Answer
600:120
Step-by-step explanation:
5+1 = 6
720/6 = 120
1 = 120
5 = 120 x 5 = 600
a. Identify the series of transformations that would map Circle A onto Circle B.
b. Identify the series of transformations that would map Circle C onto Circle A.
Answer:
Step-by-step explanation:
Assumed Knowledge
Motivation
Content
Radii and chords
Angles in a semicircle
Angles at the centre and circumference
Cyclic quadrilaterals
The alternate segment theorem
Similarity and Circles
Links Forward
Converse of the circle theorems
Coordinate geometry
Calculus
History and Applications
The Euler line
The nine-point circle
Morley’s trisector theorem
Appendix − Converses to the Circle Theorems
Answers to Exercises
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ASSUMED KNOWLEDGE
Introductory plane geometry involving points and lines, parallel lines and transversals, angle sums of triangles and quadrilaterals, and general angle-chasing.
Experience with a logical argument in geometry written as a sequence of steps, each justified by a reason.
Ruler-and-compasses constructions.
The four standard congruence tests and their application to proving properties of and tests for special triangles and quadrilaterals.
The four standard similarity tests and their application.
Trigonometry with triangles.
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MOTIVATION
Most geometry so far has involved triangles and quadrilaterals, which are formed by intervals on lines, and we turn now to the geometry of circles. Lines and circles are the most elementary figures of geometry − a line is the locus of a point moving in a constant direction, and a circle is the locus of a point moving at a constant distance from some fixed point − and all our constructions are done by drawing lines with a straight edge and circles with compasses. Tangents are introduced in this module, and later tangents become the basis of differentiation in calculus.
The theorems of circle geometry are not intuitively obvious to the student, in fact most people are quite surprised by the results when they first see them. They clearly need to be proven carefully, and the cleverness of the methods of proof developed in earlier modules is clearly displayed in this module. The logic becomes more involved − division into cases is often required, and results from different parts of previous geometry modules are often brought together within the one proof. Students traditionally learn a greater respect and appreciation of the methods of mathematics from their study of this imaginative geometric material.
The theoretical importance of circles is reflected in the amazing number and variety of situations in science where circles are used to model physical phenomena. Circles are the first approximation to the orbits of planets and of their moons, to the movement of electrons in an atom, to the motion of a vehicle around a curve in the road, and to the shapes of cyclones and galaxies. Spheres and cylinders are the first approximation of the shape of planets and stars, of the trunks of trees, of an exploding fireball, and of a drop of water, and of manufactured objects such as wires, pipes, ball-bearings, balloons, pies and wheels.
a) The series of transformations to map Circle A onto Circle B is likely a translation. b) The series of transformations to map Circle C onto Circle A is a translation, rotation, and scaling.
a. To map Circle A onto Circle B, we must determine the transformation sequence. We can scale, rotate, and translate.
Translation: An object is translated horizontally or vertically without affecting shape or orientation. To match Circle B, Circle A appears to need to be shifted right and up.
Rotation: An object rotates around a fixed point. Rotation may not be needed since Circle A and Circle B appear to be aligned.
Scaling: An object is resized by scaling. Since Circle A and Circle B are the same size, scaling doesn't seem necessary.
Thus, Circle A-to-Circle B transformations are likely translations.
b. Again, we must determine the transformation sequence to transfer Circle C onto Circle A. Translation: Based on their relative positions, Circle C needs to be shifted left and down to match Circle A.
Rotation: To align Circles A and C, they must be rotated.
Scaling: Circle A is larger than Circle C, hence Circle C should be scaled down.
Thus, translating, rotating, and scaling map Circle C onto Circle A.
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if there are 8 questions on a test and you get on all of them, what is the chance you get all 8 correct?
ASAP
Answer: or 13%
Step-by-step explanation:
Simplify the following expression.
3^3/5• 3^(-7/5)
Answer:
[tex]\frac{1}{3x^{\frac{4}{5}}}[/tex]
Step-by-step explanation:
Subtract the exponents: 3/5 - 7/5 = -4/5
Equation would become 3^-4/5
Which is equivalent to 1/3x^4/5
Joe’s Coffee is having a stained glass window installed on their front door. Approximately how much glass will be needed to create the stained glass window?
PLSS USE STEPSSS!!!!
A) 2.4
B) 9.6
C) 11
D) 38.5
[tex]\color{plum}\tt \: D) 38.5 [/tex]
Steps to derive correct answer :Diameter of the stained glass window Joey needs = 3.5
Area of the window = quantity of glass Joey needs
Area of the window :
[tex] = \tt\pi {r}^{2} [/tex]
[tex] = \tt3.14 \times 3.5 \times 3.5[/tex]
[tex] =\tt 3.14 \times 12.25[/tex]
[tex] =\tt 38.46[/tex]
38.46 can be rounded off to 38.5.
Therefore, quantity of glass needed to make the stained glass window = 38.5
What is a formula for the nth term of the given sequence? 160,200,250
Answer:
can i see the picture?
Sum of two numbers = 15 (Addition)
Difference of two numbers =3 (Subtraction)
Find the two numbers.
What is the product of those two numbers? (Multiplication)
Answer:
The numbers are x= 9 and y =6
The product of two numbers
x y = 9 × 6 = 54
Step-by-step explanation:
Step(i):-
Let x and y are two numbers
Given that the sum of two numbers
x + y = 15 ..(i)
Given that the difference of two numbers
x - y = 3 ..(ii)
adding (i) and (ii) , we get
x + y + x -y = 15 +3
2 x = 18
x =9
Step(ii):-
Substitute x = 9 in equation (i) , we get
x + y = 15
9 + y = 15
y = 15 - 9
y = 6
Final answer:-
The numbers are x= 9 and y =6
The product of two numbers
x y = 9 × 6 = 54
A bicycle was priced at $400. Later the price was reduced by 20%. What is the price after the reduction?
Answer:
320
Step-by-step explanation:
400*80/100=320
Answer:
$320 is the final price, $80 is the amount taken off
Test worth 50 points; test score of 96 write a proportion to find how many points a student needs to score on the test to get the given score.
Answer: The student needs 144 points to get a score of 96%
Step-by-step explanation:
what is the area of a 3 and a quarter inch circle?
Answer:
33.2in²Step-by-step explanation:
to find area we have to find redious first sor=d/2therefore
[tex]r = \frac{3 \frac{1}{4} }{2} [/tex]
[tex]r = \frac{ \frac{13}{2} }{2} [/tex]
[tex]r = \frac{13}{2} \div 2[/tex]
[tex]r = \frac{13}{4} [/tex]
[tex]area \: of \: a \: circle \: = \pi {r}^{2} [/tex]
[tex] = \pi (\frac{13}{4} ) ^{2} i {n}^{2} [/tex]
[tex] = \pi \times \frac{169}{16} {in}^{2} [/tex]
[tex] = \frac{169\pi}{16} i {n}^{2} [/tex]
[tex] = 33.2 \: i {n}^{2} [/tex]
What is 4/5 as a decimal?
Answer:
Umm, 0.8
Step-by-step explanation:
Is this fr?
Choose two pairs of alternate interror angles.
Answer: angle 5 and angle 10
angle 8 and angle 11
hope this helps!
The graph of which function has an amplitude of 3 and a right phase shift of ?
Answer:
The first one
Step-by-step explanation:
The amplitude is usually the first number (for example, in this equation, the 3). Then you also know that the right or left shift depends on the addition or subtraction sign. Usually, the subtraction sign means to the right and the addition sign means to the left.
We have that the graph of which function has an amplitude of 3 and a right phase shift of [tex]\phi= \frac{\pi}{4}[/tex] is
[tex]3sin2(x+\phi)[/tex]
The Correct option is D
From the Question we are told that
A graph has
Amplitude of 3
Phase [tex]\phi= \frac{\pi}{4}[/tex]
Generally the equation for the Wave Equation is mathematically given as
[tex]Asin(kx-wt+\phi)[/tex]
Therefore the Equation for this particular wave is
[tex]3sin2(x+\phi)[/tex]
Hence
The graph of which function has an amplitude of 3 and a right phase shift of [tex]\phi= \frac{\pi}{4}[/tex] is
[tex]3sin2(x+\phi)[/tex]
The Correct option is D
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73 divided by the difference between 12 and 7
Answer:
14.6
Step-by-step explanation:
difference: 12-7=5
division: 73/5=14.6
The 73 divided by the difference between 12 and 7 is equal to 14.6.
To properly calculate 73 divided by the difference between 12 and 7, we follow these steps:
Calculate the difference between 12 and 7:
12 - 7 = 5
Divide 73 by the difference obtained:
73 ÷ 5 = 14.6
Therefore, 73 divided by the difference between 12 and 7 is equal to 14.6. This means that if we take the value 73 and divide it by the difference between 12 and 7, the quotient will be 14.6. The difference between 12 and 7 is 5, and when we divide 73 by 5, we obtain 14.6. It is important to note that the result is a decimal value, specifically 14.6.
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Neeeeddddd helllppp nowwwwww!!!!
Answer:
the area is 670.32 but it's not in there
Kamil has 72 baseball cards. He wants to put the cards
in a book. He can fit 9 cards on each page of the book.
Which number sentence can be used to find the number
of pages Kamil can fill with baseball cards?
А
72x9=
B
72-9=
C
72 +9=
D
72=9=
On a coordinate plane, which theorem can be used to prove that a quadrilateral is a parallelogram if only the slopes of the sides of the quadrilateral can be calculated?
Answer: D.
Step-by-step explanation:
2 Antonio is a set designer. He is gluing ribbon on 4 square and 2 triangular posters to be used as stage props in an upcoming play. Use the system of equations to finds, the amount of ribbon needed for a square poster, and t, the amount of ribbon needed for a triangular poster. Show your work.
s=t+ 5 45 + 2t = 110
The amount of ribbon needed for a square poster will be 20.
And, The amount of ribbon needed for a triangular poster will be 15.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The system of equation are;
⇒ s = t + 5
⇒ 45 + 2t = 110
Now,
Since, The system of equation are;
⇒ s = t + 5 ..(i)
⇒ 4s + 2t = 110 ..(ii)
Solve equation (ii) for t as;
⇒ 45 + 2t = 110
⇒ 4s + 2t - 4s = 110 - 4s
⇒ 2t = 110 - 4s
⇒ t = 55 - 2s
Substitute above value in equation (i), we get;
⇒ s = t + 5
⇒ s = 55 - 2s + 5
⇒ s + 2s = 60
⇒ 3s = 60
⇒ s = 20
And, ⇒ t = 55 - 2s
⇒ t = 55 - 2 x 20
⇒ t = 55 - 40
⇒ t = 15
Thus, The amount of ribbon needed for a square poster will be 20.
And, The amount of ribbon needed for a triangular poster will be 15.
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The students in Jeremiah's grade voted to select a guest speaker. 45 students voted for a famous athlete. If there are 90 students in Jeremiah's grade, what percentage of the students voted for the athlete?
Write your answer using a percent sign (%).
Answer:
50%
Step-by-step explanation:
45 is half of 90. A percent is out of 100. So when you split 100 in half, it equals 50. The answer is 50%. Glad I could help!
Answer:
50% of the students voted for the athlete.
Step-by-step explanation:
half of 90 = 45 which means 45 + 45 = 90
so 50% of the class voted for the athlete
Help me with this circle question
Answer:
50.265482457436 inches
Step-by-step explanation:
radius = 8 inches
C = 2×pi×r
= 2×pi×8
C = 50.265482457436 inches
Which table represents a linear function?
Answer:
top right
Step-by-step explanation:
plz help due in 30mins
Answer:
y=x+5
Step-by-step explanation:
y increases by 5 so in y=mx+b b=5 and x increases by 1 so still x thus the answer is y=x+5
I NEED ANSWERS ASAP ITS DUE TODAY
Answer:
C
Step-by-step explanation:
First find the radius:
5 pi = 2 pi r
cancel out pi
5 = 2r
r = 5/2
Then find the area:
A = pi r^2
A = pi 5/2^2
A = 25/4 pi
How do you do these question and what's the answer?
-1/3 (n + 15) = -2
46 = -6t -8
Urgent. Please answer ASAP. Thanks guys!
Answer:
n= -9, t= -9
Step-by-step explanation:
1) -1/3(n+15)=-2
-1/3×n+-1/3×15=-2
-1/3×n -5= -2
-1/3 n-5+5= -2+5
-1/3×n=3
3/-1×-1/3×n=3/-1×3
n= -9
2) 46 = -6t -8
−6t−8=46
−6t−8+8=46+8
−6t=54
Divide both sides by -6
t=-9
Find the values of x and y in the d
9514 1404 393
Answer:
x = 20y = 10Step-by-step explanation:
The angle marks show that ΔRST is isosceles, so RT = RS. They also show ΔRTU to be equilateral, so UT = RT.
UT = RS
x -5 = 15
x = 20 . . . . . . add 5
__
ΔRTU is equilateral, so ∠RTU is 60°. The angle marked 3y° is complementary to that.
3y = 30
y = 10 . . . . . divide by 3
15 points PLEASE HELP!!!
Factor the following equation:
[tex]x^2+3x+4[/tex]
Step-by-step explanation:
x²+3x+4=0
x²+3x_ +2=0
x²+3x_2=-2
x²+3x_2+(3x_4)²=-2+(3/4)²
(x+3/4) =-2+9_16
x+3_4 = -32+9__16 =√-23_6
x+3_4 =-√23_4
x = -3+√-23___4
x = -3- √-23___4 , -3+√-23___4 //
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Energy and mass are related by the formula
E = mc².
m is the mass of the object
c is the speed of light
Solve the equation for the mass of the object, m.
Answer:
m=E/c².
Step-by-step explanation:
Transposing the formula
E=mc²
we divide both sides by c² then cancel out where necessary so m would stand alone
E/c²=mc²/c²
cancelling c² on the right hand side, equation becomes
m= E/c²
Please help me with this question?
Question 1- Andre says that 4x + 7 + 6x + (-1) and 15x + 5 + 1 - 5x are equivalent because they both equal 10x + 6. Do you agree with Andre? a) No b) Yes
Explain your reasoning for your choice above.
Answer:
Yes
Step-by-step explanation:
[tex]4x + 7 + 6x - 1\\10x + 6[/tex]
[tex]15x + 5 + 1 -5x\\10x+6[/tex]
They both equal 10x + 6
Answer:
no they are not equal bcz Lhs is not =Rhs
Point I is on line segment HJ. Given HI = x, IJ = 2x + 9, and H J = 4x,
determine the numerical length of IJ.
Please help it’s due at 11:59
Answer:
c=-16
Step-by-step explanation: