Answers
Answer:
[tex]\textsf{center \quad $(x,y)=\left(\; \boxed{6,-2}\; \right)$}[/tex]
[tex]\textsf{radius \quad $r=\boxed{8}$}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Given equation:
[tex]x^2+y^2-12x+4y-24=0[/tex]
Move the constant to the right side of the equation and collect like variables on the left side of the equation:
[tex]\implies x^2-12x+y^2+4y=24[/tex]
Create perfect square trinomials for the both variables by adding the square of the half the coefficient of x and y to both sides:
[tex]\implies x^2-12x+\left(\dfrac{-12}{2}\right)^2+y^2+4y+\left(\dfrac{4}{2}\right)^2=24+\left(\dfrac{-12}{2}\right)^2+\left(\dfrac{4}{2}\right)^2[/tex]
[tex]\implies x^2-12x+\left(-6\right)^2+y^2+4y+\left(2\right)^2=24+\left(-6\right)^2+\left(2\right)^2[/tex]
[tex]\implies x^2-12x+36+y^2+4y+4=24+36+4[/tex]
[tex]\implies x^2-12x+36+y^2+4y+4=64[/tex]
Factor the two perfect trinomials:
[tex]\implies (x-6)^2+(y+2)^2=64[/tex]
Therefore:
[tex]\textsf{center \quad $(x,y)=\left(\; \boxed{6,-2}\; \right)$}[/tex]
[tex]\textsf{radius \quad $r=\boxed{8}$}[/tex]
Related Questions
The technician at the store worked on the computer for 4.25 hours and charged him $141 for parts. The total was $332.25. Write and solve an equation which can be used to determine x the cost of the labor per hour.
Answers
The cost of the labor per hour is $ 45
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The total cost of the parts is = $ 141
The total number of hours worked by the technician = 4.25 hours
The total cost of repair = $ 332.25
Let the cost of the labor be = y
The total cost of labor =
Cost of the labor per hour x Number of hours worked by the technician
The total cost of labor = 4.25y
Now ,
The total cost of repairing the computer =
Total cost of labor + Total cost of the parts
The total cost of repairing the computer = 141 + 4.25y
332.25 = 141 + 4.25y
Subtracting 141 on both sides , we get
4.25 y = 191.25
Divide by 4.25 on both sides , we get
y = $ 45
Therefore cost of labor per hour y = $ 45
Hence , the total cost of labor per hour is $ 45
To learn more about equations click :
https://brainly.com/question/10413253
#SPJ1
Consider the following linear equation.
y=−43x+2
Step 1 of 2 : Determine the slope and the y-intercept (entered as an ordered pair) of the equation above. Reduce all fractions to lowest terms.
Answers
Slope: -1/9
Y-Intercept: 2
What is the equation in standard form 0f the line y=1/9x+5
Answers
Answer:
The equation in standard form of the line y=1/9x+5 is y-5=1/9(x-0)
Pleaseee help me
a +3> 14 or a -5 ≤3
Answers
Answer:
a>11
[tex]a\leq 8[/tex]
Step-by-step explanation:
a+3>14
-3. -3
a>11
a-5<=3
+5. +5
a<=8
Hopes this helps please mark brainliest
A regular polygon has 18 sides. If one of its angles measures (4h − 25)°, what is the value of h?
Answers
Answer: h = 46.25
Step-by-step explanation:
You can use the formula below to calculate the value of its interior angle:
n = number of sides = 18[tex]\frac{(n-2)*180}{n} =\frac{(18-2)*180}{18} =\frac{16*180}{18} =160[/tex]
So, each one of its interior angles is equal to 160°. Set that equal to the given angle measure and solve:
[tex]160=4h-25\\\\4h=160+25=185\\\\h=46.25[/tex]
What is the first step in estimating the quotient for 492 divided by 50?
Answers
Answer:
10
Step-by-step explanation:
Round 492 to 500, then estimate 500/50
ron picked 7/10 bushels of apples ben picked 9/10 bushels of apples how many apples did they pick all together give your answer in lowest terms
Answers
which of these statements below are true? Select all that apply
Answers
Answer:
Step-by-step explanation:
the answer is D i'm pretty sure
pls help ill give brainliest
Answers
Answer:
(- 12, 10 )
Step-by-step explanation:
2x + 4y = 16 → (1)
- 2x - 3y = - 6 → (2)
add (1) and (2) term by term to eliminate x
0 + y = 10
y = 10
substitute y = 10 into (1) and solve for x
2x + 4(10) = 16
2x + 40 = 16 ( subtract 40 from both sides )
2x = - 24 ( divide both sides by 2 )
x = - 12
solution is (- 12, 10 )
Answer:
(- 12, 10 )
Step-by-step explanation:
mark the person above me as brainliest
Getting rain at least once in 11 days if Probability of rain on each single day is 0.4
Answers
Answer:
because u can't predict the days rain will fall so u can say it will fall in ratio 0:4
This number line models the division problem 14÷5 .
What is the quotient?
Enter your answer as a fraction in simplest form by filling in the boxes.
$$
Answers
The simplest form of fraction (1/4)/5 is 1/20.
What is quotient?A quotient is the simplest or resultant value of division of two numbers. In two numbers, one number is dividend and another number is divisor,
quotient=dividend/divisor
The simplest form for fraction (1/4)/5,
(1/4)/5=1/(4×5)
= 1/20
So, the simplest form of (1/4)/5 is 1/20.
To know more about Quotient on:
https://brainly.com/question/17486526
#SPJ1
It takes a word processor 30 minutes to word process and spell check 4 pages. Find how long it takes her to word process and spell check 22 pages.
Answers
It will take the word processor 165 minutes to check 22 pages
How to determine the time to check the pages?The given parameters in the question are:
Speed = 30 minuter per 4 pages
Number of pages = 22 pages
The number of hours to check the pages can be calculated using the following equation
Time = Speed * Number of pages
Substitute the known values in the above equation So, we have the following equation
Time = 30/4 * 22
There is no unit to convert
So, we have
Time = 30/4 * 22
Evaluate
Time = 165
Hence, the time is 165 minutes
Read more about unit rates at
https://brainly.com/question/19493296
#SPJ1
what is f(2) for f(x) = 3^x--13
Answers
f(2) = -4
Step-by-step explanation:
f(2) = 3^2-13
f(2) = 9-13
f(2) = -4
Yoga pants are on sale for 1/3 off the original price. If a pair of yoga pants normally costs $60, what is sales price?
Answers
The sales price of the yoga pants is $20.
How to calculate the price?It should be noted that from the information illustrated, the Yoga pants are on sale for 1/3 off the original price and a pair of yoga pants normally costs $60.
The sales price will be:
= Fraction given × Original price
= 1/3 × $60
= $20
The price is $20.
Learn more about price on:
brainly.com/question/1153322
#SPJ1
In the past, Jessica got paid $197,980 annually. Since switching to a new career, she has been making 35% more. How much does Jessica make now?
$
thanks if you answer!!!! :")
Answers
Answer: $267,273
Step-by-step explanation:
$197,980 × 0.35 (35%) = $69,293
$197,980 + $69,293 = $267,273
Jessica now makes $267,273 annually.
I really need help on this one I am confused and if someone could explain that would be great. also I am sorry the picture is flipped I couldn't turn it.
Answers
The hourly rate that the business owner should pay the employees to obtain the desired net income of $40,000 is of:
$17.
How to calculate the net income?The net income is calculated as the subtraction of the total income by the expenses.
In the context of this problem, the expenses are given as follows:
Building and equipment: $900 a month = $10800 a year.Hearse: $200 per month = $2400 per year.Lead car: $150 per month = $1800 per year.Insurance: $1500 per year.Licensing/Certification: $250.Three employees, each working 20 hours a week = 52 x 20 = 1040 hours a year.Hence the expression for the net income is given as follows:
110000 - [10800 + 2400 + 1800 + 1500 + 250 + 3(1040x)] = 40000
93250 - 3120x = 40000
3120x = 53250
x = 53250/3120
x = $17 an hour.
More can be learned about net income at https://brainly.com/question/25895372
#SPJ1
PLEASE URGENT PLEASE
Answers
The equation of the line in slope-intercept form is y = 5x-22.
What is slope-intercept form of an equation?The slope-intercept form of a straight line is one of the most common forms used to represent the equation of a line.
The slope-intercept form of an equation is given as
Formula:
y₂-y₁/x₂-x₁ = y-y₁/x-x₁........... Equation 1Where:
y₂ = 4y₁ = 3x₂ = 10x₁ = 5Substitute these values into equation 1
(4-3)/(10-5) = (y-3)/(x-5)1/5 = (y-3)/(x-5) (y-3) = 5(x-5)y-3 = 5x-25y = 5x-25+3y = 5x-22Hence, the equation in slope-intercept form is y = 5x-22.
Learn more about slope-intercept form: https://brainly.com/question/1884491
#SPJ1
A freight train and a passenger train leave Portland at the same time on parallel tracks heading for Springfield. The passenger train goes 30 mi/hr faster than the freight train, and in 6 hr the passenger train travels three times farther. What is the speed of each train?
Answers
The passenger train traveling at 30 mi/hr faster than the freight train and traveling 3 times the distance traveled by the freight train, through the kinematic equations, indicates that the speed of the freight train is 15 mi/hr and the speed of the passenger train is 45 mi/hr.
What is kinematics?Kinematics is the study of the motion of an object without reference to the force that causes the motion.
The speed of the passenger train = 30 + The speed of the freight train
Distance traveled by the passenger train in 6 hours = 3 × The distance traveled by the freight train
Let v represent the speed of the freight train and let d represent the distance traveled by the freight train in 6 hours
From kinematic equations, we get;
Speed of the passenger train = 30 + v
Distance traveled by the passenger train in 6 hours = 3 × d
(30 + v) × 6 = 3•d
6•v = d
Which gives; (30 + v) × 6 = 3 × 6•v
180 + 6•v = 18•v
12•v = 180
v = 180 ÷ 12 = 15
The speed of the freight train is v = 15 mi/hr
The speed of the passenger train = 30 + v
The speed of the passenger train is (30 + 15) mi/hr = 45 mi/hr
Learn more about the kinematic equations here:
https://brainly.com/question/24458315
#SPJ1
Best Buy has an iPad for $540. This weekend it’s on sale for 30% off. Best Buy charges 8% sales tax. If you were to purchase this iPad this weekend, what is the amount of money do you give the clerk? Show your work.
Answers
Answer:
Step-by-step explanation:
540x0.30=378
378x0.08=30.24
378+30.24=408.24
Tan 5 pi / 9- tan 7 pi / 18 / 1+tan 5pi/ 9 tan 7pi/18
Answers
The Mathematical Final Answer:
0
Suppose that the functions and are defined as follows.
Find the following.
Answers
The expression we get from the given functions r and s defined for all real numbers x.
r( s(-3))= -38
Given that,
All real numbers x are defined by the functions r and s.
r(x) =2x+1
s(x) =-2x²-2
We have to find the expression
r( s(-3))
Take the functions,
r(x) =2x+1
s(x) =-2x²-2
Now, Take
r( s(-3))
Substitute s function first
r(-2(-3)²-2)
r(-2(9)-2)
r(-18-2)
r(-20)
Now substitute r function
2(-20)+2
-40+2
-38
Therefore, The expression we get from the given functions r and s defined for all real numbers x.
r( s(-3))=-38
To learn more about expression visit: https://brainly.com/question/14083225
#SPJ1
Find the eigenvalues and eigenvectors
Answers
Answer:
Step-by-step explanation:
6. Use the data below to make a scatter plot in Desmos and find the
exponential regression equation. Round to the nearest hundredth if
necessary. Do not type spaces.
Time (years)
7. Using your equation from #6, find out how much the Fire Dragons
comic book would be worth in 55 years.
Your answer
Answers
Answer:
I hope that the picture below helps.
Step-by-step explanation:
What happens to a parabola when you change certain elements of the equation?
Answers
Supoose a<1 compared to the parent function then parabola is wider than the parent function.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Direction the parabola opens the value of p as positive, the parabola opens up.
The focus and vertex both have the same x position, so the distance would be in terms of the y-coordinates only.
Supoose a<1 compared to the parent function then parabola is wider than the parent function
If "a" is a fraction less than one, therefore the parabola becomes wider.
Learn more about conic sections here:
brainly.com/question/12854078
#SPJ1
Present value interest rate? You expect to receive $10000 as a bonus after 5years on the job. You have calculated the parent value of this bonus and the answer is $8000 what discount rate did you use in your calculation
Answers
The discount rate used in calculator wound be 4.56%.
Given that,
You anticipate getting a bonus of $10000 after five years on the job.
We have the result of your calculation for the parent value of this bonus is $8000. what percentage of a discount rate did you use.
We know that to find the present value of a future sum of money .
PV= FV/(1+r)ⁿ
Here,
PV is present value = $8000
FV is future value = $10000
r is discount rate we have to find
n is time = 5 years
Substitute in the formula,
$8000=$10000/(1+r)⁵
(1+r)⁵=$10000/$8000
(1+r)⁵=1.25
1+r=[tex]1.25^{1/5}[/tex]
1+r=1.0456
r=1.0456-1
r=0.0456
r=4.56%
Therefore, The discount rate used in calculator wound be 4.56%.
To learn more about calculator visit: https://brainly.com/question/15380536
#SPJ1
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 5 liters of natural oil for every 6 liters of synthetic oil. In order to make 836 liters of Petrolyn oil, how many liters of synthetic oil are needed?
Answers
The liters of synthetic oil that are needed is 456 liters.
How to calculate the liters?From the information, petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 5 liters of natural oil for every 6 liters of synthetic oil.
To make 836 liters of oil, the liters of synthetic oil will be:
= 6 / (6+5) × 836
= 6/11 × 836
= 456
Therefore, 456 liters are needed.
Learn more about ratio on:
brainly.com/question/2328454
#SPJ1
132.16 kg of beef was placed into 16 packages of equal weight. what is the weight of one package beef?
Answers
The weight of one package beef is 8.26kg
What is division of numbers?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
For example, if 10 students are to share 100 oranges, if they are to share it equal, then each students will receive 100/10= 10 oranges
Similarly 132.16kg was placed into 16packages of equal weight.
Therefore the weight of each package beef will be 132.16/16= 8.26kg
learn more about division of numbers from
https://brainly.com/question/941863
#SPJ1
Deshaun's gas tank is 1/4 full. After he buys 9 gallons of gas, it is 5/8 full. How many gallons can Deshaun's tank hold?
Answers
Answer:
Step-by-step explanation:
so what is the difference from 1/4 to 5/8 ? is the question
2/8=1/4
5/8-2/8 = 3/8
9 gallons of fuel fill 3/8 of the tank
since 3/8 is 9 gallons we can see that 1/8 will be 3 gallons or 9/3=3
then multiply 3 gallons by the 8 parts for the whole tank
3*8=24 gallons.
Than tank can hold 24 gallons
Find the next 3 numbers in the sequence: 2, 9, 11, 18, 20, 27, ___, ___, ___
Answers
Answer: 29, 36, 38
Step-by-step explanation:
The sequence starts with 2 and proceeds to go to 9, which is a difference of 7.
After 9 it is 11, and the difference is 2.
After 11 it is 18 which is a difference of 7 again.
The pattern is difference of 7, difference of 2.
Since there was a difference of 7 between 20 and 27, the next difference will be 2, which is 29.
So, the pattern is +2, +7, +2 . . .
Therefore, your next three numbers will be 29, 36, 38
On a January evening in upstate New York, 8 inches of snow was on the ground. At 11pm, it began snowing 1/4 inch per hour and snowed consistently for 14 straight hours.
Answers
The slope of the linear function that models this situation is given as follows:
m = 0.25.
How to obtain the parameters of a linear function?The slope-intercept representation of a linear function is given as follows:
y = mx + b
Hence the coefficients of the function and their meaning are obtained as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the amount represented by the function, i.e., the numeric value of the function when the input variable x assumes a value of 0.In this problem, these parameters are defined as follows:
Intercept of 8, as it was the initial amount of snow on the ground.Slope of 1/4 = 0.25 inches, as it is the amount by which the amount of snow on the ground increases each hour.Hence the linear function modelling the situation is:
y = 8 + 0.25x.
Missing InformationThe problem asks for what is the slope of this situation.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1