Predict what will happen to the coordinates of a point (x,y) as the point rotates counterclockwise (CCW) about the origin to produce point (x’,y’). Choose rotation angles of 90 degrees, 180 degrees, and 360 degrees. Express your answer in terms of x and y. Be sure to watch your signs.

Predict What Will Happen To The Coordinates Of A Point (x,y) As The Point Rotates Counterclockwise (CCW)

Answers

Answer 1

Answer:

Step-by-step explanation:

If a point (x, y) is rotated counterclockwise by the angles given in the table attached,

Rule for the rotation at an angle of 90° CCW about the origin,

(x, y) → (-y, x)

Rule for the rotation at an angle of 180° CCW about the origin,

(x, y) → (-x, -y)

Rule for the rotation at an angle of 270° CCW about the origin,

(x, y) → (y, -x)

Rule for the rotation at an angle of 360° CCW about the origin,

(x, y) → (x, y)

Angle of rotation         x'         y'

90°                               -y         x                          

180°                              -x        -y

270°                              y        -x

360°                              x         y

Answer 2

Answer:

Angle of Rotation (CCW) x′ y′

90°   −y x

180°  −x −y

270°   y −x

360°        x   y


Related Questions

Evaluate 5w-w/x when w=6 and x=2

Answers

Answer:

27

Step-by-step explanation:

5×6-(6/2)

=30-3

=27

Answer:

[tex] 27[/tex]

Step-by-step explanation:

[tex]5w - \frac{w}{x} = \frac{5w}{1} - \frac{w}{x} = \frac{5(6)}{1} - \frac{6}{2} = 30 - 3 = 27[/tex]

or

[tex] \frac{5(6) }{1} - \frac{6}{2} = \frac{30}{1} - \frac{6}{2} = \frac{60 - 6}{2} = \frac{54}{2} [/tex]

6.88888888889 as a fraction

Answers

Answer:

62/9

Step-by-step explanation:

.88888888 is 8/9

Multiply 9*6 to get the whole amount

9*6 = 54

Add 8 because that's the fractional amount.

54 + 8 = 62

So 62/9 will give you 6.8888888889

What is f(a) in the given function 6x-5

Answers

Answer:

  f(a) = 6a -5

Step-by-step explanation:

Assuming your function is ...

  f(x) = 6x -5

The expression f(a) means you replace x with 'a' everywhere in the above function definition:

  f(a) = 6a -5

55 176 539 1628 in the sequence above each rem after the first is determined by multiplying by x and then adding y. If x and y are each greater than zero and if they are integers than what does the term x+y equals?

Answers

Answer: 14

Step-by-step explanation:

Given the sequence : 55 176 539 1628

Each number after the first is derived by multiplying by x and then adding y;

If x and y are > 0 and they are integers.

Taking 55 and 176:

176 = 55*x + y

539 = 176*x + y

55x + y = 176 - - - (1)

176x + y = 539 - - (2)

From (1) y = 176 - 55x

Substitute y = 176 - 55x into (2)

176x + 176 - 55x = 539

121x = 539 - 176

121x = 363

x = 363 / 121

x = 3

Put x = 3 in y = 176 - 55x

y = 176 - 55(3)

y = 176 - 165

y = 11

x = 3, y = 11

x + y = 3 + 11 = 14

If the relationships below are given in the form (input, output), which pairing always describes a function?

Answers

Answer: B

(height of a building in feet, height of the building in inches)

Martin decided to buy 2 bags of grapes weighing 5 2/3 pounds each instead of the three bags weighing 4 1/5 pounds each because the bigger bags were on sale did he end up with more grapes or less grapes buying the bigger bags

Answers

Answer:

He gets less buying the two big bags

Step-by-step explanation:

Question 7. Ezequiel's Biology marks are 8.3, 6.8 and 9.4 out of 10. His final grade in Biology is the mean of these three marks a Calculate Ezequiel's final grade in Biology. Ezequiel wrote the three marks correct to the nearest unit to find his final grade in Biology.​

Answers

Answer:

Ezequiel's final grade is 8

Step-by-step explanation:

The average (mean) of Ezequiel's grade is:

[tex]\frac{(8.3+6.8+9.4)}{3} \approx 8.16666[/tex]

which rounded to the nearest unit is 8.

Answer:

It would be 8 :)

Step-by-step explanation:

estimate the equation 12+ 19.61

Answers

QUESTION:

QUESTION:estimate the equation 12+19.61.

QUESTION:estimate the equation 12+19.61.Answer:

QUESTION:estimate the equation 12+19.61.Answer:12+19.61 =31.61.

12 + 19.61
Usually we round off the number when we do estimates
12 + 20 = 32

Iris has 120 songs on her playlist. each week, she downloads 4 new songs. Write an expression to show the total number of songs on Iris's playlist after 'w' weeks.. (Help please!)

Answers

Answer: 4w+120.
Explanation: She downloads 4 songs for every week which is represented as 4w, and she started with 120 songs which is represented as +120.

The expression that shows the total number of songs on Iris playlist is 120 + 4w

A linear expression is an expression that has only one variable. The single variable is raised to the power of 1.  An example of a linear expression is x + 10  

Iris already has 120 songs on her playlist. She increases her playlist every week by four songs.

This means that each week, her playlist increases by 4. This can be represented with the expression : 4 x w = 4w

Where w represents the number of weeks.

In week 10, her playlist increases by: 4 x 1 = 4 songs

In week 10, her playlist increases by : 4 x 10 = 40 songs

But Iris already has 120 songs

This can be represented with the expression 120 + 4w

After 1 week, the total songs she would have is 120 + 4 = 124 songs

After 10 weeks, the total songs she would have is 120 + 40 = 160 songs

A similar question was solved here: https://brainly.com/question/21262994?referrer=searchResults

Distribute: -3 (2x-4)

Answers

-6x+12 because you are multiplying -3 and 2x and -3 and -4

Answer:

24

Step-by-step explanation:

2x-4= -8×-3= 24

When you look at the P.E.M.D.A.S. method you have to do what's in the PERENTESSE first so that means 2x-4 is the first thing that I are solving and you get -8 now you have to multiply -8 by -3 then you get 24

The weight of the cardinal ( in ounces ) is 0.6x+11 after its x ounces of bird seed. How much does it weigh after it eats 2 ounces of bird seed?

Answers

Answer:

12.2 oz

Step-by-step explanation:

you would just plug in 2 for x so you get 0.6(2)+11 and which you simplify to get 1.2+11 and then you would get 12.2 as the weight

prove that points (2a,4a), (2a,6a), and (2a +√3a,5a) are the vertices of an equilateral triangle of side

Answers

Answer:

Let A (2a, 4a)

     B(2a, 6a)

    C (2a + sqrt (3a), 5a)

Side AC:

[tex]\sqrt{(2a+\sqrt{3a}-2a)^2+(5a-4a)^2 }=\sqrt{3a+a^2}[/tex]

Side BC:

[tex]\sqrt{(2a+\sqrt{3a}-2a)^2+(5a-6a)^2 }=\sqrt{3a+a^2}[/tex]

Hence AC = BC

It is an isoceles triangle.

Side AB:

[tex]\sqrt{(2a-2a)^2+(6a-4a)^2 }=\sqrt{2a^2}=2a[/tex]

It proves that the triangle is NOT an equilateral triangle.

evaluate the expression 32^((3)/(5))

Answers

Answer:

8

Step-by-step explanation:

3/5=0.6

32^0.6=8

Ans.8

ux+ rx= w; solving for x

Answers

Answer:

[tex]x = \frac{w}{(u + r)} [/tex]

Step-by-step explanation:

ux + rx = w

x(u + r) = w

x = w/(u + r)

the dash '/' represents fraction

The required solution is x = w/(u + r).

It is required to find the value of x.

What is algebra?

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given:

The given equation is

u x + r x = w

Taking common x  we get,

x(u + r) = w

Divide (u + r)  on both sides we get,

x = w/(u + r)

Therefore, the required solution is x = w/(u + r).

Learn more details about algebra here:

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Simplify the expression where possible. (picture below)

Answers

Answer:

1/ [tex]x^{-8}[/tex]

Step-by-step explanation:

when there is two powers the correct method to solve is to multiply them so

4 * -2 = -8

An elm tree is 3 and one-half times as tall as an apple tree. The apple tree is 10 and two-thirds feet tall. How tall is the elm tree?

Answers

Answer:

The elm tree is 40 5/6 inches tall

Step-by-step explanation:

Let

Tallness of the apple tree = x

Tallness of the elm tree= 3 1/2x

Apple tree = 10 2/3 feet tall

Elm tree = 3 1/2x

Where x= 10 2/3

Elm = 3 1/2 (10 2/3)

= 7/2(35/3)

= 7*35 / 2*3

= 245 / 6

= 40 5/6 inches tall

The elm tree is 40 5/6 inches tall

Rewrite the equation so that it does not have fractions 2/3x-4=5/6

Answers

Answer:

.6x - 4 = .83

Step-by-step explanation:

three sphere of radius 4cm each fit inside a tube calculate the percentage of the tube.

Answers

Answer:

66.6% (see below)

Step-by-step explanation:

Each sphere 4/3[tex]\pi[/tex]r²=4/3[tex]\pi[/tex](4²)=268.08cm³

Assuming the tube is the same width and height as the three spheres,

V=[tex]\pi[/tex]r²h=[tex]\pi[/tex](4²)24=1206.37

The three spheres are 268.08*3=804.24cm³

The tube is 1206.37cm³

I’m not sure if your question is asking the percentage of the tube that’s filled, or the percentage that’s unfilled.

Filled: 804.24÷1206.37=0.66666=66.6%

Unfilled: 1206.37-804.24=402.13

402.13÷106.37=0.33333=33.3%

Answer:

Percentage of Tube Unfilled : 33 and 1/3%

Step-by-step explanation:

It's most likely that we want to calculate the percentage of the tube unfilled, as the tube itself wouldn't be provided otherwise. We can start by calculating the volume of the tube --- (1)

The volume of a cylinder is represented by πr²h. Substituting we would receive π(4)²h. h is represented by 3 times the diameter of each sphere, as it is aligned such. Diameter = 2 * r = 2 * 4 = 8, so h = 3 * 8 = 24. Therefore Tube Volume = π(4)²(24) = π(16)(24) = 384π.

Now let's solve for the volume of a sphere, multiplying by three to receive the total volume of all 3 spheres --- (2)

Volume of 1 Sphere : 4 / 3πr³ = 4 / 3π(4)³ = 4 / 3π * 64 = 256 / 3π

Volume of all 3 Spheres : 256 / 3π * 3 = 256π

And now the volume of the tube that is unfilled, will be 384π - 256π = 128π. The total volume of the tube is 384π, so the percentage of the unfilled tube will be 128π / 384π or 128 / 384 = 0.333333333 * 100 = 33.33333...%. Therefore the percentage of the tube that is not filled will be 33.33% approximately, or 33 and 1/3% in exact terms.

Marlena places a square rug on her living room floor, which is also a square. What area of her floor is NOT covered by the rug? A. 9 ft2 C. 63 ft2 B. 12 ft2 D. 81 ft2

Answers

Answer:B - 12ft2

Step-by-step explanation:

1x + 2 = Ox + 5
Solve the equation.

Answers

Answer:

x =-3

Step-by-step explanation:

1x + 2 = 0x + 5

hence 0x simplifies x

1x-0x = 2-5

x = -3

given the midpoint and one endpoint find the other endpoint. Endpoint (2,-9) Midpoint (-2,-1)
A) (4,8)
B) (-4,-8)
C) (-6,7)
D) (6,-7)

Answers

Answer:

Step-by-step explanation:

(x + 2)/2 = -2

x + 2 = -4

x = -6

(y + (-9))/2 = -1

y - 9 = -2

y = 7

(-6, 7)

answer is C

[tex](W^{8} )^{8}[/tex]

Answers

Answer:

w^64

Step-by-step explanation:

[tex]\left(w^8\right)^8\\[/tex]

[tex]\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc}[/tex]

[tex]\left(w^8\right)^8=w^{8\times\:8}\\=w^6^4[/tex]


[tex]x {2} = \frac{25}{144} [/tex]
I don't understand at all​

Answers

Step-by-step explanation:

Hey, there!!

Let me explain you very simply, ok.

Here, according to the question,

[tex]{x}^{2} = \frac{25}{144} [/tex]

X is square so, which finding the value of x you must take it to the right side (in root form ). so,

[tex]x = \sqrt{ \frac{25}{144} } [/tex]

Now, as we know that,

sq.root of 25 = 5

sq.root of 144 = 12

Now, you write it as,

[tex]x = \sqrt{ \frac{ {5}^{2} }{ {12}^{2} } } [/tex]

[tex]or \: x = \sqrt{( { \frac{5}{12} )}^{2} } [/tex]

Now, square root and (5/12) square ( square root , square gets cancelled).

You will get as,

[tex]x = \frac{5}{12} [/tex]

And its your simplified answer.

Hope it helps...

is -3 a whole number

Answers

Answer:

No it is not -3 is an integers

Answer:

no: -3 is an integer

Step-by-step explanation:

Ms. Rothrock loves to go shopping with Ms. Cluver and Mrs. Gosch. When they went to Target Ms. Rothrock bought shirts and jeans. Each shirt cost $13 and each pair of jeans cost $15. Ms. Rothrock decided to buy 4 shirts. She spent $82. How many pairs of jeans did she buy?

Answers

Answer:

She bought 2 pairs of jeans

Step-by-step explanation:

$82- $13-$13-$13-$13=$30

$15*2=$30

$30=$30

she bought 2 pairs of jeans

Powers of 10 with positive exponents are:
less than 1
greater than 1

Answers

Answer:

greater than 1

Step-by-step explanation:

Answer:

greater than 1

Step-by-step explanation:

Which exponential equation correctly rewrites this logarithmic equation?


Answers

Answer:c

Step-by-step explanation:

This is how it should be when you are representing an exponential equation to a logarithmic equation

[tex]y=a^{x}[/tex]→log y base a =x

therefore the answer is c

The exponential equation which rewrites the logarithmic equation is given by 6ˣ = 18

What is Logarithm?

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

log₆ 18 = x

From the properties of logarithm , we get

log Aⁿ = n log A

On simplifying , we get

6ˣ = 18

where the value of x = 1.61314

Hence , the exponential equation is 6ˣ = 18

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The ideal length of a particular metal rod is 30.5 cm. The measured length may vary from the ideal length by at most 0.015 cm. What is the range of acceptable lengths for the rod.

Answers

Answer:

The range can be expressed as: [tex]30.485\leq x\leq 30.515[/tex]

which agrees with answer D

Step-by-step explanation:

If the tolerance is 0.015 cm for the final rod, then the range of acceptable lengths for the rod is between 30.5 - 0.05 and 30.5 + 0.015 . That is between

30.485 cm and 30.515 cm

Which can be expressed as:   [tex]30.485\leq x\leq 30.515[/tex]

Please help me with this question. This is urgent

Answers

Answer:

1000m (option A)

Step-by-step explanation:

[tex]10^k^-^3 = m \\=>\frac{10^k}{10^3} = m \\=> 10^k = 1000 m[/tex]

Number a !! (1,000m)

Number 8 I need help really bad

Answers

Answer:

See below.

Step-by-step explanation:

So we have the parent function:

[tex]f(x)=x^2[/tex]

And it was transformed into:

[tex]g(x)=(3x)^2+6[/tex]

First, the +6 at the very end simply tells us that the graph was shifted upwards by 6 units.

For the (3x), this is essentially saying that:

[tex]f(x)=x^2[/tex]

If we use 3x for x:

[tex]f(3x)=(3x)^2[/tex]

Therefore, we essentially multiplied the x variable by 3.

In other words, this is a horizontal compression by a factor of 3.

So, our transformations are:

1) 6 units upwards

2) Horizontal compression by 3

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