Find the center (h, k), the radius r, and the intercepts, if any of each circle.
x2 + y2 - 6x + 2y + 6 = 0
a
(h, k) = (3, -1); r = 2; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none
b
(h, k) = (3, -1); r = 4; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none
c
(h, k) = (-3, 1); r = 4; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none
d
(h, k) = (-3, 1); r = 2; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none
e
none
Answers
Answer:
A. [tex]C(x,y) = (3,-1)[/tex], [tex]r = 2[/tex], x-Intercepts: [tex]x = 3\pm\sqrt{3}[/tex], y-Intercepts: none.
Step-by-step explanation:
Let [tex]x^{2}+y^{2}-6\cdot x + 2\cdot y + 6 = 0[/tex] be the general equation of the circle, we must transform the expression into standard form to determine its center, radius and intercepts. The procedure is shown below:
1) [tex]x^{2}+y^{2}-6\cdot x + 2\cdot y + 6 = 0[/tex] Given.
2) [tex](x^{2}-6\cdot x)+(y^{2}+2\cdot y) +6= 0[/tex] Commutative and associative properties.
3) [tex](x^{2}-6\cdot x)+(y^{2}+2\cdot y) + 6 + 3 + 1 = 3 + 1[/tex] Compatibility with addition.
4) [tex](x^{2}-6\cdot x +9)+(y^{2}+2\cdot y +1) = 4[/tex] Definition of addition/Commutative and associative properties.
5) [tex](x-3)^{2} + (y+1)^{2} = 4[/tex] Perfect square trinomial/Result.
The equation of the circle centered in (h, k) in standard form is defined as:
[tex](x -h)^{2} + (y-k)^{2} = r^{2}[/tex] (Eq. 1)
Where:
[tex]h[/tex], [tex]k[/tex] - Coordinate of the center of the circle, dimensionless.
[tex]r[/tex] - Radius of the circle, dimensionless.
By direct comparison we find that circle is centered in [tex]C(x, y) = (3, -1)[/tex] and has a radius of 2.
Finally, we obtain the intercepts of the given function:
x-Intercepts ([tex]y = 0[/tex])
[tex](x-3)^{2} + (0+1)^{2} = 4[/tex]
[tex]x^{2}-6\cdot x +9+1 = 4[/tex]
[tex]x^{2}-6\cdot x +6=0[/tex]
Roots are found analitically by Quadratic Formula:
[tex]x = 3\pm\sqrt{3}[/tex]
y-Intercepts ([tex]x=0[/tex])
[tex](0-3)^{2}+(y+1)^{2} = 4[/tex]
[tex]9+y^{2}+2\cdot y +1 = 4[/tex]
[tex]y^{2}+2\cdot y +6 = 0[/tex]
Roots are found analitically by Quadratic Formula:
[tex]y = -1\pm i\,\sqrt{5}[/tex]
In a nutshell, there are no y-Intercepts.
We include a graphic including circle, center and x-Intercepts.
Finally, we came to the conclusion that correct answer is A.
Related Questions
Use algebraic means to show that x^2 + y^2 = 8 is not a function. Explain your process.
Answers
Answer:
For a single value of x function has more than one corresponding value of y which satisfies the equation.
Step-by-step explanation:
Function: A relationship between a set of inputs and a set of possible outputs, where exactly one output is associated with each input.
It means for an equation to represent a function any single value of x there should be only one corresponding value of y which satisfies the equation.
Now consider the given equation.
[tex]x^2 + y^2 = 8[/tex]
If we put x=0 then we get two value of y i.e [tex]\sqrt8[/tex] and [tex]-\sqrt8[/tex] which satisfy the equation and therefore the equation is not a function.
Need help asap PLEASE same problem just made it easier to see
Answers
Label XY with 3.
Label angle X with 53 degrees.
Label angle Y with 90 degrees.
Label angle C with 37 degrees.
Label angle A with 53 degrees.
Label BC with 4.
Label AC with 5.
Answer: i don't know if you want degrees or the lengths so i did both
∠ACB = 37°
∠BAC = 53°
∠ZXY = 53°
∠XYZ = 90°
∠XZY = 37°
∠ABC = 90°
BC = 4
AC = 5
AB = 3
YZ = 4
XY = 3
XZ = 5
Step-by-step explanation:
37 + 90 = 127
180 - 127 = 53
37 + 90 + 53 = 180
Which of the following is a binomial?
Answers
Answer:
B
Step-by-step explanation:
10,716/ 456 written as a decimal
Answers
Explanation/Answer: 23.5
The decimal value of 10716 / 456 is 23.5.
Given,
10716 / 456.
We need to convert it into a decimal value.
What is a decimal number?A number that has a decimal point is called a decimal number.
In order to convert a fraction into a decimal number, we need to divide the numerator by the denominator.
Example: 7/2 =3.5
Find the decimal number.
We have,
10716 / 456
We can directly divide or we can simplify the fraction into a simpler fraction.
10716 = 12 x 893
456 = 12 x 38
So,
= 12 x 893 / 12 x 38
= 893 / 38
Divide 893 by 38
We get,
= 23.5
Thus the decimal value of 10716 / 456 is 23.5.
Learn more about converting fractions into decimals here:
https://brainly.com/question/2362378
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Show your work:
−15x = 0
Answers
Answer:
Step-by-step explanation:
-15x = x = 0/-15
x = 0
Step-by-step explanation:
-15x=0
-15x/-15=0/-15
x=0
-15(0)=0
I need help please and thank you in advance
Answers
u/5 =13/7 solve for u
Answers
Answer:
u = 65/7
Step-by-step explanation:
u/5 = 13/7
Using the cross product
7u = 5*13
7u = 65
Divide each side by 7
7u/7 = 65/7
u = 65/7
Find the product: 5(2x2 + 4x + 3)
Answers
Answer:
10x^2+20x+15
Step-by-step explanation:
5(2x^2+4x+3)
u distributed it and u get
10x^2+20x+15
Answer: I am pretty sure it is 115+20x
Step-by-step explanation: You have to do distributive Property
10 times 10+ 20x+15
100+20x+15
115+20x
Do yoi think you can sovle this?
Free brainlest for answer, 25 points.
Answers
Answer:
23 did i get it?
Give the probability distribution for X:
x 0 1 2 3
f(x) 1/4 1/8 1/2 1/8
Find Var.
Answers
Answer:
Var(x)=1
Step-by-step explanation:
x p(x) x² x*p(x) x²*p(x)
0 1/4 0 0 0
1 1/8 1 1/8 1/8
2 1/2 4 1 2
3 1/8 9 3/8 9/8
Total 3/2 13/4
The required variance can be computed as
Var(x)=sumx²*p(x)-(sum(x*p(x)))²
Var(x)=13/4-(3/2)²
Var(x)=13/4-9/4
Var(x)=4/4
Var(x)=1
Thus, the required variance is 1.
Write and equation of a line perpendicular to y=-5x+8 and passes through (10,4)
Answers
im not sure just yet
What place value is the 5 in the following number, 123.465? earn 100 points!!!
Answers
Answer:
it will be in the thousands place for sure
Step-by-step explanation:
hope that helps =) i forgot there were a decimal point
Answer:
The place value of 5 in "123.465" is the thousandths
Step-by-step explanation:
The reason for this is because the "5" is 3 points behind the decimal, making it in the thousanths place.
To finish a certain job in 8 days in 6 workers are needed. if it is required to finish the same job in 2 days advance how many workers have to work?
Answers
Answer:
The job needs 48 worker/days.
Step-by-step explanation:
To do it in 4 days, 48/4 or 12
A college food court surveyed 325 students to see how many drink tea and how many drink coffee.
The Venn diagram below shows the results. (Each number gives the number of students who fall into that Venn diagram category.)
-All students in the survey
(a) How many of the students drink coffee?
Drink
tea
Drink
coffee
0
students
94
77
56
(b) How many of the students drink tea or coffee (or both)?
. students
98
(c) How many of the students do not drink both tea and coffee?
students
Answers
Answer:
Add the 3 then subtract that from 325
you should know part B
Step-by-step explanation:
Adam has two kinds of fruit punch left over from a party. He mixes 5 liters of fruit punch A with 10 liters of fruit punch B to create fruit
punch C. Fruit punch A contains 25% orange juice and the resulting fruit punch C contains 35% orange juice.
What percent orange juice does fruit punch B contain?
OA. 20%
OB. 50%
OC. 40%
OD 25%
Answers
Answer:
A. 20%
Step-by-step explanation:
fruit punch A is half of fruit punch B so times 35 by 2 and then subtract 50. 50 came from 25 times 2.
Solve the inequality. 12x<-144
Answers
Answer:
Step-by-step explanation:
x=-12
Answer:
x= -12
Step-by-step explanation:
Two angles of a triangle measure 12 and 40. What is the third angle?
Answers
52+X=180
X=180-52 = 128 degrees
X is the third angle of the triangle
Answer:
The third angle is 128°.
Step-by-step explanation:
We need to remember that the sum of the 3 angles of a triangle is 180°, hence if we have 2 angles, the third angle is:
[tex] 180 = \alpha + \beta + \theta [/tex]
[tex] 180 = 12 + 40 + \theta [/tex]
[tex] \theta = 180 - 52 [/tex]
[tex] \theta = 128 [/tex]
Therefore, the third angle is 128°.
I hope it helps you!
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Vanessa and Zack are playing a game where the player with the lower score wins. At the end of the game, Vanessa has a score of Negative 3 and StartFraction 5 over 8 EndFraction and Zack has a score of Negative 3 and two-thirds. Which statement explains who won?
Comparing the decimal equivalents of their scores shows that Vanessa won because –3.625 is less than Negative 3.ModifyingAbove 6 with bar.
Comparing the decimal equivalents of their scores shows that Vanessa won becauseNegative 3.ModifyingAbove 6 with bar is less than –3.625.
Comparing the decimal equivalents of their scores shows that Zack won because –3.625 is less than Negative 3.ModifyingAbove 6 with bar.
Comparing the decimal equivalents of their scores shows that Zack won becauseNegative 3.ModifyingAbove 6 with bar is less than –3.625.
Answers
Answer:
the last option D.comparing the decimal equivalents of their scores shows that Zack won because -3.6 is less than -3.625
Step by step explanation
Got it correct on edge
Answer:
D
Step-by-step explanation:
Is this a function or not a function? (Picture)
Answers
Answer:
Yes it is a function
Step-by-step explanation:
I can do math can I get brainliest?
Kyle plans to estimate the area of the figure below by identifying the full and partial squares that make up the figure.
If Kyle uses the strategy, which statement best describes the figure?
O 20 full squares and 8 partial squares
0 24 full squares and 12 partial squares
0 36 full squares and 12 partial squares
O 40 full squares and 8 partial squares
Answers
Answer:
The answer is one hundred percent D
Step-by-step explanation:
Hi
Answer:
D
Step-by-step explanation:
PLEASE HELP ASAP
Solve the following system of equations.
y = 5x – 3
y = x2 + 3x – 2
Question 4 options:
A)
(–1,8)
B)
(0,–3)
C)
(2,7)
D)
(1,2)
Answers
The Answer fam is......... D) (1,2)
The solution for the given system of equations as per linear and quadratic equation is (x, y) = (1, 2).
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1."
What is a quadratic equation?"A quadratic equation is an equation in which the highest power of the variable is always 2."
Given two linear equations are:
y = 5x – 3 (1)
y = x² + 3x – 2 (2)
Therefore, combining the two equations, we get:
5x - 3 = x² + 3x - 2
⇒ x² - 5x +3x - 2 + 3 = 0
⇒ x² - 2x + 1 = 0
⇒ (x)² - 2 × x × 1 + (1)² = 0
⇒ (x - 1)² = 0
⇒ (x - 1) = 0
⇒ x = 1
Now substituting the value of 'x' in the equation (1), we get:
y = 5 × 1 - 3
⇒ y = 2
Therefore, by solving the given two equations, we get: x = 1, y = 2.
Learn more about linear and quadratic equation here: https://brainly.com/question/26020597
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Maureen reads at an average rate of 18 pages per hour. If she reads for 3.5 hours how many pages will she read?
Answers
the answer is 63
Step-by-step explanation
18 x 3.5=63
Answer: 63 pages
Explanation: 18 times 3 equals 54 and then for half an hour that's 9 minutes added to 54 which is 63 pages.
△BCD≅△GEF . If BC=10 , CD=3x+8 and EF=4x+6 , then what is the measure of CD ?
Answers
Given :-
ΔBCD ≅ ΔGEF
Then :-
∠B <=> ∠G ( ∠B = ∠G )
∠C <=> ∠E ( ∠C = ∠E )
∠D <=> ∠F ( ∠ D = ∠F )
BC <=> GE ( BC = GE )
CD <=> EF ( CD = EF )
BD <=> GF ( BD = GF )
Using this let us find CD .
CD = EF
Which means :-
[tex] 3x + 8 = 4x + 6[/tex]
[tex]8 = 4x + 6 - 3x[/tex]
[tex]8 = 1x + 6[/tex]
[tex]1x + 6= 8[/tex]
[tex]1x = 8 - 6[/tex]
[tex]1x = 2[/tex]
[tex]x = 2[/tex]
Then :-
EF =
[tex]EF = 4x + 6 \\ = 4 \times 2 + 6 \\ = 8 + 6 \\ = 14[/tex]
CD =
[tex]CD = 3x + 8 \\ = 3 \times 2 + 8 \\ = 6 + 8 \\ = 14[/tex]
Therefore , CD = 14 .△BCD≅△GEF
The measure of CD is 14
Given :
Two triangles are congruent
△BCD≅△GEF
When triangles are congruent then the sides are equal
[tex]BC=GE\\CD=EF\\DB=FG\\[/tex]
Given that CD=3x+8 and EF=4x+6
[tex]CD=EF\\3x+8=4x+6\\3x+8-3x=4x-3x+6\\8=x+6\\8-6=x+6-6\\x=2[/tex]
The value of x=2
Now we find measure of CD
[tex]CD=3x+8\\CD=3(2)+8\\CD=14[/tex]
The measure of CD is 14
Learn more : brainly.com/question/18373823
Suppose a Hispanic Heritage festival is held in an area measuring 2,494 square yards. If the length of the festival is 58 yards, what is the width of the festival?
Answers
Answer: 43 yards.
Step-by-step explanation:
Let the shape of the area occupied for festival be rectangle.
and area of rectangle = length x width
Given: Area of the festival= 2,494 square yards.
Length of the festival= 58 yards
Then width = (Area )÷ (length)
= (2494)÷58 yards
= 43 yards
hence, the width of the festival = 43 yards.
Look at the pattern below.
0, 3, 6, 9, ...
Create a new pattern that follows the same rule as the one above.
Answers
0,5,10,15,20,
Step-by-step explanation:
I'm just adding 5 to each because I add 3 to each number
Anyone know how to do this? I’m stuck
Answers
8/9 - 1/3 equals what
Answers
Explanation: Start by making them have common denominators by multiplying the numerator and denominator by 3, so now its 8/9-3/9 then 8-3=5 so the answer is 5/9.
A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and their plan of going to graduate school. Compute the row percentages.
A. Yes = 35% and No = 65% Business = 25%, Engineering = 30%, and Others = 45%
B. Yes = 48% and No = 52% Business = 31.5%, Engineering = 36.5%, and Others = 32%
Answers
Incomplete question. Attached is an image of the table.
Step-by-step explanation:
A.
Yes = 35% = [tex]\frac{280}{800} * 100 =[/tex] 35%. and No = 65% = [tex]\frac{520}{800} * 100 =[/tex] 65%
Business = 25% = [tex]\frac{70}{280} * 100 =[/tex] 25%.Engineering = 30% = [tex]\frac{84}{280} * 100 =[/tex] 30%. and Others = 45% = [tex]\frac{126}{280} * 100 =[/tex] 45%.Find the slope of the line
Answers
Dylan mowed three lawns for $45. Determine the cost per lawn
Answers
Answer:
$15
Step-by-step explanation:
Dvide 45 by 3 to get 15.
Explanation: If he mowed 3 laws for $45, you need to do 45 divided by 3 which equals 15 to find out he makes $15 per lawn.
