H(x)= 3x^4+2x—5/x+9x^3-7, is it a polynomial? If so write in standard form, degree, type, and leading coefficient.

Answer: 4

Step-by-step explanation: To solve the equation (x/(x-2)) + (1/5) = (2/(x-2)), we can follow these steps:

Step 1: Find a common denominator for the fractions on the left-hand side of the equation. The common denominator will be (5(x-2)).

Step 2: Rewrite the equation using the common denominator:

[(5(x)/(x-2)) + (1(x-2))/(5(x-2))] = (2/(x-2))

Step 3: Simplify the equation:

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

Step 4: Combine like terms:

(6x - 2)/(5(x-2)) = (2/(x-2))

Step 5: Cross-multiply to eliminate the denominators:

(6x - 2)(x-2) = 2 * 5(x-2)

Step 6: Expand and simplify both sides of the equation:

6x^2 - 20x + 4 = 10x - 20

Step 7: Rearrange the equation to one side:

6x^2 - 30x + 24 = 0

Step 8: Divide the equation by 6 to simplify:

x^2 - 5x + 4 = 0

Step 9: Factor the quadratic equation:

(x - 4)(x - 1) = 0

Step 10: Solve for x:

x - 4 = 0 or x - 1 = 0

x = 4 or x = 1

Therefore, the solutions for x are 4 and 1.

The ratios are not equivalent.

Considering the age of Amy and sum of their ages, Jamie is 12 years old.

Let the age of Amy be x years. Thus, the age of Jamie be (x + 5) years. Forming equation as per the age -

x + x + 5 = 19

Performing addition on Left Hand Side of the equation

2x + 5 = 19

Shifting 5 to Right Hand Side of the equation

2x = 19 - 5

Performing subtraction on Right Hand Side of the equation

2x = 14

Shifting 2 to Right Hand Side of the equation

x = 14 ÷ 2

Performing division to Right Hand Side of the equation

x = 7

The age of Amy = 7 years

The age of Jamie = 7 + 5

Performing addition

The age of Jamie = 12 years

Thus, the age of Jamie is 12 years old.

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Step-by-step explanation:

2x + 4y = 36

2 × 4 + 4y = 36

8 + 4y = 36

4y = 36 - 8

4y = 28

y = 28 ÷ 4

y = 7

The density of an object is 10490kg/m^3.

Density is like rate. It tells you how much of a thing is available for each unit other thing which contains the first thing.

Density = (Total amount available)/(total space which contains that amount)

Given;

The mass of object= 73,430 kilograms

The volume of object= 7m^3

Now

D=mass/volume

D=73430/7

D=10490

Therefore, the density will be 10490kg/m^3.

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The three (3) possible combinations are

Alex should 20 hats and 20 scarves

Let the number of scarves be x and y be the number of hats

He can make at most 20 hats and 30 scarves, but no more than 40 items altogether

x ≤ 20

y ≤ 30

x + y ≤ 40 (in time of market)

x + y ≥ 25

The possible combinations are

He should choose the third option x = 20, y = 20 this allows him to take more products to the show

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Answer:

−6x^2+7x+1

Step-by-step explanation:

1)(7x+8x-4)=15x−4

2)15x-4-(6x^2+8x-5)=−6x2+7x+1

Given that the function f is linear, f(1) = −4, and f intersects the x-axis at an angle of 150° (measured counterclockwise from the x-axis, as usual). To find a formula for f and leave the answer in exact form, let's proceed as follows: Let a be the slope of the linear function, f(x) = ax + b.

Given that the function f is linear, f(1) = −4, and f intersects the x-axis at an angle of 150° (measured counterclockwise from the x-axis, as usual). To find a formula for f and leave the answer in exact form, let's proceed as follows: Let a be the slope of the linear function, f(x) = ax + b.

At point (1, -4), we have-4 = a(1) + b ...(1)

Also, given that f intersects the x-axis at an angle of 150° (measured counterclockwise from the x-axis), we can use the angle θ that f makes with the positive x-axis to find the slope as follows: tan θ = a ...(2)

Since the angle with x-axis is 150°, the angle made with the positive x-axis is 30°.

Hence, tan 30° = 1 / √3

Therefore, a = 1 / √3. Hence, from equation (1), -4 = (1 / √3) + b ⇒ b = -4 - (1 / √3)

Thus, the equation of the linear function f is

f(x) = (1 / √3)x - (4 + 1 / √3).

Therefore, the formula for f is given by f(x) = (1 / √3)x - (4 + 1 / √3).

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The statement that best describes the composition of most foods is: "They contain mixtures of the three energy nutrients, although only one or two may predominate."

Most foods contain mixtures of the three energy nutrients, namely carbohydrates, proteins, and fats. However, the relative proportions of these nutrients can vary significantly from one food to another. In some foods, one or two of these nutrients may predominate, while others may contain relatively equal amounts of all three.

Carbohydrates are a primary source of energy for the body and can be found in various forms such as sugars, starches, and fibers. Foods like grains (e.g., rice, wheat, oats), fruits, vegetables, and legumes tend to be rich in carbohydrates. However, the specific types and amounts of carbohydrates can vary widely.

Proteins are crucial for building and repairing tissues, as well as for various metabolic functions. Foods like meat, poultry, fish, eggs, dairy products, legumes, nuts, and seeds are excellent sources of protein. Again, the protein content in different foods can vary.

Fats, also known as lipids, are an important energy source and provide essential fatty acids. Foods such as oils, butter, avocados, nuts, and fatty meats are high in fats. Like carbohydrates and proteins, the fat content in foods can differ significantly.

It's worth noting that some foods may predominantly consist of one specific nutrient. For example, pure sugar is almost entirely composed of carbohydrates, while pure oil is almost entirely composed of fats. However, most whole foods, such as fruits, vegetables, grains, meats, and dairy products, contain a mixture of these energy nutrients.

Furthermore, a balanced diet typically includes a combination of these nutrients in appropriate proportions. A varied diet that incorporates a range of foods from different food groups helps ensure an adequate intake of carbohydrates, proteins, and fats, along with other essential nutrients required for optimal health.

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Answer:

18.682

Step-by-step explanation:

Given that :

E = (-7, - 2) ; x1 = - 7 ; y1 = - 2

F = (11, 3) ; x2 = 11 ; y2 = 3

EF = √((x2 - x1)² + (y2 - y1)²)

EF = √((11 - -7)² + (3 - -2)²)

EF = √((11 + 7)² + (3 + 2)²)

EF = √(18² + 5²)

EF = √324 + 25

EF = √349

EF = 18.6815

EF = 18.682 units (3 decimal places )

Answer:

Use the Substitution method

The answer to the problem is x = 10, y = -1

Answer:

Area:1298

Step-by-step explanation:

Area of a trapezoid is found with the formula, A=(a+b)/2 x h. So, for this instance to find the area the formula would be, (62+56)/2 x 22.

Hope I could help!:)

(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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E(z),the expected value of z in which at least one member has a birthday in 12 months is (11/12)^10

Define the random variable Zi’s as

\(Z_{i}\)= 1 : if no member of the club has a birthday in the month

   = 0: otherwise   for, i =1,2, ......,12 .

Now, we have,

= P (\(Z_{i}\) =1) .

=p( no member of the club has a birthday in month i).

= p, say.

Now, there are a total of 10 members in the club and their birthdays are assumed to be independently and uniformly distributed over the 12 months of the year. So, there are 12 possible choices of months for each of the 10 members for their birthday. Thus, the total no. of exhaustive mutually exclusive and equally likely no. of ways of birthdays 12^10.

Again, if no member of the club has a birthday in month 'i'; then, all of their birthdays should be on the remaining (12 - 1) = 11 months of the year. So, there are possible choices of birthday months for each of the 10 members of the club. So, the no. of cases for the event (Zi=1) is 11^10.

So, p(\(Z_{i}\)=1) = Favorable no. of cases for Zi=1) / Total no. of all possible cases

= 11^10 / 12^10

By the classical definition of probability.

= (11/12)^10

p(\(Z_{i}\) = 1) = (11/12)^10

E(Zi).= (11/12)^10

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Answer:

Step-by-step explanation:

The relationship between the sides MN, MS, and MQ in the given regular heptagon is \(\dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}\)

The area to be planted with flowers is approximately 923.558 m²

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

Required;

The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

\(A = \dfrac{7}{4} \cdot a^2 \cdot cot \left (\dfrac{180 ^{\circ}}{7} \right )\)

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

\(\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}\)

\(s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69\)

\(The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52\)

The area of the heptagon MNSRQPO is therefore;

\(A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94\)

\(MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times 21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08\)

By sine rule, we have

\(\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}\)

\(sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})\)

\(\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}\)

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

\(Area \ of \Delta MSQ = \dfrac{1}{2} \times 43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}\)

The area of the of the garden plated with flowers, \(A_{req}\), is given as follows;

\(A_{req}\) = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

\(A_{req}\)= 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, \(A_{req}\) ≈ 923.558 m²

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Answer:

   Angle at x is 75°

Step-by-step explanation:

Data :

  Angle at A = 65°

  Angle at B = 40°

According to  the porperty of triangle we know that total interior angle a triangle has is 180° irrespect of type or size

              A + B + C = 180

      65 + 40 + C = 180

        C = 180 - 65 - 40 = 75°

Mark brainliest if you understand

..no lo sé, pero como necesito puntos, ¿sí?

The graph of the solution region for the system of inequalities can be seen on the image at the end.

The solution region refers to the region where all the points are solutions of the system of inequalities.

The system of inequalities here is:

y < -x - 2

y < (1/4)x + 2

Notice that the two lines are already graphed, and "y" is smaller than the lines, so we need to shade all the region below the two lines.

The intersection of the shaded regions will be the region of solutions, the graph can be seen in the image below.

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Answer:

4 1/2

Step-by-step explanation:

2 1/3 pounds and 2 1/6 pounds

convert the 1/3 pounds into x/6 by multiplying both numerator and denominator by 2 which equals 2/6

Then add 2+2 which gives 4 and the 1/6 and 2/6 which is equal to 3/6 which simplifies into 1/2.

4 1/2

12.23  i dont know what the awnswer is bu hahahah

Answer:

Step-by-step explanation:

1. If PQ = PQ then PQ ≅ PQ

 Reflexive Property of congruence

2. If K is between J and L, then JK + KL = JL

 Segment addition property

3. EF ≅ EF

 Definition of congruence

4. If RS = TU, then RS + XY = TU + XY

 Addition property of equality

5. If AB = DE, then DE = AB

 Symmetric property of equality

If a typical somatic cell has 64 chromosomes, each gamete of that organism is expected to have 32 chromosomes.

In sexually reproducing organisms, somatic cells are the cells that make up the body and contain a full set of chromosomes, which includes both sets of homologous chromosomes. Gametes, on the other hand, are the reproductive cells (sperm and egg) that contain half the number of chromosomes as somatic cells.

During the process of gamete formation, called meiosis, the number of chromosomes is halved. This reduction occurs in two stages: meiosis I and meiosis II. In meiosis I, the homologous chromosomes pair up and undergo crossing over, resulting in the shuffling of genetic material. Then, the homologous chromosomes separate, reducing the chromosome number by half. In meiosis II, similar to mitosis, the sister chromatids of each chromosome separate, resulting in the formation of four haploid daughter cells, which are the gametes.

Since a typical somatic cell has 64 chromosomes, the gametes produced through meiosis will have half that number, which is 32 chromosomes. These gametes, with 32 chromosomes, will combine during fertilization to restore the full set of chromosomes in the offspring, creating a diploid zygote with 64 chromosomes.

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We are given the following picture

We are given the following statements

- Line BA is congruent to line OC

- Line ON is congruent to line DA

- Angle A is congruent to angle O

If we highlight the congruencies we get

where the matching colors indicate congruency. As we can see, we have a pair of sides that are congruent and the included angle are also congruent. This is the condition for the SAS theorem to apply. Hence both triangles are congruent by the SAS theorem

Answer:

Step-by-step explanation:

answer:289/4

x² + 17x + 12 = 0

x² + 17x = -12

Take half of the second coefficient, square it, then add the result to both sides.

(17/2)² = 289/4

x² + 17x + 289/4 = -12 + 289/4

(x + 17/2)² = 241/4

Answer:

i think it might be 72.5

also theres an app called air math it could possibly help with questions you have

Step-by-step explanation:

.

P(X = k) = (1 - p)^4   for k = 0
P(X = k) = 4p(1 - p)^3   for k = 1
P(X = k) = 6p^2(1 - p)^2   for k = 2
P(X = k) = 4p^3(1 - p)   for k = 3
P(X = k) = p^4   for k = 4

Note that these probabilities add up to 1, as they should for any probability distribution.

(a) The distribution of X can be modeled as a binomial distribution with parameters n = 4 and p, where p is the probability that the friend correctly identifies a milk-first cup as milk-first. Each cup that the friend tastes can either be identified correctly (success) or incorrectly (failure), and there are 4 cups that were poured milk-first in the experiment.

(b) To find the probability mass function (PMF) of X, we need to find the probability of each possible value of X. Since X is a binomial random variable, the PMF of X is given by:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where (n choose k) is the binomial coefficient, given by:

(n choose k) = n! / (k! * (n - k)!)

where n! denotes the factorial of n.

In this case, n = 4 and there are 4 cups that were poured milk-first, so we have:

P(X = 0) = (4 choose 0) * p^0 * (1 - p)^4 = (1 - p)^4

P(X = 1) = (4 choose 1) * p^1 * (1 - p)^3 = 4p(1 - p)^3

P(X = 2) = (4 choose 2) * p^2 * (1 - p)^2 = 6p^2(1 - p)^2

P(X = 3) = (4 choose 3) * p^3 * (1 - p)^1 = 4p^3(1 - p)

P(X = 4) = (4 choose 4) * p^4 * (1 - p)^0 = p^4

Since X can only take on values between 0 and 4, the PMF of X is given by:

P(X = k) = (1 - p)^4   for k = 0
P(X = k) = 4p(1 - p)^3   for k = 1
P(X = k) = 6p^2(1 - p)^2   for k = 2
P(X = k) = 4p^3(1 - p)   for k = 3
P(X = k) = p^4   for k = 4

Note that these probabilities add up to 1, as they should for any probability distribution.

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These concepts form the basis of understanding electrical systems, allowing us to analyze and design complex circuits and devices.

Electricity is a form of energy resulting from charged particles, such as electrons and protons. Key electricity terminologies include:
1. Conductor: A material that allows the flow of electric charge with minimal resistance, typically metals like copper and aluminum.
2. Electrical circuit: A closed loop through which electric current flows, comprised of a power source, conductive path, and electrical components like resistors and capacitors.
3. Current: The flow of electric charge, measured in amperes (A). It is the rate at which charge moves through a circuit.
4. Voltage: The electric potential difference between two points, measured in volts (V). It represents the force driving electric charges through a circuit.
5. Resistance: The opposition to the flow of electric current, measured in ohms (Ω). Materials with higher resistance reduce the flow of current.
6. Watts: The unit of power, symbolized as 'W.' It represents the rate of energy transfer or conversion in an electrical circuit and is calculated by multiplying voltage (V) and current (A).
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Answer:

pandas

Step-by-step explanation:

These equations represent the total distance traveled (2400 miles) being equal to the product of the effective speed (airplane's airspeed + wind rate) and the corresponding time taken.

(a) To transform the problem into simultaneous equations, let's denote the plane's airspeed as "p" and the wind rate as "w." Since the plane's speed is affected by the wind, we can set up the following equations:

For the Washington, D.C. to San Francisco trip:

2400 = (p + w) * 7.5

For the San Francisco to Washington, D.C. trip:

2400 = (p - w) * 6

(b) To transform the problem into a matrix equation, we can write the system of equations in matrix form:

⎡ 7.5 7.5 ⎤ ⎡ p ⎤ ⎡ 2400 ⎤

⎢ ⎥ ⎢ ⎥ = ⎢ ⎥

⎣ 6 -6 ⎦ ⎣ w ⎦ ⎣ 2400 ⎦

Here, the matrix on the left represents the coefficients of the variables (p and w), the column vector on the right represents the constants (2400), and the column vector in the middle represents the variables (p and w).

(c) To find the plane's airspeed (p) and the wind rate (w), we can solve the matrix equation using matrix operations. However, since the solution requires numerical calculations, it's not feasible to provide the exact values without additional information or calculations.

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The solution to the initial value problem can be written in the form:

y(x) = (1/K)∫|sin(5x)|⁵ (3x³ - csc(5x)) dx

where K is a constant determined by the initial condition.

To solve the initial value problem and find the solution y(x), we can use the method of integrating factors.

Given: dy/dx + 5cot(5x)y = 3x³ - csc(5x), y = 0

Step 1: Recognize the linear first-order differential equation form

The given equation is in the form dy/dx + P(x)y = Q(x), where P(x) = 5cot(5x) and Q(x) = 3x³ - csc(5x).

Step 2: Determine the integrating factor

To find the integrating factor, we multiply the entire equation by the integrating factor, which is the exponential of the integral of P(x):

Integrating factor (IF) = e^{(∫ P(x) dx)}

In this case, P(x) = 5cot(5x), so we have:

IF = e^{(∫ 5cot(5x) dx)}

Step 3: Evaluate the integral in the integrating factor

∫ 5cot(5x) dx = 5∫cot(5x) dx = 5ln|sin(5x)| + C

Therefore, the integrating factor becomes:

IF = \(e^{(5ln|sin(5x)| + C)}\)

= \(e^C * e^{(5ln|sin(5x)|)}\)

= K|sin(5x)|⁵

where K =\(e^C\) is a constant.

Step 4: Multiply the original equation by the integrating factor

Multiplying the original equation by the integrating factor (K|sin(5x)|⁵), we have:

K|sin(5x)|⁵(dy/dx) + 5K|sin(5x)|⁵cot(5x)y = K|sin(5x)|⁵(3x³ - csc(5x))

Step 5: Simplify and integrate both sides

Using the product rule, the left side simplifies to:

(d/dx)(K|sin(5x)|⁵y) = K|sin(5x)|⁵(3x³ - csc(5x))

Integrating both sides with respect to x, we get:

∫(d/dx)(K|sin(5x)|⁵y) dx = ∫K|sin(5x)|⁵(3x³ - csc(5x)) dx

Integrating the left side:

K|sin(5x)|⁵y = ∫K|sin(5x)|⁵(3x³ - csc(5x)) dx

y = (1/K)∫|sin(5x)|⁵(3x³ - csc(5x)) dx

Step 6: Evaluate the integral

Evaluating the integral on the right side is a challenging task as it involves the integration of absolute values. The result will involve piecewise functions depending on the range of x. It is not possible to provide a simple explicit formula for y(x) in this case.

Therefore, the solution to the initial value problem can be written in the form: y(x) = (1/K)∫|sin(5x)|⁵(3x³ - csc(5x)) dx

where K is a constant determined by the initial condition.

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