Erin and Shelby have 8 children who never finish their dinner. Tonight they are having soup. Calculate how much soup is left over after everyone has finished eating. Erin and Shelby ate all their soup. Three of their kids left 3/4 cup of soup in their bowl. Two of their kids left 1/4 cup of soup in their bowl and three of their kids left 1/2 cup of soup in their bowl. How much soup is left over?

Answer:

[tex](2x - 1)(x + 3) = [/tex]

[tex]2 {x}^{2} + 5x - 3[/tex]

A = 2, B = 5, C = -3

Answer:

The line that appears to be tangent to circle S is not actually tangent.

[tex] \sqrt{ {14}^{2} + {19}^{2} } = \sqrt{196 + 361} = \sqrt{557} [/tex]

√557 is not equal to 25.

Answer:

  not a tangent

Step-by-step explanation:

You want to know if a segment 19 units long from a point 25 units from the center of a circle of radius 14 units is a tangent.

A tangent to a circle forms a right angle with the radius to the point of tangency. You can easily check to see if the triangle shown is a right triangle by using the Pythagorean theorem.

If the triangle is a right triangle the sum of the squares of the short sides is equal to the square of the hypotenuse:

  14² +19² = 25²

  196 +361 = 625

  557 = 625 . . . . . . . . false — not a right triangle; not a tangent

__

Additional comment

The attached figure is drawn to scale. It shows line QR intersects the circle in 2 places, so is not a tangent. The angle at Q is obtuse.

Given 3 sides of a triangle, you can classify it as acute, right, or obtuse using the "form factor" computed as follows. Form the sum of the squares of the two shorter sides, and subtract the square of the longer side:

  f = 14² +19² -25² = 196 +361 -625 = -68

The interpretation is ...

The correct statement is: reducing the number of attributes in data is a data transformation subtask.

Explanation:
- Selecting the relevant data by deciding which data sources to collect is a data preparation task, not specifically a data reduction subtask.
- Converting numeric variables into discrete representations is a form of data discretization, which is a data reduction subtask.
- Normalizing observed values between 0 and 1 is a form of data scaling, which is a data transformation subtask.
- Reducing the number of attributes in data is a form of dimensionality reduction, which is also a data transformation subtask.

1. For numerical variables, normalizing the observed values between 0 and 1 is a data transformation subtask.
2. Reducing the number of attributes in data is a data transformation subtask.
In these statements, data transformation subtasks are mentioned, which involve normalizing numeric variables between 0 and 1 and reducing the number of attributes in the data. The other two statements do not fit the context of data reduction, numeric variables, or data transformation.

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Large MAD tells us that the average distance between each data value and the mean is large.

Given that;

The mean age of swimmers for all of these teams is 10.

Since, MAD is the mean absolute deviation (MAD) of a set, it tells the average distance between each data value and the mean.

Hence, It is a method to express the variance in the data set.

So, the large MAD tells us that the average distance between each data value and the mean is large.

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The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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There are many natural objects that have two or more lines of symmetry. here are two examples:

Starfish - A starfish has five arms which can be equal in shape and size, and every arm has two lines of symmetry running down the length of the arm. this means that a starfish has a total of ten strains of symmetry, with every line bisecting two fingers.

Snowflakes - Snowflakes are intricate ice crystals which can have many strains of symmetry. the precise variety of lines of symmetry depends on the form of the snowflake.

However typically, a snowflake has as a minimum six traces of symmetry that bypass via its middle factor, creating six same hands. some snowflakes could have as many as twelve strains of symmetry, making them quite symmetrical and beautiful herbal objects.

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i have no idea for answer

The derivative of F(x) is F'(x) = 2x³ - 8x² + 4x.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[1 to x²] (t³ - 4t² + 2) dt

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[1 to x²] (t³ - 4t² + 2) dt

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

F'(x) = (x²³ - 4x²² + 2) d(x²)/dx - (1³ - 4(1)² + 2) d(1)/dx   [applying the chain rule to the upper limit]

F'(x) = (x²³ - 4x²² + 2) (2x) - (1 - 4 + 2) (0)  [using the power rule for differentiation]

F'(x) = 2x(x²³ - 4x²² + 2)

F'(x) = 2x³ - 8x² + 4x

Therefore, the derivative of F(x) is F'(x) = 2x³ - 8x² + 4x.

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The equation is true for any value of x! This means that no matter how many tools Victor gives to Ilay, the ratio of their tools will never be 3:4. Therefore, there is no solution to this problem.

Let's start by using algebra to represent the given information. Let's say that the number of tools Victor has is represented by the variable "v" and the number of tools Ilay has is represented by the variable "i".

According to the problem, we know two things:

The ratio of Victor's tools to Ilay's tools is 5:2, which can be written as:

v/i = 5/2

Victor has 42 more tools than Ilay, which can be written as:

v = i + 42

Now, we want to find how many tools Victor should give to Ilay so that the ratio becomes 3:4. Let's say that the amount of tools Victor gives to Ilay is represented by the variable "x".

After giving x tools to Ilay, Victor will have v-x tools, and Ilay will have i+x tools. We want to find the value of x that makes the ratio of v-x to i+x equal to 3:4.

So, we can set up the following equation:

(v-x)/(i+x) = 3/4

Now we can substitute the expression for v and the ratio of v/i to get an equation in terms of i and x:

(i+42-x)/(i+x) = 3/4

Next, we can cross-multiply to get rid of the denominators:

4(i+42-x) = 3(i+x)

Simplifying this equation:

4i + 168 - 4x = 3i + 3x

Combining like terms:

i = 7x - 168

Now we have an equation that relates the number of tools Ilay has to the number of tools Victor gives him. We can substitute this into the equation v=i+42 to get an equation that only involves x:

v = 7x - 126

Finally, we can use this equation to find the value of x that makes the ratio 3:4.

(v-x)/(i+x) = 3/4

(7x-126-x)/(i+x) = 3/4

6x-126 = (3/4)(i+x)

6x-126 = (3/4)(7x-168+x)

6x-126 = (3/4)(8x-168)

6x-126 = 6x - 126

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The equation of the perpendicular bisector of the line segment with endpoints (-1, -8) and (7, -2) is y = (-4/3)x - 1.

The perpendicular bisector of a line segment is the line that passes through the midpoint of the segment and is perpendicular to it. To find the midpoint of the segment with endpoints (-1, -8) and (7, -2), we can use the midpoint formula: ((x₁ + x₂)/2, (y₁ + y₂)/2)

By using given the values, we get :

((-1 + 7)/2, (-8 + (-2))/2)

= (3, -5)

So the midpoint is (3, -5).

To find the slope of the line segment connecting the two endpoints. We can use the slope formula: (y₂ - y₁)/(x₂ - x₁)

By using the given values, we get:

(-2 - (-8))/(7 - (-1))

= 6/8

= 3/4

So the slope of the line segment is 3/4.

To find the slope of the perpendicular bisector, we need to find the negative reciprocal of the slope of the line segment. The negative reciprocal of 3/4 is -4/3.

To find the equation of the line in point-slope form, we can use:

y - y₁ = m(x - x₁)

y - (-5) = (-4/3)(x - 3)

y + 5 = (-4/3)x + 4

y = (-4/3)x - 1

Therefore, the equation of the perpendicular bisector of the line segment with endpoints (-1, -8) and (7, -2) is y = (-4/3)x - 1.

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Answer:

it have the property of parallelogram ,

To find the distance between objects 1 and 2 for which the net force on object 2 is zero, we need to use the equation for gravitational force:

F = G (m1m2 / d^2)
where F is the gravitational force between two objects, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.
Let's start by finding the mass of each object. We are given that:
mass of object 1 = 7 x mass of object 2
mass of object 1 = 4 x mass of object 3
We can use these equations to solve for the masses of the objects:
mass of object 2 = (1/7) x mass of object 1
mass of object 3 = (1/4) x mass of object 1
Now let's consider the gravitational force between objects 1 and 2. We want to find the distance at which the net force on object 2 is zero. This means that the gravitational force between the two objects must be equal and opposite to any other forces acting on object 2. Mathematically, we can express this as:
F_gravity = - F_other
where F_gravity is the gravitational force between objects 1 and 2, and F_other is the force acting on object 2 in the opposite direction.
We don't know what the other force is, but we do know that its magnitude must be equal to the gravitational force between the two objects. So we can set up an equation:
G (m1m2 / d^2) = G (m2m_other / x^2)
where x is the distance between objects 1 and 2 at which the net force on object 2 is zero.
Now we can plug in the masses we found earlier:
G (7m2 x m_other / x^2) = G (m2m_other / x^2)
Simplifying this equation, we get:
7m2 = m_other
So the other mass is equal to seven times the mass of object 2.
Now we can plug in the masses and solve for x:
G (7m2^2 / x^2) = G (m2 x 7m2 / x^2)
Simplifying this equation, we get:
x = distance between objects 1 and 2 = sqrt(7) x distance between objects 2 and 3
So the distance between objects 1 and 2 for which the net force on object 2 is zero is the square root of seven times the distance between objects 2 and 3.

To find the distance between objects 1 and 2 for which the net force on object 2 is zero, you need to consider the mass of each object and their gravitational forces.
Let's denote the mass of object 1 as M1, object 2 as M2, and object 3 as M3. According to the information given, we have:
M1 = 4M3 and M1 = 7M2.
Next, let's denote the distance between objects 1 and 2 as D12, between objects 1 and 3 as D13, and between objects 2 and 3 as D23.
For the net force on object 2 to be zero, the gravitational forces between objects 1 and 2, and objects 2 and 3 must be equal and opposite. Using the gravitational force equation:
F12 = (G * M1 * M2) / D12^2, and F23 = (G * M2 * M3) / D23^2.
Where G is the gravitational constant.
For net force on object 2 to be zero:
F12 = F23.
(G * M1 * M2) / D12^2 = (G * M2 * M3) / D23^2.
Now, substitute M1 and M3 in terms of M2:
(G * 7M2 * M2) / D12^2 = (G * M2 * (1/4) * 7M2) / D23^2.
Simplify the equation:
7 / D12^2 = (7/4) / D23^2.
Now, you would need more information such as the distance between object 1 and object 3 (D13) or other givendistances to find the exact values of D12 or D23. But with this equation, you have set up the relationship between the distances required for the net force on object 2 to be zero.

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The value of the test statistic is approximately -3.02. this value represents how far the sample mean is from the hypothesized population mean in terms of the standard error of the mean.

The test statistic can be calculated using the formula: t = (X - μ) / (s / √n)

where X is the sample mean (4.0 psi), μ is the hypothesized population mean (4.1 psi), s is the population standard deviation (0.7 psi), and n is the sample size (150). Plugging in the values, we get: t = (4.0 - 4.1) / (0.7 / √150) ≈ -3.02

Therefore, the value of the test statistic is approximately -3.02. This value represents how far the sample mean is from the hypothesized population mean in terms of the standard error of the mean.

A negative value indicates that the sample mean is lower than the hypothesized population mean. A value of -3.02 is quite far from zero, suggesting that the engineer's claim that the valve performs to specifications may be false.

The next step would be to determine the corresponding p-value and compare it to the level of significance to make a decision about rejecting or failing to reject the null hypothesis.

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Answer:

-√36

Step-by-step explanation:

The first (approx. 3.567) is obviously irrational, as it continues forever; the decimal values do not end.

The next (√18) is approx. 4.243 and is irrational.

The next (π/3) is irrational because it involves an irrational number, π.

The last (-√36) is -6 and is therefore rational.

The organs of static equilibrium, also known as the maculae, are located within two expanded chambers within the vestibule called the utricle and saccule.

Utricle and saccule are filled with a gel-like substance containing tiny calcium carbonate crystals called otoliths. When the head moves, the otoliths shift and stimulate the hair cells within the maculae, which send signals to the brain regarding the body's position and movement. This allows us to maintain balance and stability, especially when standing still or moving in a straight line. Any disruptions or damage to the maculae can result in issues with balance, dizziness, and vertigo.

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If 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine,  the percent by mass of I in the sample is 75%. So, correct option is D.

The percent by mass of iodine in the sample can be calculated by dividing the mass of iodine by the total mass of the sample and then multiplying by 100.

Mass of iodine = 300 g

Mass of cesium = 100 g

Total mass of sample = 300 g + 100 g = 400 g

Percent by mass of iodine = (mass of iodine / total mass of sample) x 100

= (300 g / 400 g) x 100

= 0.75 x 100

= 75%

Therefore, the correct answer is D. 75%. This means that 75% of the total mass of the sample is iodine. It is important to note that the percent by mass of cesium in the sample is 25% because the sum of the percent by mass of all components in a sample must equal 100%.

So, correct option is D.

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The sum of the squares of the first 5 terms in the Fibonacci sequence is equal to [tex]Fn - Fn+1[/tex] , but the result is not true for n[tex]= 6[/tex] .

The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding numbers, starting from [tex]0[/tex] and [tex]1.[/tex]

To show that the sum of the squares of the first n terms in the Fibonacci sequence is equal to[tex]Fn - Fn+1[/tex], we can use mathematical induction.

Inductive step:

Assume that the result is true for some value of n, and consider the case where n [tex]= 5.[/tex]

[tex]0, 1, 1, 2, 3[/tex]

The fifth and sixth terms of the Fibonacci sequence are:

[tex]F5 = 5[/tex] and [tex]F6 = 8[/tex]

So,  for n = 5 is:

[tex]Fn - Fn+1[/tex]

[tex]F5 - F6 = 5 - 8 = -3[/tex]

We can also calculate[tex]Fn - Fn+1[/tex] for n = 6 using the values of F6 and F7:

[tex]F6 - F7 = 8 - 13 = -5[/tex]

So, we have:

[tex]Fn - Fn+1 = -F(n+1)[/tex]

[tex]15 = -3[/tex]

Which is not true, so the assumption that the result [tex]Fn - Fn+1,[/tex] is true for n = 5 leads to a contradiction. Therefore, we can conclude that the result is not true for n[tex]= 6[/tex].

Therefore, we have shown that the sum of the squares of the first [tex]5[/tex] terms in the Fibonacci sequence is equal to but the result is not true for n[tex]= 6.[/tex]

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The action which best demonstrates the fairness is (c) manager hires an "older-woman" based on her "job-performance" for security position even though men have traditionally held this job.

This action demonstrates fairness because the manager made the hiring decision based on job performance, rather than on any gender or age biases.

The fact that the job was traditionally held by men, the manager recognized that the older woman was the best candidate for the position based on her qualifications and abilities.

This shows that the hiring-process was fair and unbiased, and that the manager was focused on selecting the most qualified candidate for the job, regardless of any stereotypes.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Which action demonstrates fairness?

(a) A referee position is opened at a sport organization but only men are told about the position since traditionally men perform the job.

(b) A man's application to work as a make-up artist at a department store is passed over even though he has more experience.

(c) A manager hires an older woman based on job performance for a security position even though men have traditionally held the job.

(d) A twenty-five-year-old with a strong Hispanic accent is told he is ineligible to apply for a public speaking position even though he is overqualified.

The inequality that determines the number of miles that Eddie can travel is $1.75 + $0.25x  ≤ $15 (first option).

The first step is to determine the inequality sign that would be used.

Here are inequality signs and what they mean:

The sign that would be used is (≤) less than or equal to

The form of the inequality is:

[flat fee + (cost per mile x number of miles)] ≤ total amount she has

$1.75 + ($0.25 × x) ≤ $15

$1.75 + $0.25x  ≤ $15

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The area of the region is 25/3 square units.

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.

First, let's find the equation of the tangent line to the parabola at the point (5,100). The derivative of y = 4x² is y' = 8x, so the slope of the tangent line at x = 5 is y'(5) = 8(5) = 40. Thus, the equation of the tangent line is y - 100 = 40(x - 5), or y = 40x - 100.

To find the points of intersection of the parabola and the tangent line with the x-axis, we need to solve the equations y = 4x² and y = 40x - 100 for y = 0:

4x² = 0 => x = 0

40x - 100 = 0 => x = 2.5

So the region we want to find the area of is bounded by the x-axis and the curves y = 4x² and y = 40x - 100, with x ranging from 0 to 2.5.

To find the area, we need to integrate the difference between the two functions with respect to x:

A = ∫[0, 2.5] (40x - 100 - 4x²) dx

A = [20x² - 4/3 x³]0 to 2.5

A = 20(2.5)² - 4/3 (2.5)³ - 0

A = 25/3

Therefore, the area of the region is 25/3 square units.

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It is to be noted that the probability of a randomly picked whole carton of grade A eggs to weight more than 850gm is 10.2%

Let W represent the weight of a fun carton of eggs chosen at random. W is distributed normally, with a mean of 840 grams and a standard variation of 7.9 grams.

The z-score for a weight of 850gms is:

z = 850 - 840 / 7.9 ≈ 127.

The standard normal probability table reveals that

P (W > 850) = P( Z > 1.27) ≈ 1-  0.8980 = 0.1020.

As a result, it is acceptable to assert that the likelihood of a randomly picked whole carton of grade A eggs weighing more than 850 grams is  10.2%.

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If 3 over 5 of the family income is spent on food, The amount spent on  food is $2118.6

If their total income is 3531 dollar and 3/5 is spend on food, we find the sum total of the amount of money spend on food by multiply the fraction or ratio to the total income the family gets monthly.

Therefore; Amount spent on food = monthly income x 3/5

It becomes $3531 x 3/5 or 3531 x 0.6

= $2118.6

It means that 2/5 of the income will be 2/5 x  $3531  = $1 412.4

$2118.6 + $1412.4 = 3531

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The y-intercept of the straight line crosses the x-axis at (3,0) and the y-axis at (0,2) is 2.

The point of the line is the x-axis at (3,0) and the y-axis at (0,2)

Using two-point line equation

[tex](y_{2} - y) = m(x_{2} - x)[/tex]

m = slope = change in y / change in x

m = 2-0/0-3

m = -2/3

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

3(2-y) = -2(-x)

6 - 3y = 2x

-3y = 2x - 6

y = -2/3 x + 2

On comparing equation with y = mx + c

c in y intercept we get c = 2

Hence y - intercept = 2

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Answer:

4) 24

Step-by-step explanation:

Diagonals of a rectangle are congruent and bisect each other.

AE = x + 2

BD = 4x - 16

2AE = BD

2(x + 2) = 4x - 16

2x + 4 = 4x - 16

20 = 2x

x = 10

AC = BD = 4x - 16 = 4(10) - 16 = 40 - 16 = 24

Answer: 4) 24

The market share of the four remaining companies is 29% to the nearest percent.

The market share the four remaining companies have, to the nearest percent is calculated as follows;

The revenue of the other four companies is calculated as;

R = $4,120,500 - $2,940,000

R = $1,180,500

The market share of the four remaining companies is calculated as follows;

market share = ($1,180,500 / $4,120,500) x 100

market share = 28.65% ≈ 29%.

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To divide the polynomial p(x) by d(x), we can use long division or synthetic division. Let's say we choose to use long division.

First, we need to write the polynomials in descending order of degree, with any missing terms filled in with zeros. Let's say the polynomials are:

p(x) = 3x^3 - 5x^2 + 2x + 4
d(x) = x - 2

Then, we set up the long division like this:

         3x^2 + x + 4
   x - 2 | 3x^3 - 5x^2 + 2x + 4

We divide the first term of p(x) by the first term of d(x), which gives us 3x^2. We write this above the division bar and multiply it by d(x), which gives us 3x^3 - 6x^2. We subtract this from p(x), bringing down the next term:

         3x^2 + x + 4
   x - 2 | 3x^3 - 5x^2 + 2x + 4
         - 3x^3 + 6x^2
             ----------
              -11x^2 + 2x

We repeat the process with the next term, dividing -11x^2 by x to get -11x, writing this above the division bar, and multiplying it by d(x) to get -11x + 22. We subtract this from -11x^2 + 2x, bringing down the next term:

         3x^2 + x + 4 - 11/(x-2)
   x - 2 | 3x^3 - 5x^2 + 2x + 4
         - 3x^3 + 6x^2
             ----------
              -11x^2 + 2x
              + 11x^2 - 22
              ----------
                     -20

Since we have no more terms to bring down, our remainder is -20. Therefore, the quotient p(x)/d(x) is:

p(x)/d(x) = 3x^2 + x + 4 - 11/(x-2) - 20/(x-2)^2

We can express this in the form p(x) d(x) by multiplying both sides by d(x):

p(x) = d(x) (3x^2 + x + 4 - 11/(x-2) - 20/(x-2)^2)
To answer your question, we'll first need the specific polynomials for p(x) and d(x) that you'd like to divide. However, I can still guide you through the general steps to perform the division and express the quotient.

1. Choose either synthetic or long division, depending on your preference and the complexity of the polynomials.
2. Divide p(x) by d(x) using the chosen method. Make sure to follow the steps of the division process carefully to obtain the correct quotient and remainder.
3. Once the division is complete, express the quotient p(x)/d(x) in the form p(x) = d(x) * q(x) + r(x), where q(x) is the quotient and r(x) is the remainder.

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The correct expansion of (-4x + 9)² is 16x² - 72x + 81.

We have,

Step 1: Start with the expression (-4x + 9)².

Step 2: To expand this expression, we use the formula for the square of a binomial: (a - b)² = a² - 2ab + b².

Step 3: In this case, a is -4x and b is 9.

Applying the formula, we have:

(-4x + 9)² = (-4x)² - 2(-4x)(9) + (9)².

Step 4: Simplify each term in the expansion:

(-4x)² = 16x² (square the first term).

-2(-4x)(9) = 72x (multiply -2, -4x, and 9 together).

(9)² = 81 (square the second term).

Step 5: Combine the simplified terms:

(-4x + 9)² = 16x² - 72x + 81.

Thus,

The correct expansion of (-4x + 9)² is 16x² - 72x + 81.

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We can see here that values will:

c = 6

d = 2.

A square is a geometric shape with two dimensions that has four equal sides and four equal 90 degree angles. It is a particular kind of quadrilateral and a regular polygon, which means that all of its sides and angles are congruent (equal in length).

We can see that using Pythagoras Theorem, a² = c² + d²

Triangle existence theorem = c + d > a

From the question, we see that: 6 < a < 7

Thus, 36 < c² + d² < 49

c + d > 7

c = 6, d = 2

Whenever the conditions are met, many values can still fit in.

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The pocket money that Sam had to start with is: £24

Let the amount of money he had at the beginning be x.

He spent 1/4 of the money on magazines. Thus:

Amount left = ³/₄x

He spent ²/₃ of what he had left on a present. Thus< he spent:

²/₃ * ³/₄x = ¹/₂x

Amount left = ³/₄x - ¹/₂x

He had £6 left. Thus:

³/₄x - ¹/₂x = 6

9x - 6x = 72

3x = 72

x = £24

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The surface area of the composite solid is 286 square feet.

To calculate the surface area of this composite solid,

Find the areas of each individual shape and then add them up.

The rectangular prism has a surface area of,

2(11x2 + 11x2 + 2x11)

= 2(22 + 22 + 22)

= 2(66)

= 132 square feet.

The square pyramid has a base area of,

11x11 = 121 square feet.

The area of each triangular side can be found using the formula,

1/2 x base x height.

The base of each triangle is 11 feet (since it is the same as the length of the base of the pyramid), and the height of each triangle is 7 feet.
So each triangle has an area of 1/2 x 11 x 7 = 38.5 square feet.

There are four triangular sides, so the total area of the triangular sides is 4 x 38.5 = 154 square feet.

Adding the surface area of the rectangular prism and the square pyramid, we get

132 + 154 = 286 square feet.

Therefore, the correct answer is 286 square feet.

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