Why is circle 1 similar to circle 2?
Circle 1: center (2, 3) and radius 4
Circle 2: center (2, 3) and radius 12
Answers
Circle 2 is a dilation of circle 1 with a scale factor of 3.
Answer: The answer is given below.
Step-by-step explanation: The given circles are:
Circle 1: centre (2, 3) and radius 4
Circle 2: centre (2, 3) and radius 12.
The equations of circle 1 and circle 2 are respectively given as :
[tex](x-2)^2+(y-3)^2=4^2,\\\\(x-2)^2+(y-3)^2=12^2.[/tex]
These two circles are drawn on the graph as shown in the attached figure.
We can easily see that the Circle 2 is a dilation of Circle 1 with a scale factor
[tex]S=\dfrac{12}{4}=3.[/tex]
Thus, the two circles are similar.
Related Questions
800% of what number is 4,240?
Answers
Name the property of real numbers illustrated by the equation 16(3t + 4v) = 48t + 64v.
Answers
Therefore, the answer is: Distributive property.
As you can see, you have the equation 16(3t+4v), and when you apply the Distributive property, you obtain:
16(3t+4v)
(16)(3t)+(16)(4v)
48t+64v
Which graph shows a line that is perpendicular to line QR?
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I really hope this helps you:)
A segment with the endpoint X(-6,2) and Y(-1,-3) is rotated 90 degrees about the origin. What are the coordinates of X' and Y'?
1- X' (-1,-3) Y'(-6,2)
2- X' (2,6) Y' (-3,1)
3- X' (-2,-6) Y' (3,-1)
4- X' (6,-1) Y' (1,3)
Thank you for helping, and looking. Thanks,
Answers
x' = -y
y' = x
Therefore:
X' (-2, -6)
Y' (+3, -1)
The correct answer is then option 3.
ALGEBRA 1 PLEASE HELP
5x+y=6
5x+3y=-5
The y-coordinate of the solution to the system shown as______
A) -5
B) -1
C) 1/2
D) 1
Answers
5x - 5x = 0x = 0
meaning the x terms effectively go away after subtraction
Then we do the y terms together in the same exact order
y-3y = -2y
Then finally the right hand side values
6 - (-5) = 6+5 = 11
All of that work done indicates we have 0x-2y = 11 which is the same as -2y = 11. Divide both sides by -2 and we end up with y = -11/2
This answer isn't listed so I'm thinking there's a typo your teacher made somewhere.
A watch manufacturer has two factories (FA, FB) and 60% of their watches are made at FA. It is known that 10% of them are made at FA and 15% made at FB are defective. What is the probability that a selected defective watch was manufactured at FB?
Answers
Imagine that 100 watches are made at the two factories. 60 of them would be made at Factory FA and 40 of them would be made at Factory FB.
In Factory FA, 10% of the 60 would be defective. That is 6.
In Factory FB, 15% of the 40 would be defective. That is also 6.
So if you select one of the 12 defective watches, half would come from FA and half would come from FB.
To find the slope of a line using two points on the line, you can use the slope formula. Which formula will find the slope of a line
y = rise/run
y = run/rise
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which is translated into:
[tex] \dfrac{Y_2 - Y_1}{X_2-X_1} [/tex]
Final answer:
The slope of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. The formula represents the rise over run between these points.
Explanation:
We can use a specific formula to calculate the slope of a line using two points on that line. The slope is found by taking the difference in the y-value (also known as the rise) and dividing it by the difference in x-value (also known as the run). In mathematical terms, if we have two points (x1,y1) and (x2,y2), the formula for slope (m) is as follows:
m = (y2 - y1) / (x2 - x1)
Therefore, between two given points, you subtract the y-value of the starting point from the y-value of the end point to find the rise, and then remove the x-value of the starting point from the x-value of the end point to determine the run. The slope is then the quotient of these two differences.
Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at
90
miles per hour. The eastbound train travels at
80
miles per hour. How long will it take for the two trains to be
272
miles apart?
Do not do any rounding.
Answers
272
train 2 = 80 miles per hour
90 + 80 = 170
272 / 170 = 1.6 hours = 1 hour 36 minutes
how much would 500 invested at 4 interest compounded continuously be worth after 7 years round your answer to the nearest cent?
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can some one plz help me...Banks cannot provide amortization schedules to borrowers.
A) true
B) false,
Answers
The correct answer is:
False.
Explanation:
When you take out a loan, banks provide all of the relevant information for the loan. This includes the interest rate, payment amount, and an amortization schedule, which shows the amount paid and the amount of principal this takes off of the loan every month for the life of the loan.
Construct two tangents to circle O, at A and at B, where AB is a diameter. What relationship exists between the two tangents
Answers
When two tangents are drawn to a circle at endpoints A and B of a diameter, the tangents are perpendicular to the radii at their points of tangency and are parallel to each other, forming two congruent right triangles.
Explanation:The question involves constructing two tangents to a circle from two points, A and B, where AB is the diameter of the circle. By the properties of circles and tangents, we know that a tangent to a circle is perpendicular to the radius at the point of tangency. Since AB is the diameter, points A and B are on opposite ends of the circle, and when we draw tangents at these points, each tangent will be perpendicular to the radii OA and OB respectively. Additionally, since AB is a diameter, it creates a linear pair with the two tangents, meaning that the two tangents are parallel to each other. This setup creates two congruent right triangles, namely triangle OAT and triangle OBT, where T represents the points of tangency on each tangent.
Two tangents to a circle from points A and B, where AB is a diameter, are congruent and parallel to each other, forming right angles with the diameter.
Explanation:When constructing two tangents to a circle at points A and B, where AB is a diameter, an interesting relationship exists between those tangents. By the properties of tangents to a circle from an external point, we know that two tangents drawn to a circle from the same external point are equal in length. Therefore, the two tangents you would draw from points A and B to any point on the circumference of the circle would be congruent to each other.
Additionally, since each tangent is perpendicular to the radius of the circle at the point of tangency, the tangents are parallel to each other because they are both perpendicular to the same diameter. In the context of circle O with AB as a diameter, we can also conclude that the angles formed between the tangents and the diameter AB are right angles due to the geometric properties of tangents.
What is the area of a sector with a central angle of 3π5 radians and a diameter of 21.2 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
cm²
Answers
Area of a circumference=π*r²
for diameter=21.2 cm---------> r=10.6 cm
A=π*10.6²--------> A=π*112.36 -------> A=352.81 cm²
if 2π radians (full circumference) has an area of -----------------> 352.81 cm²
3π/5 radians-------------------------------------> X
X=[(3π/5)*(352.81)]/2π---------> X=105.84 cm²
the answer is 105.84 cm²
The area of the sector has a diameter of 21.2 cm and a central angle of 3π/5 radians is 105.90 square cm.
What is a circle?It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
The central angle of 3π/5 radians and a diameter of 21.2 cm.
Then the area of the sector will be
[tex]\rm Area = \dfrac{\theta}{2\pi} *\dfrac{\pi}{4} d^2[/tex]
Then put the values, we have
[tex]\rm Area = \dfrac{\frac{3\pi}{5}}{2\pi} *\dfrac{\pi}{4} (21.2)^2\\\\\\\rm Area = \dfrac{3\pi}{10\pi} *\dfrac{3.14}{4} *449.44\\\\\\Area = \dfrac{3}{10} *\dfrac{3.14}{4} *449.44\\\\\\Area = 105.8968 \approx 105.90 \ cm^2[/tex]
The area of the sector has a diameter of 21.2 cm and a central angle of 3π/5 radians is 105.90 square cm.
More about the circle link is given below.
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Which number system BEST describes this set? {-10, 0, 28 7 , 102.9} A) integers B) natural numbers C) rational numbers D) irrational numbers
Answers
The 4 numbers in this list only all belong to the set of rational numbers. All of the other sets can be crossed off.
First, 102.9 is not an integer, so we can't select choice A.
Second, 0 is not a natural number, so we can't select choice B.
Third, none of the numbers are irrational, so we can't select choice D.
The only choice left is choice C - rational numbers.
Find the equation of the axis of symmetry for the parabola y = x2 + 4x – 5 .
Answers
[tex]x = - \frac{b}{2a} [/tex]
[tex]x = - \frac{4}{2} [/tex]
[tex]x = - 2[/tex]
You roll a number cube twice. Find the probability of the events.
1.Rolling a 3 twice
2.Rolling an even number and a 5
3.Rolling an odd number and a 2 or 4
4.Rolling a number less than 6 and a 3 or a 1
Answers
2.) (1/2)*(1/6)=1/12
3.) (1/2)*(1/3)=1/6
4.) (5/6)*(1/3)=5/18
Answer:
In a number cube, a dice, you have six sides with the numbers 1, 2, 3, 4, 5 and 6. And when you roll it, each number has the same probability of showing.
a) rolling a 3 twice.
In the first roll you get a 3, with a probability of 1/6, and with the second roll you also get a 3, also with a probability of 1/6. The probability of bot evets to happen is equal to the product of the individual probabilities.
P = 1/6*1/6 = 1/36
b) An even number and a 5.
In the first roll you can get 2, 4 or 6, so you have 3 out of 6 options, the probability is 3/6 = 1/2, in the second roll you need you get a 5, the probability is 1/6.
P = 1/2*1/6 = 1/12.
But we also have the probability where the first dice is a 5 and the second a pair number, so the real probability is 2*P = 1/6
c) an odd number and 2 or 4.
for an odd number the probability is 3/6 = 1/2, for getting 2 or 4 the probability is 2/6 = 1/3
then we have that P = 2*(1/3)*(1/2) = 1/3
d) a number less than 6, you have 5 options, then the probability is:
p = 5/6, and for 3 or 1 the probability is 2/6 = 1/3
then P = 2*(5/6)*(1/3) = 5/9
Which expression gives the area of the triangle shown below?
Answers
On this picture the base is the length of the bottom part of the triangle (c). It is the distance of the solid line only.
The height is represented as the straight line that is perpendicular to the base (forms a right/90 degree angle). X is the height of the triangle.
Therefore, 1/2cx is the answer.
The expression gives the area of the triangle shown below 1/2cx is the answer.
The reason this is the answer is because to find the area of a triangle you will find half of the base times the height.
What is the formula of the triangle?
The formula of a triangle
A=1/2bh.
In this picture, the base is the length of the bottom part of the triangle (c).
It is the distance of the solid line only.
The height is represented as the straight line that is perpendicular to the base (forms a right/90-degree angle).
X is the height of the triangle.
Therefore, 1/2cx is the answer.
So option D is correct.
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Which is a zero od the quadratic function f(x)=16x²+32x-9?
Answers
[tex]\left[\begin{array}{ccc}\Delta=b^2-4.ac\\ \\ x=\frac{-b\±\sqrt{\Delta}}{2.a}\end{array}\right][/tex]
a = 16
b = 32
c = -9
[tex] \Delta [/tex] = 32² - 4.16. (- 9)
[tex] \Delta [/tex] = 1024 - (- 576)
[tex] \Delta [/tex] = 1600
[tex] x'=\frac{-(32)+\sqrt{1600}}{2.16}=\frac{-(32)+40}{32}=\frac{8}{32}=0.25\\ \\ \\ x'' =\frac{-(32)-\sqrt{1600}}{2.16}=\frac{-(32)-40}{32}=\frac{-72}{32}=-2.25[/tex]
The rate of change of y with respect to t is proportional to 50 - y
Answers
dy/dt = k(50-t)
∫dy = ∫ k(50-t)dt
= ∫ (50k - kt) dt
therefore;
y = 50kt - k/2(t²) + C
Alternatively, can be written as
y = - k/2 (50-t)² + C)
Which statement justifies that angle XAB is congruent to angle ABC?
A. Corresponding angles of parallel lines cut by a transversal are congruent.
B. Vertical angles are congruent.
C. Same-side interior angles of parallel lines cut by a transversal are supplementary.
D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Given: m || CB
Prove: m∠ABC + m∠BAC + m∠ACB = 180°
Answers
Answer: D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Step-by-step explanation:
In the given picture m is parallel to CB .
Since m is a straight line and the angle of straight line is 180° .
Therefore, m∠XAB+m∠BAC+m∠YAC=180° ........................ (a)
Also, m is parallel to CB and AB is a transversal and because Alternate interior angles of parallel lines cut by a transversal are congruent.
⇒m∠XAB=m∠ABC and m∠YAC=m∠ACB
Put the values of m∠XAB and m∠YAC in equation (a), we get
m∠ABC + m∠BAC + m∠ACB = 180°.
Hence proved.
Statement D Alternate interior angles of parallel lines cut by a transversal are congruent is the most relevant to the congruence of XAB and ABC.
It is proved that m∠ABC + m∠BAC + m∠ACB = 180°.
For angle XAB being congruent to angle ABC, and then prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Parallel lines m and CB.
Points X, A, and Y are on line m.
To prove that angle XAB is congruent to angle ABC.
Justification for Congruence:
In this context, use the Alternate Interior Angles Theorem,
which states that when a transversal intersects two parallel lines, the alternate interior angles formed are congruent.
Here's the reasoning:
Line m is parallel to line CB.
The line XY is a transversal line that intersects m and CB.
Therefore, the alternate interior angles formed by this setup are congruent.
This means that angle XAB and angle ABC are congruent.
Now, let's prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Angle XAB is congruent to angle ABC (justified by the Alternate Interior Angles Theorem).
Now, let's consider the triangle ABC. By the angle sum property of triangles, the sum of the angles in a triangle is always 180°. Therefore:
m∠ABC + m∠BAC + m∠ACB = 180°
Since angle XAB is congruent to angle ABC, replace angle ABC with angle XAB:
m∠XAB + m∠BAC + m∠ACB = 180°
Now, the equation holds true, and you have successfully proven that m∠ABC + m∠BAC + m∠ACB = 180°.
learn more about parallel lines here
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If x is 6, then 7x = _____. 13 42 42x 76
Answers
Answer: 42
Step-by-step explanation:
x = 6 now that you know what x represents switch it out the x by the 7 with a 6 like this 7(x)- 7(6) seven times six is 42 in other words x
=42
The top of a rectangular table has an area of 100 square feet and width of 5 feet. What is the length in feet of the surface
Answers
The length of the surface of the rectangular table that has an area of 100 sq. ft is: 20 ft.
What is the Area of a Rectangle?Area of rectangle = (length)(width).
The table given has a rectangular surface.
Area of the rectangular table = 100 square feetWidth of the rectangular table = 5 feet(length)(5) = 100
Length = 100/5
Length of the rectangular table = 20 feet.
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Carl puts 1.10 in his penny bank every day in the month of July. His total savings was 55at the end of June. What’s the best estimate for Carl’s savings at the end of July
Answers
Answer:
About 85 is the answer
please help asap! 14 points
Answers
Help!! Would the answer be c??
The steps below show the incomplete solution to find the value of x for the equation 7x − 3x − 4 = −1 + 21:
Step 1: 7x − 3x − 4 = −1 + 21
Step 2: 7x − 3x − 4 = 20
Step 3: 4x − 4 = 20
Which of these is most likely the next step? (4 points)
Select one:
a. 4x = 24
b. 4x = 16
c. 4x = 5
d. 4x = 80
Answers
Answer: is a
Step-by-step explanation:
The coordinates of the vertices of / are G(–2, 3), H(–1, 2), and I(–3, 1). If / is reflected across the x-axis to create /, find the coordinates of the vertex located at point W.
Answers
Answer:
A. (–2, –3)
that is the answer
A triangle with vertices at A(20, –30), B(10, –15), and C(5, –20) has been dilated with a center of dilation at the origin. The image of B, point B', has the coordinates (2, –3). What is the scale factor of the dilation?
110110
1515
5
10
Answers
Answer:
5
Step-by-step explanation:
which expression is equivalent to 6a+12
Answers
An equivalent expression would be 2(3a+6)
What I did is simply factor a 2 out of the equation. Just add it back and you have the original expression.
Answer:
2(3a + 6) would be correct.
Hope this was helpful !
Step-by-step explanation:
Create an equation to model a population of cells which starts with 10 cells and doubles in size every day. How many days will it take to reach 1,000,000 cells?
Answers
you can do this by dividing 10 and 1,000,000
The t represents days, and we can't have a fraction of a day for the population to reach [tex]1,000,000[/tex] cells, we need to round up to the nearest whole number. Therefore, it will take approximately [tex]17[/tex] days for the population to reach [tex]1,000,000[/tex] cells.
To model the population of cells, we can use an exponential growth equation. Since the population doubles every day, the equation would be:
[tex]P(t)=P_{0} *2^{t}[/tex]
Where:
[tex]P(t)[/tex] is the population size at time t.
[tex]P_{0}[/tex] is the initial population size ([tex]10[/tex] cells in this case).
[tex]t[/tex] is the time in days.
So, for this scenario, the equation becomes:
[tex]P(t)=10*2^{t}[/tex]
Now, we want to find out how many days it will take for the population to reach [tex]1,000,000[/tex] cells. We can set up the equation:
[tex]1,000,000=10*2^{t}[/tex]
To solve for t, we need to isolate it. First, divide both sides by [tex]10[/tex] :
[tex]100,000=2 t[/tex]
Now, take the logarithm base 2 of both sides to solve for t:
[tex]log_{2} (100,000)=t[/tex]
Using a calculator, we find:
[tex]t=16.61[/tex]
Since t represents days, and we can't have a fraction of a day for the population to reach [tex]1,000,000[/tex] cells, we need to round up to the nearest whole number. Therefore, it will take approximately [tex]17[/tex] days for the population to reach [tex]1,000,000[/tex] cells.
COMPLETE QUESTION:
Create an equation to model a population of cells which starts with [tex]10[/tex]cells and doubles in size every day. How many days will it take to reach [tex]1,000,000[/tex] cells?
A valve in a full 6000 gallon water tank is slowly opening. Water flows out of the tank through the valve. The flow rate in gallons per hour is given by the function f(t)=300 t^2 where t is in minutes.
How much water flows out the tank in the first 7 minutes?
How many minutes does it take for the tank to be completely empty?,
Answers
Water flows: 34300 gallons in 7 minutes. Tank empties in about 3.914 minutes. (Rounded to three decimal places.)
To find out how much water flows out of the tank in the first 7 minutes, we need to integrate the flow rate function, [tex]\(f(t)\)[/tex], from [tex]\(t = 0\)[/tex] to [tex]\(t = 7\)[/tex]. The flow rate function is given as [tex]\(f(t) = 300t^2\)[/tex].
So, the amount of water that flows out of the tank in the first 7 minutes, denoted as [tex]\(W_{\text{out}}\)[/tex], is given by the integral of [tex]\(f(t)\)[/tex] over the interval [tex]\([0, 7]\)[/tex]:
[tex]\[W_{\text{out}} = \int_{0}^{7} f(t) \, dt\][/tex]
[tex]\[= \int_{0}^{7} 300t^2 \, dt\][/tex]
[tex]\[= 300 \int_{0}^{7} t^2 \, dt\][/tex]
To find the integral of [tex]\(t^2\)[/tex], we use the power rule for integration:
[tex]\[= 300 \left[\frac{t^3}{3}\right]_{0}^{7}\][/tex]
[tex]\[= 300 \left(\frac{7^3}{3} - \frac{0^3}{3}\right)\][/tex]
[tex]\[= 300 \left(\frac{343}{3}\right)\][/tex]
[tex]\[= 34300\][/tex]
So, [tex]\(W_{\text{out}} = 34300\)[/tex] gallons.
Now, to find out how many minutes it takes for the tank to be completely empty, we need to find the time, [tex]\(T\)[/tex], at which the tank is empty. The tank will be empty when the integral of the flow rate function from [tex]\(t = 0\)[/tex] to [tex]\(t = T\)[/tex] is equal to the total volume of the tank, which is 6000 gallons.
So, we have:
[tex]\[6000 = \int_{0}^{T} f(t) \, dt\][/tex]
[tex]\[= \int_{0}^{T} 300t^2 \, dt\][/tex]
[tex]\[= 300 \int_{0}^{T} t^2 \, dt\][/tex]
Using the power rule for integration again:
[tex]\[6000 = 300 \left[\frac{t^3}{3}\right]_{0}^{T}\][/tex]
[tex]\[= 300 \left(\frac{T^3}{3} - \frac{0^3}{3}\right)\][/tex]
[tex]\[= 100T^3\][/tex]
Now, solving for [tex]\(T\):[/tex]
[tex]\[T^3 = \frac{6000}{100}\][/tex]
[tex]\[T^3 = 60\][/tex]
[tex]\[T = \sqrt[3]{60}\][/tex]
[tex]\[T \approx 3.914\][/tex]
So, it takes approximately 3.914 minutes for the tank to be completely empty.
HELP PLEASE!!! Which figure shows a reflection of pre-image DEFG over the x-axis ? ( there’s only an A B and C )