The functions s and t are defined as follows. s (x) ニーx+5 t(x) =2x+2 Find the value of t (s (2)).

The quadratic polynomial with integer as coefficients that has four real roots including these conjugates is a² + b² - 2ab - 20a - 20b + 88 ≥ 0

One possible quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3, is:

(x - 5 - √3)(x - 5 + √3)(x - a)(x - b)

where a and b are the remaining two roots.

Expanding the first two factors using the difference of squares formula, we get:

(x - 5)² - 3

Expanding the last two factors, we get:

x² - (a + b)x + ab

Putting it all together, the quartic polynomial is:

a² + b² - 2ab - 20a - 20b + 88 ≥ 0

To ensure that a and b are also real, we can use the fact that the discriminant of a quadratic equation ax² + bx + c = 0 with real coefficients is b² - 4ac ≥ 0. Applying this to the quadratic factor in the above polynomial, we get:

(a + b)² - 4ab ≥ 0

Expanding and simplifying, we get:

a² + b² - 2ab - 20a - 20b + 88 ≥ 0

To simplify the problem, we can set a = b, since the polynomial is symmetric with respect to the roots. Then, the inequality becomes:

2a² - 40a + 88 ≥ 0

Dividing by 2 and factoring, we get:

(a - 10)² - 12 ≥ 0

This inequality is always true for real values of a, so we can choose any real value for a and set b = a to obtain a quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3.

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Answer:

Number of 2-point questions on the test as per given condition is equals to 8.

Total number of questions in a test = 28

Total points allotted for test = 100

Questions distribution as per points :

2-point questions, 4-point questions, and 5-point questions

'x' represents the 5-point questions

As per condition given,

Number of 2-point questions = 2x

Number of( 2-point  +  4-point +  5-point ) questions = 28

⇒ 2x + 4-point questions  + x = 28

⇒ 4-point questions  = 28 - 3x

Substitute the value in the given condition of the equation we get,

2(2x)+4(28-3x)+5(x) = 100

4x+112-12x+5x=100

112-3x=100

x=4

The length of each garden side is 4 ft.

Given that, Paola has 48 ft² of mulch, she wants to make three square vegetable gardens of equal sizes, we need to find the length of each garden side.

Let s be the length of the side of the gardens,

Since, she need 3 gardens,

So,

3 × side² = 48

3s² = 48

s² = 16

s = 4

Hence, the length of each garden side is 4 ft.

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The sales after 5 months is 36,000 units (since f(t) is given in thousands of units).

The given function f(t) represents the sales of a gaming product in thousands of units after t months. To find the sales after 5 months, we need to substitute t = 5 in the function f(t) and evaluate the expression. f(5) = 5(5) + 11

= 25 + 11

= 36

Therefore, the sales of the gaming product after 5 months is 36 thousand units. This means that the company has sold 36 thousand units of the gaming product within the first 5 months since the launch of the product. It also indicates that the sales are increasing by 5 thousand units every month.

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-- The given question is incomplete, the complete question is

"Let f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11. Find the sales after 5 months."

Answer:

40, 2

Step-by-step explanation:

x = number 1

y = number 2

x = 15y + 10

x + y = 42

we use the first in the second equation and get

15y + 10 + y = 42

16y = 32

y = 32/16 = 2

x + y = 42

x + 2 = 42

x = 40

Answer:

Kenyon could make a total of 7 bouquets.

Step-by-step explanation:

To find the greatest number of bouquets we need to find GCF.

We need to find GCF for 21 and 28.

The factors of 21 are: 1,3,7, and 21.

The factors of 28 are: 1,2,4,7,14, and 28

1 and 7 are the common factors between 21 and 28.

From the factors, the greatest common factor is 7.

The total number of cups of grapes and raisins include the following: 5/6 cups of grapes and raisins.

In Mathematics and Geometry, a fraction is a numerical quantity (number or numeral) that is typically expressed as a quotient (ratio) or not expressed as a whole number. This ultimately implies that, a fraction simply refers to a part of a whole number.

Based on the information provided above, the total number of cups of grapes and raisins can be calculated as follows;

Fraction = 1/2 + 2/3

Fraction = (3 + 2)/6

Fraction = 5/6 cups of grapes and raisins.

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The length of m∠WYX is equal to 12π units.

In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:

Area of sector = θπr²/360

Where:

By substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = θπr²/360

16π = θ(π/360) × 8²

Central angle, θ = 0.5π

m∠WYX = 2π - m∠WX

m∠WYX = 2π - 0.5π

m∠WYX = 1.5π

Length of m∠WYX = (1.5π)/2π × 2πr

Length of m∠WYX = (1.5π)/2π × 2π(8)

Length of m∠WYX = 12π units.

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The equation |x| = 9 has two solutions: x = 9 and x = -9. The shaded region includes all points to the left of -9 and all points to the right of 9.

The equation is given as follows:

|x| = 9

The equation |x| = 9 has two solutions: x = 9 and x = -9.

To check these solutions, we can substitute them back into the original equation and see if they satisfy it:

|x| = 9

|9| = 9 --> True

|-9| = 9 --> True

Therefore, the solutions x = 9 and x = -9 are both valid.

To graph the solution(s), we can draw a number line and mark the points x = 9 and x = -9 with closed circles (since the absolute value of x is equal to 9 at those points).

We can then shade the parts of the number line where the absolute value of x is greater than or equal to 9.

This includes all points to the right of 9 and all points to the left of -9.

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Answer

[tex]\large\textrm{There are two solutions: 9 and -9.}[/tex]

Further explanation

If we have the absolute value of x, that means x could be positive or negative.

This means that, in |x| = 9, x could be 9 or -9.

 Plug the answers into the original equation.

You should get a true statement.

because the absolute value of 9 is 9 so that's a solution

the absolute value of -9 is also 9 so that's also a solution

therefore, the solutions are 9 and -9.

The missing length is 4 in.

The volume of a rectangular prism is 32 in³.

We have,

Since the two faces of the blocks are squares.

The face that has the missing length can be considered as a square face.

i.e

The front and back faces are squares.

So,

The missing length is 4 in.

Now,

The volume of a rectangular prism.

= length x width x height

= 4 x 2 x 4

= 32 in³

Thus,

The missing length is 4 in.

The volume of a rectangular prism is 32 in³.

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The number of sides of a polygon that has 18 triangles would be 20 sides.

To determine the number of sides in a polygon consisting of 18 triangles, we can calculate the sum of the interior angles. Each triangle has total interior angle sum of 180 degrees, and since there are 18 triangles, the sum of those angles would be 18 multiplied by 180, which comes to 3, 240 degrees.

Applying the given formula for calculating the interior angles of a polygon, we obtain that (n - 2) multiplied by 180 stands for the sum of all angles within it, with n being the number of sides.

Hence, rearranging the equation gives n :

n = (sum of interior angles ÷ 180) + 2

n = (3240 ÷ 180) + 2 = 20

There must be precisely 20 sides in that particular polygon.

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2 nickels and 1 dime

4 nickels and 2 dimes

6 nickels and 3 dimes

8 nickels and 4 dimes

10 nickels and 5 dimes

We can see here that the distinct orders of light bulbs that are there if two light bulbs of the same color are considered identical is: 4,620.

We can see here that in order to find the solution, we use the permutation with repetition formula:

n! / (n1! × n2! x ... × nk!)

In order to adjust for overcounting, we divide by 3! because of the 3 red light bulbs we have. For the 2 yellow light bulbs, we divide with 2!. For the 6 pink light bulbs, we divide by 6!. This is because we are treating lights bulbs of the same color which are identical.

Therefore, the total number of distinct orders of bulbs will be:

11! / (3! × 2! × 6!) = 4,620

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Answer:

√50

Step-by-step explanation:

To solve, use distance formula.

√(9-4)^2 + (2-(-7))^2=

√5^2+5^2=

√50

Answer:

The height of the kite is 63.40 feet.

Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.

Let h represent the height of the kite. Hence, using trigonometric ratios:

sin(30) = h / 95

h = 47.5 feet

Therefore the height of the kite is 63.40 feet.

In the given system of linear equations we get,

3x - y = 4, 6x - 2y = 8 has no solution.

y = -4x - 5, y = -4x + 1 has infinitely many solutions.

- 3x + y = 7, 2x - 4y = -8 has exactly one solution.

System of linear equations can have one solution or infinitely many solution or no solution based on their form.

If two lines are parallel to each other (that is, both linear equations have same slope) then the system of linear equations has no solutions.

A system of linear equation with infinitely many solutions has both the sides of equations equal.

When a system of linear equation has exactly one value of the variables which makes the equations satisfy is said to have one solution.

Here the system of linear equations are as,

3x - y = 4

6x - 2y = 8

The two equations of the system of linear equations are parallel to each other and hence has no solution.

y = -4x - 5

y = -4x + 1

The two equations of the system of linear equations has both the sides equal to each other and hence has infinitely many solutions.

- 3x + y = 7

2x - 4y = -8

The two equations of the system of linear equations has exactly one value of x and y which satisfies the conditions and hence has one solution.

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The volume of the solid is 1922.7 in³.

The volume of a solid can be found by adding the volume of the shapes that make the solid. In this case:

Volume of solid = volume of hemisphere + volume of cylinder

Volume =  2/3πr³ + πr²h

where r = 12/2 = 6 in

height of cylinder (h) = 13 - 6 = 7 in

Volume =  (2/3 * π * 6³) + (π * 6² * 13)

Volume =  1922.7 in³

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You can use functions to complete the table as follow:

x   f(g(x))

4      2

10     4

20    6

34    8

52   10

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

We have:

f(x) = √(x+1)

g(x) = 2x - 5

When x = 4:

f(g(x)) = f(g(4))

f(g(4)) = f(2*4 - 5)

f(g(4)) = f(3)

f(g(4)) = √(3+1)      [Remember f(x) = √(x+1)]

f(g(4)) =  2

When x = 10:

f(g(10)) = f(2*10 - 5)

f(g(10)) = f(15)

f(g(10)) = √(15+1)

f(g(10)) = 4

When x = 20:

f(g(20)) = f(2*20 - 5)

f(g(20)) = f(35)

f(g(20)) = √(35+1)

f(g(20)) = 6

When x = 34:

f(g(34)) = f(2*34 - 5)

f(g(34)) = f(63)

f(g(34)) = √(63+1)

f(g(34)) = 8

When x = 52:

f(g(34)) = f(2*52 - 5)

f(g(34)) = f(99)

f(g(34)) = √(99+1)

f(g(34)) = 10

Thus, fill the values into the table to complete it.

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The degree of the polynomial 11x⁴ + 8x² + x is 4, which is the highest degree among its terms. The degrees of the terms are 4, 2, and 1 for the first, second, and third terms, respectively.

The degree of a term in a polynomial is the exponent of its variable.

In the polynomial 11x⁴ + 8x² + x, the degree of the first term 11x⁴ is 4, the degree of the second term 8x² is 2, and the degree of the third term x is 1.

The degree of the polynomial is the highest degree among its terms. In this case, the highest degree is 4, which is the degree of the first term. Therefore, the degree of the polynomial is 4.

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The triangles are similar, and the scale factor is given as follows: k = 0.8.

Similar triangles are triangles that share these two features listed as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of the missing angle is given as follows:

x + 114 + 24 = 180

x + 138 = 180

x = 42º.

Which is equals to the measure on the second triangle, hence they are similar.

The scale factor is given as follows:

k = 16/20 = 36/45 = 0.8.

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Answer: 147,456

Step-by-step explanation: 9, 18, 36, 72, 144, 288, 576, 1,152, 2,304, 4,608, 9,216, 18,432, 36,864, 73,728, 147,456

Answer: Option C.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.

Given that the diameter of the container is 24 ft, the radius (r) would be half of that, which is 12 ft.

The depth of the container (h) is given as 4 ft.

Plugging in these values into the formula, we get:

V = π(12^2)(4)

V = 3.14(144)(4)

V = 1808.6 cubic feet (rounded to the nearest tenth)

So, the storage container can hold approximately 1808.6 cubic feet of wood, rounded to the nearest tenth.

Step-by-step explanation:

The domain can be written as follows:

R - {x = n*12pi or m*4pi | n, m ∈ Z}

where pi = 3.14 and R is the set of real numbers.

Here we want to find the domain of the function:

y = tan(x/8)

The tangent is the quotient between the cosine and the sine, then we will get:

sin(x/8)/cos(x/8)

The problems of the tangent are all the values that make the denominator equal to zero, then we need to remove these.

The zeros are:

cos(x/8) = 0

We know that cos(pi/2) = cos(3pi/2)  = 0

Then:

x/8 = pi/2

x = 4pi

x/8 = 3pi/2

x = 12pi

So the domain is the set of all real numbers except the ones in the next set:

{x = n*12pi or m*4pi | n, m ∈ Z}

Where Z is the set of integers.

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As per the unitary method, each piece is 3.25 meters long by dividing the total length of the ribbon by the number of pieces.

Larry has cut a ribbon into 8 equal pieces. The total length of the ribbon is 26 m. We need to find out the length of each piece of the ribbon.

To do this, we can use the unitary method. We know that the ribbon is divided into 8 equal pieces, so each piece is 1/8th of the total length of the ribbon.

Therefore, we can find the length of each piece by dividing the total length of the ribbon by 8:

Length of each piece = Total length of ribbon / Number of pieces

Length of each piece = 26 m / 8

Length of each piece = 3.25 m

So, each piece of the ribbon is 3.25 meters long.

We used the unitary method by finding the value of one unit (1/8th of the ribbon) and then using it to calculate the value of other units (the length of each piece).

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Answer:

Step-by-step explanation: The answer is 4 all u do is add 2 to 2

Answer: 2+2=4

Step-by-step explanation: The sum of two and two results in a value of four in a quantitative analysis.

Yes, data provide convincing evident that contest has increased participation.

We have,

H₀: p = 0.12

Hₐ: p > 0.12

So, z = (p' - p)/ (√pq/n)

z = 1/6 - 0.2/ √(0.12 x 0.88) /210

z= 2.08

The test is right tailed.

So, P value = P( z> 2.08) = 0.0188

and, P- value < α, Reject H₀

Yes, data provide convincing evident that contest has increased participation.

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The ground distance of the plane is 170,138.5 ft.

The ground distance of the plane is calculated by applying trigonometry ratio as shown below;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The height attained by the plane is the opposite side, while the ground distance is the adjacent side

tan (10) = 30,000 ft/d

d = 30,000 ft/tan(10)

d = 170,138.5 ft

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