Use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.10-(-3,6)(-6,3(0,3)-10(-3,0)1010
Answers
Question:
Solution:
An equation of the circle with center (h,k) and radius r is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]This is called the center-radius form of the circle equation.
Now, in this case, notice that the center of the circle is (h,k) = (-3,3) and its radius is r = 3 so that the center-radius form of the circle would be:
[tex](x+3)^2+(y-3)^2=3^2[/tex]To obtain the general form, we must solve the squares of the previous equation:
[tex](x+3)^2+(y-3)^2-3^2\text{ = 0}[/tex]this is equivalent to:
[tex](x^2+6x+3^2)+(y^2-6y+3^2)\text{ - 9 = 0}[/tex]this is equivalent to
[tex]x^2+6x+9+y^2-6y\text{ = 0}[/tex]this is equivalent to:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]so that, the general form equation of the circle would be:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]thus, the correct answer is:
CENTER - RADIUS FORM:
[tex](x+3)^2+(y-3)^2=3^2[/tex]GENERAL FORM:
[tex]x^2+y^2+6x-6y\text{ +9= 0}[/tex]
Related Questions
What is the probability that the spinner lands on a prime number?
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Answer:
Step-by-step explanation:
50
I would like to learn the long multiplication so I can teach my fifth grader this math problem
352x20=
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Answer: 7040
Step-by-step explanation:
1
352
x20
——-
000
7040
+
———
7040
Fill in the blanks. (6x)^2 = _x^_
Answers
Step-by-step explanation:
[tex](6x) {}^{2} = -x { }^{?} - [/tex]How many times in the parabola does a line intersect?
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The line can intersect the parabola at one or two points.
See the example below.
The black line intersects the parabola at (1, -1)
The blue line intersects the parabola at two points: (0, 0) and (4, 8).
(Combining Equation)What is the result of subtracting the second equation from the first ?-2x + y = 0 -7x + 3y = 2
Answers
We are given the following two equations
[tex]\begin{gathered} -2x+y=0\quad eq.1 \\ -7x+3y=2\quad eq.2 \end{gathered}[/tex]Let us subtract the second equation from the first equation.
Therefore, the result of subtracting the second equation from the first is
[tex]5x-2y=-2[/tex]Find all the solutions and if there is an extraneous solution, identify them and explain why they are extraneous.
Answers
ANSWER
Solution: b = 3
It is extraneous
EXPLANATION
We want to solve the equation given and to see if there are any extraneous solutions.
We have:
[tex]\begin{gathered} \frac{7}{b\text{ + 3}}\text{ + }\frac{5}{b\text{ - 3}}\text{ = }\frac{10b}{b^2\text{ - 9}} \\ \Rightarrow\text{ }\frac{7}{b\text{ + 3}}\text{ + }\frac{5}{b\text{ - 3}}\text{ = }\frac{10b}{(b\text{ + 3)(b - 3)}} \\ \text{Multiply both sides by (b + 3)(b - 3):} \\ \Rightarrow\text{ }\frac{7(b+3)(b\text{ - 3)}}{b\text{ + 3}}\text{ + }\frac{5(b\text{ + 3)(b - 3)}}{b\text{ - 3}}\text{ = }\frac{10b(b\text{ + 3)(b - 3)}}{(b\text{ + 3)(b - 3)}} \\ 7(b\text{ - 3) + 5(b + 3) = 10b} \\ 7b\text{ - 21 + 5b + 15 = 10b} \\ \text{Collect like terms:} \\ 7b\text{ + 5b - 10b = 21 - 15} \\ 2b\text{ = 6} \\ Divide\text{ both sides by 2:} \\ b\text{ = }\frac{6}{2} \\ b\text{ = 3} \end{gathered}[/tex]That is the solution to the equation.
To find if the solution is extraneous, we will insert the value of b = 3 into the original equation.
That is:
[tex]\begin{gathered} \Rightarrow\text{ }\frac{7}{3\text{ + 3}}\text{ + }\frac{5}{3\text{ - 3}}\text{ = }\frac{10(3)}{(3\text{ + 3)(3 - 3)}} \\ \frac{7}{6}\text{ + }\frac{5}{0}\text{ = }\frac{30}{(6)(0)} \\ \frac{7}{6}\text{ + }\frac{5}{0}\text{ = }\frac{30}{0} \end{gathered}[/tex]An extraneous solution is a solution that derives from solving a rational equation but does not exactly satisfy the original equation, that is, it is invalid for the equation.
By inserting b = 3 into the equation, we see that the equation is undefined.
Therefore, since b = 3 is a solution, but it does not satisfy the equation, it is an extraneous solution.
Fill in the reason that justifies the step to solve for x in the diagram Given: QS = 42 X + 3 + 2x = 42 o R A. Substitution PropertyB. Segment Addition Postulate C. Simplify.
Answers
With the Segment Addition Postulate you have that:
[tex]QS=QR+RS[/tex]As you have that 42 is equal to QS, and 42 is equal to X + 3 + 2, you use
The Entertainment Center accumulates the following cost and net realizable value (NRV) data at December 31.
Inventory
Cost
Categories Data
Camera
Camcorders
DVDs
$11,600 $10,100
8,500
8,000
Market
Data
13,500
12,900
What is the lower-of-cost-or-net-realizable-value of the inventory?
Lower-of-cost-or-net-realizable-value $
Answers
The lower-of-cost-or-net-realizable-value of the inventory is $31000.
Define net-realizable-value.An asset's worth is often assessed using the net realizable value (NRV) approach for inventory accounting. It is discovered by calculating the difference between the asset's anticipated selling price and all of the expenses related to the asset's eventual sale. The cash sum that a corporation anticipates receiving is known as net realizable value (NRV). Consequently, net realizable value is also known as cash realizable value. The terms "net realizable value" and "current assets" are frequently used in relation to inventory and accounts receivable.
Given,
Camera
Cost = 11600
Market value = 10100
(Market value is less. so 10100.)
Camcorders
Cost = 8500
Market value = 8000
( Market value is less so 8000)
DVD
Cost = 13500
Market value = 12900
(Market value is less, so 12900)
the lower-of-cost-or-net-realizable-value of the inventory:
= 10100 + 8000 + 12900
= 31000
The lower-of-cost-or-net-realizable-value of the inventory is $31000.
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Please help me solve this math problemRewrite in exponential form Ln3=y
Answers
1) Let's rewrite it as a logarithmic expression of the following exponential one. Let's do it step by step.
[tex]\begin{gathered} e^6=x \\ \ln e^6=\ln x \\ \ln(x)=6 \end{gathered}[/tex]Note that when we apply the natural log on both sides, we use one of those properties that tell us that we can eliminate the log since the base of a natural log is "e", as well as, "e" is the base of that power.
2) To rewrite in the exponential form we can do the following:
[tex]\ln(3)=y\Leftrightarrow e^y=3[/tex]Note that in this case, we have used the definition of logarithms.
When should the Empirical Rule be used?
Answers
The empirical formula should be used after calculating the standard deviation and collecting the exact data needed for a forecast.
Explanations:What is the empirical rule?The empirical rule is a term used in statistics also known as the 68–95–99.7 rule. This rule is majorly used in forecasting the final outcome of events.
The empirical rule can be used to therefore determine a rough estimate of the outcome of the impending data to be collected and analyzed. This is done after calculating the standard deviation and collecting the exact data needed.
68–95–99.7 rule,
Using the formula C =5/9(F −32), find C when F is −58∘.? C∘
Answers
ANSWER
C = -50 degree Celcius
STEP-BY-STEP EXPLANATION:
What to find? The value of C in degree Celcius
Given Parameters
F = -58 degree Fahrenheit
The formula is given below
[tex]C=\text{ }\frac{5}{9}(F\text{ - 32)}[/tex]Substitute the value of into the equation
[tex]\begin{gathered} C\text{ = }\frac{5}{9}(-58\text{ - 32)} \\ \text{Solve the expression inside the parenthesis first} \\ C\text{ = }\frac{5}{9}(-90) \\ C\text{ = }\frac{-5\cdot\text{ 90}}{9} \\ C\text{ = }\frac{-450}{9} \\ C=-50^oC \end{gathered}[/tex]Hence, the value of C is -50 degrees
Jenny originally bought her car for $42,000. Four years later, she sold it to a used car salesman for $14,000. What is the ratio for the amount she sold it for to the amount that it depreciated?
Answers
SOLUTION
The amout that Jenny sold the car for is $14,000
The amout that the car depriciated will be
$42,000 - $14,000 = $28,000
The ratio for the amount she sold it for to the amount that it depreciated becomes
[tex]\begin{gathered} \frac{14,000}{28,000} \\ \\ =\text{ }\frac{1}{2} \\ \\ =\text{ 1 : 2} \end{gathered}[/tex]in a triangle one angle is three times the smallest angle and the third angle is 45 more than twice the smallest angle. find the measure of all 3 angles. Hint: the angles of a triangle add up to 180.
Please show me full steps. I need help.
Answers
The angles are 22.5°, 67.5° and 90°.
How to calculate the angle?Let the smallest angle = x
Total angles in a triangle = 180°
One angle is three times the smallest angle. This will be 3x.
The third angle is 45 more than twice the smallest angle. This will be:
= (2 × x) + 45
= 2x + 45
The angles will be:
x + 2x + 45 + 3x = 180
6x + 45 = 180
Collect like terms
6x = 180 - 45
6x = 135
Divide
x = 135 / 6
x = 22.5°
Smallest angle = 22.5°
The other angles will be calculated by substitutibg 22.5° for x. This will be:
3x = 3 × 22.5 = 67.5°
Also, 2x + 45 = 2(22.5) + 45 = 90°
This illustrates the concept for angles in a triangle.
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The function f(x) = 6x represents the number of lightbulbs f(x) that are needed for x chandeliers. How many lightbulbs are needed for 7 chandeliers? Show your work
Answers
There are a total of 42 lightbulbs needed for 7 chandeliers
How to determine the number of lightbulbs needed?From the question, the equation of the function is given as
f(x) = 6x
Where
x represents the number of chandeliersf(x) represents the number of lightbulbs
For 7 chandeliers, we have
x = 7
Substitute x = 7 in f(x) = 6x
So, we have
f(7) = 6 x 7
Evaluate the product
f(7) = 42
Hence, the number of lightbulbs needed for 7 chandeliers is 42
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The number of lightbulbs needed for 7 chandeliers would be; 42
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the given problem, the equation of the function is;
f(x) = 6x
Where
x be the number of chandeliers and f(x) represents the number of lightbulbs.
For 7 chandeliers, x = 7
Now Substitute x = 7 in f(x) = 6x
Therefore, f(7) = 6 x 7
Evaluate the product;
f(7) = 42
Hence, the number of lightbulbs needed for 7 chandeliers would be; 42
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A park has several rows of trees. Each row has 5 trees. How many trees could be in the park?
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Answer: so lets say x =the exact amount of rows
so each row has 5 tree's
then a is the answer
its an equation of x·5=a
so that would be a unknown number of trees so you assume that there is more than 1 row because there is several rows so its a incomplete question
Step-by-step explanation:
Hayley's rectangular bedroom is 6 meters by 5 meters. What is the diagonal distance from one corner to the opposite corner? If necessary, round to the nearest tenth.
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Hayley's rectangular bedroom is 6 meters by 5 meters. What is the diagonal distance from one corner to the opposite corner? If necessary, round to the nearest tenth.
Apply the Pythagorean Theorem
c^2=a^2+b^2
we have
a=6 m
b=5 m
c^2=6^2+5^2
c^2=36+25
c^2=61
square root c=7.8 m
answer is 7.8 metersDraw a sketch of f(x) = (x-4)^2+5. Plot the point for the vertex, label the coordinates as a maximum or minimum, draw and write the equation for the axis of symmetry
Answers
Given the function:
[tex]f(x)=(x-4)^2+5[/tex]the given function is a quadratic function
The graph of the function is as shown in the following picture
As shown the function has a minimum point at ( 4, 5 )
So, vertex = ( 4, 5 )
And Axis of symmetry: x = 4
write each phrase as an algebraic expression:1) n times 72) 4 minus y3) 13 added to x
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1) n times 7
times means multiplication
7n
2.Find the range of thisquadratic function.1-3-2-11y = x2 + 2x-27А-1 < y< ooB- < y < oo
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Okay, here we have this:
Considering that the range of a function is the complete set of all possible resulting values of the dependent variable (y), we can see in the graph of the function that:
The values of the variable "y" go from -1 to plus infinity, this mean that the range is:
-1≤y<∞
Finally we obtain that the correct option is the first option.
The population of Somewhere, USA was estimated to be 658,100 in 2003, with an expected increase of 5% per year. At the percent ofincrease given, what was the expected population in 2004? Round your answer to the nearest whole number.
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To solve for the expected population in 2004:
[tex]\begin{gathered} \text{Estimated population for 2003=658100} \\ \text{rate = 5 \%} \\ nu\text{mber of year = 1} \end{gathered}[/tex]Using compound interest formular to solve for the expected popupation:
Expected population = Amount
[tex]\begin{gathered} A=p(1+\frac{r}{100})^n \\ A\text{ = 658100 (1+}\frac{5}{100})^1 \\ A=658100\text{ (1+0.05)} \\ A=658100(1.05) \\ A=691005 \end{gathered}[/tex]Hence the expected population in 2004 = 691,005
What is the volume of the right triangular prism below? a 1600cm 800cm 400cm 160cm
Answers
The formula for determining the volume of a triangular prism is expressed as
Volume = area of triangular face * height of prism
The fotmula for finding the area of the triangular face is
Area = 1/2 * base * height
Looking at the diagram,
base = 8 cm
height = 10 cm
Area of triangular face = 1/2 * 8 * 10 = 40 cm^2
height of prism = 20 cm
Volume of prism = 40 * 20 = 800 cm^3
Option B is correct
y=-2x+6x+8 how do i find the vertex
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Then the vertex is (3/2, 25/2)
A general equation of a parabola is:
[tex]y=ax^2\text{ + bx + c; the vertex of a parabola is the point (h,k) where h = -b/2a}[/tex]This way you find the value of h
Since h is a value of x, you can find the corresponing value of y by using the original equation:
[tex]y=ah^2\text{ + bh + c}[/tex]and this will be the value of K
2. What is an algebraic expression for each phrase?a. the product of 9 and a number tb. the difference of a number x and 1/2c. the sum of a number m and 7.1 d. the quotient of 207 and a number n
Answers
The algebraic expression for each phrase would be the following:
a. the product of 9 and a number t would be expressed as:
9*t
b. the difference of a number x and 1/2 would be expressed as:
x - 1/2
c. the sum of a number m and 7.1 would be expressed as:
m + 7.1
d. the quotient of 207 and a number n would be expressed as:
207 / n
Ms. Wong sold 28 cars. She sold 8 fewer cars that 3/4 as many cass as Mr. Diaz. Which equation can be used to find the number of cars that Mr. Diaz sold,c?
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The equation that we can be used to find the number of cars that Mr. Diaz sold is [tex]\frac{3}{4}x[/tex]−[tex]8=28[/tex].
Ms Wong sold cars = 28.
She sold [tex]8[/tex] fewer cars that is 3/4 as many cars as Mr. Diaz.
Let Mr. Diaz sold [tex]x[/tex] cars.
Cars is 3/4 as many cars as Mr. Diaz so the term [tex]3/4x[/tex].
She sold 8 fewer cars.
Now from the statement the Ms Wong sold cars [tex]\frac{3}{4}x[/tex]−[tex]8[/tex].
As it is given that Ms Wong sold 28 cars.
So the equation must be
[tex]\frac{3}{4}x[/tex]−[tex]8=28[/tex]
So equation that we can be used to find the number of cars that Mr. Diaz sold is [tex]\frac{3}{4}x[/tex]−[tex]8=28[/tex].
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the rate of change at which the water level rises is ___ centimeters per minutes. so, involving the equation ____ for y gives a y-value equal to___
Answers
We will have the following:
The rate at which the water rises is 13/4 cm per minute.
So, solvinng the equation:
[tex]\frac{13}{4}=\frac{y}{12}[/tex]For y gives a value for y equal to:
[tex]y=\frac{13\cdot12}{4}\Rightarrow y=39[/tex]Rewrite the equation by completing the square. x^2 + 4x − 21 = 0
( x + _ )^2 = _
Answers
[tex] {x}^{2} + 4x + ( \frac{4}{2} )^{2} - 21 = 0 + ( \frac{4}{2} )^{2} \\ {x }^{2} + 4x + 4 = 4 + 21 \\ (x + 2)(x + 2) = 25 \\ {(x + 2)}^{2} = 25[/tex]
ATTACHED IS THE SOLUTION
Angie added a stone border 2 feet in width on all sides of her garden making her harder 12 by 6 feet. What is the area, in square feet, of the portion of the garden that excludes the border?
A. 4
B. 16
C. 40
D. 56
E. 72
Answers
The area, in square feet, of the portion of the garden that excludes the border is 40.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
We have been given that Angie added a stone border of 2 feet in width on all sides of her garden making her harder 12 by 6 feet.
Length = 12 ft
Width = 6 ft
The dimension of the garden that excludes the border of 2 feet are;
Length = 12 ft- 2 = 10 ft
Width = 6 ft - 2= 4 ft
Thus, Area = length × Width
Area = 10 x 4
Area = 40 square feet
Hence, the area, in square feet, of the portion of the garden that excludes the border is 40.
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A 128 ounce container of hand lotion is separated into 4 ounce sample packs. How many sample packs are created from the large
container?
Please help will give brainlest!!
Answers
Answer:
32
Step-by-step explanation:
Solution
If the total amount of hand lotion is available, then you have 128 ounces of hand lotion.
If 128 oz is put into a number of smaller containers (each one 4 oz) then you have
128/4 containers.
128 / 4 = 32.
You can make 32 containers each one holding 4 ounces. The question uses division to solve.
10(6 + 4) ÷ (2³-7)² =
Answers
Answer:
100
Explanation:
Given the expression
[tex]10\mleft(6+4\mright)\div(2^3-7)^2[/tex]First, we evaluate the bracket and exponents.
[tex]=10\mleft(10\mright)\div(8-7)^2[/tex]This then gives us:
[tex]\begin{gathered} 100\div(1)^2 \\ =100\div1 \\ =100 \end{gathered}[/tex]A linear function contains the following points.What are the slope and y-intercept of this function?
Answers
Answer: The slope is 4/5 and the y-intercept is (0,-1)
Step-by-step explanation:
What is equation of straight line in slope-intercept form?
The formula for equation of straight line in slope-intercept form is y = mx +c
where m = slope and c = y-intercept
Analysis
y2-y1/x2-x1
3-(-1)/5-(-0)
=4/5
The slope of the linear function is 4/5
The y-intercept is (0.-1)