Which one of Aiko's steps makes a false assumption? Why is it false?
Aiko's Proof:
1. Draw 2 rectangles. Label one ABCD and the other PQRS
2. Translate rectangle ABCD by the directed line segment from A to P.A' and P now coincide. The points coincide because that's how we defined
our translation
3. Rotate rectangle A'B'C'D' by angle D'A'S. Segment A"D" now lies on ray PS. The rays coincide because that's how we defined our rotation.
4. Dilate rectangle A"B"C"D" using center A" and scale factor AD. Segments A"D" and PS now coincide. The segments coincide because A" was
the center of the rotation, so A" and P don't move, and since D" and S are on the same ray from A", when we dilate D" by the right scale factor, it
will stay on ray PS but be the same distance from A" as S is, so S and D' will coincide.
5. Because all angles of a rectangle are right angles, segment A'B' now lies on ray PQ. This is because the rays are on the same side of PS and
make the same angle with it (If A'B' and PQ don't coincide, reflect across PS so that the rays are on the same side of PS.)
6. Dilate rectangle A"B"C"D" using center A" and scale factor AB Segments A'"'**" and PQ not coincide by the same reasoning as in step 4.
7. Due to the symmetry of a rectangle, if 2 rectangles coincide on 2 sides, they must coincide on all sides.

Answers

Answer 1

Answer:

6th step is wrong

Step-by-step explanation:

We have the dilation transformations we only needed one, and that is the 6th step. It would make more sense to do the dilation transformation early in the steps and we already did these steps at the beginning.


Related Questions

DONT ASNWER IF YOU DON"T KNOW THE ANSWER
Are the two triangles similar? Why or why not?

Answers

yes because they are congruent just dilated in size

Hi! Kindly give me the formula for finding the percentage of profit.


Profit and selling price are given. Thank you in advance!​

Answers

When the selling price and the cost price of a product is given, the profit can be calculated using the formula, Profit = Selling Price - Cost Price. After this, the profit percentage formula that is used is, Profit percentage = (Profit/Cost Price) × 100.

Step-by-step explanation:

Given:

Profit P and selling price Sp

Find cost price Cp first:

Cp = Sp - P

To find the percentage profit divide the profit by the cost price and multiply by 100%:

P% = P/(Sp - P)*100%

Simplify this question

Answers

[tex]\\ \sf\longmapsto √64+√-81-i^2[/tex]

[tex]\\ \sf\longmapsto 8+√81i-(-1)[/tex]

[tex]\\ \sf\longmapsto 8+9i+1[/tex]

[tex]\\ \sf\longmapsto 9i+9[/tex]

Can you help this is a lot. I don't really get it

Answers

Answer:

country is 15 30 45 60 75 90 105 120 135 150 pop is 5.75 11.5 17.25 23 28.75 34.5 40.25 46 51.75 57.5

why  you take my profile picture  hello.....

Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 68 km/h faster than the other. If the two planes are 5052 kilometers apart after 3 hours, what is the rate of each plane?

Answers

Step-by-step explanation:

the slower plane travels x km in 3 hours.

the faster plane travels x + 3×68 = x + 204 km in 3 hours.

x + x + 204 = 5052 km

2x = 4848 km

x = 2424 km (in 3 hours).

so, the slower plane's speed is 808 km/h.

the faster plane's speed is 808 + 68 = 876 km/h.

Each time Bobby rides the JUTC bus, money will be deducted from the value of his card. He rode the bus 5 times and his card was charged $100. What integer best represents the the amount by which the balance of the card changed each time it was used?

Possible Answers

A. -$500
B. $20
C. -$20
D. $500​

Answers

Answer:

b

Step-by-step explanation:

100/5= 20

he was charhed 20

can someone help me for this?​

Answers

Answer:

500000N=2m

x. =6m

cross multiply, it'll be

6×50000÷2

=150,000N

Simplify the variable expression below as much as possible.
X + 8 .z
Answer here

Answers

Answer:

It will stay at x + 8

Step-by-step explanation:

answer this pleaseeeee

Answers

Answer:

Each goat gets 3 carrots and there are 4 extra carrots left

Step-by-step explanation:

5*3=15

OR: If you wanted to do it exact you give each goat 3 carrot's and an 1/8th of one and you'd have no extra carrots left.

5*3.8=19

Answer:

the answer is simple 3 remainder of 4

Step-by-step explanation:

so he had 5 goats and 19 carrots  

19/5=3.8 which mean 3 and 4  left

PLEASE PLEASE HELP IM TIMED!! Just look at the picture

Answers

The first one A 7/2
You can just round up 6.75 -> 7 and 1.67->2
the answer is the first one :) 7/2

24 feet/second to inches/minute

Answers

Answer:

4.8 inches a minute is probably the answer

Answer:

4.8 inches a minute

Step-by-step explanation:

Can you calculate problems involving percent? pls help i WILL make as brainlyst pls i dont wanna fail

Answers

Calculating percent in easy, if you turn in into fractions like 20% is 20/100 or 2/10 if you look at it that way it should help you understand it

Answer:

45 is 150% of 30.

Step-by-step explanation:

To find what percent of 30 is 45 first we must turn it into a fraction and simplify.

fraction form: 45/30

simplified fraction form: 3/2

now to find percent you have to put a number over one hundred.

3/2 = ?/100

Right now our denominator is 2. By what number can we multiply 2 to get to 100? The answer is 50.

Now that we have multiplied the denominator by 50, we also have to multiply the numerator (3) by fifty. 3 x 50 = 150

so now we put the new numerator and denominator together and get 150/100

The answer is 150%

Can someone plz help me? :(

Answers

the answer to your question is B.) 12x

A pole 12 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Moussa measures the distance from the pole to the stake and from the pole to the tower. Find the length of the guy wire, to the nearest foot.

Answers

Answer: The answer is 189 ft.

write the equation of a line that passes through the points (-7,-4) and (-5,-6)

Answers

Answer:

y=-x-11

Step-by-step explanation:

Find the inverse function. f(x) = Vx - 1+4​

Answers

Answer:

f^-1(v)=v/x-3/x

Step-by-step explanation:

The inverse of the function f(x) = [tex]\sqrt[3]{x-1} + 4[/tex] Is f⁻¹(x) =  (x - 4)³ + 1.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

f(x) = [tex]\sqrt[3]{x-1} + 4[/tex]

y =  [tex]\sqrt[3]{x-1} + 4[/tex]

Calculate the inverse of the function as shown below,

Replace x with y,

x = [tex]\sqrt[3]{y-1} + 4[/tex]

x - 4 = [tex]\sqrt[3]{y- 1}[/tex]

Cube both sides,

(x - 4)³ = y - 1

y = (x - 4)³ + 1

Thus, f⁻¹(x) =  (x - 4)³ + 1

To know more about function:

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#SPJ2

what is the probability​

Answers

Answer:

1/4

Step-by-step explanation:

the probability on getting blue on spinner is 1/2

1/2 x 1/2 =1/4

Let f be a differentiable function. If h (x) = (2+ f (sin x))", which of the following gives a correct process for finding h' (x) ?

Answers

Answer:

[tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Basic Power Rule]:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle h(x) = [2 + f(\sin x)]''[/tex]

Step 2: Differentiate

Derivative Rule [Chain Rule]:                                                                       [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [2 + f(\sin x)]'[/tex]Rewrite [Derivative Property - Addition/Subtraction]:                                 [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' \bigg[(2)' + [f(\sin x)]' \bigg][/tex]Derivative Rule [Basic Power Rule]:                                                             [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' [f(\sin x)]'[/tex]Derivative Rule [Chain Rule]:                                                                       [tex]\displaystyle h'(x) = [2 + f(\sin x)]''' f'(\sin x)(\sin x)'[/tex]Trigonometric Differentiation:                                                                       [tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]

From here, if you would like, you can take the 3rd derivative of the last piece.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Please help, I dont know how to get the other angle measurement.

Answers

Answer:

Angle E is 88º

Step-by-step explanation:

If angle A is 46, then angle B is 46. Angle C in triangle ABC then has to be 88. Because of this, angle C in triangle CDE has to be 88 as well. Hence, E is 88.

What is the gradient of the graph shown?

Give your answer in its simplest form.

Answers

Answer:

2

Step-by-step explanation:

Choose 2 points on the graph: (0, -2) and (1, 0)

[tex]\boxed{ gradient = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

Gradient of graph

[tex] = \frac{0 - ( - 2)}{ 1 - 0} [/tex]

[tex] = \frac{0 + 2}{1} [/tex]

= 2

Answer:hope it helps!

Step-by-step explanation:

cannot be bothered

Simplify using combining like terms: 3a + 6 + 2a - 8

Answers

Answer:

a = 2

Step-by-step explanation:

Simplifying

3a + 6 = 2a + 8

Reorder the terms:

6 + 3a = 2a + 8

Reorder the terms:

6 + 3a = 8 + 2a

Solving

6 + 3a = 8 + 2a

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-2a' to each side of the equation.

6 + 3a + -2a = 8 + 2a + -2a

Combine like terms: 3a + -2a = 1a

6 + 1a = 8 + 2a + -2a

Combine like terms: 2a + -2a = 0

6 + 1a = 8 + 0

6 + 1a = 8

Add '-6' to each side of the equation.

6 + -6 + 1a = 8 + -6

Combine like terms: 6 + -6 = 0

0 + 1a = 8 + -6

1a = 8 + -6

Combine like terms: 8 + -6 = 2

1a = 2

Divide each side by '1'.

a = 2

There are 10 pens in a box. There are x red pens in the box. All the other pens are blue. Jack takes at random two pens from the box. Find an expression, in terms of x, for the probability that Jack takes one pen of each colour. Give your answer in its simplest form.​

Answers

The probability that one of each color is selected is [tex]\frac{10x - x^2}{45}[/tex]

Probabilities

The probability of an event is the chances of the said event

The given parameters are:

Total  = 10Red = xBlue = 10 - x

Calculating the required probability

The probability that one of each color is selected is calculated as follows:

[tex]P = P(Blue) \times P(Red) + P(Red) \times P(Blue)[/tex]

So, we have:

[tex]P = \frac{10 - x}{10} \times \frac{x}{9} + \frac{x}{10} \times \frac{10 - x}{9}[/tex]

This gives

[tex]P = \frac{x(10 - x)}{90} +\frac{x(10 - x)}{90}[/tex]

Take LCM

[tex]P = \frac{2x(10 - x)}{90}[/tex]

Simplify the above expression

[tex]P = \frac{x(10 - x)}{45}[/tex]

Expand

[tex]P = \frac{10x - x^2}{45}[/tex]

Hence, the probability that one of each color is selected is [tex]P = \frac{10x - x^2}{45}[/tex]

Read more about probabilities at:

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What is the simplified form of the following expression? 5 StartRoot 8 EndRoot minus StartRoot 18 EndRoot minus 2 StartRoot 2 EndRoot 2 StartRoot 2 EndRoot 5 StartRoot 2 EndRoot 9 StartRoot 2 EndRoot 15 StartRoot 2 EndRoot.

Answers

The simplified form of the given expression is [tex]5\sqrt{2}[/tex].

Given expression,

[tex]5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}[/tex].

We have to simplify the above expression.

So, [tex]5\sqrt{8} - \sqrt{18} - 2 \sqrt{2}\\[/tex]

First solve for the square root,

[tex]5\sqrt{2\times2\times2} -\sqrt{3\times3\times2} -2\sqrt{2} \\\\10\sqrt{2} -3\sqrt{2}-2\sqrt{2} \\[/tex]

[tex]7\sqrt{2} -2\sqrt{2}[/tex]

[tex]5\sqrt{2}[/tex]

Hence the simplified form of the given expression is [tex]5\sqrt{2}[/tex].

For more details follow the link:

https://brainly.com/question/2719671

I have no idea how to do this. Please help. ​

Answers

Answer:

Area is 5 cm and perimeter is 12 cm

Step-by-step explanation:

Area: top left sqare:

1cm * 1cm = 1 cm

bottom rectangle:

1cm * 3 cm = 3 cm

top right square:

1cm * 1cm = 1 cm

Perimeter:

1 cm + 2 cm+ 3 cm+ 2 cm+ 1 cm + 1 cm + 1cm + 1cm  = 12 cm

i need help on this asap

Answers

Answer:

c

Step-by-step explanation:

PLS HELP WILL MARK YOU BRAINLIEST!!
No fake answers pls

Answers

Answer:

See below

Step-by-step explanation:

1)

x + 5 = 12, subtract 5 from both sides

x = 7

Subtraction property of equality

a = ba - c = b - c

2)

x + y = 20 and y = 5, substitute 5 into first equation

x + 5 = 20

Substitution property of equality

a + b = c and b = da + d = c

3)

2x - 3 = 11, interchange the sides of equality

11 = 2x - 3

Symmetric property of equality

a = bb = a

Answer:

1. if x + 5 = 12, then x = 7

:Subtraction property of equality

2. If x + y = 20, and y = 5, then x + 5 = 20.

:Substitution property of equality

3. If 2x3 = 11, then 11 = 2x - 3.

:Symmetric property of equality

Write the equation of the line that is perpendicular to y=3x-6 and passes through the point
x, y
(2,0)

Perpendicular is the negative reciprocal so the slope is -1/3

Need to know b and the full equation

With work please. Thank you!

Answers

Answer:

y=-1/3x+2/3 (please mark brainliest)

Step-by-step explanation:

start with y=3x+6

you can get the slope of the perpendicular line by dividing the slope by -1,

so the slope of the new line is -1/3.

using the point and the slope of the new line, we can put it into point-slope form:

y-y₁=m(x-x₁)

y-0=-1/3(x-2)

simplify:

y=-1/3x+2/3

this is the final equation in the form y=mx+b

find an ordered pair that represents the vector from (-3.7, 2) to (-4, -5)


Answers

Answer is (-0.3 ,7) I am sure this answer

Where did this student make the mistake when solving this inequality?

2x + 4 > 5x - 5

-2x -2x

4 < 3x - 5

+5 +5

9 < 3x

/3 /3 (divide by 3)

3 < x

options:

When subtracting the same value from both sides you don't need to switch the inequality sign


There is no mistake, it was solved correctly


You don't subtract 2x from each side, you add 2x to each side


When dividing by 3 you should switch the inequality sign

Answers

Answer:

You don't subtract 2x from each side, you add 2x to each side

f(x) = 3/4 * x - 7 . Find x if f(x) = - 1 . PLEASE tell how to solve it bc that what i dont know, i dont want just the answer​

Answers

Answer:

[tex]x=-8[/tex] if [tex]f(x)=-1[/tex]

Step-by-step explanation:

Given --> [tex]f(x)=-\frac{3}{4}x-7[/tex]

Substitute [tex]f(x)=-1[/tex] into the equation and solve for [tex]x[/tex]:

[tex]-1=-\frac{3}{4}x-7[/tex]

[tex]6=-\frac{3}{4}x[/tex]

[tex]24=-3x[/tex]

[tex]-8=x[/tex]

So, when [tex]f(x)=-1,x=-8[/tex]

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