there are 140 more adults than children;
y = x + 140
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20/3 / 1/6 what is the miles per gallon
Answer: 20/3 / 1/6 is a division problem that can be simplified as follows:
20/3 divided by 1/6 = (20/3) * (6/1) = (206) / (31) = 120/3 = 40
The value of the division is 40. However, without knowing the context, it is impossible to know what the meaning of this value is. In particular, without knowing the units of 20/3 and 1/6, it is not possible to interpret the division as miles per gallon or any other unit.
It is important to note that 20/3 and 1/6 should be represented as mixed numbers (6 2/3 and 1/6) or as decimal numbers (6.66 and 0.16666) in order to be able to proceed with the division.
Step-by-step explanation:
elect ALL factors of 15. (Be sure to select ALL correct factors for full credit).
Question 5 options:
45
5
2
3
30
15
9
1
Answer:
1,3,5,15
Step-by-step explanation:
A factor cannot be greater then the number itself so we can scratch 30 and 45. 15 is divisible by itself and 1, as every other number. 2 is not a factor of 15 because 15 is not even. Also not 9. But it does have factors 5 and 3 because 5×3=15.
Hope that helps, let me know if you have any further questions!
The company claims that in the large bag of M&M's 20% of them were orange. Students bought a large bag of M&M and counted the candies they were 500. What is the probability of getting orange 21% more in that large bag.
The probability of getting orange 21% more in that large bag is 0.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
In this situation, the company claims that in the large bag of M&M's 20% of them were orange. Since the oranges are 20%, the probability of getting orange 21% more in that large bag is not possible. This will be zero.
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Find the measure of angles 1 and 2
Answer:
angle 1 = 118 deg
angle 2 = 62 deg
Step-by-step explanation:
To find angle one you must know that angles 1 and 118 deg are alternate angles. Therefore since these lines are parallel, angles 1 and 118 are equal.
To find angle 2 to you must know that angle 1 + angle 2 = 180.
angles on a straight line always equal 180 deg
therefore:
180
118 -
62 deg
hope this helps :)
Answer:
m<1 = 118°
m<2 = 62°
Step-by-step explanation:
The horizontal lines are parallel.
Angles 1 and 118° are alternate interior angles of parallel lines cut by a transversal, so they are congruent.
m<1 = m<2 = 118°
Angles 1 and 2 are a linear pair, so they are supplementary. That means that their measures add to 180°.
m<1 + m<2 = 180°
118° + m<2 = 180°
m<2 = 62°
can someone help me with 11 and 12
Answer:
see below
Step-by-step explanation:
11: write 3 equiv ratio of 1:3, so it' could be 3:9, 2:6, 4:12
12. 20:15 = 4:3, 12:9, 8:6
Translate the following into equivalent predicate statement :
i. There is an integer whose square is twice itself.
ii. No school buses are purple.
iii. If a real number is even, then its square is even.
i. ∃x ∈ Z, x² = 2x, ii. ∀y ∈ school buses, y is not purple and iii. ∀x ∈ R, if x is even, then x² is even.
i. The equivalent predicate statement for the first statement is:
∃x ∈ Z, x² = 2x
The symbol "∃" means "there exists", the symbol "∈" means "is an element of", and the symbol "Z" represents the set of integers.
ii. The equivalent predicate statement for the second statement is:
∀x, (x is a school bus) → (x is not purple)
The symbol "∀" means "for all", and the symbol "→" means "implies".
iii. The equivalent predicate statement for the third statement is:
∀x ∈ R, (x is even) → (x² is even)
The symbol "∈" means "is an element of", and the symbol "R" represents the set of real numbers.
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I NEED HELP ASAP
A toy manufacturer is designing a new triangular-shaped toy. The company would like the toy to have a specific area. Write the equation for the area of a triangle. Solve your formula for the height. The company specified that the area of the toy must be 60 square inches and the length of the base must be 12 inches. Use your formula to determine the height of the new toy.
The height of the triangle with area of 60 square inches and the base of 12 inches is 10 in.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
The area of a triangle is the amount of space it occupies. The area is the product of the base and height divided by 2. It expressed as:
Area = (1/2) * base * height
Given that the area is 60 square inches and the length of the base must be 12 inches. Let h represent the height
Therefore:
Area = (1/2) * base * height
60 = (1/2) * 12 * h
6h = 60
h = 10 in
The height of the triangle is 10 in.
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Mary, Ana, and Nata work at a coffee shop. Each day from Monday to Friday exactly two of them come to work. Mary works 3 days per week and Ana works 4 days per week. How many days per week does Nata work?
Based on the information, it can be inferred that Nata has to work 7 days a week.
How to calculate how many days Nata works?To calculate how many days Nata works we must perform the following mathematical operation.
We must find how many days in total Ana and Mary work together, that is, we must add the days that they work.
3 + 4 = 7Based on the above, we can say that Ana and Mary work 7 days a week, so Ana could work Monday, Tuesday and Wednesday and Mary could work Thursday, Friday, Saturday and Sunday.
So, Nata will have to accompany both of them every day, so she will have to work 7 days.
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Please help!!
Which of the following statements is true about the triangles below
Answer: ASA
Step-by-step explanation: Hello! You can use ASA to prove that the triangles ABC and ABD are congruent. This is because you are given two angles of each triangle. You know that your answer should be ASA or AAA, which are the only two triangle congruence postulates that involve two or more congruent angles. Lastly, you can use the reflexive property. An example of reflexive property is 3 = 3, which means anything is congruent to itself. You know that both triangles share line segment AB, meaning that they have one side and two angles that are congruent. Since you know that the two angles and the included side are congruent, ASA proves that both triangles ABC and ABD are congruent. I hope this helps you!
The figure shows the measurements, in inches, of a rectangular prism. 8 in 12 in 7 in What is the volume of the prism
A:92 in B: 236 in C: 472 D: 672
Answer:
672 in.³
Step-by-step explanation:
V = LWH
V = 8 in. × 12 in. × 7 in.
V = 672 in.³
Answer: D 672
Step-by-step explanation: The formula for volume is L x W x H = V so if you plug all those numbers in and multiply u get 672
A company manufactures a wash-down motor that is used in the food processing industry. The motor is marketed with a warranty that guarantees it will be replaced free of charge if it fails within the first 12,000 hours of operation. On average, the wash-down motors operate for 14,000 hours with a standard deviation of 1, 050 hours before failing. The number of operating hours before failure is approximately normally distributed.
a. What is the probability that a wash-down motor will have to be replaced free of charge?
b. What percentage of wash-down motors can be expected to operate for more than 16,100 hours?
c. If the company wants to design a wash-down motor so that no more than 1% are replaced free of charge, what would the average hours of operation before failure have to be if the standard deviation remains at 1,050 hours?
a) The probability that a wash-down motor will have to be replaced free of charge - 1,904
b) A percentage of wash-down motors can be expected to operate at 2,28 %
c) The average hours of operation before failure would be 13500 h
Normal Distribution
μ₀ = 14000 hours and σ = 1050 hours
a) Probability of X (replacement of motor free of charge)
Z = ( X - μ₀ ) / σ
Z = ( 12000- 14000) / 1050
Z = - 2000/1050
Z = - 1,904
From z Table we get
for z = -1.904 P [ X ≤ 12000 ] = 0.0262
P [ X ≤ 12000 ] = 0.0262 or 2.62 %
b) What % of motors can be expected to operate more than 16100 hours
z = ( 16100 - 14000) / 1050
z = 2100/1050 ⇒ 2
From the z table, we find with z = 2 total number of f motors operating up to 16100 hours
From the z table, we find 0,9772
Then the probability of motors operating for more than 16100 hours is:
P [ X > 16100] = 1 - 0.9772 = 0,0228
Then
P [ X > 16100] = 0,0228 or 2,28 %
c) The average hours of operation before failures if only 1% of motors would be replaced free of charge is:
1% = 0,01 Probability then z score is z = 0,4960
0,4960 = ( 14000 - X ) / 1050
0,4960 * 1050 = ( 14000 - X )
520,8 - 14000 = - X
X = 13479,2 hours as is not common such offer company could set up a guarantee for 13500 h
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a medical researcher is comparing the results of two surgical techniques to correct a skeletal deformity. there are many obvious risks of participating in this treatment trial, and participants are carefully informed about the likelihood of infection, poor treatment outcome, further damage, etc. the research design includes a questionnaire given to patients about their quality of life before and after the surgery. because this is just a simple paper and pencil questionnaire, it does not add any risks to the overall study design. is this true or false?
The questionnaire given to patients about their quality of life before and after the surgery included in the research design does add risks to the overall study design. Hence, the given statement is false.
Even though the questionnaire itself may not cause any additional physical risks, it can still have an impact on the overall study design. The questionnaire can add additional burden to the participants, who may already be dealing with physical and emotional stress from the surgery. Also, the questionnaire results may not be accurate if participants are not fully honest or unable to understand the questions being asked. Therefore, the inclusion of such a questionnaire in the research design should be carefully considered after evaluating its potential impact on the overall study.
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The heights of a species of plant are approximately Normally distributed, have a mean of 9. 31 cm, and have a standard deviation of 0. 55 cm. If 20 of the plants are randomly selected, what is the probability that the mean plant height is less than 9. 5 cm?
If heights of a species of plant are approximately Normally distributed, have a mean of 9.31 cm, and standard deviation of 0.55 cm , If 20 of the plants are randomly selected , then the probability that the mean plant height is less than 9.5 cm is 0.9388 .
We can use the Z-score formula to find the probability that a randomly selected plant has a height less than 9.5 cm:
Z = (x - mean)/(standard deviation/sqrt(sample size)) ;
Where x is the value we want to find the probability for, in this case x = 9.5
So , Z = (9.5 - 9.31)/(0.55/√20) = (0.19)/(0.123) = 1.54
Now we can use the standard normal table to find the probability that a Z-score is less than 1.54 .
From the z table ; we get , the p value is 0.9388 .
Therefore , The probability that a randomly selected plant from this species has a height less than 9.5 cm is about 0.9388 .
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Consider two stars, star A and star B. Star A is 22 light-years from Earth, and star B is 34 light-years from
Earth. Viewing from Earth, the angle between them is 60 degrees. What is the distance between star A
and star B in light-years? (Round your answer to the nearest hundredth.)
The distance that exists between star A and B is given as 29.87 light years
How to solve for the distance that exists between the the starsWe can solve this by creating a triangle where Point a Is star a, point b is star b and the point c is earth
the angle is given as 60 degrees
AC = 22 light years
BC = 34 light years
ab² = ac² + bc² - 2 *ac * bc* cos60
we would have to put in the values
ab² = 22² + 34² - 2 * 34 * 22 * cos 60
ab² = 484 + 1156 - 748
ab² = 892
square both sides
ab = 29.87 light years
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I really need help with this question please and thank you
Answer:
9. reduction, 1/2
10. enlargement, 3/2
11. enlargement, 3
12. reduction, 1/3
Step-by-step explanation:
You want to know whether the dilations shown are reduction or enlargement.
Dilation
If the image (figure B) is larger, the dilation is an enlargement. (10, 11)
If the image (figure B) is smaller, the dilation is a reduction. (9, 12)
Scale FactorThe scale factor is the ratio of a length on the image to the corresponding length on the original figure. It will also be the ratio of distances from the center of dilation (the origin) of corresponding points.
9.The ratio of line lengths B/A is 3/6, a reduction by a factor of 1/2.
10.The ratio of distances from the origin on the x-axis is 3/2, an enlargement by a factor of 3/2.
11.The ratio of distances from the origin on the x-axis is 6/2, an enlargement by a factor of 3.
12.The ratio of distances from the origin on the x-axis is 2/6, a reduction by a factor of 1/3.
An architect is designing a building. Each floor will be 12 feet tall. Write an expression for the number of floors the building can have for a given building height. Tell what the variable in your expression represents
how many pieces of data can a variable hold at a given time? group of answer choices two infinite it depends on the data type none one
None of the options are correct. A variable can only hold one piece of data at a time.
A variable is a named storage location in a computer's memory that is used to store a single value. The value can be of any data type, such as a number, a string, or a boolean. A variable can only hold one piece of data at a time, meaning that it cannot store multiple pieces of data simultaneously. This is why it is important to use multiple variables if you need to store multiple pieces of data. Each variable should be given a unique name so that it can be easily referenced and identified when needed.
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Multiple Choice 1. Which proportion can be used to determine what number is 15% of 30? (1 point) 15/30=x/100 15/100=x/30 15/100=x/30 30/100=x/15
Answer:4.5
Step-by-step explanation:
Plot a point on the coordinate plane to represent each of the ratio values in the table.
what is (8/9)^2 pls i need it
Answer: about 0.79
Step-by-step explanation:
First divide 8 by 9 --> (8/9) = about 0.8889
then square that value --> (0.8889)^2 = about 0.79.
PEMDAS is your friend!
What is the slope of the line in the graph below?
undefined
−2
2
0
Answer:
Step-by-step explanation:
The slope of the given line in the graph is "undefined".
Define the term slope of the line?Slope, usually referred to as rise over run, is the "steepness" of the line.
By dividing the difference in y values between two points by the difference in x values, we may determine slope.
A line's slope does not summarily characterize it. As a result, even if you know a line's slope, you cannot identify the exact spots the line passes through.Any two lines with the same slope are said to be parallel. When a line is rotated 90 degrees, it becomes perpendicular and becomes parallel. A horizontal line is one that has a slope of 0. Positive lines are those that rise as they move further to the right.The y-axis is an example of a vertical line that is believed to have an "undefined" slope.Thus, as the line is passing through the y axis and parallel to the x axis, the slope of the given line is undefined.
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Heyy can anyone help me in this please IMP
Answer:
Step-by-step explanation:
What would the answer be?
Answer: AAS → Makes the most sense
- They give two angles and a side for both triangles
Step-by-step explanation:
Lenny has 104 coins in his pocket made up of nickels and dimes worth
$22.00. Write and solve a system of equations to find out how many
nickels and quarters he has.
On solving the equations x + y = 104 and 0.05x + 0.25y = 22, the number of nickels and quarters Lenny has is 20 and 84 respectively.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The value of 1 nickel is = $0.05
The value of 1 quarter is = $0.25
The total amount of coins is = $22.0
The total number of coins is = 104
Let the number of nickel be = x
Let the number of quarter be = y
The equation for total number of coins =
x + y = 104 ....(1)
The equation for total amount of coins =
0.05x + 0.25y = 22 ...(2)
Multiply equation (1) by 0.05 -
0.05(x + y) = 104 × 0.05
0.05x + 0.05y = 5.2 ... (3)
Subtracting equation (3) from (2) -
0.05x + 0.25y - (0.05x + 0.05y) = 22 - 5.2
0.05x + 0.25y - 0.05x - 0.05y = 22 - 5.2
0.20y = 16.8
y = 84
Substitute the value of y in equation (1) -
x + 84 = 104
x = 104 - 84
x = 20
Therefore, the value for x and y is obtained as x = 20 and y = 84.
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On a team, 3 girls and 2 boys scored a total of 27 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 15. Each girl scored the same number of points, and each boy scored the same number of points. Find the number of points scored by each girl and each boy.
Answer:
We can start solving the problem by using algebra. Let x be the number of points scored by each girl, and y be the number of points scored by each boy. Then, based on the information given in the problem, we have the following equations:
x + y = 27 (the total number of points scored by the team)
3x - 2y = 15 (the difference between the number of points scored by the 3 girls and the 2 boys)
To solve for x and y, we can use the second equation to eliminate one of the variables. Multiplying both sides of the second equation by 2, we get:
6x - 4y = 30
Now we can substitute this into the first equation:
6x - 4y + y = 27
6x = 27 + 4y
x = (27 + 4y)/6
Now we can substitute this back into the second equation:
3((27 + 4y)/6) - 2y = 15
27 + 2y - 2y = 15
27 = 15
This is a contradiction, so the given information is insufficient to find the number of points scored by each girl and each boy.
Step-by-step explanation:
If 479,000 people each receive an average refund of $4,500, based on an interest rate of 1 percent, what would be the lost annual income from savings on those refunds? (Do not round intermediate calculations. )
As per the compound interest, the lost annual income from savings on those refunds is $21,555,000
In math the term called compound interest is defined as a type of interest that not only accrues on the principal but also on the accrued interest and the interest rates on loans are quoted in terms of annual percentage rate, which does not account for the compounding of interest, and therefore understates the true cost of borrowing.
Here we know that the 479,000 people each receive an average refund of $4,500, based on an interest rate of 1 percent.
Then the lost annual income from savings on those refunds is calculated as,
As we all know that the lost annual income is the amount of interest these people could have earned on their income, in which the extra tax had not been deducted.
Then With $4,500 each person,
Then the total amount of the deducted income is calculated as,
=> 479,000 x 4,500 = 2,155,500,000.
Here we have the 1% interest rate, then the net return on these fund if they were saved
=> 2,155,500,000 x 1% = 21,555,000.
Therefore the total lost annual income is 21,555,000
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Your parents are taking you and some of your friends to the movies tonight. Your parents might bring your grandparents and other adults to the movies as well. Adult tickets cost $11 each, and children's tickets cost $8 each. Write an equation that represents the total cost for the movie tickets. What is one combination of tickets that would total $57?
Answer:
57 = 33+24 = 3a+3c
Step-by-step explanation:
Let a= adults, c = children
total costs = 11a+8c
57 = 33+24 = 3a+3c
Answer: We can use the variables x and y to represent the number of adult tickets and children's tickets, respectively. The cost of adult tickets is $11 each and the cost of children's tickets is $8 each. So, we can use the following equation to represent the total cost for the movie tickets:
C = 11x + 8y
Where C is the total cost of the tickets, x is the number of adult tickets and y is the number of children's tickets
One combination of tickets that would total $57 is:
C = 11x + 8y = $57
x + y = 7 (number of tickets)
One way to satisfy this equation is to have 5 adult tickets and 2 children's tickets
x = 5
y = 2
C = 115 + 82 = $57
So, 5 adult tickets and 2 children's tickets is one combination that would total $57.
Step-by-step explanation:
The Stock Market Nadia is a stockbroker. She earns 14% commission each week. Last week, she sold $5,300 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011?
Answer:$742; $38,584
Step-by-step explanation: 14% of $5,300 is $742 (0.14 x 5300). There are 52 weeks in a year so $742 x 52 weeks = $38,584.
adams awesome pawnshop will lend up to 42% of the value of a borrowers collateral. andy want wants to use his 10000 signed michael jordan rookie card. his 3000 signed joe monntana cleats & his 2000 signed tiger woods golf ball as collateral for a loan. with the loan andy wants to buy a signed michael jackson white glove that costs 6500. will the loan be enough for andy to get the glove?
No, Andy do not have enough loan, he need $200 more dollars to purchase Michael Jackson white glove.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, Adams awesome pawnshop will lend up to 42% of the value of a borrowers collateral.
Andy want wants to use his $10000 signed Michael Jordan Rookie card. his $3000 signed Joe Montana cleats and his $2000 signed Tiger Woods golf ball as collateral for a loan.
Now, 42% of (10000+3000+2000)
= 42/100 ×15000
= 0.42×15000
= $6300
Cost of Michael Jackson white glove costs $6500
No, Andy do not have enough loan, he need $200 more dollars to purchase Michael Jackson white glove.
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