The equation of the circle is \(x^2 + y^2 + 6x - 18y + 65 = 0\).
Given:
Equation of the circle is \((x+3)^2+(y-9)^2=5^2\)
Expand the equation
\((x+3)^2 = (x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9\)
\((y-9)^2 = (y-9)(y-9) = y^2 - 9y - 9y + 81 = y^2 - 18y + 81\)
\(5^2 = 25\)
Then, substitute the expanded expressions into the equation
\((x+3)^2+(y-9)^2=5^2\\(x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\\)
Simplify and combine like terms
\((x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\x^2 + y^2 + 6x - 18y + 90 = 25\)
Rearrange the equation so that one side is 0
\(x^2 + y^2 + 6x - 18y + 90 = 25\\x^2 + y^2 + 6x - 18y + 90 - 25 = 0\\x^2 + y^2 + 6x - 18y + 65 = 0\)
Thus, the equation of a circle \((x+3)^2+(y-9)^2=5^2\) can be rearranged using the distributive property to form \(x^2 + y^2 + 6x - 18y + 65 = 0\), with one side equaling 0.
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Consider the matrix of 160 single digits (16 rows x 10 columns) shown in the left image of slide 6. The textbook describes how we can aid in counting the number of 7s in the matrix using the pre-attentive attributes of red hue (middle image of slide 6) and size (right image of slide 6.)
•Regardless of the specific hue and size used in the two mentioned examples, list at least three more ways you could use individual pre-attentive attributes to aid in counting the number of 7s in the matrix of first digits.
•Reassess the previous question, but this time answer it using the individual Gestalt principles of similarity, proximity, enclosure, and connection, rather than pre-attentive attributes.
Each of these attributes can be manipulated to make the 7s stand out and facilitate the counting process.
Apart from red hue and size, other pre-attentive attributes can aid in counting the number of 7s in the matrix. First, manipulating the shape of the 7s by using a distinct shape, such as circles, while using a different shape for other digits, can make the 7s visually prominent.
Second, altering the orientation of the 7s by tilting them slightly to the right or left while keeping other digits upright creates a noticeable difference, assisting in counting the 7s.
Third, applying a unique texture to the 7s, such as a textured pattern, while keeping other digits smooth, makes the 7s visually distinct and easier to identify.
Now, reassessing the question using the Gestalt principles, we can employ four principles: similarity, proximity, enclosure, and connection. By making the 7s visually similar, for example, by applying a different color or shading to them, they form a cohesive group that can be counted as a separate entity.
Utilizing the principle of proximity, positioning the 7s closer to each other compared to other digits helps to form a distinct cluster, simplifying their identification and counting. Employing enclosure by enclosing the 7s within a specific shape, such as a circle or box, sets them apart visually and aids in counting.
Lastly, using the principle of connection, visually linking the 7s using lines or curves forms a recognizable pattern, facilitating the counting process. By leveraging these Gestalt principles, the task of counting the number of 7s in the matrix can be made more efficient.
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At a sale, dresses were sold for $144 each. If the dresses originally cost $200, what percentage of its original price was a dress sold for?
Answer:
72%
80% of 200 is 160.
75% of 200 is 150.
74% of 200 is 148.
72% of 200 is 144
Just to make sure ask google or siri "What is 72% of 200?".
Hope this helps!
Answer:
28% (because it was marked down by $56 dollars)
Step-by-step explanation:
144/200 = 72%
100% (200) - 72% (144) = 28% (56)
56/200 = 28%
28% (56) + 72% (144) = 100% (200)
what is the probability that the diameter of arandomly selected tree will be at least 10 in.?will exceed 10 in.?
The probability that the diameter of a randomly selected tree for the different conditions is given by ,
a. Will at least 10 inches is equal to 0.
b. Will exceed 10 inches is equal to 1.
Probability for the diameter of a randomly selected tree
z = (x - μ) / σ
x = Diameter value
= 10in.
μ = mean
= 88
σ = standard deviation.
= -2.8
P(X ≥ 10)
X= diameter of a tree
Substituting the values we have,
z = (10 - 88) / 2.8
= -26.43
Using a standard normal distribution table or calculator
Probability that a standard normal variable is ≤ -26.43 equals to 0.
b) P(X > 10) = 1 - P(X ≤ 10)
Substituting the values we have,
z = (10 - 88) / 2.8 = -26.43
⇒ P(X > 10) = 1 - P(X ≤ 10)
= 1 - 0
= 1
Therefore, the probability that the diameter of a randomly selected tree is equal to,
a. at least 10 inches is essentially 0.
b. exceed 10 inches is essentially 1.
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The above question is incomplete, the complete question is:
Suppose the diameter at breast height in.) of trees of a certain type is normally distributed with mean 88 and sigma - 2.8. as suggested in the article "Simulating Harvester Forwarder Softwood Thinning" (Forest Products May 1997 36-41)
a. What is the probability that the diameter of a randomly selected tree will be at Wille least 10 in Will exceed 10 in.?
b. What is the probability that the diameter of a randomly selected tree will exceed in.?
8.
For which set of data is the median greater than the mean?
A.
B.
C.
D.
{8, 12, 14, 14, 20}
{8, 12, 14, 14, 22}
{9, 13, 14, 15, 19}
(9, 13, 14, 15, 20}
Answer:
B
Step-by-step explanation:
For a set of data to have a median that is greater than the mean, it must have an odd number of values and be skewed to the right. This means that the majority of the values in the set must be smaller than the median, with a few larger values on the right side of the distribution.
Out of the given options, the only set of data that satisfies these conditions is (B) {8, 12, 14, 14, 22}. This set has an odd number of values, and the median of 14 is greater than the mean of 14.4. The other options have either an even number of values, or are not skewed to the right.
Therefore, the correct answer is (B) {8, 12, 14, 14, 22}.
Please help. Also please show your work. Y/5 - 2/5
Answer:
0.2(y-2)
Step-by-step explanation:
factor out 1/5 from the expression
1/5×(y-2)
0.2(y-2)
Seven apple women possessed respectively 20,40,60,80,100,120,and 140 apples, went to market and sold all their apples at the same price,and each received the same sum of monkey.What was the price?
Answer: Each woman sold her apples at the rate of seven apples for I¢, and 3¢ each for the odd ones which were left over. this made it possible for each to receive the same amount, which is 20¢.
Step-by-step explanation:
given data:
20,
40,
60,
80,
100,
120,
140.
solution.
first woman 20 apples
= 2 + 3 * 6¢.
= 20¢.
second woman 40 apples
= 5 + 5 * 3¢.
= 20¢.
third woman 60 apples
= 8 + 4 * 3¢.
= 20¢.
fourth woman 80 apples
= 11 + 3 * 3¢.
= 20¢.
fifth woman 100 apples
= 14 + 2 * 3¢.
= 20¢.
sixth woman 120 apples
= 17 + 1 * 3¢.
= 20¢.
seventh woman 140 apples
= 20 * 1¢.
= 20¢.
Jada told Noah that she has $2 worth of quarters and dimes in her pocket and 17 coins all together. She asked him to guess how many of each type of coin she has.
Here is a table that shows some combinations of quarters and dimes that are worth $2. Complete the table
4566 x 53383= _________________
Please answer, (no explanation needed)
I'M MARKING BRAINLIEST FOR 1st RIGHT ANSWER
Answer:
243,746,778
or 243 million 746 thousand 778
Hope the answer helps!
Step-by-step explanation:
Graph the absolute value equation that represents the given situation, d = |s 250 - 50.
Then mark the points that represent the horizontal distance from the left shore where the river bottom is
20 feet below the surface.
Answer:The answer is below
Step-by-step explanation:
The bottom of a river makes a V-shape that can be modeled with the absolute value function, d(h) = ⅕ ⎜h − 240⎟ − 48, where d is the depth of the river bottom (in feet) and h is the horizontal distance to the left-hand shore (in feet). A ship risks running aground if the bottom of its keel (its lowest point under the water) reaches down to the river bottom. Suppose you are the harbormaster and you want to place buoys where the river bottom is 20 feet below the surface. Complete the absolute value equation to find the horizontal distance from the left shore at which the buoys should be placed
Answer:
To solve the problem, the depth of the water would be equated to the position of the river bottom.
h is=380 or h=100
Step-by-step explanation:
The line plot represents the wait time in line for a ride at a local fair.
A line plot titled Wait Time at the Fair. The horizontal line labeled Time in Minutes begins at 8, with every one unit labeled up to 20. There is one dot above 10, 11, 14, 16, and 17. There are two dots above 13. There are four dots above 12 and 15.
Which of the following best describes the shape of the data, and why?
The data is skewed and means that the wait times were less than 13 minutes for all the rides.
The data is bimodal, and it might mean that the wait times for the most popular rides were 12 and 15 minutes long.
The data is symmetric and means that the wait times were around 13 minutes for all the rides.
The data is skewed and means that the wait times were over 13 minutes for all the rides.
The shape of the data of the line plot is best described by the option
The data is bimodal, and it might mean that the wait times for the most popular rides were 12 and 15 minutesWhat is a line plot?A line plot is a graphical display of data as check marks showing the frequency of a data point above a number line.
The description of the line plot can be presented as follows;
The number of dota above the points marked 10, 11, 14, 16, and 17 = One dot each
The number of dots above the point marked 13 = Two dots
The number of dots above the points marked 12, and 15 = Four dots each
The above description of the line plot indicates;
The mode of the dataset are 12 and 15, therefore;
The data set is bimodalThe option that best describes the shape of the data, is therefore;
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Gary, Mary, and Rory have the same number of candies. If Gary gives Mary half of all his candies, then Mary gives Rory half of all the candies she has at the moment, and then Rory gives Gary half of all the candies he (Rory) has at the moment, Gary would have 12 more candies than he had originally. How many candies do Gary, Mary, and Rory have altogether
Gary, Mary, and Rory have 96 candies altogether.
Let's assume that the original number of candies that Gary, Mary, and Rory had is "x".
After Gary gives Mary half of all his candies, he would have x/2 candies.
Then, after Mary gives Rory half of all the candies she has at the moment, she would have x/4 candies.
And then, after Rory gives Gary half of all the candies he (Rory) has at the moment, he would have x/8 candies.
Now, we know that Gary would have 12 more candies than he had originally, which means:
x/2 + x/8 = x/2 + x/4 - 12
We can combine like terms and simplify the equation:
x/2 + x/8 = x/4 + x/4 - 12
x/8 = 12
x = 8 * 12
x = 96
Thus, Gary, Mary, and Rory have 96 candies altogether.
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The radius of the small circle is 0.5 millimeter. the area of the large circle is 28.26 square millimeters. calculate the area of the shaded region.
The area of the shaded region is approximately 8.215π square millimeters, for the given radius of small circle of 0.5 mm.
To find the area of the shaded region, we need to subtract the area of the small circle from the area of the large circle.
Given the radius of the small circle as 0.5 mm, we can find the area of the small circle using the formula for the area of a circle:
Area of small circle = πr²
where r is the radius of the small circle.
Area of small circle = π(0.5)²
= π(0.25)
= 0.785 mm²
Given the area of the large circle as 28.26 mm², we can find the radius of the large circle using the formula for the area of a circle:
Area of large circle = πR²
where R is the radius of the large circle.
28.26 = πR²
R² = 28.26/π
R² = 9
R = √(9)
R = 3 mm
Now that we know the radius of the large circle, we can find its area using the same formula:
Area of large circle = πR²
= π(3)²
= 9π mm²
Finally, we can find the area of the shaded region by subtracting the area of the small circle from the area of the large circle:
Area of shaded region = Area of large circle - Area of small circle
= 9π - 0.785
= 8.215π mm² (rounded to three decimal places)
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find the volume of the fish tank if the base is a regular octagon with side length 0.9 units and the height of the prism is 2 units
Answer:
9.2
Step-by-step explanation:
Yesterday the temperature at noon was 23-3°F. By midnight, it had decreased by
30.8°F. What was the temperature at midnight?
Answer:
-7.5°F
Step-by-step explanation:
23.3°F - 30.8°F = -7.5°F
A cylinder has a height of 20 inches and a radius of 19 inches. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.?????????HELP PLEASEEEEEEEEEEE
Answer:
22670.8 :D
Step-by-step explanation:
Volume of a cylinder: 3.12(r^2)h
Now lets solve :)
3.14(19^2)20
3.14(361)20
(1133.54)20
22670.8 :)
Have an amazing day!!
Please rate and mark brainliest!!
(x-1)²-(x-1)
Can anyone help me with factorising this
Answer:
(x - 1)(x - 2)
Step-by-step explanation:
Given
(x - 1)² - (x - 1) ← factor out (x - 1) from each term
= (x - 1)(x - 1 - 1)
= (x - 1)(x - 2)
1. A new company wants to mail out samples of its hair products. The company has a sample box that is a rectangular prism with a rectangular base with
an area of 23 1/3 sq. in. The height of the prism is 1 1/4 in. Determine the volume of the sample box
A.24 7/12 sq. inches
B. 24 7/12 cubic inches
C.175/6 sq. inches
D. 175/6 cubic inches
Answer:
Volume of rectangular prism = 175 / 6 inch³
Step-by-step explanation:
Given:
Base area of rectangular prism = 23 ¹/₃ inch² = 70 / 3 inch²
Height of rectangular prism = 1 ¹/₄ inch = 5 / 4 inch
Find:
Volume of rectangular prism
Computation:
Volume of rectangular prism = Base area of rectangular prism x Height of rectangular prism
Volume of rectangular prism = [70 / 3] x [5 / 4]
Volume of rectangular prism = [350 / 12]
Volume of rectangular prism = 175 / 6 inch³
y2−10y+24+6x−9x2
\(factorization\)
Answer:
y(2-10)2(12+3x)...
Step-by-step explanation:
first make groups of the numbers
y2 with 10 y they both have y in common
so you can write it as y(2-10)
after 24 with 6x they both have 2in common (2×12=24)
so you can write it as 2(12+3x)
and you can do the rest with the same technique
Mrs. Hanover borrows $1,413 at a
rate of 5% per year. How much
Simple Interest will she owe if it
takes her 9 months to repay the
loan? Round your answer to the
nearest cent
well, let's recall that a year has 12 months, so 9 months is really 9/12 of a year
\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1413\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (1413)(0.05)(\frac{3}{4}) \implies I = 1413(\frac{3}{80})\implies I\approx 52.99\)
set up a linear program that will determine a feasible solution to the following system of equations and inequalities if one exists. do not solve the linear program.
By following these steps, you can set up a linear program that will determine a feasible solution to a given system of equations and inequalities.
To set up a linear program to determine a feasible solution to a system of equations and inequalities, you need to follow these steps:
1. Define your variables: Start by identifying the variables in the system of equations and inequalities. Assign them letters, such as x, y, and z, to represent unknown values.
2. Write the objective function: Determine what you want to optimize or minimize in the system. This could be maximizing profit, minimizing costs, or achieving a certain goal. Translate this objective into an equation using the variables defined in step 1.
3. Formulate the constraints: Convert each equation and inequality in the system into linear constraints. Constraints restrict the feasible region where the variables can take values. For example, if you have an equation like 2x + 3y = 10, you can rewrite it as 2x + 3y ≤ 10 and 2x + 3y ≥ 10.
4. Specify the domain: Define the feasible domain for each variable. This could be based on physical constraints or limitations. For example, if x represents the number of units produced, it cannot be negative, so x ≥ 0.
5. Write the linear program: Combine the objective function and constraints to form the linear program. It should have the following general structure:
- Maximize or minimize: [Objective Function]
- Subject to: [Constraints]
- Domain: [Variable Domains]
Remember, we are not solving the linear program at this point; we are only setting it up. This means we do not need to find numerical values for the variables or determine if a feasible solution exists.
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what is (0, 1 3/4) on a coordinate plane
The simplified form of the given coordinate is (0,7/4) and the points in the coordinate plane given below:
In the given question we have to represent in given point in the coordinate plane.
The given coordinate is (0, 1 3/4).
In the given coordinate we firstly simplify the given coordinate.
We solve 1 3/4 this mixed fraction in the improper fraction.
To convert into improper fraction we multiply 1 with 4 then add with 3.
So simplified form is;
1 3/4 = 7/4
So the simplified form is (0, 7/4).
The point on the coordinate plane is given below:
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an experimenter surveyed two acres of a desert preserve and found six cactus wren nests. assuming that the habitat is fairly uniform, how many nests would he expect to be in the entire 200-acre preserve?
600 cactus wren nests the experimenter would expect to be in the entire 200-acre preserve.
To estimate the number of cactus wren nests in the entire 200-acre preserve, we can use the ratio of the area surveyed to the number of nests found.
Let's call the number of nests in the entire 200-acre preserve "N".
The ratio of the area surveyed to the number of nests found is:
2 acres / 6 nests = 200 acres / N nests
We can use this ratio to find the number of nests in the entire 200-acre preserve:
N nests = 200 acres * (6 nests / 2 acres)
N nests = 200 * 3
N nests = 600
So the experimenter would expect to find approximately 600 cactus wren nests in the entire 200-acre preserve, assuming that the habitat is fairly uniform.
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The scale factor from drawing 1 to drawing 2 is ___ %
Please help! Fill in the blank
I will give brainliest
Answer:
ghggyffxvbvucfyiyiyxozhlhzguvufcbi8
Katie wants to buy a bicycle that costs $200. This is
$20 more than twice what she saved last month. How
much did she save last month?.
Find the number,
Answer:180
Step-by-step explanation: subtract the 200 that is worth of the bike
and by the amount that is more than she had from last month and there will be your answer! hope it helps!
Pleasee help(GIVING BRAINILEST) Tyra's family is spending the afternoon in Millersville. They plan to see a movie and then explore the town. The movie will cost the family $36, and parking costs $4 per hour.
How long will the family be able to spend in Millersville if they want to spend less than $60 and they don’t have any other expenses?
Follow the steps to answer this question.
1. Write an inequality that shows that Tyra's family spends less than their limit. Explain how you wrote the inequality, and define any variables used. (2 pts)
Write your answer in the space below.
2. Solve your inequality. Show your work. What does your solution mean? (3 pts)
Write your answer in the space below.
Answer: 36+4h=60
36+4h-36=60-36
4h=24
4h÷4=24÷4
h=6
So, after the move they can spend 6 hours there. (6×4=24, 24+36=60, they will spend $60 if they spend 6 hours there, $56 if they spend 5 hours there and don't want to spend $60).
Step-by-step explanation:
2 w = 2p - 3z
a Find w when p = 8 and z = -2
Answer:
11
Step-by-step explanation:
2w = 2×8 - (-2×3)
2w = 16 - (-6)
2w = 22
w = 11
find the linear approximating polynomial for the function centered at the given point a f(x) = 32x^3/2
The linear approximating polynomial for the function f(x) = 32x^3/2 centered at a is:32a^3/2 + 48a^(1/2)(x-a)sample.
This can be obtained using the formula for the linear approximation of a function:f(x) ≈ f(a) + f'(a)(x-a)where f'(a) is the derivative of f(x) evaluated at a.To find the derivative of f(x), we use the power rule, which states that the derivative of x^n is n*x^(n-1).
Therefore, the derivative of f(x) = 32x^3/2 is:f'(x) = 3*32*x^(3/2-1) = 96x^(1/2)Evaluating this at x=a, we have:f'(a) = 96a^(1/2)Finally, substituting into the linear approximation formula, we get:f(x) ≈ f(a) + f'(a)(x-a)f(x) ≈ 32a^3/2 + 96a^(1/2)(x-a)f(x) ≈ 32a^3/2 + 48a^(1/2)(x-a) * 2 / 2f(x) ≈ 32a^3/2 + 48a^(1/2)(x-a)
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Pls help
Write the equation for a parabola with a focus at (-4,3) and a directrix at y=5
Answer:
y=(1/-4)(x+4)^2 +4
Step-by-step explanation:
Don't ask
Given g(x) = -2x + 1, solve for x when g(x) = 5.
Answer:
g(5)=-2(5)+1
g(5)=-10+1
g(5)=-9
What is 6(26x+4) simplified
Step-by-step explanation:
156x+24
..................
Answer:
156x + 24
Step-by-step explanation:
6(26x + 4) = Use the distributive property
6(26x) + 6(4) =
156x + 24