Determine if 0.515115111511115111115... is rational or irrational and give
reason for your answer.

Answer:

D. Rotation 270 degrees clockwise.

Step-by-step explanation:

The transformation used in the coordinates below was a rotation 270 degrees clockwise, whose definition is:

[tex](x', y') = (r\cdot \cos (\theta - 270^{\circ}), r\cdot \sin (\theta -270^{\circ}))[/tex]

Please note that clockwise rotation is represented by the minus sign.

Where [tex]r[/tex] is the norm of original point, defined as:

[tex]r =\sqrt{x^{2}+y^{2}}[/tex], [tex]\forall \,x,y\in \mathbb{R}[/tex]

And [tex]\theta[/tex] is the direction of the point centered at origin and with respect to +x semiaxis, measured in sexagesimal degrees:

[tex]\theta = \tan^{-1} \frac{y}{x}[/tex]

Now we proceed to prove the statement:

[tex]L (x, y) = (-1, 9) \longrightarrow L'(x,y)[/tex]

Norm

[tex]r = \sqrt{(-1)^{2}+9^{2}}[/tex]

[tex]r = \sqrt{82}[/tex]

Direction

The point is located on 2nd quadrant, which means that [tex]90^{\circ} \leq \theta \leq 180^{\circ}[/tex]. Then:

[tex]\theta = \tan^{-1}\left(\frac{9}{-1} \right)[/tex]

[tex]\theta = 96.340^{\circ}[/tex]

Rotation

[tex]L'(x,y) = (\sqrt{82}\cdot \cos (96.340^{\circ}-270^{\circ}),\sqrt{82}\cdot \sin (96.340^{\circ}-270^{\circ}))[/tex]

[tex]L'(x,y) = (-9, -1)[/tex]

[tex]M(x,y) = (-8,8) \longrightarrow M'(x,y)[/tex]

Norm

[tex]r = \sqrt{(-8)^{2}+8^{2}}[/tex]

[tex]r = \sqrt{128}[/tex]

Direction

The point is located on 2nd quadrant, which means that [tex]90^{\circ} \leq \theta \leq 180^{\circ}[/tex]. Then:

[tex]\theta = \tan^{-1}\left(\frac{8}{-8} \right)[/tex]

[tex]\theta = 135^{\circ}[/tex]

Rotation

[tex]M'(x,y) = (\sqrt{128}\cdot \cos (135^{\circ}-270^{\circ}),\sqrt{128}\cdot \sin (135^{\circ}-270^{\circ}))[/tex]

[tex]M'(x,y) = (-8, -8)[/tex]

[tex]N(x,y) = (-3,5)\longrightarrow N'(x,y)[/tex]

Norm

[tex]r = \sqrt{(-3)^{2}+5^{2}}[/tex]

[tex]r =\sqrt{34}[/tex]

Direction

The point is located on 2nd quadrant, which means that [tex]90^{\circ} \leq \theta \leq 180^{\circ}[/tex]. Then:

[tex]\theta = \tan^{-1}\left(\frac{5}{-3} \right)[/tex]

[tex]\theta = 120.964^{\circ}[/tex]

Rotation

[tex]N'(x,y) = (\sqrt{34}\cdot \cos (120.964^{\circ}-270^{\circ}), \sqrt{34}\cdot \cos (120.964^{\circ}-270^{\circ}))[/tex]

[tex]N'(x,y) = (-5, -3)[/tex]

Hence, the correct answer is D.

Answer:

y = 7x-17

Step-by-step explanation:

y=mx+ c

substitute the values,

-3=14+c

c=-17

y=7x-17

Answer:

You sure this true

Step-by-step explanation:

How you know

Answer:

OOOOOOOO THANK YOU!!!!!!

Answer:

60

Step-by-step explanation:

Answer:

Step-by-step explanation:

it's 60 5+5+5+5+5+5+5+5+5+5+5+5

Answer:

71º is measure of angle A

19º is measure of angle B

Step-by-step explanation:

complementary angles are angles that equal to 90º 

so let's add the terms (from angles A & B) and set them equal to 90º

3x+2 + x-4 = 90

4x -2 = 90

add 2 to both sides to get rid of the 2 on the left side and isolate our similar terms

4x = 92

divide both sides by 4

x=23

We're not done though, we must plug in our x value to Angle A terms and Angle B terms.

(3(23) + 2)º = measure of Angle A            (solve for both of them)

(23-4)º =  = measure of Angle B

3(23) + 2 =

3(23) = 69 (add the 2)

71º is measure of angle A

23-4 = 19º

19º is measure of angle B

double-check

71+19 = 90º

It works

Answer:

71º is measure of angle A

19º is measure of angle B

Step-by-step explanation:

Answer:

y=-3x+13

Step-by-step explanation:

y=-3x-9+4

-9+9= 0 so that cancel out

next u do

4+9=13

and thats when u drop the variables and the 13 down then it will be

y= -3x + 13

Answer:

25

Step-by-step explanation:

3 over 3 = 1

5 x (4-1)

5 x 4 = 20

5 x 1 = 5

20 + 5 = 25

Answer:

trinomial

Step-by-step explanation:

Since this polynomial has 3 different terms, this is, in fact, a trinomial.

Hope this helps :)

Answer:

The number is 4/9

Step-by-step explanation:

3(6*(4/9))=3*(2+(2/3))=8

Answer:

-6.5)7 1/4)6.57)-5 58/100)9 1/3

Step-by-step explanation:

I have no explanation

Answer:

The answer is x = 7

Step-by-step explanation:

Divide each term by  3  and simplify. Move all terms not containing  x  to the right side of the equation.

Answer:

[tex]\huge\boxed{x=7}[/tex]

Step-by-step explanation:

In order to solve for x, our goal is to isolate it on one side of the equation. We can do this by reversing the equation.

Let's apply the distributive property on the left side:

[tex](3 \cdot x) + (3 \cdot -10) = -9\\\\3x-30=-9[/tex]

Add 30 to both sides:

[tex]3x - 30 + 30 = -9 + 30\\\\3x = 21[/tex]

Divide both sides by 3:

[tex]3x \div 3 = 21 \div 3\\\\x = 7[/tex]

So x = 7.

Hope this helped!

Answer:

3

Step-by-step explanation:

well first you need to put your hand over the 3 on your keyboard and then push down once.

Answer:

Since 80 and 40 are both divisible by 40 and 10, 40 and 10 are factors of both 80 and 40.

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

That is false

If the pre-image is reflected over any axis, the image will still be congruent to it

Answer:

1.8400

Step-by-step explanation:

Answer:

y = x + 4

Step-by-step explanation:

Let the equation of the linear function represented by the table is,

[tex]y-y_1=m(x-x_1)[/tex]

where m = slope of the line

And this line passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Slope of the given line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

From the given table two points lying on the function are (-4, 0) and (1, 5).

Slope 'm' = [tex]\frac{5-0}{1+4}[/tex] = 1

Therefore, equation of the linear function passing through (1, 5) and slope 1 will be,

y - 5 = (x - 1)

y = x + 5 - 1

y = x + 4

Answer:

  4) 16√3 in²

  5) 63 cm²

Step-by-step explanation:

The formula to use in these cases is ...

  A = (1/2)ab·sin(θ)

where a, b are the side lengths and θ is the angle between them.

It helps to know the trig functions of the "special" angles used here.

  sin(120°) = sin(60°) = (√3)/2

  cos(60°) = 1/2

  sin(135°) = cos(45°) = (√2)/2

__

4) The external angle at the base is the supplement of 120°, so is 60°. Then the length of the missing segment between the end of the base and the right angle at h is ...

  x = (8 in)cos(60°) = (8 in)(1/2) = 4 in

So, the bottom edge of the triangle is 12 in - 4 in = 8 in.

The area is ...

  A = (1/2)(8 in)(8 in)sin(120°) = (1/2)64(√3)/2 in² = 16√3 in²

__

5) As in the previous problem, the difference between the given horizontal dimension and the base of the triangle is ...

  x = (18 cm)cos(180°-135°) = 18(√2)/2 cm = 9√2 cm

Then the base of the triangle is ...

  16√2 cm -9√2 cm = 7√2 cm

The area is then ...

  A = (1/2)(18 cm)(7√2 cm)(√2)/2 = 63 cm²

Answer:

11/3

Step-by-step explanation:

Multiply the 3 by the 3 and then add 2.

[tex]3 \frac{2}{3} [/tex]

[tex](3 \times 3) + 2[/tex]

[tex]9 + 2 = 11[/tex]

[tex] \frac{11}{3} [/tex]

Answer:

fiydy8dy8d8ydy8ddiydy8dyr68d8yd8yd86dy8d8yd86d86f8yf8yfiyfi6dy8f86fi6di6di6f58yfiigdfyifigfuditit8yd58dityofc8568d68r96r69d has been in H2g2g2hh2 for a year wtfor subscribing to the

Answer:

20 cm

Step-by-step explanation:

the square root of 400 is 20

since all 4 sides are equal and the formula is area = L X B

20 x 20 is 400

Answer:

115

Step-by-step explanation:Beacsue that is way smaller than usal...the angle is 180 degress so if you do 55+65=120 so it defintly isn't 120 because that is correct so ya.

Answer:

A) You would move it 2 times B) The Exponent would be 10^2

Step-by-step explanation:

This one's hard to explain..if you want you can message me about it :)

Answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 + a

Putting value of a

6 + 3 = 9

5b

Putting value of b

5(2) = 10

C - 1

Putting value of c

12 - 1 = 11

The backpack price is $38.25

Answer:

6>5

Step-by-step explanation:

I know it is true

Answer:

XDDDDDDDDDDDDDDDDDDDDDDDDD

Step-by-step explanation: