What is the equation for a circle that has a center at (−8,−5)
and a point on the circle at (−1, 1)
?
Answers
The equation for the circle with a center at (-8, -5) and a point on the circle at\((-1, 1) is (x + 8)^2 + (y + 5)^2 = 85.\)
To find the equation for a circle with a center at (-8, -5) and a point on the circle at (-1, 1), we can use the general equation for a circle:
\((x - h)^2 + (y - k)^2 = r^2,\)
where (h, k) represents the coordinates of the center of the circle, and r represents the radius.
Given that the center of the circle is (-8, -5), we can substitute these values into the equation:
\((x - (-8))^2 + (y - (-5))^2 = r^2.\)
Simplifying the equation, we have:
\((x + 8)^2 + (y + 5)^2 = r^2.\)
Now, we need to find the value of r, the radius of the circle. We know that a point on the circle is (-1, 1). The distance between the center of the circle and this point will give us the radius.
Using the distance formula, the radius can be calculated as follows:
\(r = √((x2 - x1)^2 + (y2 - y1)^2),\)
where (x1, y1) represents the coordinates of the center (-8, -5) and (x2, y2) represents the coordinates of the point (-1, 1).
Plugging in the values, we have:
\(r = √((-1 - (-8))^2 + (1 - (-5))^2)\)
\(= √((7)^2 + (6)^2)\)
= √(49 + 36)
= √85.
Substituting this value of r into the equation for the circle, we get:
\((x + 8)^2 + (y + 5)^2 = (√85)^2,\)
\((x + 8)^2 + (y + 5)^2 = 85.\)
Thus, the equation for the circle with a center at (-8, -5) and a point on the circle at (\(-1, 1) is (x + 8)^2 + (y + 5)^2 = 85.\)
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Related Questions
Kylie is preparing for the science fair that will take place in six weeks. She has three plants that she has grown from seeds, which she considers to have height 0 centimeters, and she is measuring their heights as she applies different treatments to each. The second plant is receiving Plant Food B. After 3 weeks, it is 10 centimeters tall. If it continues growing at this rate, how tall will it be after 6 weeks?
Answers
The height of plant B growing at a rate of 3.33 centimeters per week should have a height of 19.98 cms.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
First we need two points (x, y) to obtain the slope.
Assuming height to be 'y' and weeks to be 'x'.
Therefore, (0, 0) and (3, 10) are the two points.
Slope(m) = (10 0)/(3 - 0).
Slope(m) = 10/3.
Slope(m) = 3.33
Now, To obtain the y-intercept.
10 = 3(3.33) + b
b = 0.01 Or neglegible.
Therefore y = 3.3x.
Now, In the 6th week, the height of plant B will be,
y = 3.33(6).
y = 19.98 or 20 cm.
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Which is better to buy, 6 CD's for $12 or 8 CD's for $14.50?
Answers
Answer:
8 CDs for $14.50
Step-by-step explanation:
We have to divide both of the numbers by the number of CDs. Our formula is:
(price) ÷ (number of CDs) = price per CD
When we divide both of the prices by the number of CDs, we see that 6 CDs for 12.00 is worse because it is 2.00, whereas the inflation is lower when you compare to the other rate. You get $1.81.
Identify the corresponding word problem given the equation: x = 4 × 9
A) Chris and four of her friends went out to eat. They decided to split the bill evenly. If each person paid $9, what was the total bill? Eliminate B) Chris and three of her friends went out to eat. They decided to split the bill evenly. If each person paid $9, what was the total bill? C) Chris and four of her friends went out to eat. They decided to split the bill evenly. If the total bill was $36. 00, what did each person pay? D) Chris and three of her friends went out to eat. They decided to split the bill evenly. If the total bill was $36. 00, what did each person pay?
Answers
Answer: C) Chris and four of her friends went out to eat. They decided to split the bill evenly. If the total bill was $36.00, what did each person pay?
The equation x = 4 × 9 represents the total bill for Chris and her four friends. By solving the equation, we get x = 36. This corresponds to option C where the total bill is given as $36.00, and we are asked to find what each person paid after splitting the bill evenly.
Step-by-step explanation:
the census bureau reports that 27% of california residents were born outside the united states. (a) suppose that you randomly choose 4 californians. what is the probability that exactly 1 of the chosen californians were born outside the u.s.?
Answers
The probability that exactly 1 of the chosen Californians were born outside the US when 4 Californians are chosen randomly where 27% of California residents were born outside the united states is 0.42.
This is a case of Binomial distribution where there is 0.27 probability a resident of California were born outside US and 0.73 probability they were born inside the US.
In this case of Binomial distribution, the total number of successful trial(n) is the number of Californian residents chosen that is n = 4. Probability that exactly 1 of the chosen resident is
P = 4C1 × (0.27)¹ × (0.73)⁽⁴⁻¹⁾
= 4!/ ((4-1)! × 1!) × 0.27 × 0.73³
= 4 × 0.27 × 0.389017
= 0.42013836
≈ 0.42
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part 2. (6 points) normal distributions the normal distribution curve to the right displays the distribution of grades given to managers based on management performance at ford. of the large population of ford managers, 10% were given a grades, 80% were given b grades, and 10% were given c grades. a’s were given to those who scored 380 or higher and c’s were given to those who scored 160 or lower. a. (2 point) what are the z scores associated with the 10th and 90th percentiles from the standard normal distribution? recall that a z-score is value from the standard normal distribution and represents the number of standard deviations a value is away from its mean. b. (2 point) from part a, you should have two values - the z-scores associated with the 10th and 90th percentiles. using these two values and the mathematical definitions of a z-score, calculate the mean and standard deviation of the performance scores? show work. c. (2 point) suppose the company adds grades d and f so there are 5 categories to grade performance. if they want to give a’s only to those in the top 3%, what performance score must a manager exceed to get an a?
Answers
The z-scores for the 10th and 90th percentiles are -1.28 and 1.28, respectively. The mean and standard deviation of the performance scores can be determined using the z-scores and the z-score formula.
a. To find the z-scores associated with the 10th and 90th percentiles from the standard normal distribution, we can use a standard normal distribution table or a calculator. The 10th percentile corresponds to a z-score of approximately -1.28, and the 90th percentile corresponds to a z-score of approximately 1.28.
b. To calculate the mean and standard deviation of the performance scores, we can use the z-score formula and the information given. Let's denote the mean as μ and the standard deviation as σ.
For the 10th percentile (z = -1.28):
-1.28 = (380 - μ) / σ
For the 90th percentile (z = 1.28):
1.28 = (160 - μ) / σ
Solving these two equations simultaneously will give us the values of μ and σ.
c. To find the performance score a manager must exceed to receive an A grade, we need to find the z-score associated with the top 3% of the standard normal distribution. The z-score corresponding to the top 3% is approximately 1.88. Using the z-score formula, we can calculate the corresponding performance score:
1.88 = (X - μ) / σ
Solving this equation for X will give us the performance score needed to receive an A grade.
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Carter buys 20 bottles of grapefruit juice at the corner store for a total
cost of $15. Assume each bottle of juice is the same price. If c
represents the total cost in dollars and cents of the juice for any
number, j, of bottles of juice, write a proportional equation for c in
terms of j that matches the context.
Answers
Answer:
c = 3/4 j your welcome hope this helps
Need help would appreciate it :D
Answers
Answer:
Step-by-step explanation:
i can not see the attachment
Answer:
i would say C if not A i maybe wrong on both but dont hate me, i tried
Step-by-step explanation:
i will give you brainiest if correct
Which situation can be represented by the inequality?
x<90
A. There are 90 children at summer camp.
B. Betty is over the age of 90.
C. A kiddie pool holds under 90 liters of water.
D. A refrigerator weighs more than 90 kilograms.
Answers
Answer:
c
Step-by-step explanation:
Help me with the answer?? Answer please answer to answer ??
Answers
We want to find the value of x, which is the hypotenuse of the triangle on the image.
We will see that the value of x is 5.77 units.
How to find the value of x?On the figure we can see a right triangle, we want to find the value of x, which is the hypotenuse of this triangle.
To do so, we can use the trigonometric relation:
cos(θ) = (adjacent cathetus)/(hypotenuse)
Where θ is an internal angle of the triangle, and the adjacent cathetus is the cathetus that forms the angle.
Here we can use θ = 30°, and the adjacent cathetus is the one that has a measure of 5 units, then the value of x is given by the equation:
cos(30°) = 5/x
Solving that for x we will get:
x = 5/cos(30°) = 5.77
The hypotenuse measures 5.77 units.
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1) Use the method of cylindrical shells to find the volume generated by rotating the region bounded by y=e^(?x^2), y=0, x=0, and x=1 about the y -axis.
2) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
y=sqrt(x?1), y=0, x=5 about the line y=5
3) Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions y=x^2 , y=8?x^2 and to the right of x=1.5 about the y -axis.
Answers
Answer: Number Question #1 - To find the volume generated by rotating the region bounded by y=e^(−x^2), y=0, x=0, and x=1 about the y-axis using the method of cylindrical shells, we can integrate the volume of each cylindrical shell. The radius of each shell will be x, and the height will be e^(−x^2).
Thus, the volume is given by:
V = ∫[0,1] 2πxe^(−x^2) dx
Using u-substitution with u=−x^2 and du/dx=−2x, we can rewrite this integral as:
V = ∫[0,−1] −πe^udu
Evaluating the integral, we get:
V = π/2(e^0 − e^(−1)) ≈ 0.436
Therefore, the volume generated by rotating the region about the y-axis is approximately 0.436 cubic units.
Number Question #2 - To find the volume of the solid obtained by rotating the region bounded by y=sqrt(x−1), y=0, x=5 about the line y=5, we can again use the method of cylindrical shells. In this case, the radius of each shell will be 5−y, and the height will be x−1.
Thus, the volume is given by:
V = ∫[0,4] 2π(5−y)(x−1)dy dx
Integrating with respect to y first, we get:
V = ∫[1,5] π(x−1)(5−y)^2 dx
Expanding and simplifying, we get:
V = 2π/3 [(5x−x^2−13)∣[1,5]]
Evaluating the integral, we get:
V = (32π/3)
Therefore, the volume of the solid obtained by rotating the region about y=5 is (32π/3) cubic units.
Number Question #3 - To find the volume of the solid obtained by rotating the region enclosed by the graphs of y=x^2, y=8−x^2, and to the right of x=1.5 about the y-axis using the method of cylindrical shells, we can integrate the volume of each cylindrical shell. The radius of each shell will be x, and the height will be (8−x^2)−x^2=8−2x^2.
Thus, the volume is given by:
V = ∫[1.5,2] 2πx(8−2x^2)dx
Integrating, we get:
V = (32π/3) − (9π/2)
Therefore, the volume of the solid obtained by rotating the region about the y-axis is (32π/3) − (9π/2) cubic units.
Solve the system of equations using elimination
Answers
Step-by-step explanation:
\(2x + y = 5 \\ - x + y = 2\)
\(y = 2 + x\)
\(2x + x + 2 = 5 \\ 3x + 2 = 5 \\ 3x = 3 \\ x = 1 \\ y = 2 + x \\ y = 3\)
(3x + 12 + 2x³ + x²)/(x + 2)
Answers
Answer: If your simplifying it's: 2x (power of 3) + x (power of 2) + 3x + 12x +2. Dividing would be 2x (power of 2) − 3x + 9 − 6/x+2. Have a nice day ;)
A 20 oz. smoothie cost $3.59. What is the unit price rounded to the nearest cent?
Answers
the area of a square is 7 square meters. is the perimeter of the square a rational or irrational number of meters? explain.
Answers
The perimeter of the square is a rational number of meters. However, the product of a rational number and an irrational number is always irrational.
If the area of a square is 7 square meters, then each side of the square is √7 meters long. The perimeter of the square is simply the sum of the four sides, which is 4√7 meters.
To determine whether 4√7 is a rational or irrational number, we need to check if √7 is rational or irrational. Since √7 is not a perfect square, it cannot be expressed as a fraction of two integers. Therefore, √7 is an irrational number.
However, the product of a rational number and an irrational number is always irrational. Since 4 is a rational number and √7 is irrational, the product 4√7 is also an irrational number.
Therefore, the perimeter of the square is an irrational number of meters.
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One section of the reporting period test in history had 35 true or false questions. Maria answered 75% of the questions correctly. How many of the questions did she answer incorrectly?
Answers
Answer:
29 correct
Step-by-step explanation:
i honestly dont know how to explain this so its probably wrong but you know...
Which of the following is the equation of the line that has a slope of 3 and passes through the point (0, 9)?
Answers
Answer:
Step-by-step explanation:
y - 9 = 3(x - 0)
y - 9 = 3x - 0
y = 3x + 9
If Judy has 4 blouses and 5 skirts, how many different outfits of a blouse and skirt can she wear?
Answers
Answer:
20
Step-by-step explanation:
i think but not fur shure
So you have 1 shirt , all 5 skirts can go with that shirt.
Shirt # 1: 5 fits & same for all others - so the correct answer would be 20 outfits.
Are null and alternative hypotheses statements about samples, about populations, or does it depend on the situation? explain.
Answers
Alternative and null hypotheses are always based on populations.
A population cannot have both the alternative hypothesis and the null hypothesis be true. A hypothesis test determines whether to accept or reject the null hypothesis based on sample data.
null assumption (H0)
Under the null hypothesis, a population parameter (such as the mean, standard deviation, and so on) is equal to an assumed value. Often, the first claim that constitutes the null hypothesis is based on prior research or expert knowledge.
alternative hypotheses (H1)
A population parameter is either less, greater, or different from the value assumed by the alternative hypothesis, according to the former. The alternative hypothesis is what you could believe to be accurate or what you aim to prove.
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A Ferris wheel rotates 9π/8 radians prior to making a stop. The total height of the Ferris wheel is 246 ft. How far around did the Ferris wheel travel?
Answers
Answer:
The ferris wheel travelled 434.717 ft.
Step-by-step explanation:
Assuming that the ferris wheel is a perfect circle, then it's height is the same as the diameter of the circle, therefore it's radius is:
radius = height/2 = 246/2 = 123 ft
The distance travelled by the ferris wheel is the same as the length of the arc created by a angle of (9pi/8). The length of an arc is given by:
length = r*(angle in radians)
length = 123*(9pi/8)
length = 434.717 ft
The ferris wheel travelled 434.717 ft.
How will the difference of two numbers change if:(−3) is added to the subtrahend?
Answers
Answer:
When you add (-3) to the subtrahend, the difference between two numbers will decrease by 3. For example, if the two numbers are 6 and 3, then the difference between them is 3. If you add (-3) to the subtrahend (3), then the difference will become 0 (3 - (-3) = 6).
Which relation is a function?
Answers
Answer:
I think B every input has one output. let me know if I was wrong or right
Young Professional magazine was developed for a target audience of recent college graduates who are in their first 10 years in a business/professional career. In its two years of publication, the magazine has been fairly successful. Now the publisher is interested in expanding the magazine’s advertising base. Potential advertisers continually ask about the demographics and interests of subscribers to Young Professional. To collect this information, the magazine commissioned a survey to develop a profile of its subscribers. The survey results will be used to help the magazine choose articles of interest and provide advertisers with a profile of subscribers. As a new employee of the magazine, you have been asked to help analyze the survey results.what do young professional be a good advertising outlet for online brokers justify your conclusion with statistical data?
Answers
The majority of Young professional subscribers are interested in personal finance and investment opportunities.
Young Professional magazine would be a good advertising outlet for online brokers because its target audience consists of recent college graduates who are in their first 10 years in a business/professional career. This demographic is likely to have a high level of education, which means they are more likely to understand and be interested in investment opportunities. Additionally, as young professionals, they are likely to have a higher disposable income and a desire to invest and grow their wealth.
According to the survey results, the majority of Young Professional subscribers are interested in personal finance and investment opportunities. This makes the magazine an ideal outlet for online brokers to advertise their services and reach potential customers. The survey also revealed that the majority of subscribers are tech-savvy and comfortable with online transactions, which makes them more likely to be interested in using online brokers for their investment needs.
Overall, the demographics and interests of Young Professional subscribers make it a good advertising outlet for online brokers. By advertising in the magazine, online brokers can reach a highly educated, tech-savvy, and financially motivated audience that is likely to be interested in their services.
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i need help with this
Answers
Answer:
7x^2 + 8x-7
7×4^2 + 8×4-7
7×16+32-7
112+25
137
15 On Saturday, Luisa paints for 2 hours.
On Sunday, she paints for 40 minutes.
How many minutes does Luisa paint
for in total on these two days?
Answers
Answer:
160 minutes
Step-by-step explanation:
Find out how many minutes are in a hour. 60 min in one hour. 60 x 2 = 120
120 + 40 = 160
PLEASE HELP FAST!!
8. Find the unknown side of the triangle below. Show your work. 17 in 8 in X
Answers
Answer:
the unknown side of triangle is 15 in :)
In a certain youth soccer league, there are 10 teams. Each game in the season is a match between two teams from the league. If each team plays each of the other teams exactly one time, how many games are played in a season?
Answers
There are 45 games played in a season of the youth soccer league with 10 teams.
In a youth soccer league with 10 teams, each team will play against every other team exactly once.
To determine the number of games played in a season, we can use the combination formula, which calculates the number of ways to choose 2 teams from a set of 10 teams. Each combination represents a unique game.
The formula for combinations, also known as the binomial coefficient, is:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items and r is the number of items to be chosen.
In this case, we have 10 teams, and we need to choose 2 teams for each game.
Using the combination formula, we can calculate the number of games played as:
C(10, 2) = 10! / (2! * (10 - 2)!)
= 10! / (2! * 8!)
= (10 * 9) / (2 * 1)
= 45
Therefore, 45 games are played in a season.
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1 Point
Which statement best describes the end behavior of the following function?
F(x) = 3x +4x3 - X+11
A. The graph of the function starts low and ends high.
B. The graph of the function starts high and ends high.
C. The graph of the function starts low and ends low.
D. The graph of the function starts high and ends low.
Answers
Answer:
The graph of the function starts high ends low
Step-by-step explanation:
I put the equation into Desmos
The captain of a ship must use extreme caution when approaching an iceberg, because only 0.125 of it is above the surface of the water. What percent of the iceberg is NOT visible above the water?
Answers
The percent of the iceberg which is not visible above the water could be 12.5%.
What is percentage ?
percentage can be defined as the product of ratio of value and total value and 100 .
Given, the captain of a ship must use extreme caution when approaching an iceberg, because only 0.125 of it is above the surface of the water
so the percent of the iceberg which is not visible could be
0.125 * 100 = 12.5 %
Hence , the percent of the iceberg which is not visible above the water could be 12.5%.
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➡) Which ratios have a unit rate of 3? Choose ALL that apply. 2 cups : 2 3 cup 3³14 3- cups: 2 cups 4 2 3 cup: 1 cup 1 1 cup: cup 15 K 1 2 cups cup 2 15 2 5 6 1 cups: 22 2 cups
Answers
The ratios that have a unit rate of 3 include the following:
A. 15/2 cups: 2 1/2 cups
C. 2 cups: 2/3 cups
F. 2 1/2 cups: 5/6 cups
What is the unit rate?In Mathematics, the unit rate is sometimes referred to as unit ratio and it can be defined as the quantity of material that is equivalent to a single unit of product or quantity.
15/2 cups : 5/2 cups
15/2 ÷ 5/2 : 5/2 ÷ 5/2
15/2 × 2/5 : 1
3 : 1 (True)
1 cup: 1/4 cups
1 × 4 : 1/4 × 1
4 : 1 (False)
2/3 cups: 1 cup
2/3 × 3/2 : 1 × 3/2
1 : 3/2 (False)
3 3/4 cups: 2 cups
(4 × 3 + 3)/4 : 2
15/4 : 2
15/8 : 2/2
15/8 : 1 (False).
2 cups: 2/3 cups
2 × 3/2 : 2/3 × 3/2
3 : 1 (True).
2 1/2 cups: 5/6 cups
(2 × 2 + 1)/2 : 5/6
5/2 : 5/6
5/2 × 6/5 : 5/6 × 6/5
3 : 1 (True).
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Complete Question:
Which ratios have a unit rate of 3? Choose all that apply.
15/2 cups: 2 1/2 cups
1 cup: 1/4 cups
2/3 cups: 1 cup
3 3/4 cups: 2 cups
2 cups: 2/3 cups
2 1/2 cups: 5/6 cups
I need help on how to find a surface area! I will send the full photo!
Answers
we are asked to determine the surface area of the figure. To do that we need to find the areas of each face and add them together. The front face is a trapezoid, and its area is:
\(A_{tz}=\frac{b+B}{2}h\)Where "b" is the upper base, "B" is the lower base and "h" is the height. Replacing the values:
\(A_{tz}=\frac{9ft+4ft}{2}\times4.3ft\)Solving the operations:
\(A_{tz}=28ft^2\)the upper face is a rectangle, its area is the product of its side:
\(A_{uf}=(10ft)(9ft)=90ft^2\)The area of the lower face is also a rectangle, therefore its area is:
\(A_{lf}=(4ft)(10ft)=40ft^2\)The side face is also a rectangle, and its area is:
\(A_{sf}=(5ft)(10ft)=50ft^2\)Now we add the areas having into account that the front and side faces repeat themselves. the total surface area is:
\(A=2A_{tz}+A_{uf}+A_{lf}+2A_{sf}\)replacing the values:
\(A=2(28ft^2)+(90ft^2)+(40ft^2)+2(50ft^2)\)Solving the operations:
\(A=286ft^2\)Therefore, the surface area is 286 square feet.