What is the equation of the circle shown in the graph ? (Blank)^2 + (Blank)^2 = blank
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[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{4}{ k})\qquad \qquad radius=\stackrel{6}{ r} \\\\\\\ [x-(-6)]^2+[y-4]^2=6^2\implies (x+6)^2+(y-4)^2=36[/tex]
The equation of the circle shown in the graph is equal to [tex](x + 6)^2 + (y - 4)^2 = 36[/tex]
Form the graph, we can deduce the following points:
The center of the circle is denoted by the black dot and we can see that the values are -6 and 4 respectively.
Center (h, k) = (-6, 4)Also, the diameter of the circle is:
Diameter = 12 units
Radius = [tex]\frac{Diameter}{2} = \frac{12}{2} = 6 \;units[/tex]
Mathematically, the standard form of the equation of a circle is given by;
.....equation 1
Where;
h and k represents the coordinates at the center.r represents the radius of the circle.Substituting the values into eqn 1, we have:
[tex](x - [-6])^2 + (y - 4)^2 = 6^2\\\\(x + 6)^2 + (y - 4)^2 = 36[/tex]
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Related Questions
how do the graphs of f(x)=x^3 and g(x)=(1/3x)^3 relate?
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The function F(x) = log0.5 x is increasing. The answer is B. False. Just finished taking the quiz I had guessed.
A. True
B. False
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Answer:
The statement is false
B is correct
Step-by-step explanation:
Given: [tex]f(x)=\log_{0.5}x[/tex]
Increasing function.
Log function:
[tex]y=\log_ax[/tex]
If 0<a<1 then y is decreasing function.
If a>1 then y is increasing function.
Now, we compare the given function
[tex]\log_ax\rightarrow \log_{0.5}x[/tex]
a=0.5
0.5<1
If 0<a<1 then y is decreasing function.
Therefore, f(x) is decreasing. But we are given f(x) is increasing.
Hence, The statement is false
Problem:
The standard form of a circle is (x-h)2+(y-k)2=r2 and for the parabola, y-k=a(x-h)2. The (h,k) pair will be the center of the circle and the vertex of the parabola. The radius of the circle is ‘r’ and the focal length of the parabola is f=1/(4a). For the following General Conic Equation: x2+y2-4x-6y-12=0 complete the following problems showing all your work:
A-Complete the square showing all your work to convert to Standard Form:
B-If this is a circle, state the coordinates of the center and give the radius. If this is a parabola, state the coordinates of the vertex and give the focal length. Show all your work.
C -Sketch the Conic. Label the values you found in part B. Be sure to draw or show the radius or focal length.
Answers
x²+y²-4x-6y-12=0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(x²-4x)+(y²-6y)=12
Complete
the square twice. Remember to balance the equation by adding the same constants
to each side
(x²-4x+4)+(y²-6y+9)=12+4+9
Rewrite as perfect squares
(x-2)²+(y-3)²=25the answer part A) is
(x-2)²+(y-3)²=5²-----> this is the standard form of the equation of a circle
Part B) (x-2)²+(y-3)²=5²
the center is the point (2,3) and the radius is r=5 units
Part C)
using a graph tool
see the attached figure
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. find the probability that the number drawn is a multiple of 77 or a multiple of 4.
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Multiples of 77: 1, 7, 11
Multiples of 4: 1, 2, 4
Therefore, multiples of 77 or 4 are: 1, 2, 4, 7, 11 = 5 numbers
P (multiples of 7 or 4) = 5/25 = 1/5 = 0.2
Which of the following holds about 800 milliliters o f water?
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The soup can is 6 cm tall and has a radius of 3.5cm. If you were to pull the label off the can in one complete piece,what would the area of the label be ? Use 22/7 for p.
Please help !!!
A)22 sq.cm
B)42 sq.cm
C)132 sq.cm
D)152 sq.cm
Answers
3,14*7=21.98
21.98*6=131,88≈132
The soup can is 6 cm tall and has a radius of 3.5cm. If you were to pull the label off the can in one complete piece,what would the area of the label be ? Use 22/7 for p.
Please help !!!
A)22 sq.cm
B)42 sq.cm
C)132 sq.cm
D)152 sq.cm
Solution:
Radius of cylindrical soup can= 3.5 cm
Height of cylindrical soup can= 6 cm
Area of cylinder =2πrh
So, Area of label of cylindrical soup can=2πrh
Plugging in the value of r and h in the formula
Area of label=2*π*3.5*6
Multiplying the constants, we get
Area=2*π*21
Area=42π
Plugging in the value of π
Area=42*[tex]\frac{22}{7}[/tex]
Multiplying the numerators
Area=[tex]\frac{924}{7}[/tex]
Area=132 sq.cm
Answer: Option (C)
Area of label= 132 sq. cm
Miss Nelson Has a rectangular flower box that is 5 ft long 2 ft tall she wants the width of the box to be no more than 5 ft if the width is a whole number what are the possible volumes for the flower box
Answers
A homeowner plants two flowerbeds around his garage. What is the total area he will have planted. Round to nearest tenth.
Answers
The hyperbola (x-5)^2/7 - (y+3)^2/9 = 1 is shifted to the right by 4 units and upward by 3 units. the new center of the hyperbola is
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(5, -3) +(4, 3) = (9, 0)
Answer:
( 9 ,0)
Step-by-step explanation:
Given : [tex]\frac{(x -5)^{2}}{7} - \frac{(y+3)^{2}}{9} = 1.[/tex] is shifted to the right by 4 units and upward by 3 units
To find : New center of the hyperbola .
Solution : We have given
[tex]\frac{(x -5)^{2}}{7} - \frac{(y+3)^{2}}{9} = 1.[/tex]
Center of hyperbola is ( 5 , -3)
By the transformation rule f(x) →→ f(x -h) + k it mean f(x) is shifted to right by h unit and k unit up.
Then Center of hyperbola is shifted to the right by 4 units and upward by 3 units.
( 5 , -3) →→ (5 + 4 , -3 + 3
( 5 , -3) →→ ( 9 ,0)
Therefore, new center is ( 9 ,0).
17.5% as a fraction in simplest form?
Answers
solve the system of equations 5x-2y=88 3x+4y=58 show all work
Answers
5x - 2y = 88
3x + 4y = 58
Multiplying the 1st equation by 2, we get the new set of equations as:
10x - 4y = 176
3x + 4y = 58
Adding the two equations, we get:
10x - 4y + 3x + 4y = 176 + 58
13x =234
x = 18
Using the value of x in 1st equation, we get:
5(18) - 2y = 88
- 2y = 88 -5(18)
-2y = -2
y = 1
So, the solution of the equation is (18, 1)
[tex]3x+4\cdot(2.5x-44)=58\\3x+10x-176=58\\13x-176=58\ \ \ |\text{add 176 to both sides}\\13x=234\ \ \ \ |\text{divide both sides by 13}\\x=18\\\\\text{substitute value of x to the equation}\ 1^o\\\\y=2.5\cdot18-44=45-44=1\\\\Answer:\ \boxed{\left\{\begin{array}{ccc}x=18\\y=1\end{array}\right}[/tex]
It took Alex 2.5 hours to cover a certain route walking at a rate of 3.6 km/h. How long would it take Alex to cover the same route if he walked at a rate of 4.5 km/h
Answers
Answer:
2 hours
Step-by-step explanation:
5.
Find the present value of the annuity.
Amount Per Payment: $6,225
Payment at End of Each: Quarter
Number of Years: 6
Interest Rate: 8%
Compounded: Quarterly
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where
[tex]PV[/tex] is the present value
[tex]P[/tex] is the periodic payment
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]k[/tex] is the number of payments per year
[tex]t[/tex] is the number of years
We know for our problem that [tex]P=6225[/tex] and [tex]t=6[/tex]. To convert the interest rate to decimal form, we are going to divide it by 100%:
[tex]r= \frac{8}{100} [/tex]
[tex]r=0.08[/tex]
Since the interest is compounded quarterly, it is compounded 4 times per year, so [tex]n=4[/tex]. Similarly, since the payment is made at the end of each quarter, it is made 4 times per year; therefore, [tex]k=4[/tex].
Lets replace the values in our formula:
[tex]PV=P[ \frac{1-(1+ \frac{r}{n})^{(-kt)} }{ \frac{r}{n} }] [/tex]
[tex]PV=6225[ \frac{1-(1+ \frac{0.08}{4})^{(-(4)(6)} }{ \frac{0.08}{4} }] [/tex]
[tex]PV=117739.19[/tex]
We can conclude that the present value of the annuity is $117,739.19
Vernon has obtained a $105,000, 5/1 30-year ARM at 5%. During the first 3 years, he has an option of paying interest only. If he accepts this offer, what would be his initial payment?
Answers
Answer: 437.50
Step-by-step explanation:
hey can you please help me posted picture of question
Answers
The solutions are:
[tex] \frac{3 + i}{2} [/tex] and [tex] \frac{3 - i}{2} [/tex]
Explanation:
The general form of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
2x² - 6x + 5 = 0
By comparison:
a = 2
b = -6
c = 5
Now, to get the solutions of the equation, we will have to use the quadratic formula shown in the attached image.
By substituting in the formula, we would find that:
either x = [tex] \frac{6 + \sqrt{(-6)^2 - 4(2)(5)} }{2(2)} = \frac{3 + i}{2} [/tex]
or x = [tex] \frac{6 - \sqrt{(-6)^2 - 4(2)(5)} }{2(2)} = \frac{3 - i}{2} [/tex]
Hope this helps :)
Hey can you please help me posted picture of question
Answers
In given case, Karen has to find the probability of a number greater than 4 which can appear when a die is rolled. The possible outcomes in this case are 2 i.e. 5 and 6
Since, the number of possible outcomes is more than 1, the event is a compound event.
So answer is true
Find the length of AB , given that DB is a median of the triangle and AC = 24.
Answers
Answer:
AB = 12 units
Step-by-step explanation:
We are given the following information in the question:
DB is the median of the triangle.
AC = 24 units
Property of median of a triangle:
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.Thus, a median divides the side of triangle in two equal parts.Thus, DB divides AC in two equal parts.
Thus, we could say:
AB = BC
We have to find the length of AB.
[tex]\text{AB} = \displaystyle\frac{AC}{2} = \frac{24}{2} = 12\text{ units}[/tex]
Thus, AB is 12 units.
Which of these shows 8 + 3m rewritten using the commutative property of addition? 8m + 3 8 − 3m 3m − 8 3m + 8
Answers
Reason:
★Commutative Property★
The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around.
For addition, the rule is:
"a + b = b + a"
Hope this helps!
Answer:(3m+8)
Step-by-step explanation:
One endpoint of a line segment is at (4, 2). The line is bisected by placing the midpoint of the line segment at (−2, −1). What are the coordinates of the other endpoint?
A) (−4, −6)
B)(−8, −4)
C)(10, 5)
D)(−8, 4)
Answers
hello can you please help me posted picture of question
Answers
[tex] \frac{25-y^2}{16} + \frac{y^2}{9} = 1[/tex]
Explanation:
For the first given equation, we will need to isolate the x². This can be done as follows:
x² + y² = 25
x² + y² - y² = 25 - y²
x² = 25 - y² ..................> I
For the second given equation:
We will remove every x² and substitute with its equivalence from I as follows:
[tex] \frac{x^2}{16} + \frac{y^2}{9} = 1[/tex]
[tex] \frac{25-y^2}{16} + \frac{y^2}{9} = 1[/tex]
Hope this helps :)
It is the c)25-y^2-y^2 by 16-9 = 1
What is the vertex of the quadratic y=-2x^2-4x-5
Answers
We will need to complete square to write the equation in the vertex form.
y=-2(x²+2x)-5
y=-2(x²+2x+1)-5+2
y=-2(x+1)² - 3
Vertex (-1,-3)
Answer:
(-1,-3)
Step-by-step explanation:
I just took the test, and I got 100%!!!
the scatter plot shows the number of students per class al monida middle school and the number of magazine subscription each class sold for a fund raiser.About how many subscription did the class of 30 students sell
Answers
We have then:
For x = 30:
The value of y is given by:
y = 175 (approximately)
Answer:
y = 175 subscriptions
About how many subscription did the class of 30 students sell,
We need to consider the Given which is x = 30:
So The value of y is given by:
y = 175 (approximately)
So the answer would be the third option.
Help with the graph and answer below
Answers
From the graph we can see that the function does not cross the x-axis at any point. Hence it has no x-intercept and thus no real zero. Both the zeros will be complex.
So, the correct answer is option B.
Function has exactly 2 complex solutions.
This means that 1 value of y is equal to two values of x
so the answer is D. Function f has two real solutions
The ratio of sugar to flour is 2:3. If there are 6 cups of sugar, how many cups of flour are there
Answers
cross multiply
5x=2x1
simplify
5x=2
divide each side by 5 to find x
x=2/5
2/5 or 0.4 cups of flour are needed
answer= 2/5
Identify the figure shown and find its surface area. Explain how you found your answer.
Answers
To find the surface area you need to first find the areas of the triangles, then the square, in the end you have to add them together.
Since we know the area of a triangle is 1/2bh we know that one if the triangle in the figure is
9*16/2=72(in^2)
there are four of these so we multiply it by 4
4*72=288(in^2 aka squared inches)
Then we need to find the area of the square. side * side=9*9=81 (in^2)
Add them together we get the surface area.
288+81=369 (in^2)
hello can you please help me posted picture of question
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If Disc > 0, the function has two distinct roots
If Disc = 0, the function has repeated roots
If Disc < 0, the function has complex roots
The turning away of the function indicates a repeated root at that point.
Thus, the given quadratic equation has a repeated root at x = 2. So the discriminant of the function is zero.
Therefore, the correct answer is option B
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2 − 108x + 6, [−3, 4]
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The absolute minimum on the interval is -237 at x=3.
The absolute maximum on the interval is 138 at x=-2.
Answer:
The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.
Step-by-step explanation:
To find the absolute extrema values of [tex]f(x) = 6x^3 - 9x^2 - 108x + 6[/tex] on the closed interval [−3, 4] you must:
1. Locate all critical values. We need to find the derivative of the function and set it equal to zero.
[tex]\frac{d}{dx}f(x)= \frac{d}{dx}\left(6x^3-9x^2-108x+6\right)=\\\\f'(x)=\frac{d}{dx}\left(6x^3\right)-\frac{d}{dx}\left(9x^2\right)-\frac{d}{dx}\left(108x\right)+\frac{d}{dx}\left(6\right)\\\\f'(x)=18x^2-18x-108[/tex]
[tex]18x^2-18x-108=0\\18\left(x^2-x-6\right)=0\\18\left(x+2\right)\left(x-3\right)=0\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=-2,\:x=3[/tex]
2. Evaluate f(x) at all the critical values and also at the two values -3 and 4
[tex]\left\begin{array}{cc}x&f(x)\\-3&87\\-2&138\\3&-237\\4&-186\end{array}\right[/tex]
3. The absolute maximum of f(x) on [-3, 4] will be the largest number found in Step 2, while the absolute minimum of f(x) on [-3, 4] will be the smallest number found in Step 2.
Therefore,
The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.
Heong cut a slice of birthday cake. The slice formed the angle shown. What is the measure of the angle shown?
Answers
There are 2,000 eligible voters in a precinct. 548 of the voters are randomly selected and asked whether they planned to vote for the democratic incumbent or the republican challenger. of the 548 surveyed, 474 said they would vote for the democratic incumbent. using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the democratic incumbent?
Answers
Point estimate, p = 474/548 = 0.865 or 86.5%
Z at 0.99 confidence coefficient = 2.58
Confidence limits = p +/- Z*Sqrt [p(1-p)/n] = 0.865 +/- 2.58 Sqrt [0.865(1-0865)/548] = 0.865 +/- 0.0378 = (0.8272,0.9028) or (82.72%,90.28)
Hey can you please help me posted picture of question
Answers
you are flipping the coin 3 times
so there is 2^3 outcomes = 8 leaves required
3 coins
so 2^3 = 8;
the answer is A. 8 leaves