Given the equation of a circle, x^2 + y^2 - 6x + 2y + 1 = 0, find the coordinates of the center and the length of the radius
Answer:
Center: (3,-1)
Radius: 3
Step-by-step explanation:
Given:
[tex]\displaystyle \large{x^2+y^2-6x+2y+1=0}[/tex]
First, we have to convert the following standard circle equation to this:
[tex]\displaystyle \large{(x-h)^2+(y-k)^2=r^2}[/tex]
where h is horizontal shift, k is vertical shift and r is radius.
That means we have to complete the square for both x-term and y-term.
Rearrange the equation:
[tex]\displaystyle \large{x^2-6x+y^2+2y+1=0}\\\displaystyle \large{(x^2-6x)+(y^2+2y+1)=0}[/tex]
For [tex]\displaystyle \large{y^2+2y+1}[/tex], can be converted to perfect square as [tex]\displaystyle \large{(y+1)^2}[/tex]. Hence:
[tex]\displaystyle \large{(x^2-6x)+(y+1)^2=0}[/tex]
For the x-terms, we have to find another value that can complete the square. We know that [tex]\displaystyle \large{(a\pm b)^2 = a^2 \pm 2ab + b^2}[/tex].
For [tex]\displaystyle \large{x^2-6x}[/tex] can be [tex]\displaystyle \large{x^2-2(x)(3)+3^2 \to x^2-6x+9}[/tex]. So our another value is 9.
[tex]\displaystyle \large{(x^2-6x+9-9)+(y+1)^2=0}[/tex]
From above, we add -9 because the original expression isn’t actual perfect square.
Separate -9 out of [tex]\displaystyle \large{x^2-6x+9}[/tex]:
[tex]\displaystyle \large{(x^2-6x+9)-9+(y+1)^2=0}[/tex]
Transport -9 to add another side:
[tex]\displaystyle \large{(x^2-6x+9)+(y+1)^2=9}[/tex]
Complete the square:
[tex]\displaystyle \large{(x-3)^2+(y+1)^2=9}[/tex]
Finally, we have our needed equation to find radius and center. The coordinate of center is defined as the point (h,k) from [tex]\displaystyle \large{(x-h)^2+(y-k)^2=r^2}[/tex] and the radius is defined as r.
Hence, from the equation:
The coordinate of center is (3,-1) with radius equal to 3.
CAN SOMEONE PLS ANSWER THIS QUESTION FAST
WILL MARK BRAINLIEST
Answer:
C. 9 miles/gallon
Step-by-step explanation:
Answer:
Maybe 10? I'm sure though
Step-by-step explanation:
Find the value of the expression 1/2x + 3 if x = 12
Step-by-step explanation:
please mark me as brainlest
the table of value shows a linear relationship
Answer:
I believe your answer is A
Step-by-step explanation:
Rise is over run, the run (x) is increasing by five but, the rise (y) is decreasing by 8 so the answer would be -8/5
Hope this helps! :)
Beth Hazelton purchased a compact vehicle with an $18,240.00. MSRP including the delivery and title fee. She selected a leather interior which costs 5 times the upgraded stereo system. If the total cost of the vehicle, including a 7% sales tax, was $21,365.20 find the cost of the (a) stereo system and (b) leather interior. Use the example in the book to help you with solving this problem.
Answer:
price of leather thingy= $2906.62
price of stereo system = $581.33
Step-by-step explanation:
final cost minus cost of total before adding the leather.
21,365.20
- 18,240.00
= $3125.2
to find the exact price of the leather since the 7% tax was included in the price we mulitply by .93
3125.2 x .93 = 2906.62
we know the stereo is 1/5 of the price of the leather so we divide by 5 2906.63 ÷ 5 = 581.33
there u go! pls give brainliest :D
Answer for brainliest
25 X 1 =
;)
The answer is 25
25x1 is 25
anything multiplied by 1 Is itself
The ratio of blue jays to Robin's was 6 to 7. If there were 84 Robins, how many blue jays were there?
Answer:
72
Step-by-step explanation:
Since the ratio of blue jays to robin's was 6 to 7 then if there were 84 robins how many blue jays were there.
6 to 7 can also be express as 6/7
Thus, we can set up a proportion
6/7 = x/84
Now, we have to solve for x
x = 72
Hence, if there were 84 robin there would be 72 blue jays.
~lenvy~
44. What three-dimensional figure can be made by folding the net?
ASSESSMENT 1
A rectangular pyramid
B. triangular pyramid
C. triangular prism
D. square pyramid
Answer:
Its B square pyramid
Step-by-step explanation:
Because
Brand X rice sells for $70 per kg. Brand Y rice sells for $20 per 400 g. Both brands have similar qualities 8 . Which brand is the better buy? Why do you think so?
Answer:
Brand Y would have a better deal.
Step-by-step explanation:
Step 1. There are 1,000 grams in 1 kilogram. Knowing this, you can see that it would be $70 for 1,000 grams of rice and $20 for 400 grams of rice.
Step 2. You would have to do 70 divided by 1000 (0.07) and 20 divided by 400 (0.05) to see which has the better deal.
Step 3. Brand X is 7 cents per grain and Brand Y is 5 cents per grain, making Brand Y the better deal. I hope that this helps! :)
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Step-by-step explanation:
by using formula a+b+c=180
what is the intial value of the function f(x)=3{5/4}^x
Answer:
3
Step-by-step explanation:
The "initial value" of a function is the value when the independent variable is zero.
f(0) = 3(5/4)^0 = 3×1 = 3
The initial value of the function is 3.
Evaluate the limit
[tex]\lim \limits_{x\to 0} \dfrac{\ln \left(1-\dfrac x4 \right) - (1-x)^{\tfrac 14} +1}{x^2}[/tex]
Answer:
1/16
Step-by-step explanation:
Place x=0 and you can see [tex]\frac{0}{0}[/tex] indefinitness. So you can apply the l'hosptial rule. Its basic you should
[tex]\lim_{x \to \ 0} \frac{g(x)}{f(x)} = \\[/tex] [tex]lim_{x \to \ 0} \frac{g'(x)}{f'(x)}[/tex] so apply the derivative
[tex]\frac{\frac{1}{x-4} +\frac{1}{\sqrt[4]{(1-x})^3 } }{2x}[/tex] and replace the x=0 and you'll see same answer [tex]\frac{0}{0}[/tex] re-apply the l'hospital rule and answer
[tex]\frac{\frac{-1}{(x-4)^2} + \frac{3}{16\sqrt[4]{(1-x)^7} } }{2}[/tex] and replace the 0 you can see the answer [tex]\frac{1}{16}[/tex]
Solve for b. -36 + 2.5 = 4
Answer:
False
Step-by-step explanation:
The sides are not equal
Aidan earned a total of $117 in one week. His babysitting job pays him $15 per hour. His after-school job at a barber shop pays him $9 per hour. He worked a total of 9 hours that week. The system of linear equations represents this situation, where x represents the number of hours Aidan spent babysitting and y represents the number hours he worked at the barber shop.
x + y = 9
15x + 9y = 117
How many hours did Aidan work at each job?
The hours worked at the babysitting job is 6 hours.
The hours worked at the barber shop is 3 hours.
What are the hours worked at the babysitting job?
Given the two linear equations:
x + y = 9 equation 1
15x + 9y = 117 equation 2
Multiply equation 1 by 9
9x + 9y = 81 equation 3
Subtract equation 3 from 1
36 = 6x
x = 6
What are the hours worked at the barber shop?
Substitute for x in equation 1
6 + y = 9
y = 9 - 6
y = 3 hours
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
Solve -5(3n + 4) = 40.
Which of the following is the solution to the equation 4 over 5 times n = 20
N = 4
N= 12
N = 16
N = 25
Answer:
(d) N = 25
Step-by-step explanation:
The solution to a one-step linear equation can be found by performing the inverse of the operation that is performed on the variable.
(4/5)N = 20
(5/4)(4/5)N = (5/4)(20) . . . . . multiply by the inverse of the coefficient
N = 25 . . . . . simplify
What is the area of a pillow that is 12 1/2 inches long and 15 1/2 inches wide?
Answer:
193.75in or 193 3/4 in.
Step-by-step explanation:
To find the area, multiply the length x width.
12.5 x 15.5 = 193.75in
:)
Answer:
193.75 inch
Step-by-step explanation:
Area= Length ×Width
12.5*15.5
Find P (Freshman(Girl) Hint: P(A and B)
P(B)
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5 7 12
Junior 2 3 5
Senior 1
4 5
12 18
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.
Answer:
[tex]\sf \dfrac29[/tex]
Step-by-step explanation:
From the table:
Total number of Girls = 18Total number of students = 30Total number of Girls who are Freshman = 4[tex]\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}[/tex]
[tex]\sf \implies P(Girl)=\dfrac{18}{30}[/tex]
[tex]\sf \implies P(Freshman \cap Girl)=\dfrac{4}{30}[/tex]
[tex]\begin{aligned}\sf P(Freshman|Girl)& = \sf\dfrac{P(Freshman \cap Girl)}{P(Girl)}\\\\ & = \sf \dfrac{4}{30} \div \dfrac{18}{30}\\\\ & \sf=\dfrac{4}{30} \times \dfrac{30}{18}\\\\ & = \sf \dfrac29\end{aligned}[/tex]
X2 -2x -24=0 is equivalent to
Answer(S):
Answer:
x= 6, -4
Step-by-step explanation:
x^2 - 2x - 24 = 0
(x-6) (x+4) = 0
x = 6, x= -4
Help me please with math for points
Answer:
The answer is 72
Step-by-step explanation:
because you take the 8 times it by the 9
9×8=72 square³
PLEASE HELP I WILL GIVE BRAINLIEST
Answer:
65 degrees
Step-by-step explanation:
The angles will sum up to 360, just do 360 - all known angles
360 - 90 - 128 - 77 = 65
Answer:
Step-by-step explanation:
Sum of all angles is 360 degrees
Let the measure of angle M equal x.
x+90+77+128=360
x=65
Measure of angle M is 65 degrees
As a cold front passed, the temperature dropped steadily
2 degrees each hour. It dropped a total of 10 degrees. How
many hours did it take for the temperature to drop this far?
Answer:
5
Step-by-step explanation:
because 10 divided by 2 is 5
Naomi was measuring and cutting yarn in inches for an art project.she cut 9 pieces of the yarn.
Answer:
i don't know this question but you can just measure it
The figure is made up of a cylinder and a half sphere. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth.
A cylinder and half sphere. Both have a radius of 4 millimeters. The cylinder has a height of 7 millimeters.
Recall the formulas V = B h and V = four-thirds pi r cubed
Answer:
351.68 millimeters for the cylinder and 8 23/75 millimeters for the half circle.
Step-by-step explanation:
Volume Cylinder = 3.14(16)(7) = 351.68
Volume Half sphere = 2/3(3.14)(4) = 8 23/75
If you want both of them together just add up the two numbers.
Answer:
351.68 millimeters cylinder
8 23/75 millimeters half circle
Step-by-step explanation:
what is the derivative and the slop of the tangent line of f(x)=3x+5 at (1,8)
Step-by-step explanation:
To find the derivative of
3x+5, apply sum rule
[tex] \frac{d}{dx}(3x + 5) = \frac{d}{dx} 3x + \frac{d}{dx} 5[/tex]
The derivative of
[tex] \frac{d}{dx} kx = k[/tex]
And
[tex] \frac{d}{dx} c = 0[/tex]
So we have
[tex] \frac{d}{dx} 3x + 5 = 3[/tex]
So the derivative of the function is 3,
Since linear equations have a constant slope, the slope at any point will be 3.
So the slope of the tangent line is 3.
Which of the following is true for the function y = log3(x)?
It is the inverse of the function y = x3.
It is the inverse of the function y = 3x.
It is the reciprocal of the function y = x3.
It is the reciprocal of the function y = 3x.
Answer:
B
Step-by-step explanation:
ED
2. On the first day of a month, Leann's savings account had $176. During the
month, Leann deposited $198 and spent $160 of her money. What was
Leann's account balance at the end of the month?
⚫️-138 dollars
⚫️534 dollars
⚫️214 dollars
⚫️-182 dollars
What are the x-intercepts of this conic section?
no x-intercepts
(0, −3) and (0, 3)
(−5, 0) and (5, 0)
(−3, 0) and (3, 0)
Answer:
D. (-3, 0) (3, 0)
Step-by-step explanation:
An x-intercept is means when the line/shape crosses the x axis, or when y=0
So in this case, we can see that the shape crosses the x axis when
x = -3 and 3
So to put it in coordinate form (x, y)
It is: (-3, 0) and (3, 0)
(Whenever it crosses the x-axis, the y coordinate will always be 0)
I'LL MARK AS THE BRAINLIEST!!!!! a− (10 − a) = 30
Answer:
a=20
Step-by-step explanation:
a-10+a=30
a+a-10=30
2a-10=30
2a=30+10
2a=40
a=20
Let f(x)=3/4x2-1 The function g(x) is a vertical stretch of f(x) by a factor of 8.What is the equation of g(x)?
Answer:
g(x) = 6x^2-1
Step-by-step explanation:
f(x)=3/4x^2 −1.
A vertical stretch by a factor of 8 you multiply the number with x by the factor:
3/4 x 8 = 6
g(x) = 6x^2-1