The equation of a circle is (x−2)2+(y+6)2=100. Find the equation of a circle that is externally tangent to the given circle and has a center at (14, 3).
Answer:
(x-14)^2+(y-3)^2=9
Step-by-step explanation:
equation of a circle is (x-h)^2+(y-h)^2=r^2
so center is (14,3) and is tangent externally means
(x-14)^2+(y-3)2=3^2
(x-14)^2+(y-3)^2=9 answer
The equation of a circle is externally tangent to the given circle and has a center at (14, 3) is [tex](x-14)^2 + (y-3)^2=9[/tex]
The standard formula for finding the equation of a circle is expressed as:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where
(a, b) is the centre
r is the radius
Given the center at (14, 3)
If the equation of a circle is externally tangent to the given circle and has a center at (14, 3), then the radius will be 3
Substitute the radius and the centre into the expression above to have:
[tex](x-14)^2 + (y-3)^2=3^2\\(x-14)^2 + (y-3)^2=9[/tex]
Hence the equation of a circle is externally tangent to the given circle and has a center at (14, 3) is [tex](x-14)^2 + (y-3)^2=9[/tex]
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ASAP Mr. Morris used the greatest common factor and the distributive property to rewrite the sum 45 + 27. What did he write? please show your work YOU CAN GET BRAINLIEST
Answer: its 3( 15+9 ) or 9( 5+3 ) go with your gut im srry if im wrong
Step-by-step explanation:
Daichi wo fumishimete
Kimi wa mezameteiku
How many edges are there on a cylinder?
Answer:
There are 0 number of edges on a cylinder
The standard height from the floor to the bull’s-eye at which a standard dartboard is hung at 5 feet 8 inches. A standard dartboard is 18 inches in diameter. Suppose a standard dartboard is hung at standard height so that the bull’s-eye is 10 feet from the wall to its left. Sasha throws a dart at the dartboard that land at point 10.25 Feet from the left wall and 5 feet above the floor. Does Sasha’s dart land on the dartboard? Drag the choices into the boxes to correctly complete the statements.
Answer:
Hello! I'm sorry I couldn't get to your question sooner. I just completed this quiz!
The equation of the circle that represents the dartboard is (x-10)^2 + (y-17/3)^2 = 9/16, where the origin is the lower-left corner of the room and the unit of the radius is feet.
The position of Sasha's dart is represented by the coordinates (10.25,5). Sash's dart does land on the dartboard.
This quiz was completed on k12, lesson 3.03.
The question is an illustration of equation of circles.
The equation of the dartboard circle is: [tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]Sasha's dart lands on the dartboard becauseFrom the question, we understand that:
[tex]\mathbf{h = 5\ ft\ 8\ in }[/tex] ---- the height at which the dartboard was hung
[tex]\mathbf{d = 18\i n }[/tex] ---- the diameter of the dartboard
[tex]\mathbf{B = 10ft}[/tex] --- the bull's eye
[tex]\mathbf{D = (10.25ft, 5ft)}[/tex] --- Sasha's dart
Equation of the circle
First, we convert all units to feet
This is done by dividing inches units by 12
[tex]\mathbf{h = 5\ ft\ 8\ in }[/tex]
[tex]\mathbf{h = 5\ ft\ + \frac{8}{12}\ ft }[/tex]
[tex]\mathbf{h = 5\ ft\ + \frac{2}{3}\ ft }[/tex]
Take LCM
[tex]\mathbf{h = \frac{15 + 2}{3}\ ft }[/tex]
[tex]\mathbf{h = \frac{17}{3}\ ft }[/tex]
[tex]\mathbf{d = 18\i n }[/tex]
[tex]\mathbf{d = \frac{18}{12}ft}[/tex]
[tex]\mathbf{d = \frac{3}{2}ft}[/tex]
Divide by 2 to calculate radius
[tex]\mathbf{r = \frac{3}{2*2}ft}[/tex]
[tex]\mathbf{r = \frac{3}{4}ft}[/tex]
The equation of the circle is represented as:
[tex]\mathbf{(x - a)^2 + (y - b)^2 = r^2}[/tex]
In this case:
[tex]\mathbf{a = B = 10ft}[/tex] -- the distance between the bull's eye and the wall
[tex]\mathbf{b = h = \frac{17}{3}\ ft }[/tex] ---- the height at which the dartboard was hung
So, we have:
[tex]\mathbf{(x - a)^2 + (y - b)^2 = r^2}[/tex]
[tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = (\frac 34)^2}[/tex]
Evaluate the exponents
[tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]
Hence, the equation of the circle is: [tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]
Does Sasha’s dart land on the dartboard?
Yes her dart lands on the dartboard because
[tex]\mathbf{D = (10.25ft, 5ft)}[/tex] is within the circumference of the dartboard
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someone help fast please
Answer:
c. supplementary angles
Step-by-step explanation:
Determine the midpoint of the segment with endpoints of (-3, 8) and (-3,
-2).
Answer:
(-3,3)
Step-by-step explanation:
Write 9/18 as a decimal. Identify the decimal as terminating or repeating.
a. 0.5; repeating
b. 0.9; terminating
c. 0.5; terminating
d. 1; repeating
Answer:
it is c
Step-by-step explanation:
Answer:
C.) 0.5; Terminating
Step-by-step explanation:
Answer:
918=0.5
Showing the work
You can first reduce this fraction by dividing both the numerator and denominator by the Greatest Common Factor of 9 and 18 using
GCF(9,18) = 9
9÷918÷9=12
We know that
12
is the same as
1÷2
Then using
Long Division for 1 divided by 2
=0.5
Hope I helped
Brainliest plz
Alex is making a candy that contains 75% white chocolate and the rest peppermint sticks. The candy has 3 pounds
of peppermint sticks.
Part A: Write an equation using one variable that can be used to find the total number of pounds of white
chocolate and peppermint sticks in the candy. Define the variable used in the equation. (5 points)
Part B: How many pounds of white chocolate are present in the candy? Show your work. (5 points)
Answer:
163
Step-by-step explanation:
Which rule describes a composition of transformations that maps pre-image PQRS to image P"Q"R"S"?
270 degree rotation about point 0 composition. Translation of negative 2 units x, 0 units y.
Translation of negative 2 units x, 0 units y composition 270 degree rotate about point 0.
270 degree rotation about point 0 composition reflected across the y-axis
Reflected across the y-axis composition 270 degree rotation about point 0.
Answer:
270 degree rotation about point 0 composition .translations of negative 2 units
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Took the test
An Airliner has a capacity for 300 passengers. If the company overbook a flight with 320 passengers, What is the probability that it will not be enough seats to accommodate all passengers. Assume that the probability that a randomly selected passenger shows up to the airport is 0.96. Find the probability using the normal distribution as an approximation to the binomial distribution.
Answer:
The probability is [tex]P(X >300 ) = 0.97219 [/tex]
Step-by-step explanation:
From the question we are told that
The capacity of an Airliner is k = 300 passengers
The sample size n = 320 passengers
The probability the a randomly selected passenger shows up on to the airport
[tex]p = 0.96[/tex]
Generally the mean is mathematically represented as
[tex]\mu = n* p[/tex]
=> [tex]\mu = 320 * 0.96[/tex]
=> [tex]\mu = 307.2[/tex]
Generally the standard deviation is
[tex]\sigma = \sqrt{n * p * (1 -p ) }[/tex]
=> [tex]\sigma = \sqrt{320 * 0.96 * (1 -0.96 ) }[/tex]
=> [tex]\sigma =3.50 [/tex]
Applying Normal approximation of binomial distribution
Generally the probability that there will not be enough seats to accommodate all passengers is mathematically represented as
[tex]P(X > k ) = P( \frac{ X -\mu }{\sigma } > \frac{k - \mu}{\sigma } )[/tex]
Here [tex]\frac{ X -\mu }{\sigma } =Z (The \ standardized \ value \ of \ X )[/tex]
=>[tex]P(X >300 ) = P(Z > \frac{300 - 307.2}{3.50} )[/tex]
Now applying continuity correction we have
[tex]P(X >300 ) = P(Z > \frac{[300+0.5] - 307.2}{3.50} )[/tex]
=> [tex]P(X >300 ) = P(Z > \frac{[300.5] - 307.2}{3.50} )[/tex]
=> [tex]P(X >300 ) = P(Z > -1.914 )[/tex]
From the z-table
[tex]P(Z > -1.914 ) = 0.97219[/tex]
So
[tex]P(X >300 ) = 0.97219 [/tex]
FOR EXAMPLE:
Christa and her family went out for pizza and it cost $28. In Tennessee we have a sales tax that is 7% which has to be paid along with $28. What is the sales tax on $28?
Maggie claims that there are transformations that preserve the length of the rectangle's sides. Which of the following transformations could be used to support Maggle's claim? Select all that apply.
reflection over the side RS
a translation of 10 units to the right
a rotation of 90' clockwise about vortex Q
a vertical stretch of scale factor 2 through contor C
a dilation of scale factor 1 through conter
Answer: B,D,E. Step-by-Step explanation
Transformation that preserve lengths are rigid transformation.
The options that support Maggie's claim are:
reflection over the side RS a translation of 10 units to the right a rotation of 90' clockwise about vortex QAll transformations are rigid transformation, except dilation.
Dilation are of two types
StretchCompressEither of the two above, do not preserve length
This means that:
Options (d) and (e) will not preserve the lengths of the rectangle, because they represent dilation
Hence, the correct options that will preserve the length of the rectangle are: (a), (b) and (c)
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which of the following choices is equal to 22+36
Answer:
58
Step-by-step explanation:
2. Which of the following is an irrational number?
A. 3
B. 3.5
C. 36
D. 15
Answer:
C. 36
because can not be expressed as a ratio
f(x)=x-5
g(x) = 2x+1
Write the expressions for (f-g)(x) and (f+g)(x) and evaluate (fg)(4).
Answer:
(f - g)(x) = -x - 6
(f + g)(x) = 3x - 4
(f*g)(4) = -9
Step-by-step explanation:
These are your equations:
f(x) = x - 5
g(x) = 2x + 1
To find (f - g)(x), subtract g(x) from f(x).
(f - g)(x) = x - 5 - (2x + 1)
(f - g)(x) = x - 5 - 2x - 1
(f - g)(x) = -x - 5 - 1
(f - g)(x) = -x - 6
To find (f + g)(x), add f(x) with g(x).
(f + g)(x) = x - 5 + 2x + 1
(f + g)(x) = 3x - 5 + 1
(f + g)(x) = 3x - 4
To find (f*g)(4), you need to first find (f*g)(4). You can do this by multiplying f(x) wih g(x).
(f*g)(x) = (x - 5)(2x + 1)
(f*g)(x) = 2x² - 9x - 5
Now that you have (f*g)(x), solve with x as 4.
(f*g)(4) = 2(4)² - 9(4) - 5
(f*g)(4) = 2(16) - 9(4) - 5
(f*g)(4) = 32 - 36 - 5
(f*g)(4) = -9
The required expression for (f-g)(x), (f+g)(x) and (fg)(4) are given as 3x - 4, -x - 6 and 11.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
f(x)=x-5
g(x) = 2x+1
According to the question,
[f + g ](x) = x - 5 + 2x + 1 = 3x - 4
[f + g ](x) = 3x - 4
[f - g ](x) = x - 5 - 2x - 1
[f - g ](x) = -x - 6
(f.g)(x) = (x - 5)(2x + 1)
(f.g)(x) = 2x² -4x -5
(f.g)(4) = 2[4]² - 4[4] - 5
= 32 - 16 - 5
= 11
(f.g)(4) = 11
Thus, the required expression for (f-g)(x), (f+g)(x) and (fg)(4) are given as 3x - 4, -x - 6 and 11.
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#SPJ2
solve the equation
–12p = 24
Answer:
p = -2
Step-by-step explanation:
24 divided by -12
p= -2
In an alloy of gold and silver the ratio of the amount of gold to the amount of silver is 2:5. What is the weight of silver in the alloy if there are 18g of gold?
Answer:
45
Step-by-step explanation:
equate the two equations
2/5=18/x
Answer:
45grams
Step-by-step explanation:
2
[tex] 2 \times 2[/tex]
Answer:
4
Step-by-step explanation:
2 × 2 = 4
A ball is hit into air at time t=0 seconds.its height above the ground is given by the equation h=25t-9.8t².what is the value of t when the ball lands on the ground?
Answer:
The ball lands on the ground at t=2.55 seconds
Step-by-step explanation:
Quadratic Equation
The following function models the height above the ground of a ball hit into the air at time t seconds:
[tex]h=25t-9.8t^2[/tex]
We need to find the value of t when the ball hits the ground.
At ground level, h is zero, thus:
[tex]25t-9.8t^2=0[/tex]
This is an incomplete quadratic equation that can be easily solved by factoring:
[tex]t(25-9.8t)=0[/tex]
There are two solutions:
t=0
t=25/9.8=2.55 s
The first solution corresponds to the moment when the ball is hit, and the second is when it returns to the ground, thus:
The ball lands on the ground at t=2.55 seconds
Find atleast 5 numbers between 1/2 and 1/3.
Answer:
12.2 12.3 12.4 12.5
Step-by-step explanation:
HELP PLEASE BRAINLESS ANSWER GETS 20 POINTS
An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Using d for distance in kilometers and t for number of hours, an
equation that represents this situation is d-50t.
Enter the smaller of the two constants of proportionality.
Answer:
t=8
Step-by-step explanation:
400 divided by 50 hopefully that helps with your question
Which of the following is the correct factored form of the given equation?
4x 2 - 11x + 6 = 0
(2x + 3)(2x + 2) = 0
(2x - 3)(2x - 2) = 0
(4x - 3)(x - 2) = 0
Answer:
(4x - 3)(x-2) = 0
Step-by-step explanation:
4x² - 11x + 6 = 0
To factorize this equation,
-11
4x6
These numbers are the key to the solution:
find two numbers whose sum is -11 and the product is + 24 (4 x 6)
So, the numbers are -3 and -8
4x² - 8x - 3x + 6 = 0
4x(x -2) - 3(x - 2) = 0
(4x - 3)(x-2) = 0
Answer:
(4x - 3)(x - 2) = 0
That's your answer!!
a spring of original length 25 cm was stretched to a new length of 28 cm when a force of 12 n was applied. what would its new length be if the applied force is doubled?
a. 31 cm
b. 35 cm
c. 50 cm
d. 45 cm
Answer:
A. 31 cm
Step-by-step explanation:
Hopefully its right :)
What is 6√2⋅√11−2√22 expressed in simplified form?
Hope this help you!!! :))
A river has a current of 2km per hour. Find the rate of Fred’s boat in still water if it travels 30 km downstream and the same time it takes to travel 14 km upstream.
Answer:
32km
Step-by-step explanation:
A pice of lumber 2 1/4 feet long is to be cut into 3 equal pieces. How long will each piece be? Give the measurements in feet and inches.
Answer: The required length of each piece of wood is or 9 inches.
Step-by-step explanation: Given that a piece of lumber is feet long is to be cut into 3 equal pieces.
We are to find the length of each piece of wood in feet and in inches.
We will be using the UNITARY method to solve the given problem.
The length of 3 pieces of wood is equal to
Therefore, the length of each piece of wood will be
Thus, the required length of each piece of wood is or 9 inches.
UCF is a major Metropolitan University located in Orlando Florida. UCF is advertising their bachelor in Economics with the statistic that the starting salary of a graduate with a bachelor in economics is $ 48,500 according to Payscale (2013-13). The Director of Institutional Research at UCF is interested in testing this information. She decides to conduct a survey of 50 randomly selected recent graduate economic students. The sample mean is $43,350 and the sample standard deviation is 15,000. Alpha = 0.01
Answer:
The claim is rejected
Step-by-step explanation:
Claim: UCF is advertising their bachelor in Economics with the statistic that the starting salary of a graduate with a bachelor in economics is $ 48,500 according to Payscale (2013-13).
Null hypothesis: [tex]H_0: \mu = 48500[/tex]
Alternate hypothesis :[tex]H_a : \mu \neq 48500[/tex]
n = 50
Since n is more than 30 .
So we will use Z test
x=43350
Standard deviation = 15000
[tex]Z=\frac{x-\mu}{\frac{s}{\sqrt{n}}}\\Z=\frac{43350-48500}{\frac{15000}{\sqrt{50}}}\\Z=-2.42[/tex]
Refer the z table
p value = 0.00776
[tex]\alpha = 0.01[/tex]
p value < [tex]\alpha[/tex]
So, We are failed to accept null hypothesis
Hence The claim is rejected
This is a 2x2 identity matrix:
True
Or
False
Answer:
i think it is false
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
An identity matrix has a 1 in each position of the main diagonal (diagonal from upper left to lower right) and zeros elsewhere. This matrix has the 1s and 0s in the wrong places to be an identity matrix.
This is what a 2x2 identity matrix looks like:
[tex] \begin{bmatrix} 1 & 0\\ 0 & 1\end{bmatrix} [/tex]
This question only for JungKookLuver and JungKookLuver.... is this right...
Answer: Yes it is right.
Step-by-step explanation: Have a blessed day!
Answer: Yes, it’s correct!
Step-by-step explanation: Have A Great Day Bro! :)
Please help me answer the question in the photo! Will give brainlist :)
Answer:
the answer is B because it make a 90* angle