Apply the Pythagorean Theorem to find the distance between points A and C.
A)
129 units
B)
V40 units
C)
158 units
D)
V116 units

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.

To know more about transformations

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Answer:

umm  it think it is 14

Step-by-step explanation:

Answer:c

Step-by-step explanation:

Answer:

I believe the answer is 4. Please correct me if I’m wrong.

Step-by-step explanation:

================================================

Work Shown:

A = old velocity = 2 m/s

B = new velocity = 10 m/s

C = change in time = 5 seconds

D = average acceleration

D = (change in velocity)/(change in time)

D = (B-A)/C

D = (10-2)/5

D = 8/5

D = 1.6 m/s^2

The acceleration 1.6 m/s^2 means that the velocity is increasing by 1.6 m/s for every second.

Answer:

there is no solution for x

Step-by-step explanation:

BTW you can use math.way

Answer:

can you type out the entire equation? i'll do my best to solve it. don't screen shot the question tho because for some reason my laptop won't let me see them.

Step-by-step explanation:

Answer:

It would be 5

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

A triangle being translated upwards shows only a vertical translation. Option A is correct.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

When a shape is translated vertically, it moves up or down along the y-axis, maintaining its shape and size. In the case of a triangle being translated upwards, the y-coordinates of its vertices are increased, resulting in a vertical shift of the entire triangle.

When a shape is translated horizontally, it moves left or right along the x-axis, maintaining its shape and size.

When a shape is translated diagonally, it moves in both the horizontal and vertical direction, changing its position but maintaining its shape and size.

Learn more about transformation here:

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Answer:

as an instinct i thought that i should multiply 11 and 5, so im saying 55 different selections

Step-by-step explanation:

sorry if im wrong

Answer:

12.75

Step-by-step explanation:

The computation of the geometric mean of sqrt 77 and sqrt 343 is given below:

As we know that

Geometric mean = [tex]\sqrt{ab}[/tex]

where

a is the first number = [tex]\sqrt{77}[/tex]

And, the b is the second number = [tex]\sqrt{343}[/tex]

Now first we have to convert into a number

For a it, is = 8.78

And, for b, it is = 18.52

Now the geometric mean is

[tex]= \sqrt{8.78 \times 18.52}[/tex]

= 12.75

Answer: I am pretty sure the answer is A, 120.

Step-by-step explanation:

Answer:

10 three point and 14 5 point

Step-by-step explanation:

Ive answered this same question a lot

Answer:

r≈7cm

Step-by-step explanation:

Using the formula

V=4

--------= πr^3

    3

r=(3V

-------------

4π)⅓=(3·1436

4·π)⅓≈6.99877cm

the answer is 7cm

Answer:

C. 7 cm

Step-by-step explanation:

Took the quiz. Trust

Answer:

the expression is 3 + ( - 4) so as you can tell there are more

negative than positive as you can see in the table you first add 3 than you add -4 which you get -1

Step-by-step explanation:

hope it helps!

Answer:

y = 5(3)+3

= 15 +3

= 18

y = 18

hope it's helpful ❤❤❤❤

THANK YOU.

Answer:

40.25 i believe

Step-by-step explanation:

Answer:

Please check the explanation.

Step-by-step explanation:

Given the statement:

''Twice the difference of a number and 2 is added to 6 and the result is 4 more than 3 times the number''.

Let us break down the statement into an algebraic expression.

First Portion:

Let the number be: n

The difference of a number n and 2: n -2

Twice the difference of a number n and 2: 2(n-2)

Twice the difference of a number and 2 is added to 6 = 2(n-2) + 6

Second Portion:

3 times the number n:  3n

4 more than 3 times the number: 3n + 4

Combine the First portion and Second Portion:

Twice the difference of a number and 2 is added to 6 and the result is 4 more than 3 times the number:

2(n - 2) + 6 = 3n + 4

Therefore, the required algebraic expression is:

BONUS SOLUTION to determine the number n

Let us solve the expression

2(n - 2) + 6 = 3n + 4

2n - 4 + 6 = 3n + 4

flip the equation

3n + 4 = 2n - 4 + 6

3n + 4 = 2n + 2

3n - 2n = 2 - 4

n = -2

Thus, the value of n = -2

Answer:

You payed for 18 months.

Step-by-step explanation:

420-60=360

360÷20=18

Answer:

The equation is y=3/2x

Step-by-step explanation:

Answer:

junk personally

Answer:

junk

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

2/3 of 15 is 10

Answer:

x=7

Step-by-step explanation:

∠STP=∠SWT+∠TSW(exterrior ∠ of Δ)

15x=7x+1+7x+6

x=7

Answer:

45.56923076923077

Step-by-step explanation:

Work out 51.6 x 12 which is 619.2 and subtract that from 1804.80 then x your answer which is 1,184.8 and divide by 26 to get your answer which is 45.569....

Answer:

3.25

Step-by-step explanation:

answer:

2. 3/2

1. y=-7

Step-by-step explanation:

Answer:

el precio de la biciclete entre 3 es lo que van a pagar cada quien.

Step-by-step explanation:

4,20

i think that the answer