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The length and width of the rectangle are 12.5 cm and 22 cm, respectively.

Let L be the length of the rectangle, and W be the width of the rectangle, then we have that:

L x W = 297 sq cm 1.

If the length is increased by 3 cm and width decreased by 1 cm, then we have that:

(L + 3) x (W - 1) = 297 + 3 sq cm -......(2).

Expand equation 2, we have:

LW + 2L - W = 300 sq cm-.......(3)

We have two equations from 1 and 3:

LW = 297 sq cm         LW + 2L - W = 300 sq cm 3.

Substitute equation 1 into equation 3.

297 + 2L - W = 300 sq cm

2L - W = 3 sq cm  

2L - W = 3 sq cm

2L = W + 3 sq cm

L = (W + 3)/2 sq cm

W x (W + 3)/2 = 297 sq cm

W² + 3W - 594 = 0 (W + 27) (W - 22) = 0

Therefore, the width of the rectangle is either 22 cm or -27 cm. Since the width cannot be negative, we discard the value of -27 cm. Therefore, the width of the rectangle is 22 cm. Finally, let's calculate the length of the rectangle:

L = (W + 3)/2 sq cm L = (22 + 3)/2 sq cm L = 25/2 sq cm L = 12.5 sq cm

Therefore, the length and width of the rectangle are 12.5 cm and 22 cm, respectively.

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Answer:

$5

Step-by-step explanation:

Let x = price of 1 bag of popcorn.

Let y = price of 1 souvenir cup

First family:

4x + 5y = 50

Second family:

6x + 4y = 54

We have a system of 2 equations with 2 variables.

4x + 5y = 50

6x + 4y = 54

We are asked for the price of 1 bag of popcorn, x, so we will eliminate y and solve for x.

Multiply both sides of the first equation by -4. Multiply both sides of the second equation by 5.

-16x - 20y = -200

30x + 20y = 270

Add the equations to eliminate y.

14x = 70

x = 70/14

x = 5

Answer: $5

Answer:

$5

Step-by-step explanation:

I took the test

hypothetically, say the popcorn WAS 5 dollars. 5x4 = 20

$50 - $20 = 30 that makes the souvenirs $6 because 30/5 = 6.

If we use this for the next family, 5x6 is 30 for the popcorn plus 6x4 for the souvenirs totals at 54 making this equation correct.

Answer:

wow thats some good information there!

Step-by-step explanation:

The complete equation using the numbers from1 to 9 will be:

2:2 = 3×3:9 = 4×4 =16.

A contrast between two numbers in arithmetic, this is referred to as a proportion. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

In the question given:

By using the digits 1 to 9 at one time each, we have to form the equation to make the equality true.

Now,

All the numbers from 1 to 9 are = 1, 2 ,3, 4, 5, 6, 7, 8 and 9

Let the proportion be = 1

Hence, the equivalent ratios are:

1:1, 2:2. 3:3

Now, according to the question the required equation will be:

2:2 = 3×3:9 = 4×4 =16.

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The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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The equilibrium price and quantity for each pair of demand and supply functions are as follows:

a. Q = 10 - 2P

To find the equilibrium, we set the quantity demanded equal to the quantity supplied:

10 - 2P = P

By solving this equation, we can determine the equilibrium price and quantity. Simplifying the equation, we get:

10 = 3P

P = 10/3 ≈ 3.33

Substituting the equilibrium price back into the demand or supply function, we can find the equilibrium quantity:

Q = 10 - 2(10/3) = 10/3 ≈ 3.33

Therefore, the equilibrium price is approximately $3.33, and the equilibrium quantity is also approximately 3.33 units.

b. Q = 1640 - 30P

Setting the quantity demanded equal to the quantity supplied:

1640 - 30P = P

Simplifying the equation, we have:

1640 = 31P

P = 1640/31 ≈ 52.90

Substituting the equilibrium price back into the demand or supply function:

Q = 1640 - 30(1640/31) ≈ 51.61

Hence, the equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In summary, for the demand and supply functions given:

a. The equilibrium price is approximately $3.33, and the equilibrium quantity is approximately 3.33 units.

b. The equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In the first paragraph, we summarize the steps taken to determine the equilibrium price and quantity for each pair of demand and supply functions. We set the quantity demanded equal to the quantity supplied and solve the resulting equations to find the equilibrium price. Substituting the equilibrium price back into either the demand or supply function allows us to calculate the equilibrium quantity.

In the second paragraph, we provide the specific calculations for each pair of functions. For example, in case a, we set Q = 10 - 2P equal to P and solve for P, which gives us P ≈ 3.33. Substituting this value into the demand or supply function, we find the equilibrium quantity to be approximately 3.33 units. We follow a similar process for case b, setting Q = 1640 - 30P equal to P, solving for P to find P ≈ 52.90, and substituting this value back into the function to determine the equilibrium quantity of approximately 51.61 units.

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Answer:

2 is irrational

3/4 is rational

pi is irrational

last on is irrational

Step-by-step explanation:

The equivalent expression that could she also use to find the total cost is  (1+0. 2)35 (option d).

To find an equivalent expression that can be used to find the total cost, we need to understand the components of the original expression. The number 1.20 represents 100% of the bill plus the 20% tip, which can also be written as 1 + 0.20. The number 35 represents the cost of the meal before the tip was added.

Using this knowledge, we can rewrite the original expression as (1 + 0.20)35, which simplifies to option D, (1+0.2)35. This expression represents the total cost of the meal plus the tip, which is equal to 120% of the original cost of the meal.

Therefore, the correct equivalent expression is D, (1+0.2)35, which represents the total cost of the meal plus tip.

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Answer:

Volume=2/6cu.ft

Step-by-step explanation:

.........................

option B

Answer:

A

Step-by-step explanation:

5/8=0.625

0.42=0.42^2

Answer:

$24.00

Step-by-step explanation:

It cost $3.00 a book.  

8 x 3 = 24

The graph is proportional.  The cost per book would be any point on the graph in the form y/x.

For example the point (4,12) would be 12/4 = 3.  This is the cost per book.  I could have used the point (6,18) would be 18/6 = 3.

A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

We have to given that;

Tiffany’s mother bought a car for $9000 five years ago.

And, She wants to sell it to Tiffany based on a 15% annual rate of depreciation.

Now, We have;

the exponential growth formula is,

⇒ y = a(1 − r)ˣ

Here, We have;

⇒ a = 9000

⇒ r = 15%

Thus, We get;

The equation correctly models the context of the problem is,

⇒ y = a(1 − r)ˣ

⇒ y = 9000 (1 - 0.15)ˣ

⇒ y = 9000 (0.85)ˣ

Therefore, We get;

A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

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Answer:

Step-by-step explanation:

Add 7x-2 to both sides and collect terms.

  2x +2 -6x +7x -2 > -4 -7x +7x -2

  3x > -6

  x > -2 . . . . . . . divide by 3

__

Solve these one at a time, and form the union of the answers.

  1 +7n ≤ 15 . . . .given

  7n ≤ 14 . . . . . . subtract 1

  n ≤ 2 . . . . . . . divide by 7

__

  -2n -2 ≤ -18 . . . given

  -2n ≤ -16 . . . . . add 2

  n ≥ 8 . . . . . . . . divide by -2

The solution is n ≤ -2 or n ≥ 8.

Answer:

B

Step-by-step explanation:

We want to simplify \(\frac{15x^{2} }{9x}\). The numerator and denominator both have a common factor of 3x, and when we simplify by 3x, we get 5x/3, or B.

Answer:

The price elasticity of demand, when using the midpoint​ formula, would be B.1.29.

How to find the price elasticity of demand ?

Price elasticity of demand = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))

where:

Q1 = initial quantity demanded = 20 units

Q2 = final quantity demanded = 15 units

P1 = initial price = $8

P2 = final price = $10

Substituting the values:

Price elasticity of demand = ((15 - 20) / ((15 + 20) / 2)) / (($10 - $8) / (($10 + $8) / 2))

= (-5 / 17.5) / (2 / 9)

= (-0.2857) / (0.2222)

= -1.2857

= 1. 29

Answer:

-4/6, -8/12, -16/24, etc. look at the picture.

Step-by-step explanation:

Brainliest Please!!! Also, Tip: show the multiple choice options.

Answer:

4/6

Step-by-step explanation:

The probability that they win the coin toss in exactly 10 of their 16 games.

What is the probability?

Probability is a mathematical concept that deals with the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur. The probability of an event A, denoted as P(A), is calculated as the number of favorable outcomes divided by the number of possible outcomes.

P(getting heads on one toss) =  1 / 2 because the coin is unbiased.

So P(getting all heads in 10 tosses).

= \((1/2)^{10}\)

=  1/ 1024

= .0009765

Hence, the probability that they win the coin toss in exactly 10 of their 16 games.

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Answer:

25

Step-by-step explanation:

So consecutive integers, just means they're separated by a value of 1. This can be generally expressed as "a, a+1" where these two values would be consecutive integers assuming "a" is an integer.

So let's express Hassan's age as the variable "x", since it's unknown. Since Cameron is older, and by definition of a consecutive integer, Cameron's can be expressed as "x+1"

So the equation we need to set up is Cameron's age + 5(Hassan's age) = 145

So we can substitute the variables we defined to express Cameron and Hassan's age: \((x+1) + 5(x) = 145\)

Distribute the 5: \(x+1+5x\)

Add like terms: \(6x+1 = 145\)

Subtract 1 from both sides: \(6x=144\)

Divide both sides by 6: \(x=24\)

Since we used "x" to represent Hassan's age, Hassan's age is 24. Since we used "x+1" to represent Cameron's age, Cameron's age is "24+1" which is just 25

The closest option is D. $-0

To determine the gain or loss on the repurchase of stock, we need to compare the repurchase price with the original sale price.

Original sale price: 500,000 shares * $50 per share = $25,000,000

Repurchase price: 12,000 shares * $40 per share = $480,000

To calculate the gain or loss, we subtract the repurchase price from the original sale price:

Gain or Loss = Original Sale Price - Repurchase Price

            = $25,000,000 - $480,000

            = $24,520,000

Since the result is a positive value, it represents a gain. Therefore, the company will recognize a gain of $24,520,000 on its income statement.

The given options do not include this exact amount, so the closest option is D. $-0-. However, it is important to note that the gain is not zero but rather $24,520,000.

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The value of opposite side of angle θ would be,

⇒ EF

Since, A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that,

A right triangle EFD is shown in figure.

And, At angle E, right angle is shown.

We know that;

The Opposite side of a angle is called perpendicular side.

Hence, The value of opposite side of angle θ would be,

⇒ EF

Thus, Option A is true.

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Answer:

6 feet

Step-by-step explanation:

Because diameter=radiusx2

                    6 feet=3 feetx2

To determine if the given set is a subspace of $P_n$, we need to check if it satisfies the three conditions for being a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.

Let's consider the set of polynomials of the form $p(t) = at^2$, where $a \in \mathbb{R}$.Firstly, let's check if the set is closed under addition. Take two arbitrary polynomials $p_1(t) = a_1t^2$ and $p_2(t) = a_2t^2$ in the set. Then, their sum is $p_1(t) + p_2(t) = (a_1 + a_2)t^2$, which is still in the set of polynomials of the form $at^2$. Therefore, the set is closed under addition.

Next, we need to check if the set is closed under scalar multiplication. Take an arbitrary polynomial $p(t) = at^2$ in the set and a scalar $c \in \mathbb{R}$. Then, $cp(t) = cat^2$, which is still in the set of polynomials of the form $at^2$. Thus

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The sample space of rolling a six-faced dice is {1, 2, 3, 4, 5, 6}.

The sample space of an experiment is the set of all possible outcomes of the experiment. In the experiment of rolling a six-faced dice, the sample space is the set of all possible values that the dice can show when it is rolled.

Since a dice has six faces, each with a distinct number (1, 2, 3, 4, 5, or 6), the sample space of the experiment of rolling a six-faced dice is {1, 2, 3, 4, 5, 6}. This means that any time the dice is rolled, it can only show one of these six values.

It's important to note that the sample space is a finite set, as there are only a limited number of possible outcomes. In this case, the sample space contains only six elements, each representing one of the faces of the dice that can show up when it is rolled.

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The value of x where by exterior angles theorem, ∠DCO equals 2·x, 69° equals the sum of ∠DCO and x° is x = 23°

The exterior angles theorem states that the exterior angle of a triangle is equal to the sum of the opposite interior angles.

The given parameters are;

Points on the circle are; ABCD

Straight lines = AOBE and DCE

Segment CO = Segment CE

∠AOD = 69°

∠CEO = x°

∠OCD = ∠ODC base angles of isosceles triangle

69° = ∠x° + ∠ODC exterior angle of a triangle

∠DOC = 180 - 2×∠ODC (Angle sum property of a triangle)

180 - 2×∠ODC + x° + 69° = 180° (Sum of angles on a straight line are supplementary)

x° + 69° - 2×∠ODC = 0

∠ODC = 2·x° (exterior angle of a triangle is equal to the sum of the opposite interior angles)

69° = x° + ∠ODC = x° + 2·x° = 3·x° (substitution property of equality)

69° = 3·x°

x = 69° ÷ 3 = 23°

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The given geometric series as shown in the question is seen to; Be converging with its' sum as 81

We are given the geometric series;

27 + 18 + 12 + 8 + ...

Now, we see that;

First term; a₀ = 27

Second Term; a₁ = 2(27/3)

Third term; a₂ = 2²(27/3²)

Fourth term; a₃ = 2³(27/3³)

Thus, the formula is;

2ⁿ(27/3ⁿ)

Applying limits at infinity gives;

2^(∞) * (27/3^(∞)) = 0

Since the  terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

S_n = a/(1 - r)

S_n = 27/(1 - (2/3)

S_n = 81

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(a) The matrix representation [T]ᴮ of the linear operator T, relative to the standard basis ᴮ = {E₁₁, E₁₂, E₂₁, E₂₂}, in M₂x₂(R) is [T]ᴮ = [[4, 0, 0, 8], [0, 4, 9, 0], [0, 0, 4, 0], [9, 0, 0, 4]].

(b) The determinant of [T]ᴮ is det([T]ᴮ) = -70.

(a) To find the matrix representation [T]ᴮ of the linear operator T, we need to determine the images of the basis vectors E₁₁, E₁₂, E₂₁, and E₂₂ under the operator T.

For E₁₁:

T(E₁₁) = 4E₁₁ + 9(E₁₁)ᵀ = 4E₁₁ + 9E₁₁ = 13E₁₁.

The coefficients of E₁₁ in the standard basis representation of T(E₁₁) are [13, 0, 0, 0].

For E₁₂:

T(E₁₂) = 4E₁₂ + 9(E₁₂)ᵀ = 4E₁₂ + 9E₂₁ = [4, 0, 9, 0].

The coefficients of E₁₂ in the standard basis representation of T(E₁₂) are [4, 0, 9, 0].

For E₂₁:

T(E₂₁) = 4E₂₁ + 9(E₂₁)ᵀ = 4E₂₁ + 9E₁₂ = [0, 4, 0, 9].

The coefficients of E₂₁ in the standard basis representation of T(E₂₁) are [0, 4, 0, 9].

For E₂₂:

T(E₂₂) = 4E₂₂ + 9(E₂₂)ᵀ = 4E₂₂ + 9E₂₂ = 13E₂₂.

The coefficients of E₂₂ in the standard basis representation of T(E₂₂) are [0, 0, 0, 13].

Combining the coefficients, we obtain the matrix representation [T]ᴮ = [[13, 0, 0, 0], [4, 0, 9, 0], [0, 4, 0, 9], [0, 0, 0, 13]].

(b) To compute det([T]ᴮ) using cofactor expansion along a row, we choose the first row. We expand along the first row using the formula:

det([T]ᴮ) = 13 × det([[0, 9, 0], [4, 0, 9], [0, 4, 0]]) - 0 × det([[4, 9, 0], [0, 0, 9], [0, 4, 0]]) + 0 × det([[4, 0, 9], [0, 4, 0], [0, 9, 0]]) - 0 × det([[4, 0, 9], [0, 9, 0], [0, 4, 0]]).

Evaluating the determinants of the 3x3 matrices, we get:

det([T]ᴮ) =

13 × (0 - 36) - 0 × (0 - 0) + 0 × (0 - 36) - 0 × (36 - 0) = -468 - 0 + 0 - 0 = -468.

Therefore, det([T]ᴮ) = -468.

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13 is the value of z from the given figure.

The properties of the triangle are:

From the given figure,

∠ABE + ∠EBC =. 180

∠EBC = 180- ∠ABE

∠EBC = 180 - 9z -----(1)

∠ECB + 115 = 180

∠ECB = 65-----(2)

IN ∆EBC

∠BEC + ∠ECB + ∠EBC = 180

4Z + 180- 9Z + 65 = 180 ---------(from eq i & ii)

-5Z = -65

Z = -65/-5y

Z = 13

The value of z from the given figure is 13.

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Complete question:

Answer:

180 degrees

Step-by-step explanation:

You can see that the shapes are the opposite of each other. This is a clue that they were rotated 180 degrees :)

The figure ABCD is rotated counterclockwise-wise about the origin by 180degrees ABCD is rotated the answer is 180 degrees.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have:

ABCD is rotated counterclockwise-wise about the origin.

As we know, It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.

The ABCD is a square on a coordinate plane shown in the picture.

From the figure,

The two shapes are in opposition to one another. That they were 180 degrees rotated is indicated by this.

ABCD is rotated counterclockwise-wise about the origin by 180degrees was ABCD rotated

Thus, the figure ABCD is rotated counterclockwise-wise about the origin by 180degrees ABCD is rotated the answer is 180 degrees.

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Answer:

No, because the Pythagorean theorem does not prove it to be a right triangle

Step-by-step explanation:

is 9² + 12² = 18²?

81 + 144 ≠ 324