A right triangle is shown in the graph.
Part A: Use the Pythagorean Theorem to derive the standard equation of the circle, with center at (f, g) and a point on the circle at (x, y). Show all necessary math work. (3 points)
Part B: If (f, g) = (3, –1) and h = 8, determine the domain and range of the circle. (4 points)
Part C: Is the point (10, –4) inside the border of the circle if (f, g) = (3, –1) and h = 8? Explain using mathematical evidence. (3 points)
Answers
A) The standard equation of the circle, with center at (f, g) and a point on the circle at (x, y) is; (x - f)² + (y - g)² = h²
B) The domain and range of the circle are respectively;
[-5, 11] and [-9, 7]
C) Yes the point (10, –4) is inside the border of the circle
How to find the domain and range of a circle?A) Using the Pythagorean theorem will generate the equation for a circle as follows;
Sum of squares of sides = square of hypotenuse
From the given image, we have;
(x - f)² + (y - g)² = h² . . . . . . circle centered on (f, g) with radius h
B) The circle is defined for values of x in the domain f ± h, and for values of y in the range g ± h.
Domain: 3 ± 8 = [-5, 11]
Range: -1 ± 8 = [-9, 7]
C) The distance from point (10, -4) to (f, g) calculated as;
h² = (10 - 3)² + (-4 - (-1))²
h² = 7² + (-3)²
h² = 49 + 9 = 58
h = √58 < 8
Thus, the distance to the point is less than h=8 and it implies that the point is inside the circle.
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Related Questions
what is the ration that equivalent to 6/7
Answers
An equivalent ratio of the given ratio 6/7 is; 12/14
How to find Equivalent Ratios?To find equivalent ratios, we will just multiply the given ratio by any number that is equivalent to 1 such as 2/2, 3/3, 4/4, 5/5 e.t.c
Now, we want to find equivalent ratio of 6/7. Applying the procedure above, we can say that;
Equivalent ratio = (6/7) * (2/2) = 12/14
Thus, an equivalent ratio of 6/7 is; 12/14
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Dina's mother is four times older than Dina. Dina is 35 years younger than her father. Dina's father was 5 years older than Dina's mother when Dina was born. How old is Dina now?
Answers
Answer:
10 years old
Step-by-step explanation:
Let m = mother's age
Let f = father's age
Let d = Dina's age
m = 4d d = f-35 f = m+5
Substitute the middle equation in to the first equation
m = 4(f - 35) Use the distributive property
m = 4f - 140 subtract 4f from both sides
*m -4f = -140
In equation 3 above, subtract m from both sides to get
f = m+5
f - m = 5 rearrange so that the m term is first
*-m + f = 5
Now add the equations together that have *
m -4f = -140
-m + f = 5
-3f = -135 Divide both sides by -3
f = 45 This is the father's age. To find Dina's age, plug 45 into the second equation above:
d = f -35
d = 45 -35
d = 10.
To find the mom's age, use the third equation:
f = m+5
45 = m + 5
40 = m
You can check this by plugging the answers you found and you can see that all three equations are solved.
m = 4d d = f - 35 f = m + 5
40 = 4(10) 10 = 45 - 35 45 = 40 + 5
40 = 40 10 = 10 45 = 45
Explaining the Error in a Propo
A student uses the ratio of 4 oranges to 6 fuld ounces
find the number of oranges needed to make 24 fluid
ounces of juice. The student writes this proportion:
24
4
=
6 16
Explain the error in the student's work.
Answers
Answer:
16
Step-by-step explanation:
The student uses the ratio of 4 oranges to 6 fluid ounces.
When there are 24 fluid ounces, the number of oranges will be:
= 4/6 × 24
= 16 oranges
3. Which of the following best describes the reflection in the graph below
Reflection across y = -x
Reflection across x = 2
Reflection across x = 1
Reflection across y = x
Answers
Answer: Reflection across x=2.
Step-by-step explanation:
x=2 is the perpendicular bisector of segment UU'.
an economic research commission claimed that among the 500 stores there are 308 dealing with european companies, 266 dealing with asian companies 103 dealing with both sides regularly and 59 not dealing with either side. i) what is the probability that the stores deal with european or asian companies? ii) what is the probability that the stores do not deal with european companies? iii) what is the probability that the stores only deal with asian companies? iv) what is the probability that stores do not deal with only one type of company
Answers
Step-by-step explanation:
Let S be the set of all the stores in the sample, A be the set of stores dealing with Asian companies and E but the set of stores dealing with European companies
i. The set of stores that deal with European or Asian companies is A ∪ E. The inclusion-exclusion principle states that |A ∪ E| = |A| + |E| - |A ∩ E| = 266 + 308 - 103 = 471. So P(A ∪ E) = 471/500 = 0.942
ii. E' = S - E. |S-E| = 500 - 308 = 192. So P(E') = 192/500 = 0.384
iii. |A - E| = |A| - |A ∩ E| = 266 - 103 = 163. So P(A - E) = 163/500 = 0.326
iv. Stores that do not deal with only one type of company, must deal with both Asian and European companies. We are given that |A ∩ E| = 103. So P(A ∩ E) = 103/500 = 0.206
Easy, right?
Then mark as brainlist!
A football field is 160 feet wide and 360 feet in length. what is the distance around the field?
Answers
Answer:
Step-by-step explanation:
Distance around = 2*160 + 2*360
= 320 + 720
= 1080 feet.
The distance around the field is 1040 feet.
It is required to find the distance around the field.
What is rectangle?A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.
Given that:
A football field is 160 feet wide and 360 feet in length.
A football field is in the shape of rectangle.
So, we know that ,
Perimeter of rectangle= 2(length +breadth)
Distance around
= 2(160 + 360)
=2(520)
= 1040 feet.
Hence, the distance around the field is 1040 feet.
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A designer is hanging a mirror that is 101 centimeters (cm) wide in a room.
The center of the wall is 190 cm from the right end of the wall. If the designer
hangs the mirror so that the center of the poster is located at the center of the wall,
how far will the left and right edges of the poster be from the right end of the wall?
Answers
Answer:
240.5 cm and 139.5 cm, respectively
Step-by-step explanation:
101 cm / 2 = 50.5 cm
The right edge of the mirror is 50.5 cm to the right of the center line.
The right end of the wall is 190 cm from the center line.
190 cm - 50.5 cm = 139.5 cm
139.5 cm + 101 cm = 240.5 cm
240.5 cm and 139.5 cm, respectively
please help i need help solving this
Answers
Answer:
1.D 2.C 3.A 4.B
Step-by-step explanation:
hope this helped
Which of the following is equal to the fraction below?
(4/5)^6
A. 6(4/5)
B. 4^6/5
C. 4^6/5^6
D. 24/30
Answers
Answer:
C. 4^6 / 5^6
Step-by-step explanation:
(4/5)^6
= 4^6 / 5^6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{(\dfrac{4}{5})^6}[/tex]
[tex]\mathbf{= \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}\times \dfrac{4}{5}\times\dfrac{4}{5}\times\dfrac{4}{5}}[/tex]
[tex]\mathbf{= \dfrac{4\times4\times4\times4\times4\times4}{5\times5\times5\times5\times5\times5}}[/tex]
[tex]\mathbf{= \dfrac{16\times16\times16}{25\times25\times25}}[/tex]
[tex]\mathbf{= \dfrac{256 \times 16}{625\times25}}[/tex]
[tex]\mathbf{= \dfrac{4,096}{15,625}}[/tex]
[tex]\mathbf{\approx \dfrac{4^6}{5^6}}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{Option\ C. \dfrac{4^6}{5^6}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
can someone please help me
Answers
Answer:
A=120
B=165
C=240
Step-by-step explanation:
How do I find and construct the geometric mean in this problem?
Answers
x would be the side-length of a square that has the same area as a rectangle with width b and length a.
√(a*b) = x
How to find the value of x?Notice that you have two "lengths" which are a and b.
And you want to find x such that:
a/x = x/b
Now, notice that w e can rewrite the above expressions as:
a*b = x*x
This means that x would be the side-length of a square that has the same area as a rectangle with width b and length a.
Now, if you know the values of a and b (you can get these by using a ruler for example)
Then you can replace them in the equation:
a*b = x*x
√(a*b) = x
And find the value of x that meets the given condition.
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Find the equation of a circle centered on the origin going through the point (-5,3)
Answers
The given center and point on the circle of (0,0) and (-5, 3), respectively
gives the equation of the circle as [tex]x^{2} +y^{2} =\sqrt{34}[/tex].
The general form of the equation of the circle is presented as follows
(x - h)² + (y - k)² = r²
Where,(h, k) is the center of the circle and r is the radius of the circle
Here (h, k) is centered about the origin and the radius of the circle
Radius of the circle = √[(-5-0)² + (3-0)²]
= √(25+9)
=√34.
The equation of a circle centered on the origin going through the point (-5,3)
[tex]x^{2} +y^{2} =\sqrt{34}[/tex]
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Which is the population standard deviation of the data set: 8, 9, 10, 11, 12?
a. 10.123
1.414
b.
2.654
Please select the best answer from the choices provided
A
C.
d. 10
B
Answers
The population standard deviation of the data set is 1.414.
What is standard deviation?Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.
How is standard deviation calculated?Determine the mean of the observationDetermine the difference between each value and the mean and then square the resultDetermine the mean of the sum of the squared differences and then find the square root of the mean:Mean = (8 + 9 + 10 + 11 + 12) / 5 = 10
Sum of squared differences: (8 - 10)² + (9 - 10)² + (10 - 10)² + (11 - 10)² + (12 - 10)² = 10
√10/5 = 1.414
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17
Post Test: Transformations and Congruence
Select the correct answer from each drop-down menu.
Consider Undefined control sequence \triangle HJI.
H
सौ
Triangle HJIis
triangle HJI, the triangles
#
triangle EFG. Since triangle EFGuses
Reset
Next
Answers
It should be noted that mathematical transformations involve changing an image in some prescribed manner.
What is a transformation?Your information is incomplete. An overview will be given. A transformation is a general term for the specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
It should be noted that the original shape of the object is called the pre-Image and the final shape and position of the object is the image under the transformation.
There are four main types of transformations: translation, rotation, reflection and dilation. Also, in geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other
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Answer:
1. a translation and reflection
2. only rigid transfotmations
3. are congruent
Step-by-step explanation:
right on edmentum
What is the probability of on-time arrival in class given that the subject is biology?
Answers
The probability of on- time arrival in class given that the subject is biology is 82.4%.
Given the following table relating to subject on tie assignment submission and on time arrival in class.
Subject On time submission On time arrival
Physics 89.7% 82.3%
Maths 88.2% 88.7%
Chemistry 89.4% 83.1%
Biology 90.1% 82.4%
Total 88.5% 84.7%
We have to find the probability of on time arrival in class given that the subject is biology.
We have been given the corresponding percentages and percentages in itself shows some quantity. Percentage is the ratio of total favourable outcome to total outcome.
From the table the probability of on time arrival in class given that the subject is biology is 82.4%
Hence the probability of on- time arrival in class given that the subject is biology is 82.4%.
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Question is incomplete as it should includes the following table:
Subject On time submission On time arrival
Physics 89.7% 82.3%
Maths 88.2% 88.7%
Chemistry 89.4% 83.1%
Biology 90.1% 82.4%
Total 88.5% 84.7%
Answer:
82.4%.
Step-by-step explanation:
the graph of f(x) can be stretched vertically and flipped over the x-axis to produce the graph of g(x). if f(x)
Answers
The correct option is D: G(x) = -5x².
The equation of G(x) will be -5x² after vertically stretching and flipping.
What is meant by stretching vertically and flipping?A function change called a stretch or compression makes a graph bigger or narrower without moving it horizontally or vertically.
Vertical stretching: A function's graph is stretched or compressed vertically in proportion to the graph of the original function when we multiply it by a positive constant. We obtain a vertical stretch if the constant is bigger than 1, and a vertical compression if the constant is between 0 and 1.flipped over the x-axis: In order to reflect over the X axis, one must negate the value of each point's y-coordinate while maintaining its x-value. The graph reflects across the x-axis prior to transformation when the parent function f(x) = x² has an a-value smaller than 0. The function f(x) = -x² is the result.To know more about the vertical stretch, here
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The complete question is -
The graph of F(x) can be stretched vertically and flipped over the x-axis to produce the graph of G(x). If F(x) = x², which of the following could be the equation of G(x)?
A: G(x) = -1/5x²
B: G(x) = 5x²
C: G(x) = 1/5x²
D: G(x) = -5x²
A probability that it will rain on a given day during the rainy season in Miami is 70%. If there are 140 days in the rainy season. On how many days should you except it to rain?
Answers
Answer:
98 days
Step-by-step explanation:
140*70%=140*(7/10)=14*7=98
Which type of mathematical problem is too complex for a classical computer to solve efficiently?
Answers
Calculating the circumference of a circle based on the circle's diameter.
What kind of problems can a quantum computer solve?
Yet another difficult area that quantum computers cater to is that of solving difficult combinatorics problems. The algorithms within quantum computing aim at solving difficult combinatorics problems in graph theory, number theory, and statistics.10 Difficult Problems Quantum Computers can Solve Easily-
Quantum encryption. Simulation of quantum systems. ab initio calculations.Solving difficult combinatorics problems.Supply chain logistics. Optimization.Finance. Drug development.Learn more about quantum computer
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The complete question is -
Which type of mathematical problem is too complex for a classical computer to solve efficiently?
a. converting an irregular fraction to an approximate decimal value
b. multiplying two numbers that both have a large number of digits
c. finding two prime factors that result in a specific value when multiplied
d. calculating the circumference of a circle based on the circle's diameter
The average of a set of 18 consecutive integers is 22.5.what is the smallest set in the integer
Answers
Answer:
(y+17)÷18=22.5
y+17=22.5×18
y+17=405
y=405-17
y=388
Can someone help me out with these problems and show work please !!
Answers
Answer:
13. 10a^4b²
14. -5y³ + 35y² - 10y
Step-by-step explanation:
Question 13:
(5a³b) (2ab) =
=10a^4b²
Question 14:
5y (-y² + 7y - 2) =
= -5y³ + 35y² - 10y
Hope this helps!
Someone help me please
Answers
The angle m∠ABC is 70 degrees.
How to find angle in a rhombus?The angle in a rhombus can be found as follows;
The opposite angle of a rhombus are congruent.
Therefore,
∠B = 140 degrees
Hence, the diagonal of a rhombus bisect an angle.
Therefore,
m∠ABC = 140 / 2
m∠ABC = 70 degrees.
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a set of data has the values 11,14,23 and 16 what value would have to be added to set for the mean of the 5 numbers to be 18
Answers
Answer:
26.
Step-by-step explanation:
(11+14+23+16+x) / 5 = 18 where x is the value to be added.
(64 + x) / 5 = 18
64 + x = 90
x = 90 - 64
= 26.
In Bayes Theorem, you have some starting information, then you collect some new information so that you can _______ the original probabilities so you now have better information.
Answers
In Bayes Theorem, apart from the already starting information, some new information so that you can update or transform the original probabilities so you now have better information.
What is Bayes Theorem?
The Bayes' theorem was named after Thomas Bayes and it is used in probability theory and statistics as one of the fundamental theorems. It estimates the likelihood of an event based on knowledge of circumstances that might be connected to it in the past.
The Formula for Bayes' Theorem
The Bayes' theorem is given as,
P(A|B) = P(A).P(B|A) / P(B)
Here, for two events A and B,
P(A|B) is the probability for likelihood of A when B is true
P(B|A) is probability for likelihood of B when A is true
P(A) is the independent probability of event A
P(B) is the independent probability of event B
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3.
There was an earthquake in San Francisco April 18, 1906. More recently there was another earthquake in Columbia June 27, 2014. Earthquakes are measured using the associated amplitude on the Richter scale. Let a1 be the amplitude for the San Francisco earthquake and a2 be the amplitude for the Columbian earthquake.
San Francisco earthquake equations is below
Columbia earthquake below (view image)
a. Use the properties of logs to determine how many more times severe was the San Francisco earthquake? The severity is equal to the ratio below:
a1/a2
Answers
Using the properties of logarithms, it is found that the San Francisco earthquake was 24.71 times more severe than the Columbian earthquake.
How to find the ratios of the intensity of earthquakes?As given in the problem, the intensities of the earthquakes are given by logarithms of base 10. Then, supposing that the intensities are [tex]R_1, R_2, R_1 > R_2[/tex], the ratio of the intensities is given by:
[tex]R = 10^{\frac{R_1}{R_2}}[/tex]
For this problem, the intensities are:
[tex]R_1 = 7.8, R_2 = 5.6[/tex]
Hence the ratio is:
[tex]R = 10^{\frac{7.8}{5.6}} = 24.71[/tex]
The San Francisco earthquake was 24.71 times more severe than the Columbian earthquake.
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find the area of a semicircle with the height of 33 ft in the diameter of 66 ft
Answers
Answer:
Step-by-step explanation:
Comment
The radius is 33 feet. The height is really a radius. The diameter consists of 2*r
r = diameter / 2
diameter = 66 feet
r = 66 /2 = 33
So you have 2 ways of finding the radius.
Solution
Area of a full circle = pi r^2
Area of a full circle = pi * 33^2
Area of a full circle = 1089 pi
Area of a semicircle = area of a full circle / 2
Area of a semicircle = 1089 * pi /2
Area of a semicircle = 544.5 * pi
Answer
Exact answer in terms of pi is 544.5 * pi
Approximate answer using 3.14 for pi = 3.14*544.5 = 1709.73
Answer:
Area=
πr2
2
Step-by-step explanation:
3.14159⋅(33)2
2
=1710.5958
Proving Theorems about Parallelograms: Tutorial
?
Given: Quadrilateral ABCD is a parallelogram. Prove: ZBAD ZDCB, and ZABO ZODA. Match each
statement to its corresponding reason. Scroll down to see all the choices. Click the links in the statements to view
related diagrams. Drag the items on the left to the correct location on the right.
AB CD
BO ADview diagram)
Let A, B, C, and D form a parallelogram.
Draw ACand BD. (view diagram)
AB=CD
BC=AD
AABCE ACDA
AABD ACDB
ZBAD ZDCB(view diagram)
LABC ZCDA(view diagram)
ACAC, and BD BD
given
9 of 2
Opposite sides of a
parallelogram are .
line segments have
equal measures.
drawing line segments
Reflexive Property of
Equality
SSS criterion for
Corresponding angles
of triangles are
Answers
A parallelogram is a type of quadrilateral that has opposite sides to be equal, and opposite angles to be equal.
Thus to complete the given proof in the question, the required statements and reasons are stated below:
STATEMENT REASONS
1. AB ≅ CD, Opposite sides of a
BC ≅ AD parallelogram are equal
2. A, B, C, and D form a paralelogram Given
3. Draw AC and BD Drawing line segments
4. AB = CD, Equal line segments have
BC = AD equal measures
5. ΔABC ≅ ΔCDA SSS criterion for equal
ΔABD ≅ ΔCDB triangles
6. <BAD ≅ <DCB Corresponding angles of equal
<ABC ≅ <CDA triangles are equal
7. AC = AC, and BD = BD Reflective property of equality
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The function f(x) = 200(0.5)x/50 models the amount in pounds of a particular
radioactive material stored in a concrete vault, where x is the number of years since
the material was put into the vault. Find the amount of radioactive material in the
vault after 140 years. Round to the nearest whole number.
Answers
Answer:
29 years
Step-by-step explanation:
Given the function [tex]f(x)= 200(0.5)^{\frac{x}{50} }[/tex], where x stands for the number of years since the material was put into the vault, we can plug 140 into x to find the amount leftover.Another way of doing this is to change the function to [tex]f(x)=200(0.5^{\frac{1}{50} })^{x}[/tex] which are equivalent functions, and then plug 140 into x. This function is helpful if you also needed to find the rate. I'll use the 1st function because the question doesn't ask for the rate[tex]f(x)= 200(0.5)^\frac{140}{50}}[/tex]
From here I'll just use a calculator & get 28.7, or 29 years.
The movement of the progress bar may be uneven because questions can be worth more or less
(including zero) depending on your answer.
What are the exponent and coefficient of the expression 46-³?
The exponent is 3 and the coefficient is -4.
The exponent is -3 and the coefficient is 4.
O
The exponent is -3 and the coefficient is -4.
The exponent is 4 and the coefficient is -3.
Answers
Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative one and negative four.
Answers
The equation of the parabola graphed is given as follows:
y = a(x + 1)² - 4.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
Considering the vertex given, we have that h = -1, k = -4, hence the equation is:
y = a(x + 1)² - 4
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You purchase 9.25 gallons of gasoline at $3.15/gallon. You also buy gum ($1.10) and
windshield wiper fluid ($4.97). The state has a food tax of 4% and you give the clerk $30.00
cash. You pay the rest with your debit card. How much is charged to your debit card?
Answers
Answer:
$ 5.25 is charged to debit cardStep-by-step explanation:
Add 4% food tax:
1.1*1.04 = 1.14 (rounded)Total amount of purchase is:
9.25*3.15 + 1.14 + 4.97 = 35.25Subtract $30 paid in cash:
35.25 - 30 = 5.25Answer:
$5.25
Step-by-step explanation:
Cost of gasoline
9.25 gallons at $3.15 per gallon:⇒ 9.25 × $3.15 = $29.1375
Cost of gum
$1.10 plus 4% food tax:
⇒ $1.10 × 1.04 = $1.144
Total cost of purchases
Gasoline + gum + Windshield wiper fluid
⇒ $29.1375 + $1.144 + $4.97 = $35.2515 = $35.25 (nearest cent)
If $30.00 was paid by cash and the rest was paid for by debit card:
Debit card charge = $35.25 - $30.00 = $5.25