Identify the center and the radius of a circle that has a diameter with endpoints at (−5, 9) and (3, 5)
Answers
Check the picture below, so the circle looks more or less like that one.
well, the center of it is simply the Midpoint of those two points, and its radius is simply half-the-distance between them.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 3 -5}{2}~~~ ,~~~ \cfrac{ 5 + 9}{2} \right)\implies \left( \cfrac{-2}{2}~~,~~\cfrac{14}{2} \right)\implies \stackrel{center}{(-1~~,~~7)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[3 - (-5)]^2 + [5 - 9]^2}\implies d=\sqrt{(3+5)^2+(-4)^2} \\\\\\ d=\sqrt{8^2+16}\implies d=\sqrt{80}\implies d=4\sqrt{5}~\hfill \stackrel{\textit{half the diameter}}{\cfrac{4\sqrt{5}}{2}\implies \underset{radius}{2\sqrt{5}}}[/tex]
Related Questions
Could someone help, I need help with math, this is the question. The ratio of ducks to geese is 5:3. There are 50 ducks. How many geese are there?
Answers
There are 30 geese.
STEP-BY-STEP EXPLANATION:
Let y be the total no. of animals
Share= ratio/total ratio X total
50= 5/8 X y
50= 5y/8
50 X 8= 5y
y= 400/5
y= 80
The total no. of animals is 80
80-50=30 ans.
Solve the given system of differential equations by systematic elimination. Dx dt = 2x − y dy dt = x
Answers
The solution to the given system of differential equations is x(t) = t + C₁ and y(t) = t²/2 + C₁t + C₂.
1. dx/dt = 2x - y
2. dy/dt = x
Substituting y = -dx/dt into the second equation,
dy/dt = x - t
-d²x/dt² = x - t
Now, assume a particular solution of the form x = At + B,
where A and B are constants.
Substituting this into the differential equation,
-A = At + B - t.
Equating the coefficients of t on both sides,
A = -1 and B = 0.
Thus, the particular solution is x = -t.
Now, integrating dx/dt = -yt,
x = -yt + C₁
Finally, substituting x into the particular solution x = -t,
-t = -yt + C₁.
Solving for y, obtain y = t²/2 + C₁t + C₂.
Therefore, the solution is x(t) = t + C₁ and y(t) = t²/2 + C₁t + C₂.
Learn more about systematic elimination here:
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can anybody please help me with this math problem?
Answers
Answer:
B. (15, 19)
Step-by-step explanation:
To check to see if a particular ordered pair is a solution to an equation, use the values for the variables and see if the equation is true.
A. 4/5(0) +7 = 7 ≠ 1
B. 4/5(15) +7 = 19 . . . . . . is a solution
C. 4/5(-5) +7 = 3 ≠ 11
D. 4/5(-2) +7 = 27/5 ≠ 1
__
A calculator can help with this.
A news report says that 28%
28
%
of high school students pack their lunch.
Your high school has 600
600
students.
How many students in your high school would you expect to pack their lunch?
Answers
600 x 28% = 168
600-168= 432
you would guess that 432 students pack don’t pack lunch and 168 pack lunch
The cheetah is the fastest land animal in the world. During a sprint, the number of feet a cheetah runs y varies directly with the amount of time in seconds x as shown in the table. Write and solve a direct variation equation to determine how far the cheetah can run in 5.5 seconds.
Answers
Step-by-step explanation:
[tex] \hookrightarrow \sf y = kx [/tex]
[tex] \sf where \: k \: is \: constant[/tex]
[tex] \sf \: k = \frac{y}{x} [/tex]
[tex] \hookrightarrow \sf \: k = \frac{y}{5.5} [/tex]
Equation = [tex] \sf \: k = \frac{y}{5.5} [/tex]
If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from proportions from the various samples will have what approximate shape?.
Answers
Using the Central Limit Theorem, the shape of the frequency curve will be approximately normal.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].
Hence, the shape of the frequency curve will be approximately normal.
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
Label the probabilities in the tree diagram below and determine what is the probability of wearing a red shirt and black jeans?
Answers
The probability of wearing a red shirt and a black jean is the likelihood of the shirt and jean
The probability of wearing a red shirt and a black jean is is 1/6
How to determine the probability?From the tree diagrams, we have the following parameters
Total combination = 6
Red shirt and Black Jean = 1
The probability of wearing a red shirt and a black jean is calculated as:
P = n(Red shirt and Black Jean)/Total combination
This gives
P = 1/6
Hence, the probability of wearing a red shirt and a black jean is is 1/6
Read more about probability at:
https://brainly.com/question/251701
No chi-square The principal in Exercise 7 also
asked the random sample of students to record
whether they did all of the homework that was
assigned on each of the five school days that week.
Here are the data:
Monday Tuesday Wednesday Thursday Friday
School day
Number who did
all homework
34
29
32
28
19
Explain carefully why it would not be appropriate
to perform a chi-square test for goodness of fit using
these data.
oh
Answers
The random sample of the students is an illustration of sampling
The chi-square test for goodness of fit is inappropriate because the variable under study is not categorical.
How to determine the reason chi square is not appropriate?The dataset is given as:
Monday 34
Tuesday 29
Wednesday 32
Thursday 28
Friday 19
The variable of the above dataset is a not a categorical dataset.
One of the conditions of the chi-square test for goodness of fit test is that the variable under study must be categorical.
Hence, the chi-square test for goodness of fit is inappropriate because the variable under study is not categorical.
Read more about chi-square test at:
https://brainly.com/question/19959558
What is the standard form of the equation of a parabola that opens left or right? A. Y = ax2 + bx + c B. X = ay2 + by + c C. X = a(y - v)2 + h D. Y = a(x - h)2 + v
Answers
Answer:
The equation of the parabola which opens left or right is (B) x= ay^2 + by + c
:)
Is the figure defined by points H, I, J, and K a rhombus?
Yes, HIJK is a rhombus. Based on the coordinates, opposite sides are parallel, and all sides are congruent.
No, HIJK is NOT a rhombus. Based on the coordinates, opposite sides are parallel, but all sides are not congruent.
No, HIJK is NOT a rhombus. Based on the coordinates, all sides are congruent, but opposite sides are not parallel.
Yes, HIJK is a rhombus. Based on the coordinates, opposite sides are not parallel, and all sides are not congruent.
Answers
Answer:
b
Step-by-step explanation:
Change the following decimals to fractions give your answers in their simplest form a) 0.3 b) 0.46 c) 0.075
Answers
Answer:
[tex]0.3 = \frac{3}{10}\\\\ 0.46 = \frac{23}{50} \\\\0.075 = \frac{3}{40}[/tex]
Step-by-step explanation:
To convert decimals to fractions, you look at the place of the last digit of the fraction (i.e. the digit that the farthest right from the decimal)
For 0.3, 3 is in the tenths place, so we end up with the fraction [tex]\frac{3}{10}[/tex]
For 0.46, 6 is in the hundreths place, so before simplifying we have [tex]\frac{46}{100}[/tex]
The GCF of 46 and 100 is 2 so we divide the fraction by [tex]\frac{2}{2}[/tex] to get [tex]\frac{46}{100}[/tex] ÷[tex]\frac{2}{2}[/tex] = [tex]\frac{23}{50}[/tex]
For 0.075, the 5 is in the thousandths place, so before simplifying we have [tex]\frac{75}{1000}[/tex]
The GCF of 75 and 1000 is 25 so we decide the fraction by [tex]\frac{25}{25}[/tex] to get [tex]\frac{75}{1000}[/tex] ÷[tex]\frac{25}{25}[/tex] = [tex]\frac{3}{40}[/tex]
A student filled a right rectangular prism shaped box with one inch cubes to find the volume in cubic inches the students work is shown explain why the students reasoning is incorrect provide the correct volume in cubic inches and why the students reasoning is incorrect in your answer
Answers
The volume of the right rectangular prism is the amount of cubes in it
The formula to determine the volume of the right rectangular prism is V(n) = n
How to determine the volume?The question is incomplete; as the figure is not given.
So, I will provide a general solution
The volume of a one inch cube is:
[tex]V = 1^3[/tex]
[tex]V = 1[/tex]
Assume the number of one inch cubes used to fill the right rectangular prism is n.
Then the volume of the right rectangular prism would be:
[tex]V(n) = n * 1[/tex]
This gives
[tex]V(n) = n[/tex]
Hence, the general formula to determine the volume of the right rectangular prism is V(n) = n
Read more about volumes at:
https://brainly.com/question/1972490
please help this question is hard (25 POINTS!!)
An experiment involves rolling two dice simultaneously. The following table shows the possible outcomes using the format of (die 1,die 2).
1 2 3 4 5 6
1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
What is the probability of rolling 2 even numbers?
Enter your answer as a reduced fraction, like this: 3/14
Answers
Answer:
1/9
Step-by-step explanation:
Sum = 4: (1,3) (2,2) (3,1)
Sum = 12: (6,6)
4/36 = 1/9 or 0.111
hope that helps
The radius of Circle A is 6 cm. The radius of Circle B is 2 cm greater than the radius of Circle A. The radius of Circle C is 3 cm greater than the radius of Circle B. The radius of Circle D is 2 cm less than the radius of Circle C. What is the area of each circle?
Answers
Answer:
circle a: 3.14x36= 113.04
circle b: 3.14 x 64 = 200.96
circle c: 3.14 x 121= 379.94
circle d : 3.14 x 81 = 254.34
Step-by-step explanation: circle a is 6cm, circle b is 8 cm, circle c is 11 cm and circle d is 9cm.
and (Area = π r²) example: circle a 6²=36 and π=3.14 so 3.14x36=113.04
Hi Mehta06 heres my question that i told you
Answers
Answer:
1. WEA and and TSE
2.WES
3.50
Step-by-step explanation:
the inscribed angles are AWE, AWS, EST
As W is the center, ES is the Diameter
arc AE = 180-AWS
= 180-100
=80 degrees
MARK ME AS BRAINLISTHELP ME PLEASE
Solve for x: -6 – 5x = 29
Answers
Answer:
x = -7
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (&Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, add 6 to both sides of the equation:
-5x - 6 = 29
-5x - 6 (+6) = 29 (+6)
-5x = 29 + 6
-5x = 35
Next, divide -5 from both sides of the equation:
(-5x)/-5 = (35)/-5
x = 35/-5
x = -7
-7 is your answer for x.
~
What is the area of this polygon?
Answers
Answer:
The formula to calculate the area of a regular polygon is, Area = (number of sides × length of one side × apothem)/2, where the value of apothem can be calculated using the formula, Apothem = [(length of one side)/{2 ×(tan(180/number of sides))}].
Step-by-step explanation:
please help i will give brainly?
Answers
Explanation:
8:00-> 12:00= 4 hours
12:45->17:30= 5.45 hours
4+5.45=9.45 hours
9.45 x 15 = 141.75
if 45% of an item is 72.00 what is the original price. someone help me
Answers
Answer:
45% x 72.00 = 32.4
Step-by-step explanation:
hope this helped :)
Answer:
If 45% of an item is 72.00 what is the original price is, $160.00
Step-by-step explanation:
to the Kansas River Crossing.
Last year the depth of the river was 4.2 feet deep.
This year it dropped 17%.
Find the depth of the river this year to cross it.
Answers
Answer:
3.486 feet (1.06 m) or 3 feet (0.91 m) five inches
Step-by-step explanation:
17 percent of 4.2 is 0.714 and 4.2–0.714 is 3.486
Step-by-step explanation:
Solve: 2|x 7|−4 ≥ 0 express the answer in set-builder notation.
Answers
The correct answer for the given inequality is {x | x ≤ -9 or x ≥ -5}.
What is inequality?Inequality is a statement shows greater the, greater then equal to, less then,less then equal to between two algebraic expressions.
To solve an absolute inequality, first step is to isolate absolute value expression.
Hence remove -4 from the left side. So, add 4 to each sides of the inequality.
2|x + 7|−4 ≥ 0
2|x + 7|−4 +4≥ 0 +4
2|x + 7| ≥ 4 Combine the like terms.
Divide each sides by 2.
[tex]\dfrac{2|x + 7| }{2} \geq \dfrac{4}{2}[/tex]
|x + 7| ≥2
Next step is to remove the absolute value sign. So,
x + 7≥2 and x+7≤-2.
x≥2-7 and x≤-2-7
x≥-5 and x≤-9
So, the correct choice is {x | x ≤ -9 or x ≥ -5}.
To know more about inequality, follow
https://brainly.com/question/24372553
Answer:
1st one is: C
2nd one is: A
Step-by-step explanation:
Roman purchased 2 1/2 pounds of chocolate covered peanuts for $9.75 what was the price per pound?
Answers
Answer:
$3.90
Step-by-step explanation:
2 1/2 pounds = 2.5 pounds
To determine the price per pound, divide $9.75 by 2.5:
[tex]\sf \dfrac{9.75}{2.5}=3.9[/tex]
Therefore, the price per pound was $3.90
please answer 100 points
Divide. 6 from 3/5
10
30
20
15
Answers
Answer:
Step-by-step explanation:
What is 6 divided by 3/56 ÷ 3 5. The trick to working out 6 divided by 3/5 is similar to the method we use to work out dividing a fraction by a whole number. ... 6 x 5 3 = 30 3. So, the answer to the question "what is 6 divided by 3/5?" ... 30 3. ... 10 1. ... 10 1 = 10.
Answer:
The numbers in 6 divided by 3/5 are labeled below:
6 = whole number
3 = numerator
5 = denominator
To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:
6 x 5
3
=
30
3
Thus, the answer to 6 divided by 3/5 in fraction form is:
30
3
To make the answer to 6 divided by 3/5 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
30 / 3 = 10
The answer is rounded to the nearest two decimal points if necessary.
30/3 can be simplified to 10/1.
10/1 is an improper fraction and should be written as 10.Step-by-step explanation:
A bakery sells chocolate cupcakes and vanilla cupcakes. It sold 143 chocolate cupcakes in a day. 35% of the cupcakes sold that day were vanilla. How many total cupcakes did the bakery sell that day?
Answers
Answer:220
Step-by-step explanation:
An expression is given
3(3 squared2 -4)
Answers
Answer:
0.728 to nearest thousandth.
Step-by-step explanation:
3(3 squared2 -4)
= 9√2 - 12
= 0.728 to nearest thousandth.
John drove 737 miles in 11 hours At the same rate, how many miles would he drive in 5 hours?
Answers
Answer:
Step-by-step explanation: 737/ 11= 67
sooooo 67 x 5= 335
please help: Simplify 6÷(4-2)+4
Answers
Answer:
7
Step-by-step explanation:
6/(2)+4
3+4
7(BODMAS)
But if you use calculator it we give you
5
For the rotation 379°, find the coterminal angle from 0 <0 360°, the quadrant
and the reference angle,
Answers
To find the coterminal angle, it is similar to going around the entire circle once and then a bit more.
379 - 360 = 19
Coterminal Angle = 19 degrees
---All the way around and a bit more
Quadrant = 1
---Where the angle is
Reference Angle = 19 degrees
---Distance between the x-axis and the angle
Hope this helps!
solve pls brainliest
Answers
Answer:
[tex]\frac{1}{3} - \frac{1}{9} = \frac{3}{9} - \frac{1}{9} = \frac{2}{9}[/tex]
The first one: 3
The second one: [tex]\frac{2}{9}[/tex]
Step-by-step explanation:
To find the common numerator, you can multiply by 3 on both the numerator and denominator.
Help help help help help help help help I just need the answer for 13, 15, 16
Answers
Answer:
13) Squares, Rectangles. 14) Rhombus, Square.
15) Parallelogram, rectangle, rhombus, square
Step-by-step explanation: