1. Each equation below represents a circle. Place its equation in standard form and then state the coordinates of its center and the length of its radius.
(a) x² + 8x + y2 – 2y = 8
(b) x2 - 6x + y2 - 20 y =12 -
(c) x2 –16x + y2 +10y+88 =
(d) y2 + x2 +8x = 84
Answers
Completing the squares, it is found that the center and the radius of the circles are given as follows:
a) The center is (-4,1) and the radius is 5.
b) The center is (3, 10) and the radius is 11.
c) The center is (8,-5) and the radius is 1.
d) The center is (-4,0) and the radius is 10.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
Item a:
x² + 8x + y² - 2y = 8
Completing the squares:
(x + 4)² + (y - 1)² = 8 + 4² + 1²
(x + 4)² + (y - 1)² = 25
Comparing to the standard equation: The center is (-4,1) and the radius is 5.
Item b:
x² - 6x + y² - 20y = 12
(x - 3)² + (y - 10)² = 12 + 3² + 10²
(x - 3)² + (y - 10)² = 121
The center is (3, 10) and the radius is 11.
Item c:
x² - 16x + y² + 10y + 88 = 0
(x - 8)² + (y + 5)² = -88 + 8² + 5²
(x - 8)² + (y + 5)² = 1
The center is (8,-5) and the radius is 1.
Item d:
x² + 8x + y² = 84
(x + 4)² + (y - 0)² = 84 + 4²
(x + 4)² + (y - 0)² = 100
The center is (-4,0) and the radius is 10.
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Related Questions
A bag has 5 red and 8 blue marbles. What is the probability of drawing a red then blue, if the first marble has not been replaced after it has been drawn?
Answers
Answer:
5/13
Step-by-step explanation:
5+8=13
Red = 5/13
Blue = 8/13
Complete the sentence below.
The expression 52x – 169 is equivalent to
Answers
Answer:
Read the explanation below.
Step-by-step explanation:
2(26x-84.5)
13(4x-13)
Here is an inequality: -2x > 10.
list 3 values for x that would make this inequality true.
1) x=
2) x=
3) x=
Answers
Answer:
x=-10 x=-11 x=-12
Step-by-step explanation:
-10*-2=20 since -10*2=-20 and a negative number multiplied by a negative number is positive. 20>10 is true. -11*-2 is equal to 22, 22>10, -12*-2=24, 24>10.
Question
The scatterplot shows data related to the number of oil changes a car owner gets per year and the amount of money, in dollars, the owner spends on repairs during that year. The equation of the line of best fit is y=−99x+725.
Answers
A diagonal of a cube measures 15 cm and the length of an edge of the cube is V75 cm.
What is the length of the diagonal of a face of the cube? Round to the nearest tenth.
Answers
Answer:
the diagonal of a face of the cube = 12.2 (Rounded to the nearest tenth)
Step-by-step explanation:
[tex]\text{diagonal of the cube} =\ \left( \text{edge} \right) \times \sqrt{3}[/tex]
[tex]=\sqrt{75} \times \sqrt{3}[/tex]
[tex]=\sqrt{225}[/tex]
[tex]=15[/tex]
[tex]\text{diagonal of the face} =\left( \text{edge} \right) \times \sqrt{2}[/tex]
[tex]=\sqrt{75} \times \sqrt{2} \\\\=\sqrt{150} \\\\=12.247448713916[/tex]
HELP ILL GIVE BRAINLEST
What is the area of this figure?
Enter your answer in the box
Answers
Answer:
The area of that figure is 16
Step-by-step explanation:
tell me if im wrong
A 20 foot ladder is leaning against the side of a building. If the bottom of the ladder is 12 feet away from the base of the building, how far up the side of the building does the ladder reach? Draw a picture and show your work. (2 points)
Answers
Answer:
The ladder reaches is 16 feet far up the side of the building
picture below
Step-by-step explanation:
PLEASE HELP ME I'M DESPERATE.
Delta Math Question!!!
Answers
Answer:
cos S = [tex]\frac{7}{25}[/tex]
Step-by-step explanation:
this is a 7- 24- 25 right angle with RS = 7 , then
cos S = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{RS}{QS}[/tex] = [tex]\frac{7}{25}[/tex]
if 5% of an item is .50 cents what is original price
Answers
Answer:
$10.00
Step-by-step explanation:
5 % of 100 is 55 × 20 = 100so just multiply .50 by 20 and that comes out to 10 dollars19 cm 15 cm triangle and I don’t know the other side
Answers
Answer:
well it looks equal to 15 cm so its probably 15 cm
Give brainliest :)
As the degrees of freedom increase, the t distribution approaches the _____ distribution.
Answers
Using statistical concepts, it is found that as the degrees of freedom increase, the t distribution approaches the z-distribution.
When should the t-distribution and the z-distribution be used?If we have the standard deviation for the sample, the t-distribution should be used.If we have the standard deviation for the population, the z-distribution should be used.For large sample sizes, that is, a large number of degrees of freedom in the t-distribution, the t distribution approaches the z-distribution.
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Write an equation in slope-intercept form for the line with slope 1/5 and y-intercept - 2. Then graph the line.
Answers
Answer:
Slope intercept form: y = 1/5x -2
Step-by-step explanation:
Algebra 2!! Which graph represents the following piecewise defined function?
-2x, x <-1
f(x) = -1,-1
x-1, x>2
Answers
The graph that defines the following piece-wise function is given by:
f(x) = -2x, x < -1.[tex]f(x) = -1, -1 \leq x < 2[/tex].[tex]f(x) = x - 1, x \geq 2[/tex].What is a piece-wise function?It is a function that has different definitions based on the input.
In this problem, for x less than -1, the function is a line going through points (-1,2) and (-2,4), hence the slope is:
m = 4 - 2/(-2 - (-1)) = -2.
The slope of -2 means that it also passes through (0,0), hence the function is:
y = -2x.
For x between -1(inclusive) and 2(exclusive), it is a constant function at y = -1.
For x equal or greater than 2, the function is a line going through points (2,1) and (4,3), hence the slope is:
m = (3 - 1)/(4 - 2) = 1.
The slope of 1 means that the function passes through (0,-1), hence the function is:
y = x - 1.
Hence the piece-wise function is defined by:
f(x) = -2x, x < -1.[tex]f(x) = -1, -1 \leq x < 2[/tex].[tex]f(x) = x - 1, x \geq 2[/tex].More can be learned about piece-wise functions at https://brainly.com/question/24734454
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Answer:
A
Step-by-step explanation:
9. how many small cubes aside 4 cm can be filled in a rectangular box with an internal dimension of 1.6 dm long. 1.4 dm and 1.2 dm high?
pls pasagot ayan nalang kailangan ko po pls
appreciate it ko kung kahit wala nang solution basta pls sagot lang po
Answers
[tex] \small \blue{\boxed{{\colorbox{white}{42}}}} [/tex]
that's my answer
2. Let's pretend I'd give you a penny today, two pennies
tomorrow, four pennies the next day, etc. Write a function
that expresses the amount of money I'd be giving you on
thenth day. Give us your function in the initial post and give us
a little explanation about how it works.
Would you rather have me give you 40 days of this money
scheme or a billion dollars?
Answers
-f(n+1) = f(n) x 2
-on the 10th day you'd receive $512
-this function works by taking the output of the last input and multiplying it by 2 to find the new output.
-i'd rather take 40 days of this money scheme.
example of use:
f(10) = f(9) x 2
output of f(9) is 256 so f(10) = 256 x 2
Can you pls help me with this
Answers
Answer:
it's (1, 2)
Step-by-step explanation:
you just look at where the 2 lines cross
i dont understand this at all, please dont give me an answer i just need someone to explain it to me if so, thank you <3
Answers
Answer: Multiply the diameter by Pi, which in school lessons usually just use 3.14
Step-by-step explanation:
So 3.14 multiplied by the diameter of 9.
please mark brainliest
How many radians is each angle of an equilateral triangle?
Answers
Answer:
[tex]\displaystyle \frac{\pi}{3}[/tex] radians
Step-by-step explanation:
As an equilateral triangle has all angles congruent to each other, each angle is measured 60°
To convert from degrees to radians, we multiply by π/180
Hence, [tex]\displaystyle 60^\circ*\frac{\pi}{180}=\frac{60\pi}{180}=\frac{\pi}{3}[/tex]
If a parallelogram has congruent
diagonals, then it is a rectangle.
Choose the equivalent statement.
A. Ifa parallelogram is not a rectangle, then it does not have
congruent diagonals.
B. If parallelogram does not have congruent diagonals, then it is a
rectangle.
C. If a parallelogram is a rectangle, then it does not have congruent
diagonals.
Answers
Answer: A
Step-by-step explanation:
The contrapositive of a statement is logically equivalent to the original statement.
if you put one penny in a room at 12:00 every minute that penny doubles, in 1 hour at 1:00 the room is full. at what time was the room halfway full?
Answers
Answer: It would be 1 min since it doubles every minute. Similarly, it'll be half full the minute before its full is 59.
Step-by-step explanation:
2.8 meters less 2.5 meters equals how many centimeters
Answers
Answer: 30 centimeters
Step-by-step explanation:
We will subtract and then convert units.
2.8 meters less 2.5 meters = 2.8 meters - 2.5 meters = 0.3 meters
0.3 meters * 100 = 30 centimeters
If this problem is not asking for 2.8 meters minus 2.5 meters - and is stating something else - please comment so I can fix my answer.
Help me please I will mark the brainiest and give many points
Answers
Only the arrangement and order Is different else all are similar
in first method Kiran created a table which produces all values in the order [1,6] to H and T.
In second method Priya created a flow chart type tree diagram which produces all values in order H and T to [1,6]
So they both produce same answers as both are like inverses of each other ,
If you try to understand then think about relations
Kiran:[1,6]—>{H,T}Priya:{H,T}—»[1,6]So they are ought to form same values just in different order .
#2
Second method is more applicable as its more understandable and easier
7) Find the number of rotations
needed for this wheel to travel 100
feet if the radius of the wheel is 1
foot?
IL
Answers
Answer:
16 full rotations
Step-by-step explanation:
If the radius is 1 foot, cirumference is what we need to get in order to figure out how many rotations are necessary.
Circumference = 2 pi r
[tex]2 * \pi * r = 6.28\\100 / 6.28 = 15.92[/tex]
Hope this helps
Graham and hunter are circus performers. a cable lifts graham into the air at a constant speed of 1.5 ft/s. when graham’s arms are 18 ft above the ground, hunter, who is standing directly underneath graham, throws graham a ball as the cable continues to lift him higher. hunter throws the ball from a position 5 ft above the ground with an initial velocity of 24 ft/s. which system of equations can be used to model this situation? startlayout enlarged left-brace 1st row h = 18 1.5 t 2nd row h = 5 24 t minus 16 t squared endlayout startlayout enlarged left-brace 1st row h = 18 1.5 t 2nd row h = 5 24 t 16 t squared endlayout startlayout enlarged left-brace 1st row h = 18 1.5 t 2nd row h = 5 24 t endlayout startlayout enlarged left-brace 1st row h = 18 1.5 t minus 16 t squared 2nd row h = 5 24 t 16 t squared endlayout
Answers
Therefore, the system of equations that can be used to model this situation is h= 5 + 24t -16t^2.
What is the system of equation about?The equations that were given in the system above are :
h = 18 + 1.5t
h = 5 + 24t - 16t^2
Note that:
The rate of Speed = distance divided by time
Since Speed = 1.5ft/s
Distance = 18ft
To know the time which was not given, the equation will be:
1.5ft/s = 18ft/t
1.5t=18
The equation to know height h= 18 + 1.5t
Since Graham moved another 5ft along with a velocity of 24ft/s
Therefore, the system of equations that can be used to model this situation is h= 5 + 24t -16t^2 and as such, option A is correct.
Learn more about the equation from
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Answer:
so its A
Step-by-step explanation:
edge 2023
what is 35x 67 solve the question
Answers
Answer:
2,345
Step-by-step explanation:
This is a simple multiplication problem.
35 × 67 = 2345
B. Solve the inequalities. Show your work as it is done in the examples. (Hint: One answer will be "no solution" and one answer will be "all real numbers".) See Exs. 3 thru 12.
4. |x| > -11
Answers
Como diferenciar em uma imagem o angulo nulo do angulo meia volta?
Answers
Answer: Hay 360° en un giro completo, 180° en medio giro y 90° en un cuarto de giro. Un cuarto de vuelta se llama ángulo recto.
Step-by-step explanation:
1. Which is the best method for solving the quadratic equation? Explain why using a sentence. Then solve the quadratic equation using the method chosen. Leave all answers in simplest radical form.
Try to only choose each method once, but you may use a method twice.
• Take the square root of each side.
• Factor and use the zero-product property.
• Complete the square.
• Use the quadratic formula.
A. 2a2 = 72
B. x2 -10x +16= 0
C. y2 + 6y = 2
Answers
Answer:
Below.
Step-by-step explanation:
A. Take the square root of each side.
2a^2 = 72
a^2 = 36
a = -6, 6.
B. Factor and use the zero-product property
(x - 2)(x - 8) = 0
x = 2, 8.
C. Complete the square.
y^2 + 6y = 2
(y + 3)^2 - 3^2 = 2
(y + 3)^2 = 2 + 9 = 11
Taking square roots:
y + 3 = +/- √11
y = -3 + √11, -3 - √11
Help me out yall PLEASE
Answers
hope this helps :D
Use the FOIL Method to simplify completely:
(3p+2)(5p - 7)
8p² + 11p - 14
O 15p² + 11p + 14
○15p² – 11p – 14
O 8p² + 11p - 14
Answers
Answer:
15p^2 - 11p - 14 (thus answer three is correct)
Step-by-step explanation:
I uploaded an image of how this question is completed for an extended visual. Your welcome and have a great day :))))
