if a circle passe though point (-4,2) and is tangent to the x-axis at (2,0), determine the coordinates of its center.
Answers
The coordinates of its center will be (2,10)
How can we express the equation of the circle?(x - h)²+ (y - k)² = r² is the formula for the equation of a circle, where (h, k) stands for the circle's center's coordinates and r for the radius.
A circle with a radius of r and a center is represented as
(x - a)² + (y - b)² = r² where (a, b) is the center of the circle.
Circle passes points (-4, 2) and (2, 0):
Both (-4 - a)² + (2 - b)² and (2 - a)² + (-b)² are equal to r²
Currently, the center's x coordinate (a) is 2 due to the tangent at (2, 0)
The equations then read:
6² + (2 - b)² = r²
b² = r²
⇒ 36 + (2 -b)² -b² = 0
⇒ 36 + 4 + b² - 4b - b² = 0
⇒ 4b = 40
⇒ b = 10.
So, the center is (2,10)
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Related Questions
What is the interest of an investment of $2,000 made at 6% simple interest per year for a time period of 9 mo.?
Answers
Answer:The answer would be $1080.
bruce and krista are going to buy a new furniture set for their living room. they want to buy a couch, a coffee table, and a recliner. they have narrowed it down so that they are choosing between 4 couches, 5 coffee tables, and 9 recliners. how many different furniture combinations are possible? PLEASE ANSWER
Answers
Answer:
180
Step-by-step explanation:
This is becuase 4*5*9 is equal to 180, to find the total number of combinations, you multiply how many of each there are.
What is the greatest possible error for a measurement of 0.05 metric tons?
Answers
Answer:The greatest possible error of a measurement is considered to be one-half of the measuring unit. If you measure a length to be 4.3 cm. (measuring to the nearest tenth), the greatest possible error is one-half of one tenth, or 0.05. This means that any measurements in the range from 4.25 cm. to 4.35 cm. are perceived as correct.
Step-by-step explanation:
Answer:
The greatest possible error for a measurement of 0.05 metric tons would depend on the accuracy of the measurement device or technique being used. Without more information about the specific measurement method, it is impossible to determine the greatest possible error.
Step-by-step explanation:
María tiene en su libreta de ahorros un capital de 123.000,si deposita el día lunes la cantidad de 12.670 .El día miércoles por una urgencia , realiza un giro de 56.000¿cual es el nuevo capital que posee? Escribe la operación utilizando números enteros
Answers
Answer:
$79.670.
Step-by-step explanation:
Dado que María tiene en su libreta de ahorros un capital de $ 123.000,si deposita el día lunes la cantidad de $12.670, y el día miércoles por una urgencia, realiza un giro de $56.000, para determinar cuál es el nuevo capital que posee se debe realizar el siguiente cálculo:
123.000 + 12.670 - 56.000 = X
135.670 - 56.000 = X
79.670 = X
Así, el nuevo capital que María posee en su cuenta es de $79.670.
7. The quality control division of Rothschild's Blueberry Farm randomly inspects 100 of the containers in the truck being
sent to Stop and Shop. Identify the population and sample given in this scenario.
Answers
The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Population: The containers of blueberries that are being sent to Stop and Shop.
Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
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4) Sara took a ferry to a nearby island that lasted for 5 days. Although she forgot to check the date when she departed, during the trip she heard someone say the date was August 14". When she arrived on the island, a native told Sara it was August 16th. What date did Sara start her trip?
Answers
In triangle ABC, the size of angle B is 5 times the size of angle A, and the size of angle C is 11 degrees less than 4 times the size of angle A.
Find the size of the angles.
Answers
Answer:
A = 19.1°
B = 95.5°
C = 65.4°
Step-by-step explanation:
B = 5A
C = 4A-11
We know that a triangle has a total of 180° so:
180 = A + B + C
Which can be written as:
180 = A + (5A) + (4A - 11)
180 = 10A - 11
10A = 191
A = 19.1°
With A, we can work out B and C:
B = 5(19.1)
B = 95.5°
C = 4(19.1) - 11
C = 76.4 - 11
C = 65.4°
The coffee shop on the corner of the street has 14 cheese croissants and 21 plain croissants. If
buy 1 cheese croissant will the ratio of each cheese croissant to plain croissant remain the
same? Explain your answer."
Plss helpppp
Answers
Does anyone understand this? Please answer
Answers
Answer:
Step-by-step explanation:
So pretty much, when you have a negative exponent, it is the reciprocal of the number.
So, 28796^-1 = 1/28796
671 x 1/28796
=671/28796
I'm not sure if your teacher wants you to simplify or put your answer in a decimal, but I hope this helped.
$9000.00 decreased by 0.5% is what?
Answers
Answer:
8955$
It got deleted because an idiot reported me.
ola has 4
1
2
cups of rice. She uses
3
4
of the rice to make sushi rolls for dinner. She uses the rest of the rice to make rice pudding for dessert. How much rice does Lola use for the rice pudding?
Answers
The amount of cups that Lola uses to make the rice pudding for dessert is 3 3/4 cups.
How many cups were used to make rice pudding?
A fraction is a number that is made up of numerator and denominator. An example of a fraction is 3/4.
Number of cups were used to make rice pudding = number of cups Ola has - number of cups used to make sushi rolls
4 1/2 - 3/4
4 4 2-3/4 = 3 3/4 cups
What is fraction ?
A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.
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find the cost of four score of plate at 50k each and three dozens of spoon at 20k each
Answers
= 260K
1.
If'C is the midpoint of the line segment joining points A(4,1) and
B(2,3), then y-coordinate of point ' C is 4
TRUE
FALSE
Answers
Answer:
false
Step-by-step explanation:
Answer:false
Step-by-step explanation:
a can of soda has a height of 4.8 inches. its diameter is 2.6 inches. what is the volume of the can
Answers
Volume = Base area × height
V = ( π × r^2 ) × 4.8
V = ( π × ( 2.6/2 )^2 ) × 4.8
V = ( π × (1.3)^2 ) × 4.8
V = ( π × 1.69 ) × 4.8
V = π × 1.69 × 4.8
V = 8.112 π in^2
The volume of the can is 8.112π cubic inches.
What is volume?The space occupied by an object in three-dimensional space is called the volume of an object. In simple words, space is taken by an object.
Given:
A can of soda has a height of 4.8 inches.
Its diameter is 2.6 inches.
Then the radius is 2.6/2 = 1.3 inches.
The volume of the can,
= the volume of the cylinder
= πr²h
= π(1.3)²(4.8)
= 8.112π
Therefore, the volume is 8.112π cubic inches.
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15.35m rounded to the nearest whole number
Answers
Answer:
The answer is 15m
Step-by-step explanation:
The meaning whole number means an actual whole number, decimals are just part's of a whole number, so excluding decimals:
If you look at 5 and compare it to 3 following next, 3 is not higher then 5 and therefore is rounded down.
Hope this helps!
New game You pay 10 and roll a 6 die. If you get a you win 50 If not, you get to roll again. If you get a 6 this time, you get your 10 back.a) Create a probability model for this game.b) Find the expected value and standard deviation of your prospective winnings.c) You play this game five times. Find the expected value and standard deviation of your average winnings.d) 100 people play this game. What's the probability the person running the game makes a profit?
Answers
The probability mode for the given value is created. The expected value and standard deviation of prospective winnings are -$0.28 and $18.33. The expected value and standard deviation if the game is played five times are -$1.40 and $40.99. The probability that the person running the game makes a profit is 0.561.
Probability is a way to determine how likely something is to happen. It is computed by dividing the frequency of the event by the total number of outcomes. The formula then becomes P(X) = frequency of the event÷total number of outcomes.
The product of the probabilities determines the likelihood that two or more occurrences will coincide. This is given by, P(A and B) = P(A)P(B).
a) To create a probability model follow the steps. Let X is an occurrence of an event. The table is attached here.
b) The expected value is calculated using the formula, E(X) = μ = ∑ x P(x).
\(\begin{aligned}E(X)=\mu&=x_1p_1+x_2p_2+x_3p_3\\&=40\left(\frac{1}{6}\right)+0\left(\frac{5}{36}\right)+(-10)\left(\frac{25}{36}\right)\\&=-\$ 0.28\end{aligned}\)
Also,
\(\begin{aligned}E(X^2)&={x_1}^{2}p_{1}+{x_2}^{2}p_{2}+{x_3}^{2}p_{3}\\&=(40)^2\frac{1}{6}+(0)\frac{5}{36}+(-10)^2\frac{25}{36}\\&=(1600)\frac{1}{6}+(0)\frac{5}{36}+(100)\frac{25}{36}\\&=266.67+69.44\\&=336.11\end{aligned}\)
And the standard deviation is calculated using the formula, σ=√Var[X].
\(\begin{aligned}\sigma=\sqrt{\text{Var}(X)}&=\sqrt{E(X^2)-E(X)^2}\\&=\sqrt{336.11-0.08}\\&=\sqrt{336.03}\\&=\$18.33\end{aligned}\)
c) The expected value and standard deviation for playing the game 5 times are calculated as follows.
The expected value is,
\(\begin{aligned}5\times E(X)&=5(-\$0.28)\\&=-\$1.40\\\end{aligned}\)
The standard deviation is,
\(\begin{aligned}\sigma&=\sqrt{5\times\tex{Var}(X)\\&=\sqrt{5\times336.03\\&=\sqrt{1680.15}\\&=\$40.99\end{aligned}\)
d) The dice rolling is random and the winning chance is independent. The probability the person running the game makes a profit (P(x<0)) is given by,
The population mean, μ(Y) = -$0.28
The standard deviation for a population of 100 is,
\(\begin{aligned}\sigma&=\sqrt{\frac{\text{Var}(X)}{n}}\\&=\frac{18.33}{\sqrt{100}}\\&=1.83\end{aligned}\)
The z-score for mean winning is,
\(\begin{aligned}z&=\frac{x-\mu}{\sigma}\\&=\frac{0-(-0.28)}{1.83}\\&=0.153\end{aligned}\)
For a person to make a profit, the mean winning of the player should be less than the z-score. Then,
The P-value from the z-table, P(z<0.153)=0.5608
The answer is 0.561.
The complete question is -
You pay $10 and roll a die. If you get a 6, you win$50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What’s the probability the person running the game makes a profit?
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An elevator has a placard stating that the maximum capacity is 1884 lb-12 passengers. So, 12 adult male passengers can have a mean weight of up to 1884/12=157 pounds. If the elevator is loaded with 12 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 157 lb. (Assume that weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.) Does this elevator appear to be safe? BICICIE The probability the elevator is overloaded is (Round to four decimal places as needed) Does this elevator appear to be safe? OA. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity OB. No, 12 randomly selected people will never be under the weight limit. OC. Yes, there is a good chance that 12 randomly selected people will not exceed the elevator capacity OD. Yes, 12 randomly selected adult male passengers will always be under the weight limit. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275. Round to four decimal places. www OA. 0.4332 OB. 0.9332 OC. 0.5000 OD. 0.0668 Find the value of the linear correlation coefficient r. The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Cost 9 2 3 5 9 10-> 4 2 68 67 Number 52 55 85 A. 0.235 OB. 0.708 OC. 0.246 OD. -0.071 86 83 73
Answers
The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.
Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:
Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.
We can write as below:
Maximum capacity per person=1884/12=157lb.
And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586
Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.
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How are ROC (rate of change) and slope related AND different
Answers
Answer:
Rate of change and slope is the same since they are both terms of every rate, but rate of change can be said in any terms as in exponential and linear, etc. While slopes are only for linear equations.
Step-by-step explanation:
Hope this helps :)
Help! i don't understand :/
Answers
Answer:
Option C
Step-by-step explanation:
Given inequality is,
-3(2x - 4) ≤ 7(3 - x)
Solve the given inequality further,
-6x + 12 ≤ 21 - 7x
(-6x + 12) + 7x ≤ (21 - 7x) + 7x
x + 12 ≤ 21
(x + 12) - 12 ≤ 21 - 12
x ≤ 9 Or {x real | x ≤ 9}
Therefore, Option C will be the correct option.
Answer:
this is your answer look it once
Alex defeated 10 gyms today! She started with four hundred and forty coins and now has five hundred and forty coins
Find the Percent of increase
Answers
The percentage increase is 22.72%
How to determine the percentage increase?The given parameters are:
Initial = 440 coins
Final = 540 coins
The percentage increase is calculated as:
%Increase = (Final - Initial)/Initial * 100%
So, we have:
%Increase = (540 - 440)/440 * 100%
Evaluate the difference
%Increase = 100/440 * 100%
Evaluate the quotient
%Increase = 0.2272 * 100%
Evaluate the product
%Increase = 22.72%
Hence, the percentage increase is 22.72%
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The area of a square whose side is 5 cm is
Answers
Answer:
25
Step-by-step explanation:
5 x 5 = 25
Answer:
the area is 20
Step-by-step explanation:
each side is 5 and a square has 4 sides
5x4=20
pls help me thank you!
Answers
Answer:
5%
Step-by-step explanation:
Simple interest formula I = Prt
I is the interest
P is the principal
r is the rate
t is the time
so
1400 = (4000)r(7)
r = 1400/(4000 x 7)
r = 0.05 or 5%
The table shows the cost of 4 movie tickets at two theaters. Theater Cost ($) Movies Galore 30 Star Cinema 31 What equation can be used to model the total cost y for x tickets at Star Cinema? Write the equation in the form
Answers
The cost of x tickets for Star Cinema is; y = 7.5x
How to create equation word problems?
From the given table, we see that;
Cost of 4 tickets at Movie Galore = $31
Cost of 4 tickets at star Cinema = $30
Thus, we can find the cost of one ticket for each of the cinema's as;
Cost per ticket for Movie Galore = 31/4 = $7.75
Cost per ticket for Star Cinema = 30/4 = $7.5
Thus, cost of x tickets for Star Cinema is;
y = 7.5x
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Answer:
Step-by-step explanation:
The price of an item has risen to $207 today. Yesterday it was $180. Find the percentage increase
Answers
Answer:
15% '
Step-by-step explanation:
Price yesterday = $180
Price today = $207
Increase in price = $(207 - 180)
=> $27
Percent increase =
Increase / Price of yesterday
=> 27 / 180 * 100
=> 3 / 2 * 10
=> 30 / 2
=> 15
15%
Therefore, the rise in the price of the item = 15%
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What are the zeroes of f(x) = x2 + 5x + 6? (1 point) x = −2, −3 x = 2, 3 x = −2, 3 x = 2, −3
Answers
Answer:
\(x = - 2 - \sqrt{2i} \: \: - 2 + \sqrt{2i} \)
Step-by-step explanation:
\(1. \: x - {x}^{2} - 5x - 6 = 0 \\ 2. \: - 4x - {x}^{2} - 6 = 0 \\ 3. \: x = \frac{4 + 2 \sqrt{2i} }{ - 2} \: \: \frac{4 - 2 \sqrt{2i} }{ - 2} \\ 4. \: x = - 2 - \sqrt{2i} \: \: - 2 + \sqrt{2i} \)
Khali and Juan are using ribbon to decorate their art project. The ratio of the length of Khali’s ribbon to the length of Juan’s ribbon is 8:5.
If Khali used a total of 72 cm of ribbon, how much did Juan use?
Answers
Answer:
45 cm
Step-by-step explanation:
First, you want to clarify the ratio:
Khali = 8 cm = 72 cm
____ _____ ______
Juan = 5 cm = x cm
To find the missing variable, cross multiply and simplify for x:
8x = 72(5)
8x = 360
x = 45
So, Juan used 45 cm of ribbon if Khali used 72 cm.
If area of rectangle is 42 cm and length is 2/5 cm what is width??
Answers
i want one halve of a cupcake for myself 4 halves for my friend and 3 halves for my other friend
Answers
Answer: Split it into 8 pieces.
Step-by-step explanation: If there is 4 halves for your friend, and 3 halves for your other friend, that will be 7. If you add another one, it will be 8. Therefore, you should split the cupcake into 8 pieces.
Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class,
5
55 want an ice cream party,
7 77 want a movie party,
10 want a costume party, and the rest are undecided.
If 20% percent want an ice cream party, how many students are in the class?
Answers
Step-by-step explanation:
let 'x' represent the total number of students in the class
5 = 20% of x
0.20x = 5 divide both sides by 0.20
x = 25 students
there are 25 students in the class.
I'm not sure about the answer but still I think its right.....
A shirt is on sale 60% of the Original price.The oiginal price is $28 more then the sale price.What was the original price
Answers
Step-by-step explanation:
To solve for this problem you can write and equation with × being the original price:
6x + 28 = X
Solving for x you you can get:
28 = 4x
× = 70