FREE BRAINLIEST IF CORRECT: Write the following without the absolute value sign: |a^2| if a>0

Answer:

9x^3+6x^2+21x-8

Step-by-step explanation:

(3x-1) (3x ^ 2 + 3x + 8) =3x(3x ^ 2 + 3x + 8) +(-1)(3x ^ 2 + 3x + 8)  =9x^3+9x^2+24x-3x^2-3x-8 = 9x^3+6x^2+21x-8

Answer:

\(\huge\boxed{\sf 9x^3+6x^2+21x-8}\)

Step-by-step explanation:

= \((3x-1)(3x^2+3x+8)\)

\(Expand\)

\(= 3x(3x^2+3x+8)-1(3x^2+3x+8)\\\\Multiply\\\\=9x^3+9x^2+24x-3x^2-3x-8\\\\Combine \ like \ terms\\\\= 9x^3+9x^2-3x^2+24x-3x-8\\\\= 9x^3+6x^2+21x-8\\\\\rule[225]{225}{2}\)

Answer:

1 minute and 44 seconds... 1 minute and 37 seconds. a pattern of -7 seconds

The score located at -3sx (standard deviation) from the mean in a normal distribution is 75. This is because in a normal distribution, the mean is the center and -3sx is three standard deviations away from the mean. Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

To further explain, a normal distribution is a probability distribution characterized by a symmetrical bell-shaped graph, and it's determined by the mean and standard deviation of the dataset. In this case, the mean is 120 and the standard deviation is 15. Therefore, the data would have an average score of 120 and an average range of 30 (15 plus and minus from the mean). If the score is located at -3sx, it would be three standard deviations away from the mean and the score would be 75.

Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

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Answer:

2660 miles

Step-by-step explanation:

All you need to do is find 33% of 2000 then add the answer to 2000.

33% of 2000= 660

2000+660= 2660

Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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The correct answer choice for the MPC (marginal propensity to consume) when the multiplier is 6 is not provided among the options A. 0.16, B. 0.83, C. 0.71, or D. 0.86.

The MPC is calculated as the ratio of the change in consumption to the change in income. When the multiplier is given, we can derive the MPC using the formula MPC = 1 / (1 + MPC). In this case, the multiplier is stated to be 6.

To find the corresponding MPC, we can solve the equation 1 / (1 + MPC) = 6 for MPC.

Rearranging the equation, we have 1 + MPC = 1 / 6. Subtracting 1 from both sides, we get MPC = 1 / 6 - 1 = -5 / 6.

The result MPC = -5 / 6 implies a negative MPC, which does not align with any of the given answer choices.

Additionally, all the answer choices provided (0.16, 0.83, 0.71, and 0.86) are positive values, further confirming that none of them represents the correct MPC when the multiplier is 6.

Therefore, the correct answer choice for the MPC when the multiplier is 6 is not listed among the options A. 0.16, B. 0.83, C. 0.71, or D. 0.86.

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It can be inferred that there is a statistically significant result if the confidence interval excludes the value of zero effect.

Confidence Interval;

In statistics, confidence is another word for probability. For instance, if you create a confidence interval with a 95% confidence level, you can be sure that 95 times out of 100 the estimate will fall between the upper and lower values indicated by the confidence interval.

Therefore,

The confidence level is 95% if your significance level is 0.05. The hypothesis test is statistically significant if the P value is lower than your significance (alpha) level. The findings are statistically significant if the confidence interval excludes the null hypothesis value. 0

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Answer:

3x² – 5x + 2 is a polynomial because:

Exponents are whole numbers, and the expression has at least 1 term.

Exponents other than whole numbers can take the form of variables in denominators, and roots which we don't want.

The percent of the variance in the dependent variable unexplained by the independent variable is 81%

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively correlated, the value either rises or falls together.

9 percent of the variance is explained by the independent variable if the correlation coefficient is 0.3.

The correlation coefficient is therefore represented as follows:

\(r = 0.3\)

The explained variance is found using the following formula:

\(R^{2} = r^{2} \\R^{2} = (0.3)^{2} \\R^{2} = (0.3)*(0.3)\\R^{2} = 0.9\)

Thus, 81% of the variance remains unexplained by variations in the independent variable.

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Answer:

a) pentagon

b) concave

c) not regular

Step-by-step explanation:

a) this polygon has 5 sides, known as a pentagon

b) it is concave because you can connect the top two vertices with a diagonal which will be outside the shape

c) a regular polygon is equilateral (all sides equal) but the markings show that is not the case with this shape

The expression we have to evaluate is:

and we need to substitute the value of x = 8:

Next, we solve the multiplication between 2 and 8, which is equal to 16:

And finally we add and substract the corresponding terms:

Answer: 22

The volume of the given solid is πa³/4 cubic units.

Given that the base of a solid is a quadrant of a circle of radius a and each cross-section perpendicular to one edge of the base is a semicircle whose diameter lies in the base.

To find the volume of the solid, we'll integrate the area of the cross-section over the height of the solid.

Let us consider a cross-section with thickness dx at a distance x from the vertex of the quadrant, as shown in the figure below.

Here, the diameter of the semicircle forming the cross-section is 2(x + a).

Therefore, the radius of the semicircle is (x + a).

Area of the cross-section = Area of the semicircle= π[(x + a)²]/2

Volume of the solid = ∫Area dx from 0 to a= ∫π[(x + a)²]/2 dx from 0 to a= π/2 ∫(x² + 2ax + a²) dx from 0 to a= π/2 [(a³/3 + 2a²/2 + a³/2) - (0)] = πa³/4 cubic units

Therefore, the volume of the given solid is πa³/4 cubic units.

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Answer:

x ≤ 39/5

Step-by-step explanation:

To solve for the inequality, isolate the x variable.

5x - 7 ≤ 32​

Add 7 to both sides.

5x ≤ 39

Divide both sides by 5.

x ≤ 39/5

Creo que es 3,300, si aunque no entiendo bien

The correct graph that models this exponential decay would show a decreasing trend as x (the number of years) increases. we need to consider the information given regarding its decrease in value.

The piece of machinery decreases in value by 22.5% each year. This means that its value after one year is \(100\% - 22.5\% = 77.5\%\) of its original value. In other words, its value is 0.775 times its original value.

To model the value of the machinery after x years, we need to consider the exponential decay function. The general form of an exponential decay function is:

y = \(a(1 - r)^x\)

Where:

- y represents the value after x years.

- a represents the initial value.

- r represents the decay rate (expressed as a decimal).

In this case, the initial value (a) is $150,000 and the decay rate (r) is 22.5% or 0.225.

Therefore, the equation representing the value of the piece of machinery after x years would be:

y = \(\$150,000 * (1 - 0.225)^x\)

Simplifying the equation further, we have:

y = \(\$150,000 * (0.775)^x\)

From this equation, we can see that the value of the machinery decreases exponentially over time. The correct graph that models this exponential decay would show a decreasing trend as x (the number of years) increases.

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The change in potential energy of the car coasts along the hill will be 662,292.459 Joule.

We have,

Length of coasts along the hill = 62.2 meters,

And,

The angle car make with the ground = 28.3°,

And,

The mass of the car = 1234 kg,

Now,

We know,

From the Work Energy Theorem that,

The change in Potential energy = The work done on the mass.

And,

Work done i.e. W = F × s × CosΘ

Here,

F = Force,

s = Distance car cover,

And,

Θ = Angle car make with the ground,

And,

We know that,

Force i.e. F = mass × acceleration due to gravity = m × g

And,

g= Acceleration of gravity = 9.8 m/s²

So,

Now,

Putting values,

i.e.

F = 1234 × 9.8 = 12093.2 Newton

Now,

Using the Formula of Work done,

i.e.

W = F × s × CosΘ,

Putting values,

i.e.

W = 12093.2 × 62.2 × Cos(28.3°)

On solving we get,

W = 662,292.459 Joule

So,

Chane in potential energy = 662,292.459 Joule

Hence we can say that the change in potential energy of the car coasts along the hill will be 662,292.459 Joule.

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(a) The statement is true , (b) The statement is false.

(a) The statement is true. If a function f is smooth (differentiable), then its gradient vector is defined as ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k,

where i, j, and k are the unit vectors in the x, y, and z directions, respectively.

Taking the curl of the gradient vector yields the expression

curl(∇f) = (∂(∂f/∂z)/∂y - ∂(∂f/∂y)/∂z)i + (∂(∂f/∂x)/∂z - ∂(∂f/∂z)/∂x)j + (∂(∂f/∂y)/∂x - ∂(∂f/∂x)/∂y)k.

∵ the second derivatives of f are continuous (smooth function), these partial derivatives commute, resulting in each term being zero.

∴ curl(∇f) = 0→i + 0→j + 0→k.

(b) The statement is false. If a vector field →G is a smooth curl field, it means that the curl of →G is zero, i.e., curl(→G) = 0. However, it does not imply that the divergence of →G is zero. The divergence of a vector field →G is defined as

div(→G) = ∂Gx/∂x + ∂Gy/∂y + ∂Gz/∂z,

where Gx, Gy, and Gz are the components of →G in the x, y, and z directions, respectively. Even if curl(→G) = 0, the individual partial derivatives in the divergence expression may not cancel out, resulting in a non-zero value. Therefore, in general, div(→G) ≠ 0 for a smooth curl field →G.

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Answer:

9 x 10^16

Step-by-step explanation:

2 + 7 = 9

Keep the base 10 and exponent 16.

10^16

Put it all together,

9 x 10^16

The point- slope form of the line is y-5 = -0.25(x+6).

What is line?

A line is an one-dimensional figure. It has length but no width. A line can be made of a set of points which is extended in opposite directions to infinity. There are straight line, horizontal, vertical lines or may be parallel lines perpendicular lines etc.

A line with a slope of –1/4 passes through the point (–6,5)

Any line in point - slope form can be written as

y - y₁= m(x -x₁) -------(1)

where,

y= y coordinate of second point

y₁ = y coordinate of first point

m= slope of the line

x= x coordinate of second point

x₁ = x coordinate of first point

In the given problem (x₁ , y₁) = (-6,5) and m= -1/4

Putting all these values in equation (1) we get,

y-5= (-1/4) (x- (-6))

⇒ y-5 = -0.25(x+6)

Hence, the point- slope form of the line is y-5 = -0.25(x+6).

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Calculate the height of the upper triangle, using the Pythagoras theorem

The length of the vertical diagonal = 2 x 24

The length of the vertical diagonal = 48m

Answer:

Length of the Rectangle is to be considered as the circumference of the resulting cylinder and the width of the rectangle should be considered as the height of the cylinder only then we get the maximum volume of the cylinder which is 47.77\(in^3\)

Step-by-step explanation:

The given dimensions are

Width of the rectangle is  6inches.

Length of the rectangle 10inches.

Now we need to choose in what orientation we need to use the length and the width of the rectangle so that it can be rolled into a rectangle and we get the maximum volume of the resulting cylinder.

so lets consider two cases

CASE-1: width of the rectangle is to be rolled as the circumference of the cylinder and length of the rectangle is to used as the height of the cylinder

 2*pi*r = 6

      r = \(\frac{6}{2pi}\)

      r = \(\frac{3}{pi}\) Inch

and the height = 10inch.

Volume of the resultant cylinder will be

   = \(pi*r^2*h\)

   = \(pi*(\frac{3}{pi} )^2*10\)

   = \(\frac{9}{pi}*10\)

   = \(\frac{90}{pi}\) = 28.662 \(in^3\)

CASE-2: When the length of the rectangle is to used as the circumference of the resultant cylinder and the width of the cylinder is used as the height of the cylinder.

2*pi*r= 10

         r =  \(\frac{5}{pi}\)

and the height of the cylinder is 6 inch

Now the volume of the cylinder will be

 Volume= \(pi*r^2*h\)

              = \(pi*(\frac{5}{pi} )^2*6\)

              = \(\frac{25}{pi}*6\)

              = \(\frac{150}{pi}\) = 47.77\(in^3\)

Clearly we have the second case in which the resulting Cylinder will have the maximum volume.

Therefore the CASE-2 will provide the maximum Volume of 47.77\(in^3\) to the resulting cylinder in which the length of the rectangle is to be considered as the circumference of the Cylinder and the width of the rectangle is to be considered as the height of the cylinder.

The solution of the system of equation is as follows;

when x = -2 , y = -4

when x = 4, y = 8

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Let solve the system of equation by substitution method.

Therefore,

y = 2x

y = x² - 8

Using substitution,

2x = x² - 8

x² - 2x - 8 = 0

x² + 2x - 4x - 8 = 0

x(x + 2) - 4(x + 2) = 0

(x - 4)(x + 2) = 0

x = -2 or 4

Hence,

when x = -2

y = 2(-2) = -4

when x = 4

y = 2(4) = 8

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Answer:

x = 83 degree

Step-by-step explanation:

x + 43 = 126 (sum of two interior opposite angle is equal to the exterior angle formed)

x = 126 - 43

x = 83 degree

Answer:

83 degrees

Step-by-step explanation:

To find this you first find the angle opposite to 126. To do this you subtract 126 from 180 as 180 degrees is a straight line, and we are looking for that missing angle.

This equals 54 degrees.

Now, 54 + 43 equals 97.

Because all interior angles of a triangle always equal 180, you can find that last angle by subtracting 97 from 180. This leaves you with 83 degrees.

20 m longer it is to walk from A to B along the diagonal of the walk than to walk along the edges of the park.

Given:

Assume ABCD is a rectangular park of right triangles ABC of length = 40m, width = 30m, ∠C = 90

In the right-angled triangle ABC,

By Pythagoras' theorem,

AB² = AC² + BC²

AB² = 30² + 40²

AB² = 900 + 1600

AB² = 2500

AB² = \(\sqrt{2500}\)

AB = 50m

The distance from A to B along the diagonal of the park = 50m

The distance from A through to C = 30m.

The distance from A through C to B = 30 + 40 = 70m.

Therefore, 20 m longer it is to walk from the diagonal of the park to walk along the edges of the park.

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Answer:

Carl Friedrich Gauss hope this helps.

The first name of the mathematician who developed Gauss's law is Carl Friedrich. Gauss's law is just one of the many examples of his genius, and it remains an essential tool for physicists and engineers to this day.

Carl Friedrich Gauss was a German mathematician and physicist who lived from 1777 to 1855. He is best known for his work in mathematics, particularly in the field of number theory, but he also made significant contributions to physics. Gauss's law, named after him, is a fundamental law of electromagnetism that relates electric charge to the electric field it creates.

Carl Friedrich Gauss was one of the most influential mathematicians of all time. He made significant contributions to many areas of mathematics, including number theory, geometry, and statistics. Gauss's law is one of his most important contributions to physics. It states that the total electric flux through any closed surface is proportional to the total electric charge enclosed within that surface. Gauss's law is a fundamental principle of electromagnetism, and it is used to calculate the electric field due to a distribution of charges. The law was first published by Gauss in 1835, and it has been a cornerstone of physics ever since.

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Answer:

i wish i could tell you

Step-by-step explanation: