The volume of a rectangular prism is represented by the expression (2x ^ 3 + 7x ^ 2 - 9) the height of the prism is (2x + 3) what are expressions for the length and width of the prism?

The composite function value is 2t - t^2

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

f(x) = x^2 - 2x - 6

A composite function involves combining multiple functions to a single function

When the function f(2) is calculated, we have

f(x) = 2^2 - 2(2) - 6

Evaluate

f(2) = -6

When the function f(t) is calculated, we have

f(t) = t^2 - 2t - 6

So, we have

f(2) - f(t) = 2t - t^2

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Answer: No, it is not proportional.

Step-by-step explanation: X will be the mystery number here. So first, we want to find a common denominator. 5 times x equals 20. We want to divide 20 by 5. 20/5 equals 4. X = 4. So now we want to multiply the 4 from 4/5 by 4. 4 times 4 equals 16.

4/5 = 16/20

The height of the cylinder with radius of 7 yards and given volume of 2,923.34 cubic yards is calculated as; h = 19 yards

A cylinder is defined as a 3D solid shape that consists of two identical and parallel bases linked by a curved surface.

Now, the formula to find the volume of a cylinder is;

V = πr²h

where;

r is radius

h is height

V is volume

The parameters are;

Radius; r = 7 yards

Volume; V = 2923.34 cubic yards

Thus;

2923.34 = π * 7² * h

h = 2923.34/(49π)

h = 19 yards

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The length, in units, of the rectangle is 9 units.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Length = x

Width = x - 8

Area = 9 square units

Now,

The area of the rectangle = length x width

9 = x (x - 8)

9 = x² - 8x

x² - 8x - 9 = 0

Solve for x.

x² - 8x - 9 = 0

x² - (9 - 1)x - 9 = 0

x² - 9x + x - 9 = 0

x(x - 9) + 1(x - 9) = 0

(x - 9) (x + 1) = 0

x - 9 =0 and x + 1 = 0

x = 9 and x = -1 (rejected)

Now,

Length = 9

Width = 9 - 8 = 1

Thus,

Length is 9.

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A total of 0.7142 gallons of paint is needed to cover 250.0 square feet of walls.

The formula to calculate the number of gallons of paint required to cover a certain area is by dividing the area in square feet by the coverage of one gallon of paint, which in this case is 350 square feet. Hence, the formula becomes:

Using the input value of 250.0 square feet, we can apply this formula to calculate the number of gallons needed.

This means that to cover 250 square feet of wall, 0.714285714286 gallons of paint are required. The result is expressed as a decimal value as the area is not necessarily a multiple of the coverage of one gallon of paint.

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Complete Question:

Finish the program to compute how many gallons of paint are needed to cover the given square feet of walls. Assume 1 gallon can cover 350.0 square feet. So gallons = the square feet divided by 350.0. If the input is 250.0, the output should be:

Answer: 22 divided by 40 would equal 0.55.

The degree of the polynomial that best describes the data is (c) cubic

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

See attachment

Find the first dfference D1 between the consecutive y-values

D1:   10     28.4     56.4    94

Calculate the second difference

D1:   18.4     28     37.6

Calculate the third difference

D3:   9.6     9.6

The third difference are equal

Hence, the degree is (c) cubic

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Option(a) is the correct answer.

The inequality is:

|X+6|- 12 < 13

Here we can add 12 to both sides:

|X+6| <13 + 12

⇒|X+6| <25

⇒|X+6| < 25

We can separate it into two equations:

if x > -6, then |X+6|  = x + 6

⇒ (x + 6) < 25

⇒x < 25 - 6

⇒ x <  19

if x < -6, then |X+6|  = -(x + 6)

⇒-(x + 6) < 25

⇒ -x < 31

 ⇒ x > -31      (changing the sign)

And with those two equations, we get the:

-31 < x < 19

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There does not exists a rational number t such that  [tex]t^2 = 2[/tex].

Suppose the contrary, that there exists a rational number t such that[tex]t^2 = 2[/tex]. Then t can be written in its lowest terms as t = p/q, where p and q are integers, with q≠ 0. Then squaring both sides gives[tex](p/q)^2 = 2[/tex], so [tex]p^2 = 2q^2[/tex]. Since both [tex]p^2[/tex] and [tex]q^2[/tex] are integers, this implies that 2 is a perfect square, which it is not. Thus, there does not exist a rational number t such that[tex]t^2 = 2.[/tex]

In detail, assume t = p/q where p and q are integers and q ≠ 0. Then [tex]t^2 = 2[/tex] can be written as [tex]t^2 = 2[/tex].. This implies [tex]p^2 = 2q^2[/tex]. Since both [tex]p^2[/tex] and [tex]q^2[/tex] are integers, it implies 2 is a perfect square, which it is not. Therefore, there does not exist a rational number t such that   [tex]t^2 = 2[/tex].

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Complete question

Does there exist a rational number t such that [tex]t^2 = 2[/tex].?

Congruent figures are figures that are exactly the same size and shape, option A.

A figure is considered congruent when it is exactly the same size and shape as another figure. In other words, two figures are congruent if they can be superimposed on each other perfectly, without any stretching or distortion.

Congruence can also be defined as: if one of the figures can be obtained after a series of rigid motions of the other, the figures are said to be congruent. They both have congruent sides and angles.

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The value of the functions are;

f(0) = 1

f(1) = 3

f(-1) = 4

A function can be described as a rule, law or expression explaining the relationship between two variables.

These variables are called;

From the information given, we have that;

F(x) = 2x + 1 when x is greater than or equal to zero

Also,

f(x) = -2x - 1 when x is less than zero

Then for f(0)

f(0) = 2(0) + 1

expand the bracket

f(0) = 1

For f(1) = 2(1) + 1

expand the bracket

f(1) = 3

f(-1) = -2(-1) + 1

expand the bracket

f(-1) = 4

Hence, the values are 1, 3 and 4

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Two negative angles in radians are -π/2 and -π.

To find the points that correspond to these angles, we can use the formula: (cos θ,sin θ). For -π/2, this yields (0, -1) and for -π, this yields (-1, 0).Two negative angles in radians are -π/2 and -π.

Three positive angles in radians are 0, π/4 and π/2. For 0, the point is (1, 0); for π/4, the point is (0.707, 0.707); and for π/2, the point is (0, 1). To calculate these points, we can use the same formula, (cos θ,sin θ). For 0, this yields (1, 0); for π/4, this yields (cos π/4, sin π/4) = (0.707, 0.707); and for π/2, this yields (0, 1).

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Answer:

Student Ethan chose three lengths that could form a triangle.

Step-by-step explanation:

In order for three lengths to form a triangle, the sum of the lengths of the two shortest sides must be greater than the length of the longest side. In this case, 10 cm + 16 cm > 24 cm, and so the three lengths chosen by Ethan can form a triangle.

Answer: Ethan would be it

Step-by-step explanation: I took the k12 TFAR.

0.23 as:

23% (0.23 * 100 = 23)

A decimal is a number that expresses fractional values with a base of 10. It uses the place value system where the position of a digit determines its value relative to other digits. Decimals are written using a decimal point to separate the whole number part from the fractional part. For example, 3.14 is a decimal representation of the fractional value pi.

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K * K > N, because if the square of K is greater than N, it is not possible to add K distinct odd integers to get N.

If you square an integer (multiply it by itself), the result will always be an even number. If K is an odd number, then K * K will be an odd number plus one, which makes it even.

For example, if K = 3, then K * K = 9, which is an even number. If we take the square root of 9, we get 3, which is K. This means that the square of K will always be greater than K itself.

Now, if we want to add K distinct odd integers to get N, then N must be greater than K * K. This is because the sum of K odd numbers will always be less than K * K, and we need N to be greater than this sum.

Therefore, if K * K > N, it means that it is not possible to add K distinct odd integers to get N, because N is smaller than K * K, and the sum of K odd numbers will be smaller than N.

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Answer:

0.3

Step-by-step explanation:

To solve this, I asked, "If 7 divided by 21 is 3, then 7 divided by 22 would have little to no difference in the tenths place, right?" And that question is correct. Answering this question, the decimal place could not be greater than 5, because 7/22 is the formula for another, more accurate, albeit shorter version of pi, but backwards. 7/22 is 0.31, and 0.31's tenths place has a 1 in it, so this, according to the laws of rounding, rounds downward. Therefore, the correct answer would be 0.3.

Hope this helps!

x is not an integer, and is instead an irrational number that lies between -1/6 and 1/9.

We can solve this problem using the law of sines. The law of sines states that for a triangle, the ratio of the side opposite an angle to the sine of that angle is equal for all three angles. Therefore, we can solve for x by setting up two equations, one for angle W and one for angle X.

For angle W, the equation is:

18x - 2 = sin-1(VX/WY)

For angle X, the equation is:

12x + 2 = sin-1(VW/YX)

Since we know the ratio of the sides of the triangle, we can solve for x by substituting these values into the equations.

For angle W, we get:

18x - 2 = sin-1(VX/WY)

18x - 2 = sin-1(2/2)

18x - 2 = 0

18x = 2

x = 1/9

For angle X, we get:

12x + 2 = sin-1(VW/YX)

12x + 2 = sin-1(2/2)

12x + 2 = 0

12x = -2

x = -1/6

Since these two answers do not match, we can conclude that x is not an integer, and is instead an irrational number that lies between -1/6 and 1/9.

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The triangles are similar by SSS.

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;

The sides of first triangle are, 6, 9.6, 12.3

And, The sides of second triangle are, 2, 3.2, 4.1

Now, The ratio of corresponding sides of triangle are,

⇒ 6 / 2 = 3

⇒ 9.6 / 3.2 = 3

⇒ 12.3 / 4.1 = 3

Thus, The triangles are similar by SSS.

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The entropy of X (number of defective chips) in bits is a measure of uncertainty about the value of X.

The entropy of a random variable represents the amount of uncertainty or randomness associated with the outcome of the variable. To calculate the entropy of a discrete random variable, we need to determine the probability distribution function and use the formula:

H(X) = -Σ P(X=x) log2(P(X=x))

In this case, the random variable X represents the number of defective chips in 5 randomly chosen chips from a box of 50, with 3 defective chips. The possible outcomes are 0, 1, 2, 3, and 4, with probabilities:

P(X=0) = (47/50)^5

P(X=1) = (5 * (3/50) * (47/50)^4)

P(X=2) = (10 * (3/50)^2 * (47/50)^3) / 2!

P(X=3) = (5 * (3/50)^3 * (47/50)^2) / 3!

P(X=4) = (3/50)^4 / 4!

By plugging in the probabilities into the entropy formula, we can find the entropy in bits.

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The area of the walkway around the garden as the sum of two terms is,  2(w + l) = 2(8x + 21).

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

Let's call the width of the garden w and the length of the garden l.

Then, the area of the garden is,

wl = 6(2.5x + 1.5).

The combined area of the garden and the walkway is 7.5(4x + 5).

We can write this as wl + 2(w + l), since the walkway goes around the perimeter of the garden.

Equating the two expressions for the combined area, we have:

wl + 2(w + l) = 7.5(4x + 5)

Substituting wl = 6(2.5x + 1.5), we get:

6(2.5x + 1.5) + 2(w + l) = 7.5(4x + 5)

Expanding both sides, we get:

15x + 9 + 2w + 2l = 30x + 37.5

Solving for w + l, we get:

w + l = 15x + 28.5 - 7.5 = 8x + 21

So the area of the walkway around the garden can be expressed as 2(w + l) = 2(8x + 21).

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Principal amount in each account is $200 for Account A and $600 for Account B. Simple interest is most earned for Account B.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Simple interest is calculated by the formula,

SI = P × r × t,

where P is the principal amount, r is the interest rate and t is the time in years.

Account A :

t = 6 months = 0.5 year

S.I = $3.30

r = 3.3% = 0.033

Substituting in the formula,

3.30 = P × 0.033 × 0.5

P = 200

Principal amount in Account A is $200.

Simple interest earned in the first month = 200 × 0.033 × (1/12) = $0.55

Account B :

t = 30 months = 2.5 years

S.I = $37.50

r =  2.5% = 0.025

Substituting in the formula,

37.50 = P × 0.025 × 2.5

P = 600

Principal amount in Account B is $600.

Simple interest earned in the first month = 600 × 0.025 × (1/12) = $1.25

Account B earned more interest in the first month.

Hence Account B earned most interest in the first month with am amount of $1.25.

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Answer:

The function is translated down 2 and and to the right 3

Step-by-step explanation:

[tex]f(x)=(x-h)+k[/tex]

h = transition left or right

k = transition up or down

Answer: 3

Step-by-step explanation:

2 1/4 cups of brown sugar + ¾ cup of white sugar.=the total amount of sugar in this recipe

2 1/4 + 3/4 =3

or

2 1/4=2.25 and 3/4=.75

2.25+.75=3

The guidelines for developing the intervals are

An interval in math is calculated in terms of numbers. An interval comprises all the numbers that come between two particular numbers. This range includes all the real numbers between two numbers.

A closed interval is an interval that includes all its limit points and is denoted with square brackets. For example, [0, 1] means that greater than or equal to 0 and less than or equal to 1.

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The point at which the beam must be supported so that it may rest horizontally is; 9 meters from the left side

The parameters are;

Mass of beam = 50 kg

Length of beam = 12 m

Mass suspended at left end = 30kg

Mass suspended at right end = 40 kg

Let the support that will make the beam rest horizontally be x from the left side.

Thus, taking moment about the point x from the left side is;

30x + 50(6 - x) = 40(12 - x)

30x + 300 - 50x = 480 - 40x

20x = 180

x = 180/20

x = 9 m

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The Marginal Revenue MR(29) 11513 dollars per unit.

The velocity is v(t) = 24t² - 96t - 120.

The velocity equals zero at t = 5.

The acceleration of the particle is a(t) = 48t - 96.

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

Suppose a product's revenue function is given by R(q) = -7q² + 600q,

where R(q) is in dollars and q is units sold.

We have to determine a numeric value for the marginal revenue at 29 units

As per the question we have

R(q) = -7q² + 600q

Substitute the value of q = 29, and we get

R(29) = -7(29)² + 600(29)

R(29) = 11513

Thus, the Marginal Revenue MR(29) 11513 dollars per unit

Let s(t) = 8t³ - 48t² - 120t be the equation of motion for a particle.

To find the velocity, we need to differentiate the equation for the position of the particle, s(t).

v(t) = ds/dt = d/dt (8t³ - 48t² - 120t) = 24t² - 96t - 120

To find the t-values where the velocity is equal to zero, we need to set v(t) equal to zero and solve for t.

0 = 24t² - 96t - 120

This is a quadratic equation, and we can solve for t by factoring the GCF

(t - 5)(t + 1) = 0

(t - 5) = 0 and (t + 1) = 0

t = 5 and t = -1

So the velocity equals zero at t = 5

To find the acceleration, we need to differentiate the velocity function, v(t).

a(t) = dv/dt = d/dt (24t² - 96t - 120) = 48t - 96

So the acceleration of the particle is a(t) = 48t - 96.

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A formula for the function g(x) obtained when the graph of f(x) = 1/x is shifted down 7 units and to the right 5 units is g(x) = 1/(x - 5) - 7.

In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image or function.

In Mathematics, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.

Where:

By translating the graph of f(x) = 1/x down 7 units and 5 units to the right , we have:

g(x) = f(x - 5) - 7

g(x) = 1/(x - 5) - 7

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The length RS is equal to the length PQ and the length QR is congruent to SP.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The lines RS║PQ and QR║SP.

In triangles ΔSPQ and ΔQRS, then we have

∠SPQ = ∠QRS     (Alternate angles)

∠PQS = ∠RSQ     (Alternate angles)

SQ = SQ               (Common side)

ΔSPQ ≅ ΔQRS    (Congruent triangles)

RS = PQ and QR = SP

The length RS is equal to the length PQ and the length QR is congruent to SP.

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Answer:

1/64

Step-by-step explanation:

There is a 1/2 chance of getting heads each time, so you multiply 1/2 by itself 6 times

1/2*1/2*1/2*1/2*1/2*1/2 =