What is the center and radius for the circle with equation 2x2 - 8x + 2y2 +12y + 14 = 0?
A A
(2,-3); r = 6
B
00
(293); r = 16
(-2,3); r = 6
0
D
(-2,3); r = 16
Answers
Answer:
[tex](2,\, -3)[/tex].
[tex]r = \sqrt{6}[/tex].
Step-by-step explanation:
Let [tex](a,\, b)[/tex] denote the center of this circle. Let [tex]r[/tex] ([tex]r > 0[/tex]) denote the radius of this circle. The equation of this circle would be:
[tex](x - a)^{2} + (y - b)^{2} = r^{2}[/tex].
Expand to obtain an equivalent equation:
[tex]x^{2} + (- 2\, a) + y^{2} + (- 2\, b) + (a^{2} + b^{2} - r^{2}) = 0[/tex].
Since this equation and the given equation describe the same circle, their corresponding coefficients should match.
Notice that the coefficients of [tex]x^{2}[/tex] and [tex]y^{2}[/tex] in this equation are both [tex]1[/tex]. However, the corresponding coefficients in the given equation are both [tex]2[/tex]. Thus, divide both sides of the given equation by [tex]2\![/tex] to match the coefficients of the [tex]x^{2}[/tex] and [tex]y^{2}[/tex] terms:
[tex]x^{2} + (- 4\, x) + y^{2} + 6\, y + 7 = 0[/tex].
Coefficients of [tex]x^{2}[/tex] and [tex]y^{2}[/tex] are now matched after the division.Coefficients of [tex]x[/tex] should match: [tex](-4) = (-2\, a)[/tex], such that [tex]a = 2[/tex].Coefficients of [tex]y[/tex] should match: [tex]6 = (-2\, b)[/tex], such that [tex]b = (-3)[/tex].The constants should also match. Thus:
[tex]a^{2} + b^{2} - r^{2} = 7[/tex].
Substitute in [tex]a = 2[/tex] and [tex]b = (-3)[/tex]; given that [tex]r > 0[/tex], the value of [tex]r[/tex] would be:
[tex]r = \sqrt{2^{2} + 3^{2} - 7} = \sqrt{6}[/tex].
Related Questions
Shannon is building a rectangular garden that is 18 feet wide and 27 feet long. Write an equation that represents the area of Shannon’s garden. In your equation, let g represent the area of Shannon’s garden. Then solve your equation
Answers
15 burritos in five minutes how many burritos can be made in one hour
Answers
Answer:
180 burritos
Step-by-step explanation:
15 burritos = 5 mins
x burritos = 60 mins
cross multiply
5x = 60 ×15
5x = 900
x = 900/5
therefore x = 180 burritos
please answer this question
Answers
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Here, we will use the concept of integration and algebric identities
Integration is the process of finding function that is a derivate of given function Three important trigonometric identities :-[tex]\sf{ sin^{2}{\theta}+ cos^{2}{\theta} = 1 }[/tex][tex]\sf{ 1 + tan^{2}{\theta} = sec^{2}{\theta} }[/tex][tex]\sf{ 1 + cot^{2}{\theta} = cosec^{2}{\theta} }[/tex]Let's Begin :-We have,
[tex]\bold{\displaystyle\int}{\bold{\dfrac{ cos^{2}x}{1 + sinx}}}{\bold{dx}}[/tex]
By using trigonometric identity,
[tex]\sf{ sin^{2}{\theta}+ cos^{2}{\theta} = 1 }[/tex][tex]\sf{\displaystyle\int}{\sf{\dfrac{ 1 -sin^{2}x }{1 + sinx}}}{\sf{dx}}[/tex]
By using algebraic identity :-
[tex]\sf{ a^{2} - b^{2} = ( a + b) (a - b) }[/tex][tex]\sf{\displaystyle\int}{\sf{\dfrac{ (1 + sinx) (1 - sinx) }{1 + sinx}}}{\sf{dx}}[/tex]
[tex]\sf{\displaystyle\int}{\sf{( 1 - Sinx)dx}}[/tex]
[tex]\sf{ {\displaystyle\int} dx - {\displaystyle\int}sinxdx}[/tex]
We know that,
[tex]\sf{{\int\displaystyle}sin{\theta} d{\theta} = - cos {\theta} + C }[/tex][tex]\sf{ x - (-cosx) + c}[/tex]
[tex]\bold{ x + cosx + c}[/tex]
Hence, The answer is x + Cosx + c.
We are given with an integral and need to solve the integral , so let's start ;
[tex]{:\implies \quad \displaystyle \int \sf \dfrac{\cos^{2}(x)}{1+\sin (x)}dx}[/tex]
As we know that sin²(x) + cos²(x) = 1 , using this
[tex]{:\implies \quad \displaystyle \int \sf \dfrac{1-\sin^{2}(x)}{1+\sin (x)}dx}[/tex]
Can be further written as
[tex]{:\implies \quad \displaystyle \int \sf \dfrac{1^{2}-\sin^{2}(x)}{1+\sin (x)}dx}[/tex]
[tex]{:\implies \quad \displaystyle \int \sf \dfrac{\cancel{\{1+\sin (x)\}}\{1-\sin (x)\}}{\cancel{\{1+\sin (x)\}}}dx\quad \qquad \{\because a^{2}-b^{2}=(a+b)(a-b)\}}[/tex]
[tex]{:\implies \quad \displaystyle \int \sf \{1-\sin (x)\}dx}[/tex]
Now , as integrals follow distributive property , so ;
[tex]{:\implies \quad \displaystyle \int \sf 1\: dx-\int \sin (x)dx}[/tex]
Now , as antiderivative (Integration) of sin(x) is -cos(x) + C and that of dx is x + C So ;
[tex]{:\implies \quad \displaystyle \bf \therefore \underline{\underline{\int \bf \dfrac{\cos^{2}(x)}{1+\sin (x)}=x+\cos (x)+C}}}[/tex]
This is the Required answer
Solve this Question and Write the method how to find LCM.
Answers
Answer:
8a²b
Step-by-step explanation:
Least common multiple: The smallest number that is a multiple of two or more numbers
As 2a² has a² and 8ab has b, then the least common multiple will include a²b.
8 is a multiple of 2
Therefore, the LCM is 8a²b
which propety of multiplication is shown
9 x (2 x 12) = (12 x 9) x 2
Answers
Answer:
216
Step-by-step explanation:
9*(2*12)
9*(24)
9*24
216 ans
Compare the numbers 289.4 and 289.400 using >,<, or =
Answers
Answer:
289.4 = 289.400
Step-by-step explanation:
no matter how many 0s are added to the end theyre always gonna be the same
On a jogging trail, you take a random sample of the speed of 50 joggers and determine that their average speed is 5.3 mph. Which statement is true?
A) You conclude that the average speed of all joggers is close to 5.3 mph.
B) You conclude that the speed of all joggers on this trail is exactly 5.3 mph.
C) You conclude that the average speed of all joggers on this trail is close to 5.3 mph.
D) You conclude that the speed of more than half of the joggers on this trail is less than 5.3 mph.
Answers
I need help on this one question! Can anyone help me?
Answers
substitute the first equation into the second. you will get 2(0.25x-1)=(2/3)x+6.
that simplifies to .5x=(2/3)x+8 solve from there to get x=-48. substitute that into the first equation to get y=(-48/4)-1 therefore, x=-48 and y=-13
Pomegranate, Papaya, and Lychee
Answers
Answer:
they're fruits
Step-by-step explanation:
i dont really know what the question is... they help against heart disease, cancer and diabetes
man helppppp oooooooooo
Answers
your answer is right since your going to the right +3 and decreasing -9 units
Which of the following is not a linear function?
Answers
Answer:
Step-by-step explanation:
Answer:
A is not linear.
Step-by-step explanation:
This is my proof when I put it on my graphing calculator.
PLEASE HELP 55 POINTS
In this activity, you will analyze a statistical study for a given situation and apply randomization to collect data from which valid conclusions may be drawn.
To meet the company’s sales goals, the sales director for the pet food company decided to provide training for some of the sales representatives in the Midwest and Northeast regions. After conducting a one-month training program, the sales director analyzed the effectiveness of the program by conducting a statistical study.
Question 1
The purpose of the sales director’s study is to determine whether attending the training program caused an increase in sales for representatives from the two regions. So the sales director collected sales data from both groups (those receiving training and those receiving no training) for three months after the one-month program and compared the number of orders secured by those who attended the training program with the number of orders secured by those who didn’t attend.
Part A
Question
Select the correct answer from each drop-down menu.
The sales director conducted because a treatment applied to the sales representatives.
This is the best statistical study for this situation because the sales director is trying to establish .
Part B
Suppose there are 1,000 total sales representatives in the Midwest and Northeast regions, with 500 sales reps in each region. Describe the best way for the sales director to include 200 sales representatives, with an equal number from each region and an equal number in each group, while yielding valid conclusions in the study.
Type your response in the box.
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Characters used: 0 / 15000
Question 2
For three months after the training program, the sales director collected the sales data for the 200 sales representatives from the Midwest and Northeast regions. The director then broke down the number of sales orders for the representatives according to whether they received training or not. This data is shown in the table.
Three Months’ Sales Orders
Training No Training
Midwest 234 196
Northeast 252 178
Question
Use the data shown in the table to complete each statement.
Select the correct answer from each drop-down menu.
For the Midwest region, the average number of sales orders per representative for the group that had training is more than the average number of sales per representative for the group that had no training.
For the Northeast region, the average number of sales orders per representative for the group that had training is more than the average number of sales per representative for the group that had no training.
The data from the sales director’s study indicates that the one-month training program sales.
Answers
Question 1 - The sales director was inclined to conduct an experiment because a treatment was applied to the sales representative.
A causality statistical study would be best.
Question 2 - In the Midwest region, the difference between those with training and without led to a 0.38 difference.
In the Northeast, the difference between those with training and without led to a 0.74 difference.
This means that a one-month training program increases sales.
What does the data show?The data shows that because a treatment was applied to sales representatives in that some of them were trained, the best way to find out the effect of this treatment would be an experiment.
This experiment would show if there is a causality relationship between training and sales numbers.
What is the difference in amount sold?Midwest:
= (234 - 196) / 100
= 0.38
Northeast:
= (252 - 178) / 100
= 0.74
Those with training in the Midwest sold 0.38 more than those without training. And those with training in the Northeast sold 0.74 more.
This means that the training does indeed increase sales.
Find out more on the effects of training at https://brainly.com/question/12427808.
The diameter of a circle is 6 kilometers.
What is the circle's circumference?
d=6km
Use 3.14 for
Pie.
Answers
Answer:
rea = pi x radius squared
area = 3.14 x (6 km)² - assuming pi i is about 3.14
area = 113.04km²
Step-by-step explanation:
The volume of the rectangular prism is 35/15yd. Determine the missing measurement using a one step equation
Area=4/5yd
Height= ?
Answers
Answer:
let x yd be the height of the rectangular prism.
4/5x = 35/15
x= 2 11/12 yd
Step-by-step explanation:
since the formula for the volume of cuboids is base area times height, we can use that equation to find out! :D
WILL GIVE BRAINLIEST. Explain how you would prove that this is an identity. (Please explain in understandable terms)
Answers
Answer:
Step-by-step explanation:
I would first expand out the numerator since it would become [tex]\sin^{2} x+2\sin x \cos x+\cos^{2}x[/tex], which would allow me to use the double angle formula for sine and the Pythagorean identity.
What is the header for this page? A) Algebra 1, B) Linear Functions, C) The slope, D) Ordered Pairs. Will Mark Brainliest if answered correctly .
Answers
What is the header for this page?
The slopeHeader means the text written at the top of the page. The word written at the top of our page is The slope. Hence, it is the header for the page...~
Select all the expressions that are equivalent to 9 + 7x – 3y.
Answers
Answer:
4 or 9+7x+(-3y) is the only expression equivalent
Step-by-step explanation:
Number 4 is the only expression that comes out to be equivalent because the rest of the answer choices have something wrong with them.
Step-by-step explanation:
Ms. Fitzgerald had 2 1 /4 gallons of fruit punch. She served 3 /8 gallon of the fruit punch
to her family at lunch.
How many gallons of fruit punch did Ms. Fitzgerald have left after lunch?
Answers
Answer:
1 7/8
Step-by-step explanation:
1/4=2/8
2+2/8-3/8= 1 7/8
The amount of the fruit punch in gallons after serving 3/8 gallons of the fruit punch at dinner is 15/8.
What is subtraction?It simply means to deduct something from the object or number of group, place, etc. Subtraction means to take away from the group or a number of objects.
Ms. Fitzgerald had 2 and 1/4 gallons of fruit punch. She served 3/8 gallons of the fruit punch to her family at lunch.
The amount of the punch she has
[tex]\rightarrow 2 + \dfrac{1}{4} \\\\\rightarrow \dfrac{8 + 1}{4}\\\\\rightarrow \dfrac{9}{4}[/tex]
Then the 3/8 gallons of fruit punch to her family at lunch. Then we have
[tex]\rightarrow \dfrac{9}{4} - \dfrac{3}{8}\\\\\\\rightarrow \dfrac{18-3}{8}\\\\\\\rightarrow \dfrac{15}{8}[/tex]
More about the subtraction link is given below.
https://brainly.com/question/4319655
If an object is shot upward with an initial velocity, vo, in feet per second (ft/s), the velocity, v, in ft/s is given by the formula v = vo - 32t where t is time in seconds. Find
the initial velocity of an object if the velocity after 3 seconds is 44 ft/s
Answers
Answer:
3s
Step-by-step explanation:
the answer is 3 seconds
Which of these is an equation?
F
6 + x + 24
G 6 + x = 24
U I
H
6 + X - 24
J
6 + X
Answers
Answer:
the answer is 6+x=24
Step-by-step explanation:
awesome
Answer:
6 + x = 24
Step-by-step explanation:
This is an equation because it has an EQUAL SIGN "=". an expression with an equal sign makes an equation.
It's in the name "EQUATION" (EQUAL)
A representation " = "
The slope of a line is given by the formula:
horizontal change
m
vertical change
True
False
Answers
Answer:
False
Step-by-step explanation:
The defining characteristic of a line is that is has a constant average rate of change.
That is, for a given line, for whatever two points are selected, the average rate of change between then will be the same. This constant average rate of change is called the slope of the line.[tex]slope=\frac{rise}{run}=\frac{verticalchange}{horizontal change} =\frac{y}{x} =\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
The first two versions are more geometric in nature (applied problems)The second two version are more algebraic (points on the x-y plane) Slope is Positive when the line rises from left to right.Negative when the line falls from left to rightZero when the line is horizontal ( no change in y)Undefined when the line is vertical (no change in x)Write the equation of the line through the given points :
I need help please
Answers
Answer:
[tex]y=-3x+5[/tex]
Step-by-step explanation:
The equation for slope is:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can substitute the given coordinates into the equation:
[tex]Slope=\frac{3-0}{\frac{2}{3}-\frac{5}{3}}=\frac{3}{\frac{2-5}{3}}=\frac{3}{\frac{-3}{3}}=\frac{3}{-1}=-3[/tex]
The slope is -3
The equation for a line is:
[tex]y=mx+b[/tex]
m: slope
b: y-intercept
x, y: (x, y) coordinate pair
Now, plug in the slope and one of the (x, y) coordinate pairs to solve for the y-intercept.
[tex]y=mx+b\\y=-3x+b\\0=-3(\frac{5}{3})+b\\0=\frac{-15}{3}+b\\0=-5+b\\$Add 5 to both sides\\b=5[/tex]
Therefore the equation is:
[tex]y=-3x+5[/tex]
PLEASE SHOW ALL WORK
Shannon won $10,000. She will be paid $20 a day until the money runs out. How many days will the money last?
Group of answer choices
500 days
499 days
480 days
Answers
Find the volume of 4 in 12 1/8 in 1 1/4 in
Answers
Mixed number:1 1/2
Decimal 1.5
Henry's mom bought a candle with a circumference of approximately 45.1846 cm. What was the diameter of the candle?
Use 3.14 for π.
A. 14.29 cm
B. 14.32 cm
C. 14.36 cm
D. 14.39 cm
Answers
Answer:
[tex]\huge\boxed{\sf d = 14.39\ cm}[/tex]
Step-by-step explanation:
Given:
Circumference = c = 45.1846 cm
π = 3.14
Required:
Diameter = d = ?
Formula:
C = πd
Solution:
Rearrange formula
d = C / π
d = 45.1846 / 3.14
d = 14.39 cm
[tex]\rule[225]{225}{2}[/tex]
Please help me! A dealership recently sold a 4-door sedan, which it purchased for $18,000, at 15% markup. It accepted a trade-in for it, and it paid $5000 for the trade. Next, it marked the trade-in up 25% and sold it in a week. What was the dealership's profit on these two vehicles?
Answers
Step-by-step explanation:
The answer is 3950 $
First we will calculate the two profits the dealership earned.
1. Profit on purchase.
18000 x 15% = 18000 x 0.15
=2700 $
2. Profit on Sale:
5000 x 25% = 5000 x 0.25
= 1250$
3. Adding both profits:
Total profit = 2700 + 1250 = 3950 $
-2(3x-5)=4(x+3)+8
Please will give brainlyest
Answers
Answer:
x=-1
Step-by-step explanation:
-2(3x-5)=4(x+3)+8
-6x+10=4(x+3)+8
-6x+10=4x+12+8
-6x+10=4x+20
-6x+10-10=4x+20-10
-6x=4x+10
-6x-4x+10-4x
-10x=10
[tex]\frac{-10}{-10}= \frac{10}{-10}[/tex]
x=-1
help me fast pleas-
help meeeeeeeeeeeeee
Answers
y= 9 x 6 + 25
= 79
Road-Less-Traveled Tours:
the function is y= 12x
y= 12 x 6 = 72
Bowman Bros:
The line is y -30 over x -1 = 50 - 30 over 3 - 1
y= 10x + 20
y= 10 x 6 + 20 = 80
72 < 79 < 80
So chose Road-Less-Travelled Tours
Impuesto de venta Un agente de ventas necesita calcular el
costo de un artículo cuyo impuesto de venta de 8.25%. Escriba
una ecuación que represente el costo total c de un artículo que
cuesta x dólares.
Answers
Answer:
costo total = c
costo del artículo = x
impuesto = 8,25 % = 0,0825 {cambiar el porcentaje a decimal moviendo el punto decimal dos a la izquierda}
Para encontrar impuestos:
- multiplique el costo del artículo por el porcentaje de impuestos (como decimal)
= .0825x
Para encontrar el costo total:
- agregue el costo del artículo más impuestos
= x + .0825x
c = x + .0825x {costo del artículo más impuestos}
Step-by-step explanation:
Jason sees a tall building from across town. He
turns 90° and walks 100 yards. Jason then turns to
face the building, and the angle between his line
of sight and his path is 35º as shown below. Which
of the following is the closest to the distance from
Jason's original position to the building, in yards?
Answers
Answer:
Jason's original position is 70.02 yards, or 70 yards
Step-by-step explanation:
These types of questions are understood better when drawn out.