Answer:
(x + 5)² + (y - 4)² = 17
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Here (h, k ) = (- 5, 4 ) , then
(x - (- 5) )² + (y - 4)² = r² , that is
(x + 5)² + (y - 4)² = r²
r is the distance from the centre to a point on the circle
Calculate r using the distance formula
r = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = (- 5, 4) and (x₂, y₂ ) = (- 1, 5)
r = \(\sqrt{(-1+5)^2+(5-4)^2}\)
= \(\sqrt{4^2+1^2}\)
= \(\sqrt{16+1}\)
= \(\sqrt{17}\) ⇒ r² = (\(\sqrt{17}\) )² = 17
Then
(x + 5)² + (y - 4)² = 17 ← equation of circle
Answer:
x² + y² + 10x - 8y + 24 = 0
Step-by-step explanation:
equation of a circle :-
equation of a circle :-(x - h)² + (y - k)² = r²
(h, k) is the center of the circle R is the radius of the circlefor this circle :-
h = -5k = 4R = ?finding radius of the circle
we've been given a point ( -1, 5) that lies on the circle and hence should satisfy the equation of the circle
putting x = -1 and y = 5
=> (-1 - (-5))² + (5 - 4)² = r²
=> (-1 + 5)² + 1² = r²
=> 4² + 1 = r²
=> 17 = r²
\( = > r = \sqrt{17} \)
the radius if the circle is √17 units
__________________________________
finding the equation of the circle
=> (x + 5)² + (y - 4)² = (√17)²
=> x² + 25 + 10x + y² + 16 - 8y = 17
as for any two variables a and b, (a + b)² = a² + b² + 2ab=> x² + y² + 10x - 8y + 24 = 0
A bank account starts with a balance of £8000 and pays compound interest of 5% per year. Work out the balance of the account after 1 year and after 2 years.
The balance of the account after 1 year and after 2 years 16400 and 16820 is respectively.
A bank account starts with a balance, P = $8000
rate of interest = 5%
compound interest for 1 year is :
\(CI = P(1 + R/100)^n\)
CI = 8000(1 + 5/100)
CI = 8000(1 + 1/20)
CI = 8000(21/20) = 8400
A = CI + P = 8000 + 8400 = 16400
compound interest for 1 year is :
\(CI = P(1 + R/100)^{2n}\)
CI = 8000(1 + 5/100)^2
CI = 8000(1 + 1/20)^2
CI = 8000(21/20)^2 = 8820
A = CI + P = 8000 + 8820 = 16820
The balance of the account after 1 year and after 2 years 16400 and 16820 is respectively.
To know more about interest
https://brainly.com/question/25845758
#SPJ1
Write the measurement indicated using the picture
Answer:
8 centimeters
Explanation:
We know that the ruler indicates it's from 76 - 92. In order to find out the measurement indicated you just need to know where the arrow ends and begins. Once you do you subtract the difference. Therefore, 92 - 84 is equal to 8.
find a b, 2a 3b, |a|, and |a − b|. a = 3, −4 , b = −3, 4
10 , [ -3 , 4 ] and [ 0 , 0 ] are the values in linear equation .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
a = [ 3, -4 ]
b = [ -3,4 ]
a + b = [ 3, -4 ] + [ -3,4 ]
= [ 0 , 0 ]
2a + 3b = 2 [ 3, -4 ] + 3 [ -3,4 ]
= [6 , -8 ] + [-9 , 12 ]
= [ -3 , 4 ]
l a - b l = l [ 3, -4 ] - [ -3,4 ]
= l [ 6 , -8 ] l
= √36 + 64
= √100
= 10
Learn more about linear equation
brainly.com/question/11897796
#SPJ4
consider the following data values of variables x and y. x 2 4 6 8 10 13 y 7 11 17 21 27 36 the slope of the least squares regression line is approximately which of the following: a. 1.53 b. 2.23 c. 2.63 d. 2.08
The slope of the least squares regression line for the given data values of variables x and y is approximately 2.08. This indicates that, on average, for every unit increase in x, y is expected to increase by approximately 2.08 units.
The slope of the least squares regression line, calculated using the given data values of variables x and y, is approximately 2.08.
The least squares regression line is used to determine the relationship between two variables by minimizing the sum of the squared differences between the observed values of y and the predicted values based on x. In this case, the data points suggest a positive relationship between x and y. The slope of the regression line represents the change in y for every unit change in x. By calculating the least squares regression line using the given data, the slope is determined to be approximately 2.08.
Learn more about regression here: https://brainly.com/question/29753986
#SPJ11
i need a bit help. Mason has 2 hours of free time. He spent 20 minutes playing outside, 25 minutes on his phone, and the rest of the time practicing his instrument. What percent of his time was spent playing his instrument?
Answer:
Step-by-step explanation:
He spent 62.50 percent of his time playing his instrument. In minutes he spent 75 playing his instrument.
Please Help !!!
Sam found that if the product of 5 and a number is increased by 40, the
result is 121 more than the product of 2 and the number. What is the
number?
Answer:
the number is 45
Step-by-step explanation:
factorize 5y^2- 125z^2
Answer:
\(5\left(y+5z\right)\left(y-5z\right)\)
Step-by-step explanation:
\(\mathrm{The \;given \;equation \;is \; 5y^2-125z^2}\)
\(\mathrm{Factor\:out\:common\:term\:}5:\quad 5\left(y^2-25z^2\right)\\\\= 5\left(y^2-25z^2\right)\)
\(\left y^2-25z^2\right\)
\(25z^2 = \left(5z\right)^2\)
==> \(\left y^2-25z^2\right = y^2-\left(5z\right)^2\)
\(\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)\)
\(y^2-\left(5z\right)^2=\left(y+5z\right)\left(y-5z\right)\)
So the factored expression is
\(5\left(y+5z\right)\left(y-5z\right)\)
helppp asap pleaseee!
Answer:
FOR (i) The answer will be 40
FOR(ii) Draw a rectangle and two intersecting circles.
The middle intersection part will have 20
The left circle (TEA) will have 40
Right circle (COFFEE) will have 55
Outside then circle, put 10.
FILL THE BLANK.a ______ is the product of one number multiplied by another number A.Factor B.Prime C.Multiple D.Factorization
A factor is the product of one number multiplied by another number. When you multiply two or more numbers together, the original numbers are called factors.
Consider the following example: Factor pairs are two numbers that, when multiplied together, produce a specific product. The factor pairs of 12 are:1 x 12 = 122 x 6 = 123 x 4 = 12A factor is a number that divides into another number evenly. A factor is a divisor. Every number has at least two factors: one and itself.
A factor of a number is any number that divides into it evenly, leaving no remainder. Therefore, the correct answer to the given blank is A. Factor.
Factors are numbers that are multiplied to obtain a result, and they are commonly used in mathematics. They're an important component of problem-solving. In factoring, you'll break down an equation into smaller parts to make it more manageable, and then combine those smaller parts to solve the problem.
Factorization is the process of writing a number as a product of two or more factors. For example, the factorization of 12 is 2 × 2 × 3. The prime factorization of a number is the factorization in which all factors are prime.
Learn more about factor from the given link
https://brainly.com/question/14549998
#SPJ11
What is the value of 3-(-2)?
Answer:
5
Step-by-step explanation:
keep change flip
3 - -2
3 + 2
- x3 + 4x2 – 3x + 12 when x = -2
Answer: 42
Explanation:
Image below
Answer choices
It is positive and increasing
It is positive and decreasing
It is negative and increasing
It is negative and decreasing
Answer:
A
Step-by-step explanation:
the graph goes up and the value of y increases
Which digits are in the millions period of the number 21,468,127,471?
The digits in millions period of the number is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.
Given the number is 21,468,127,471.
The digits in which are given in the large numbers are in groups of three places. The groups are called periods. Commas are usually used to separate the periods.
The groups of numbers are 3 digit group and which is starting from the right to left.
As we all know that we read the group of periods as ones, tens, hundreds, thousand, ten thousand, hundred thousand, million, ten million, hundred million, billion etc.
From the above, we find that the given number 21,468,127,471 contains digit 1 is in the ones place, 7 is in the tens place, 4 is in the hundredth place, 7 is in the thousand place, 2 is in the ten thousand place, 1 is in the hundred thousand place, 8 is in the million place, 6 is in the ten million place, 4 is in the hundred million place , 1 is the billion place and 2 is in the ten bilion.
Hence, the digits in millions period of the given number 21,468,127,471 is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.
Learn more about millions from here brainly.com/question/17806392
#SPJ9
Show work how you know it’s a function or not a function for each problem. PLEASE SOMEONE HELP ME OUT
Answer: Function, not a function, Function, not a function
Step-by-step explanation:
For it to be a function, each value of x has to map onto one value of y.
This is a function.Not a function since x=-1 has more than one y value.This is a functionNot a function since x=-6 has more than one y value.Write a story that can be represented using the equation y=x+1/5x
A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.
This can be illustrated as:
y = x + 1/5x
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
-10a+1/2(-8a+4) simplify the expression
Whenever a sample is taken, the survey will reflect: Select one: a. The entire population. b. Sample size. c. The subpopulation. d. Sampling error.
Whenever a sample is taken, the survey will reflect sampling error.
Option D is the correct answer.
We have,
Whenever a sample is taken, the survey will reflect sampling error.
Sampling error refers to the discrepancy or difference between the characteristics or values observed in a sample and the true characteristics or values of the entire population.
It arises due to the fact that a sample is only a subset of the population and may not perfectly represent the entire population.
Sampling error can occur due to various factors such as random sampling variation, non-response bias, sampling bias, and other sources of error in the sampling process.
It is important to consider and account for sampling errors when interpreting the results of a survey or study based on a sample.
Thus,
Whenever a sample is taken, the survey will reflect sampling error.
Learn more about sampling error here:
https://brainly.com/question/29974523
#SPJ4
The thickness of a conductive coating in micrometers has a density function of 600x-2 for 100 ?m < x < 120 ?m. What is the mean of the coating thickness (in ?m). What is the variance of coating thickness (in ?m2 ). If the coating costs $0.50 per ?m of thickness on each part, what is the average cost of the coating per part? (in dollars)
Given that a conductive coating in micrometers has a density function of 600x-2 for 100 ?m < x < 120 m.
We are to determine the mean and variance of the coating thickness and the average cost of the coating per part.
Step 1: Mean of the coating thickness: Mean μ = ∫xf(x)dx, where f(x) is the probability density function of x.μ = ∫100x(600x-2)dx [120-100]μ = 196.078 μm
Therefore, the mean of the coating thickness is 196.078 μm.Step 2: Variance of the coating thickness: Variance σ² = E(x²) - [E(x)]² where E(x²) and E(x) are the expected values of x² and x respectively(x²) = ∫x²f(x)dx, [120-100]E(x²) = 13,336.40μ²E(x) = ∫xf(x)dx, [120-100]E(x) = 38,422.59μ²σ² = E(x²) - [E(x)]²σ² = 2,193,272.27 μ²
Therefore, the variance of the coating thickness is 2,193,272.27 μ².Step 3: Average cost of the coating per part:We have been given that the cost of the coating is $0.50 per μm of thickness on each part.
Hence, the average cost of the coating per part is:$0.50 x 196.078$ = $98.04
Therefore, the average cost of the coating per part is $98.04.
For more information on average cost visit:
https://brainly.com/question/14415150
#SPJ11
PLEASE HELP Ten years ago, Elijah bought shares of stock
at $1.65 each. The value of the stock is now
1.4 times higher than it was when he
purchased it. How much is the stock worth
per share now?
Answer:
2.31
Step-by-step explanation:
1.65 * 1.4 = 2.31
Please help me due tomorrow morning
Answer: Y=-5
Step-by-step explanation:
The reason is because if you look down the y axis from the origin you can see the location where the line crosses over the y axis in this case it was at (0,-5)
The two shorter sides of a triangle measure 12 cm and 18 cm. which of the following could be the length of the longest side of the triangle?
1. 30 cm
2. 17 cm
3.27 cm
4. 11 cm
A rock thrown to the right with an initial horizontal velocity of 4 m/s lands after 5 seconds. What horizontal distance has the rock traveled? (hint: there is no air resistance).
20m of horizontal distance the rock traveled during its time of flight.
s= v*t . (when there is no air resistance )
where s is horizontal distance travelled by the rock
v is horizontal speed
t is time of flight
given v= 4m/s , t = 5s
so s = 4 m/s * 5s = 20 m
So the horizontal distance covered by the rock is 20m
To know more about time of flight click on link below:
https://brainly.com/question/29630737#
#SPJ4
If a company starts using 100% of its resources on one product, what automatically happens to all other products made? A. All other products will reach full production. B. All the other products will not be produced. C. Production will double. D. All the products will be evenly produced.
Answer:
B. All the other products will not be produced.
Step-by-step explanation:
The answer to what automatically happens to all other products made is (B) All the other products will not be produced.
If a company starts using 100% of its resources on one product, it means that it is devoting all of its available time, money, and labor to that product. This means that there will be no resources left over to produce other products. As a result, all other products will not be produced.
This is because a company's resources are limited. There is only so much time, money, and labor that a company can have. If a company decides to focus all of its resources on one product, it means that it is choosing to give up on producing other products.
This is a common strategy for companies that are trying to launch a new product or that are trying to increase the production of a popular product. By focusing all of their resources on one product, companies can increase their chances of success. However, this strategy also means that other products will not be produced.
Here are some additional things to consider:
The company may be able to produce a limited number of other products, but the quality of those products will likely suffer.
The company may be able to produce other products in the future, but it will need to invest in new resources.
The company may decide to outsource the production of other products to other companies.
The decision of whether or not to focus all of a company's resources on one product is a complex one. There are many factors to consider, such as the company's goals, its resources, and the competitive landscape.
Hence, (B) All the other products will not be produced.
To learn more about products here:
https://brainly.com/question/1281499
#SPJ2
What are 2 factors of 8 have in one this is a perfect square
Answer:
2 and 4
Step-by-step explanation:
The factors of 8 are 1, 2, 4, 8
4 is a perfect square , then
8 = 2 × 4
Using control charts, define five situations in which a process
is out of control and how it is recognizable on a control
chart.
Control charts are used to monitor and identify when a process is out of control. There are several situations that indicate an out-of-control process, and these can be recognized on a control chart. Here are five such situations:
A point falls outside the control limits: If a data point falls above the upper control limit or below the lower control limit, it indicates that the process is out of control. This suggests that there may be a significant change or variation in the process.
Nonrandom patterns: Nonrandom patterns in the data points on a control chart, such as a consistent upward or downward trend, cycles, or oscillations, suggest that the process is not stable. These patterns indicate the presence of special causes of variation.
Runs and streaks: A run or streak refers to a series of consecutive data points that are either above or below the central line on the control chart. Runs or streaks suggest a lack of randomness and indicate that the process is not in control.
Lack of points within control limits: If there are long stretches of data points that are consistently clustered near one control limit or the central line without points within the control limits, it suggests that the process is not stable and may be exhibiting a systematic bias or shift.
Excessive variation: If there is excessive variation in the data points on the control chart, indicated by a wide spread of points around the central line, it suggests that the process is not under control. This can be recognized when the data points exceed the expected range of variation. These situations provide clear indications that a process is out of control and requires investigation and corrective actions to address the underlying causes of the variations. Control charts help in quickly identifying these situations and facilitating timely interventions to maintain process stability and quality.
Learn more about data here: brainly.com/question/29117029
#SPJ11
HELP PLEASE
Activities K, M, and S immediately follow activity H, and their latest start times are 14, 9, and 11. The latest finish time for activity H is \( 11 . \) cannot be determined. is \( 9 . \) is \( 14 .
Based on the information provided, we can determine the latest finish time for activity H, which is 9.
In the given scenario, we have activities K, M, and S immediately following activity H. The latest start times for these activities are as follows:
Activity K has a latest start time of 14.Activity M has a latest start time of 9.Activity S has a latest start time of 11.To determine the latest finish time for activity H, we need to consider the earliest start time among the activities that follow H. In this case, the earliest start time is 9, which corresponds to activity M.
Since activity H needs to be finished before activity M can start, the latest finish time for activity H must be earlier than or equal to the earliest start time of activity M, which is 9.
To learn more about scenario: https://brainly.com/question/30275614
#SPJ11
Calculate the volume of a parallelepiped whose sides are described by the vectors, A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm, You can use the vector triple product equation Volume = A . (BXC)| .
The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.
The given vectors are:
A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm
In order to calculate the volume of parallelepiped, we will use vector triple product equation:
Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.
Step-by-step solution:
We have, A = [-4, 3, 2] cm
B = [2,1,3] cm
C = [1, 1, 4] cm
Now, let's find BXC, using the cross product of vectors B and C.
BXC = | i j k| 2 1 3 1 1 4 | i j k | = -i + 5j - 3k
Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.
The volume of the parallelepiped is given by:
Volume = A . (BXC)|
Therefore, we have: Volume = A . (BXC)
\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)
Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.
To know more about parallelepiped, visit:
https://brainly.com/question/30627222
#SPJ11
The perimeter of an equilateral triangle is 11 inches more than the perimeter of a square, and the side of the triangle is 6 inches longer than the side of the square. find the side of the triangle.
Answer:
13 inches
Step-by-step explanation:
Let P(t) and P(s) be the perimeters of the equilateral triangle and square respectively. Similarly, t and s be the side lengths of equilateral triangle and square respectively.
According to the first condition :
(Perimeter of an equilateral triangle is 11 inches more than the perimeter of a square)
\( \implies P(t) = P(s) + 11\)
\( \implies 3t = 4s + 11....(1)\)
According to the second condition :
(The side of the triangle is 6 inches longer than the side of the square)
\( \implies t = s + 6....(2)\)
From equations (1) & (2)
3(s + 6) = 4s + 11
3s + 18 = 4s + 11
3s - 4s = 11 - 18
-s = - 7
s = 7 inches
\( \because t = s + 6\)
\( \because t = 7 + 6\)
\( \because t = 13\: inches\)
Thus the side of the triangle is 13 inches long.
Write
1
16
as a decimal.
A) 0.00625
B) 0.0625
C) 0.625
D) 6.25
Answer:
b) 0.0625
Step-by-step explanation:
Answer:
b) 0.0625
Step-by-step explanation:
just couse
Write a word problem to fit each number sentence. Solve.
5 × 1 =
Answer: 5
Step-by-step explanation: add 5 by itself 5 times
Answer:
Step-by-step explanation:
the answer is 5
trust me