How can I prove that I can use millions of dirhams wisely and start a successful business?

The range of the function g(x) = x^2 - 2, when the domain is {-2, -1, 1, 3}, is C. {-7, -2, -1, 1}.

To find the range of the function g(x) = x^2 - 2, we need to substitute each value from the given domain into the function and observe the corresponding outputs.

For x = -2, g(-2) = (-2)^2 - 2 = 4 - 2 = 2.

For x = -1, g(-1) = (-1)^2 - 2 = 1 - 2 = -1.

For x = 1, g(1) = (1)^2 - 2 = 1 - 2 = -1.

For x = 3, g(3) = (3)^2 - 2 = 9 - 2 = 7.

Thus, when the domain is {-2, -1, 1, 3}, the corresponding range values are {-7, -2, -1, 1}. Therefore, the correct option is C. {-7, -2, -1, 1}.

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Mark has the better job because he makes $0.50 more per hour than John. This is evident from the information provided, where Mark earns $7 per hour for mowing lawns while John's hourly wage is unspecified.

According to the given information, Mark's job involves mowing lawns and pays $7 per hour. On the other hand, John's job at the ice cream parlor doesn't specify his hourly wage. Since the question states that Mark has the better job, we can infer that the wage of John must be less than $7 per hour.

Therefore, by default, Mark's job is superior because he earns $0.50 more than John, as mentioned in option (a). The answer is not option (b) because it incorrectly suggests that John makes $0.50 more than Mark. The answer is also not option (c) as it states that Mark makes $6.50 per hour, which contradicts the given information. The answer is not option (d) because it assumes they make the same amount of money, which is not supported by the information provided.

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Inish must wash at least 12 cars in order to have at least $45 spending money left after putting away his savings.

To determine the minimum number of cars Inish must wash, we need to solve the inequality:

6.25x - 25 ≥ 45

Let's solve it step by step:

Add 25 to both sides of the inequality:

6.25x - 25 + 25 ≥ 45 + 25

Simplifying:

6.25x ≥ 70

Divide both sides of the inequality by 6.25:

[tex](6.25x)/6.25 ≥ 70/6.25[/tex]

Simplifying:

x ≥ 11.2

Since the number of cars cannot be a fraction or a decimal, we need to round up to the nearest whole number. Therefore, the minimum number of cars Inish must wash is 12. So, Inish must wash at least 12 cars in order to have at least $45 spending money left after putting away his savings.

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The correct answer is:p = 3 × 4

Let's write the equation for the given statement:

Randy baked 4 pies

Let the number of pies that Liza baked be p

Liza baked 3 times as many pies as Randy.

Thus, the equation for the above statement can be written as:

p = 3 × 4Simplifying the above equation we get:p = 12Thus, Liza baked 12 pies.

So, the equation that can be used to find how many pies Liza made is:

p = 3 × 4The equation can be simplified to p = 12.

Therefore, the correct answer is:p = 3 × 4

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To calculate the earnings per share, we need to divide the company's profit by the number of outstanding shares. The given information includes the company's profit of $117,667,008 and the share price of $56.97.

To determine the earnings per share, we need to know the number of outstanding shares. Since the number of outstanding shares is not provided in the given information, it is not possible to calculate the earnings per share with the given data alone.

The earnings per share (EPS) is calculated by dividing the company's profit by the number of outstanding shares. It represents the portion of the company's profit that is allocated to each outstanding share. By dividing the profit by the number of shares, we can determine how much profit is attributable to each individual share.

However, without the number of outstanding shares, we cannot calculate the exact earnings per share. The market capitalization and current share price do not provide enough information to determine the number of shares outstanding. Additional information, such as the number of shares issued by the company, is needed to calculate the earnings per share accurately.

In summary, the earnings per share cannot be determined with the given information alone. The calculation requires the number of outstanding shares, which is not provided. The earnings per share is a measure of the company's profitability allocated to each share, obtained by dividing the company's profit by the number of outstanding shares. To calculate the earnings per share accurately, the number of shares outstanding must be known.

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the weight of the crackers originally in the box was 120/23 pounds.

Let the weight of the entire box be x pounds. Now, Roger served 5/8 pound of crackers, which was 2/3 of the entire box.

Therefore, the weight of the crackers left in the box = (1 - 2/3) x = 1/3 xSince the crackers served by Roger was 5/8 pound, the weight of the crackers left in the box = x/3, then we can set up the following equation to find the value of x:5/8x + 1/3x = x

Multiplying the equation by 24 (the least common multiple of 8 and 3) on both sides gives us:

15x + 8x = 24x

Therefore, 23/24 x = 5/8 pound of crackers served by Roger.So, x = (5/8) x (24/23) pounds = 15/23 pounds

To solve the given question, let us suppose that the weight of the entire box of crackers is x pounds. Now, the given information is that Roger served 5/8 pound of crackers which was 2/3 of the entire box.

Therefore, the weight of the crackers left in the box = (1 - 2/3) x = 1/3 x.Now, we need to find out the original weight of the crackers in the box, which is the value of x.

To do that, we can set up an equation as follows:5/8x + 1/3x = xMultiplying both sides by the least common multiple of 8 and 3, which is 24, we get:15x + 8x = 24x

Simplifying further, we get:23x = 120x = 120/23 poundsThis is the weight of the entire box of crackers.

Therefore, the weight of the crackers originally in the box was 120/23 pounds.

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Based on the information given, the combination of loaves of zucchini bread and banana bread that Hayley can make is option D: 4 loaves of zucchini bread and 6 loaves of banana bread.

To determine the possible combinations, we need to ensure that Hayley has enough sugar and butter for each loaf. Let's analyze the options:

Option A: 8 loaves of zucchini bread and 4 loaves of banana bread

This combination requires a total of 8 cups of sugar and 8 sticks of butter, which exceeds Hayley's available supply.

Option B: 6 loaves of zucchini bread and 8 loaves of banana bread

This combination requires a total of 14 cups of sugar and 12 sticks of butter, which exceeds Hayley's available supply.

Option C: 2 loaves of zucchini bread and 12 loaves of banana bread

This combination requires a total of 16 cups of sugar and 16 sticks of butter, which exceeds Hayley's available supply.

Option D: 4 loaves of zucchini bread and 6 loaves of banana bread

This combination requires a total of 12 cups of sugar and 10 sticks of butter, which can be accommodated within Hayley's available supply.

Hence, option D is the correct combination based on the given quantities of sugar and butter.

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The division of x^4 + 7 by x - 3 yields a quotient of x^3 + 3x^2 + 9x + 27 and a remainder of -74.

To divide x^4 + 7 by x - 3, we use long division. The first step is to divide x^4 by x, which gives us x^3. Then, we multiply x - 3 by x^3, which gives us x^4 - 3x^3. Subtracting this from x^4 + 7, we get 3x^3 + 7. Next, we divide 3x^3 by x, resulting in 3x^2. Multiplying x - 3 by 3x^2 gives us 3x^3 - 9x^2. Subtracting this from 3x^3 + 7, we obtain 9x^2 + 7. We repeat these steps for each term, dividing 9x^2 by x, which gives us 9x. Multiplying x - 3 by 9x gives us 9x^2 - 27x. Subtracting this from 9x^2 + 7, we get 27x + 7. Finally, we divide 27x by x, resulting in 27. Multiplying x - 3 by 27 gives us 27x - 81. Subtracting this from 27x + 7, we obtain -74. Therefore, the quotient is x^3 + 3x^2 + 9x + 27, and the remainder is -74.

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In 175 graduants, 100 could be expected to seek higher education

From the question, we have the following parameters that can be used in our computation:

Rate = 4 out of every 7 graduating seniors

Graduating seniors = 175

using the above as a guide, we have the following:

Higher education seeker = Rate * Graduating seniors

Substitute the known values in the above equation, so, we have the following representation:

Higher education seeker = 4/7 * 175

Evaluate

Higher education seeker = 100

Hence, 100 could be expected to seek higher education

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the correct answer is 2.39 ft, which corresponds to option 2.

To determine the height of the cylindrical rain barrel, which has a radius of 2 feet and holds 30 cubic feet of water, we need to solve for the height using the given information and the formula for the volume of a cylinder. The answer choices provided are: 1. 58 ft, 2. 39 ft, 3. 57 ft, and 4. 78 ft.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, we are given the radius as 2 feet and the volume as 30 cubic feet.

Substituting the given values into the formula, we have:

30 = 3.14 * 2² * h

Simplifying the equation:

30 = 12.56 * h

h = 30 / 12.56

h ≈ 2.39 ft

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Answer: The given function is y = f(x), defined as follows:

f(x) = x^2 * sin(4x) + 36, if x ≠ 0

f(x) = 0, if x = 0

The function f(x) combines the quadratic function x^2 with the sinusoidal function sin(4x), and then adds a constant term of 36.

For x ≠ 0, the function f(x) is determined by the product of x^2 and sin(4x), with an additional constant term of 36.

For x = 0, the function f(x) is simply equal to 0.

The domain of the function is (-∞, ∞), meaning it is defined for all real numbers.

If you have any specific questions or require further analysis of the function, please let me know and I'll be glad to assist you.

To find the missing angles, we have to use the fact that the sum of the angles of a triangle is 180°. So, we add up the known angles, and then subtract the sum from 180°. For problem 3:Let x be the measure of the missing angle at the bottom right corner of the triangle.

We know that the other two angles are 65° and 43°.Therefore,x + 65° + 43° = 180°x + 108° = 180°x = 72°So the measure of the missing angle is 72°.For problem 4:Let y be the measure of the missing angle at the bottom left corner of the triangle. We know that the other two angles are 70° and 50°.Therefore,y + 70° + 50° = 180°y + 120° = 180°y = 60°So the measure of the missing angle is 60°.Hence, the measures of the missing angles for problems 3 and 4 are 72° and 60°, respectively.

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Marcus ends up paying $37.70 for the two shirts.

To calculate the final price, we need to follow these steps:

1. Calculate the discounted price of each shirt:

  - Shirt 1: $28.99 - 30% = $20.29

  - Shirt 2: $30.29 - 30% = $21.20

2. Apply the additional 10% off the already reduced prices:

  - Shirt 1: $20.29 - 10% = $18.26

  - Shirt 2: $21.20 - 10% = $19.08

3. Calculate the total cost of the shirts before tax:

  - Total cost = $18.26 + $19.08 = $37.34

4. Add the 6% sales tax:

  - Sales tax = 6% of $37.34 = $2.24

5. Calculate the final price including tax:

  - Final price = $37.34 + $2.24 = $39.58

Therefore, Marcus ends up paying $39.58 for the two shirts. None of the provided options match the calculated amount, so none of the given options are correct.

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The specific solutions to the equation cos θ = sin θ on the interval [0, 2π) are θ = 0, π, 2π, 3π.

To find the specific solutions to the equation cos θ = sin θ on the interval [0, 2π), we can use trigonometric identities and properties.

Let's rewrite the equation cos θ = sin θ as sin θ - cos θ = 0.

We know that sin θ = cos (π/2 - θ) from the complementary angle identity.

So, we can rewrite the equation as sin θ - sin (π/2 - θ) = 0.

Using the identity sin A - sin B = 2 sin((A - B)/2) cos((A + B)/2), we get:

2 sin((θ - (π/2 - θ))/2) cos((θ + π/2 - θ)/2) = 0.

Simplifying further:

2 sin(θ/2) cos(π/4) = 0.

Since cos(π/4) = 1/√2 is a nonzero constant, the equation reduces to:

sin(θ/2) = 0.

Now, we need to find the values of θ/2 that make sin(θ/2) = 0.

Sin(θ/2) = 0 when θ/2 = 0, π, 2π, 3π, ...

So, θ = 0, π, 2π, 3π are the specific solutions to the equation cos θ = sin θ on the interval [0, 2π).

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You will need to weigh out approximately 313 grams of flour to make the cake with 5 eggs.

To determine the amount of flour needed to make the cake with 5 eggs, we can use the given ratio of 4 eggs to 250 g of flour.

Let's set up a proportion to find the amount of flour required:

4 eggs = 250 g of flour

5 eggs = x g of flour (unknown)

We can cross-multiply and solve for x:

4 eggs * x g of flour = 5 eggs * 250 g of flour

4x = 1250

Dividing both sides of the equation by 4:

x = 1250 / 4

x = 312.5

Therefore, to the nearest gram, you will need to weigh out approximately 313 grams of flour to make the cake with 5 eggs.

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A polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.

A polynomial in standard form with a degree of 6 is written as P(x) = a₆x⁶ + a₅x⁵ + a₄x⁴ + a₃x³ + a₂x² + a₁x + a₀, where a₆ ≠ 0 and a₀, a₁, a₂, a₃, a₄, a₅, and a₆ are coefficients.

To ensure that the polynomial has only complex solutions, we need to make sure that all of its roots are complex numbers.

Complex numbers have the form a + bi, where a and b are real numbers and i is the imaginary unit (√(-1)).

By factoring the polynomial into linear factors, we can ensure that each factor (x - zᵢ) contributes a complex root.

Here, z₁, z₂, z₃, z₄, z₅, and z₆ represent complex numbers.

Since the polynomial has a degree of 6, we need six complex factors to form the polynomial.

The product of these factors will give us the desired polynomial with complex solutions.

Therefore, the polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.

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Use the expression to complete the statements: (0.5)^(10) is the exponentiation of (0.5) and 10 is the base of (0.5)^10.

In the given expression, (0.5)^(10), we have a base of 0.5 and an exponent of 10.

Exponentiation is the mathematical operation of raising a base to a certain power. In this case, we are raising 0.5 to the power of 10.

To calculate the value, we multiply the base (0.5) by itself 10 times:

(0.5)^(10) = 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5

When we perform the calculation, we find that (0.5)^(10) is equal to 0.0009765625.

Now let's move on to the second statement. The statement "10 is the base of (0.5)^10" means that the base of the expression (0.5) raised to the power of 10 is 10.

However, this statement is not correct. The base of the expression (0.5)^10 is actually 0.5, not 10. The base is the number that is raised to the exponent. In this case, 0.5 is being raised to the power of 10.

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To determine the missing term in the perfect square trinomial, we need to look at the pattern and properties of perfect square trinomials.

A perfect square trinomial has the form (a ± b)^2 = a^2 ± 2ab + b^2. In this case, we have x^2 + 40x + 100, which fits the form of a perfect square trinomial.

We can identify the missing term by finding the square of half of the coefficient of the linear term, which in this case is 40. Half of 40 is 20, and squaring 20 gives us 400.

So, the missing term is 400. The complete perfect square trinomial is:

x^2 + 40x + 400

Therefore, the missing term in the perfect square trinomial x^2 + 40x + 100 is 400.

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The correct inequality for the given condition is,

⇒ x + 75 ≥ 200

We have,

Minimum amount to be saved = $200

And, She has $75 saved.

Let x is the amount needed to reach her good.

Hence, The correct inequality for the given condition is,

⇒ x + 75 ≥ 200

Therefore, Option A is correct.

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Complete question is shown in attached image.

The price of a 40-pound bag of chicken feed would be approximately $23.98.

Yes, we can use proportional reasoning to find the price of a 40-pound bag of chicken feed based on the given information.

Let's set up a proportion to determine the price of the 40-pound bag:

50 pounds of chicken feed = $29.98

25 pounds of chicken feed = $15.49

Let's assume the price of the 40-pound bag is x dollars. We can set up the proportion as:

50 pounds / $29.98 = 40 pounds / x

To find the value of x, we can cross-multiply and solve for x:

50 * x = 40 * $29.98

50x = 1199.2

Dividing both sides of the equation by 50:

x = 1199.2 / 50

x = 23.98

Therefore, using proportional reasoning, the price of a 40-pound bag of chicken feed would be approximately $23.98.

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The length of AD, denoted as x, is less than 3/2.

Let's denote the length of AD as x.

According to the given information:

AB is 4 times as large as AD, so AB = 4x.

AC is 3 more than AD, so AC = x + 3.

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Applying this rule to triangle ABC, we can set up the following inequalities:

AD + AC > AB

x + (x + 3) > 4x

Simplifying the inequality:

2x + 3 > 4x

Subtracting 2x from both sides:

3 > 2x

Dividing both sides by 2:

3/2 > x

Therefore, the length of AD, denoted as x, is less than 3/2.

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The

length

of the playing alley is 25 meters, and the width is 5 meters.

To find the length and width of the playing alley, we can set up a

system of equations

based on the given information. Let's assume the width of the playing alley is represented by "w" meters.

According to the problem, the length of the alley is five times the width. Therefore, the length can be represented as "5w" meters.

The perimeter of a rectangle is given by the formula:

perimeter

= 2(length + width). In this case, the perimeter is given as 60 meters.

Setting up the equation, we have:

60 = 2(5w + w)

60 = 2(6w)

60 = 12w

w = 5

Substituting

the value of "w" back into the expression for the length, we find:

Length = 5w = 5(5) = 25

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Given that a telephone pole casts a shadow of 20 feet when the angle of elevation of the sun is directly away from the pole, the task is to determine the length of the pole to the nearest tenth of a foot.

We can use the concept of similar triangles to solve this problem. The telephone pole, the shadow, and the sun form two right triangles that are similar to each other. Let's assume the height of the pole is h feet. The length of the shadow is given as 20 feet. Since the angle of elevation of the sun is directly away from the pole, the angle between the shadow and the height of the pole is 90 degrees.

By considering the two similar triangles, we can set up a proportion: the length of the shadow / the height of the pole = the length of the adjacent side / the length of the opposite side. This can be written as 20 / h = tan(angle of elevation).To solve for h, we can rearrange the equation: h = 20 / tan(angle of elevation).

Since the angle of elevation is not given in the problem, we cannot calculate the exact length of the pole. However, if the angle of elevation is provided, we can substitute it into the equation to find the length of the pole to the nearest tenth of a foot.

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There were 54 adults who attended the basketball game between Chester High School and Pearson High School.

To find the number of adults who attended the game, we need to subtract the number of students from the total number of spectators. The total number of spectators at the game was 240. Among them, 9th graders accounted for 60, 10th graders accounted for 50, 11th graders accounted for 36, and 12th graders accounted for 40.

To find the number of adults, we subtract the sum of student attendees from the total number of spectators: 240 - (60 + 50 + 36 + 40) = 240 - 186 = 54.

Therefore, there were 54 adults who attended the basketball game between Chester High School and Pearson High School.

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One and one/third times four and two/fifths` is equal to `88/15`.

To find the value of `one and one/third times four and two/fifths`, lets convert these mixed numbers to improper fractions, then multiply them and simplify the result :

Step 1: Converting mixed numbers to improper fractions`one and one/third` can be written as:

$$1\frac13 = \frac{3}{3}+\frac{1}{3}=\frac{4}{3}$$`

four and two/fifths` can be written as:

$$4\frac{2}{5}=4+\frac{2}{5}=\frac{20}{5}+\frac{2}{5}=\frac{22}{5}$$

Step 2: Multiplying the improper fractions$\frac43\times\frac{22}{5}=\frac{4\times 22}{3\times 5}=\frac{88}{15}$

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The answer to the expression "One and one-third times four and two-fifths" is 6/5.

To multiply fractions, follow these steps:

Step 1: Multiply the numerators together.

Step 2: Multiply the denominators together.

Step 3: Simplify the result obtained in step 1 and step 2 by reducing it to the lowest term possible.

Let's calculate the given expression:

One and one-third can be converted to an improper fraction by multiplying the denominator 3 by 1 and adding the numerator 1 to the product, which gives 4/3.

The same can be done with four and two-fifths. 5 is multiplied by 4, resulting in 20. Then, 2 is added to 20, resulting in 22/5.

Now we have:

One and one-third times four and two-fifths = 4(4) + 2 / 5(3) = 16 + 2 / 15 = 18/15 = 6/5

Therefore, the answer to the expression "One and one-third times four and two-fifths" is 6/5.

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The tension force in the string at the top of the circle is approximately 11.39 Newtons.

To find the tension force in the string at the top of the circle, we need to consider the forces acting on the ball at that point.

At the top of the circle, the ball is moving in a circular path. The two main forces acting on the ball are the tension force (T) exerted by the string and the gravitational force (mg) acting downward.

Since the ball is moving in a circular path, there is a centripetal force acting inward toward the center of the circle. This force is provided by the tension force in the string.

At the top of the circle, the tension force and the gravitational force combine to provide the net centripetal force required for circular motion.

Therefore, we can set up the following equation:

[tex]T - mg = mv^2 / r[/tex]

where T is the tension force, m is the mass of the ball, g is the acceleration due to gravity, v is the velocity of the ball, and r is the radius of the circle.

Plugging in the values, we have:

[tex]T - (0.40 kg)(9.8 m/s^2) = (0.40 kg)(4.3 m/s)^2 / 0.80 m[/tex]

Simplifying, we find:

T - 3.92 N = 7.47 N

Adding 3.92 N to both sides, we have:

T = 11.39 N

Therefore, the tension force in the string at the top of the circle is approximately 11.39 Newtons.

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Equation BBB is obtained from Equation AAA by simplifying and combining like terms.

To get Equation BBB from Equation AAA, we can simplify the expression by combining like terms and applying the rules of algebra.

In Equation AAA, we have:

5x - 2 + x / (5x + x) = x - 4

First, we can simplify the denominator in the fraction by combining the terms 5x and x:

5x + x = 6x

So, the equation becomes:

5x - 2 + x / 6x = x - 4

Next, we can multiply both sides of the equation by 6x to eliminate the fraction:

(5x - 2 + x) * 6x / 6x = (x - 4) * 6x

This simplifies to:

(6x)(5x - 2 + x) = 6x(x - 4)

Expanding both sides:

[tex]30x^2 - 12x + 6x^2 = 6x^2 - 24x[/tex]

Combining like terms:

[tex]36x^2 - 12x = 6x^2 - 24x[/tex]

Subtracting 6x^2 and adding 24x from both sides:

[tex]30x^2 + 12x = 0[/tex]

Dividing both sides by 6x:

5x^2 + 2x = 0

Now we have Equation BBB:

[tex]5x^2 + 2x = 0[/tex]

So, Equation BBB is obtained from Equation AAA by simplifying and combining like terms.

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The Rational Zero Theorem can be used to find the zeros of a polynomial function. The Rational Zero Theorem says that if a polynomial function with integer coefficients has any rational zeros, then they will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In the given function, f(x) = 0.4x^2 - 3x + 2.2. The constant term is 2.2, and the leading coefficient is 0.4. Therefore, the possible rational zeros will have the form of p/q, where p is a factor of 2.2 and q is a factor of 0.4. The factors of 2.2 are 1, 2, and 2.2. The factors of 0.4 are 1, 2, 4, and 0.2. So, the possible rational zeros are: ±1, ±2, ±0.2, and ±2.2. To check which of these are actual zeros of the function, we can use synthetic division or long division.

However, it can be observed that none of the possible rational zeros give a remainder of zero when substituted into the function. Therefore, the function does not have any rational zeros. Long answer is not necessary as the answer can be given in a few lines.

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After comparing the two sets, we find that 6 and 12 are the common elements of A and B. Therefore, the intersection of A and B is {6, 12}.

The set A is the set of multiples of 3 between 1 and 15 inclusive which are 3, 6, 9, 12, and 15.  The set B is the set of even natural numbers up to and including 20. The set B is {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}.To find A ∩ B, we must determine the elements that A and B have in common. The common elements of A and B are 6 and 12. Thus, the intersection of A and B, A ∩ B, is {6, 12}. To find the intersection of sets A and B, we look for the common elements in the two sets. The set A is the set of multiples of 3 between 1 and 15, while the set B is the set of even natural numbers up to and including 20.

Therefore, we have A = {3, 6, 9, 12, 15} and B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}. The intersection of the two sets A and B is the set of elements they share in common. Therefore, we have to look for elements that appear in both sets. After comparing the two sets, we find that 6 and 12 are the common elements of A and B. Therefore, the intersection of A and B is {6, 12}.

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The 27th term of the arithmetic sequence with the first term [tex]\(a_1 = -13\)[/tex] and a common difference of 4 is 91.

To find the 27th term of an arithmetic sequence, we can use the formula:

[tex]\[a_n = a_1 + (n - 1)d\][/tex]

where [tex]\(a_n\)[/tex] represents the [tex]\(n\)[/tex]th term, [tex]\(a_1\)[/tex] is the first term, [tex]\(d\)[/tex] is the common difference, and [tex]\(n\)[/tex] is the term number.

Given that [tex]\(a_1 = -13\)[/tex] and the common difference [tex]\(d = 4\)[/tex], we will simply substitute these values into the given formula:

[tex]\[a_{27} = -13 + (27 - 1) \cdot 4\][/tex]

Simplifying the equation, we have:

[tex]\[a_{27} = -13 + 26 \cdot 4\][/tex]

Calculating the expression, we get:

[tex]\[a_{27} = -13 + 104\][/tex]

Finally, evaluating the sum, we find:

[tex]\[a_{27} = 91\][/tex]

Therefore, the 27th term of the arithmetic sequence with the first term [tex]\(a_1 = -13\)[/tex] and a common difference of 4 is 91.

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