A rectangle has width twice its height. If the perimeter is 12cm what are the dimensions of the rectangle?

Answer:

Step-by-step explanation:

y4−

(y2−9)(y2+9)

9

Distribute:

=y4+

−1

9

y4+9

Combine Like Terms:

=y4+

−1

9

y4+9

=(y4+

−1

9

y4)+(9)

=

8

9

y4+9

Answer:

=

8

9

y4+9

The polynomial expression is divisible by 9

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the polynomial be represented as A

Now , A = y⁴ - (y² - 9)(y² + 9)

To prove that the expression y⁴ - (y² - 9)(y² + 9) is divisible by 9 for any value of y, we can use algebraic manipulation and factorization.

First, we can simplify the expression inside the parentheses:

y² - 9 = (y - 3)(y + 3)

y² + 9 = (y + 3i)(y - 3i)

where i is the imaginary unit, i.e., i² = -1.

Substituting these expressions back into the original equation, we get:

y⁴ - (y² - 9)(y² + 9) = y⁴ - (y - 3)(y + 3)(y + 3i)(y - 3i)

Now, we can factor out (y − 3)(y + 3) from the second term:

y⁴ - (y² - 9)(y^2 + 9) = y⁴ - (y² - 9)(y² + 9) + 9(y - 3)(y + 3)

= y⁴ - (y² - 3^2)(y² + 3²)

= (y²)² - (3²)²

= (y² + 3²)(y² - 3²)

= (y² + 9)(y² - 9)

= (y + 3i)(y - 3i)(y + 3)(y - 3)

Now, we can see that the expression is equal to the product of four factors: (y + 3i), (y - 3i), (y + 3), and (y - 3). Note that either (y + 3i) and (y - 3i) or (y + 3) and (y - 3) must have the same residue modulo 3, since there are only three residues modulo 3 (0, 1, and 2) and four factors. In either case, the product of the two factors that have the same residue modulo 3 is divisible by 3, and therefore the entire expression is divisible by 3.

Moreover, since (y + 3) and (y - 3) are both odd or both even, the product of (y + 3) and (y - 3) is divisible by 8, which implies that the entire expression is also divisible by 8.

Hence , the expression y⁴ - (y² - 9)(y² + 9) is divisible by both 3 and 8 for any value of y, and therefore it is also divisible by their least common multiple, which is 9

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Answer:

$3690

Step-by-step explanation:

Let's first find what percent of the original price it is being sold for.

100%-18%=82%

The water cooler is being sold for 82% of its original price.

Let's now find 82% of 4500.

0.82*4500=3690

The selling price is $3690

Answer:

3690

Step-by-step explanation:

the original price is 4500

for decreasing or discount we use this formula x discount upo 100 multiply by the original price. so for this question if we apply the formula it will be

18upon 100 x4500. the answer comes as 810. noww we subtract the original price from the discounted price. so 4500-810=3690. comes as ur selling price

mutlak değerden + veya- çıkar.

|X-4|<3

-3 <x-4 <3

-3+4 <x <3+4

1 <x <7

The solution to the inequality |x-4| < 3 is x> 1 or x<7

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality,

|x-4| < 3.

Simplifying,

-3 < x - 4 < 3

Adding 4 to all sides,

1 < x < 7

Therefore, the solution is 1 < x < 7.

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Answer:

im sorry but google?

Step-by-step explanation:

i guess

Answer:

4.5 pi

Step-by-step explanation:

First find the area of a circle with the same radius

The diameter is 6 so the radius is 1/2 d = 1/2(6) =3

A = pi r^2

A = pi (3)^2

A = 9 pi

This is a semi circle of half a circle so the area is 1/2

A  of the semicircle

9/2 pi

4.5 pi

Answer:

The area of the base is 14.5π in²

Step-by-step explanation:

The volume of a cylinder is given by

Volume =base\:area \times height

Or

V=Bh

It was given that the volume of the cylinder is 174π in³.

The height was given as 12 inches.

We substitute to get,

174π=12B

Divide both sides by 12 to get:

B=14.5π in²

Hence the area of the base is 14.5π in²

Answer:

area of base =  14.5π in²

Step-by-step explanation:

the area of the base of a cylinder with a volume of 174π in^3 and a height of 12 inches is found by applying the formula for the volume of a cylinder:

V = πr²h

Here  the area of the base of a cylinder with a volume of 174π in³ and a height of 12 inches, and so:

V = πr²(12 in) = 174 π in³

Dividing both sides by 12 in isolates πr², which is the area of the base:

                                   174π in³

area of base = πr² = --------------- = 14.5π in²

                                     12 in

Answer:

Original side of triangle = 6 units

Step-by-step explanation:

Given:

Perimeter = 45 units

Scale factor = 2.5 (Increase)

Find:

Original side of triangle = ?

Computation:

Original Perimeter = Perimeter / Scale factor

Original Perimeter = 45 units / 2.5

Original Perimeter = 18 units

Perimeter of an equilateral triangle = 3 (Side)

18 units = 3 (Side)

Side = 6 units

Original side of triangle = 6 units

Answer:

The equation of a circle using the center [tex](2,0)[/tex] and the radius [tex]7[/tex]

[tex](x-2)^2+(y-0)^2= 49[/tex]

Step-by-step explanation:

-Directions:

To determine the following circle on a graph, you need the to look for a point that lands exactly on the center of the circle and to find the radius, you need look for a point that lands exactly on the outline of the circle and start counting from the center, to the point. Then, use both the center and the radius for the equation of a circle. After putting the center and radius on the equation of a circle, simplify the radius by the exponent [tex]2[/tex], because according to the equation of a circle, the radius is [tex]r^2[/tex].

-The equation of a circle

[tex](x-h)^2+(y-k)^2=r^2[/tex]

-Finding the center and the radius for the equation of a circle:

Center: [tex](2,0)[/tex]            Radius: [tex]7[/tex]

[tex](x-2)^2+(y-0)^2= 49[/tex]

Answer:

17.80236

Step-by-step explanation:

Look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

Area is: 1,728 inches

Perimeter is: 168 inches

Step-by-step explanation:

Area= Length times width

Perimeter= length plus length plus width plus width.

Answer:

1.728 is the perimeter. the area is 84.

Step-by-step explanation:

all you do multiply for perimeter and add for area.

Answer:

x =83

Step-by-step explanation:

supplementary angles add to 180 degrees

x+y = 180

We know y is 97

x+97= 180

Subtract 97 from each side

x+97-97= 180-97

x =83

Answer:

It is 83

Step-by-step explanation:

Supplementary is 180 degrees

180-97=83

Answer:

Step-by-step explanation:

But there is not a question?

The numerical expression shows the amount of video games Alina has left after selling half will be (4 + 8 + 6):2. Then the expression C is correct.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Alina has been collecting video games for a year. The table below shows how many games she has received over the year.

                          Amount of video games

Birthday                             4

Holidays                            8

School trades                    6

Then the total number of the video games will be

⇒ 4 + 8 + 6

At the end of the year, she went to a store and sold half of her video games.

⇒ (4 + 8 + 6) / 2

⇒ (4 + 8 + 6) : 2

Then the expression C is correct.

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Answer:

8

Step-by-step explanation:

It is in the one's place, so it is just 8x1, which is 8

Answer:

1 is the out lier

Step-by-step explanation:

if you put them in order: 1, 4, 4, 4, 5, 5, 5, 6, 7, 7, 8, 9, 9

They are in order exept for the one.

So the right answer is of option D

Look at the attached picture

Hope it will help you...

Good luck on your assignment

Answer:

The length and width of the field are 68ft and 32ft respectively

Step-by-step explanation:

Given:

Rectangular Playing Field

Perimeter. P = 200 ft

Required

The dimension of the field (Length and Width)

Let L and W represent the length and the width of the field.

From the question, L is 4 more than twice of W.

This means

L = 4 + 2W

Provided that the playing field is rectangular in shape;

We need to make use of the formula of perimeter of a rectangle.

P = 2(L + W)

Substitute 200 for P

200 = 2(L + W)

Divide through by 2

[tex]\frac{200}{2} = \frac{2(L + W)}{2}[/tex]

100 = L + W

Recall that L = 4 + 2W

Substitute 4 + 2W for L

100 = L + W becomes

100 = 4 + 2W + W

100 = 4 + 3W

Subtract 4 form both sides

100 - 4 = 4 + 3W - 4

96 = 3W

Divide both sided by 3

[tex]\frac{96}{3} = \frac{3W}{3}[/tex]

32 = W

W = 32

Recall that L = 4 + 2W

Substitute 32 for W

L = 4 + 2(32)

L = 4 + 64

L = 68

Hence the length and width of the field are 68ft anf 32ft respectively

Answer:

Exactly 1 solution

Step-by-step explanation:

First we must disrupte3y+27=12y+13

Next we switch one number to the other side27=9y+13

Now we must switch the other number14=9y

Now we must solve by dividing 14 by 9y=1.555

This is one solution, so we now have our answer.

The equation has only one solution. Then the correct option is A.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equations are given below.

3y = -6x + 9

y = -2x + 3       ...1

y = -6x + 9      ...2

From equations 1 and 2, then we have

-2x + 3 = -6x + 9

4x = 6

x = 6/4

x = 1.5

Then the value of the variable 'y' is calculated as,

y = -2x + 3

y = -2(1.5) + 3

y = - 3 + 3

y = 0

The solution of the equation y = -2x + 3 and y = -6x + 9 will be (1.5, 0). Then the equation has only one solution. Then the correct option is A.

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Answer:

74

Step-by-step explanation:

you find the volume of each one by doing length * width * height and once you find the volume of all of them which is 36, 2, 36 you add them all together and you get 74

Answer:

74 ft

Step-by-step explanation:

Volume = length x width x height

For the 1st square - 3 x 3 x 4

For the rectangle in the middle - 1 x 1 x 2

For the last big square - 3 x 3 x 4

___________________________________

3 x 3 x 4 = 36

3 x 3 x 4 = 36

1 x 1 x 2 = 2

___________________________________

36 + 36 + 2 = 74

___________________________________

The volume of this figure is 74 ft

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Answer:

2x-3>15 and 3-7x>17 =  

3-7x>17

-7x>14

x<-2

Step-by-step explanation:

Sorry this is not a proper equation. I think you meant this equation.

2x-3>15 and 3-7x>17

for this equation the answer is

3-7x>17

-7x>14

x<-2

75.34

Step-by-step explanation:

1.To find the circumference, you have to multiply the diameter times pi (3.14).

2.The radius (12) is half of the diameter

3. The diameter (12x2) is 24.

4. 24x3.14 is 75.36

So, the approx. circumference is 75.36.

Answer:

Step-by-step explanation:

Answer:75ft

Answer:

The answer is B.

Step-by-step explanation:

Answer: Yes

Step-by-step explanation: It is equal because each side has a chance of it rolling on either 1,2,3,4,5, and 6.

Answer:

45

Step-by-step explanation:

Because this is an isosceles triangle, two of the angles must be equal. Since the third angle is 90 degrees, the other two must be 90/2=45 degrees. Hope this helps!

Answer:

10x + 8 = 21

x = 1.3

Step-by-step explanation:

a)

In pentagon ABCDE,

AB = DE = 2x + 3 and BC = CD = x + 1

Perimeter of pentagon ABCDE = 21

4x + 2(2x + 3) + 2(x + 1) = 21

4x + 4x + 6 + 2x + 2 = 21

[tex] \purple {\boxed {\bold{10x + 8 = 21}}} [/tex]

b)

10x = 21 - 8

10x = 13

[tex]x = \frac{13}{10} \\ x = 1.3 \: cm [/tex]

Answer:

2 or more percents add up to 100% or one percent is 100%

Step-by-step explanation:

Answer:

First one:

4 x minus 5 y = negative 5 and 3 x + 10 y = negative 20

Step-by-step explanation:

4 x - 5 y = -5 (1)

3 x + 10 y = -20 (2)

Multiply (1) by 2 and add to (×)

8x - 10y = -10

3x + 10y = -20

11x = -30

x = -30/11 = -2.727272

x = -2.7

4(-30/11) - 5y = -5

5y = -65/11

y = -13/11 = -1.18181818

y = -1.2

Answer:

4 x - 5 y = - 5 and 3 x + 10 y = - 20

Step-by-step explanation:

4 x - 5 y = -5 (1)

3 x + 10 y = -20 (2)

Multiply (1) by 2 and add to (×)

8x - 10y = -10

3x + 10y = -20

11x = -30

x = -30/11 = -2.727272

x = -2.7

4(-30/11) - 5y = -5

5y = -65/11

y = -13/11 = -1.18181818

y = -1.2

hope this helps..

Answer:

C. The sum of the measures of the interior angles

Step-by-step explanation:

An exterior ∠ is equal to the addition of the two Δ angles not right next to it.The 2 exterior angles at each vertex are = in measure because they are vertical angles.

• The exterior angles (taken one at a vertex) always total 360º

Answer:

yes it is sas

Step-by-step explanation:

because one side is shared, they both have right angles and the other side is a given.

Answer:

SAS

Step-by-step explanation:

The sides are all equivalent so it is indeed a SAS triangle.