Determine the domain of the following graph:

Answer:

x = {-5, 2}

Step-by-step explanation:

unfamiliar with the notation 7;2

will solve for |2x + 3| = 7

Solution I -  the quanity inside the absolute value is 7

2x + 3 = 7

2x = 4

x = 2

Solution II -  the quanity inside the absolute value is –7

2x + 3 = –7

2x = -10

x = -5

-----------------

x = {-5, 2}

The marginal revenue curves for the given demand curves are: MR = -0.5  Q + 12 In a monopoly market, the marginal revenue curve is always below the demand curve. This is because a monopolist can only increase their revenue by decreasing the price of their product, and therefore they must lower the price for all units sold, not just the last one.

For the first demand curve, P = -5Q + 25, the marginal revenue curve can be found by taking the derivative of the demand curve with respect to Q. This gives us:

MR = dP/d Q = -5

So the marginal revenue curve is a horizontal line at MR = -5. Adding the intercept of the demand curve at P = 25, we get:

MR = -5Q + 25

For the second demand curve, P = -0.5Q + 12, the marginal revenue curve can be found in the same way:

MR = dP/dQ = -0.5

So the marginal revenue curve is a horizontal line at MR = -0.5. Adding the intercept of the demand curve at P = 12, we get:

MR = -0.5Q + 12

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If a matrix A is 5 x 3 and the product AB is 5x7, the size of B is 3x7.

The product of two matrices A and B, denoted as AB, is possible only if the number of columns of A is equal to the number of rows of B. In this case, A is 5x3, which means it has 3 columns.

And since the product AB is 5x7, it means the resulting matrix has 7 columns. Therefore, the number of columns of B must be equal to 7. And since A has 3 columns, the number of rows of B must be equal to 3 for the product to be possible.

Thus, the size of B is 3x7.

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Answer:

3x(7+y+2x)

Step-by-step explanation:

1) Find the Greatest Common Factor (GCF).

A. What is the largest number that divides evenly into 21x, 3xy, and 6x²?

It is 3.

B. What is the highest degree of x that divides evenly into 21x, 3xy , and 6x²?

It is x.

C. hat is the highest degree of y that divides evenly into 21x, 3xy, and 6x²?

It is 1, since y is not in every term.

D. Multiplying the results above,

The GCF is 3x.

2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

\(3x(\frac{21x}{3x} +\frac{3xy}{3x} +\frac{6x^{2} }{3x} )\)

3)  Simplify each term in parentheses.

\(3x(7+y+2x)\)

\(21x+3xy+6x^{2} = 6x^{2}+3xy+21x=3x.2x +3xy+3x.7 =3x.(2x+y+7)\)

ok done. Thank to me :>

Answer:

2m+3r-2x-2y

Step-by-step explanation:

2m+3r=2m+3r

-2×x=-2x

-2×y=-2y

answer=2m+3r-2x-2y

the answer is option 2....

Answer:

Option 2

Step-by-step explanation:

when the power appears as a fraction, take the root of the number based on the denominator of the fraction when numerator is equal to 1

He made $480 in commission last month

This refers to the fee paid to an agent or employee for transacting a piece of business or performing a service

First, convert 8% into a decimal

8%/100

= 0.08

Multiply the decimal by his sales

0.08 * 6000

480

Therefore, he made $480 in commission last month

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Answer:

The right option is option e.T-shaped.

Step-by-step explanation:

The molecular geometry or shape of clf3 is T-shaped. It acquires such shape because of presence of two lone pairs which take equatorial position and there are greater repulsions. The hybridisation is sp3d and it has 2 lone pairs

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Option e) T-shaped

The shape or molecular geometry  of ClF₃ is T-shaped. It acquires such a shape due to the presence of two lone pairs in the equatorial position and has greater repulsion. The hybrid is sp³d and it has 2 lone pairs.

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Answer:

The sample space is 29........

The rotational inertia of the block about an axis of rotation through one of the corners of the block which is perpendicular to the large faces will be M(a²+b²)/3.

Any item that can be rotated has the property of rotational inertia. It is a scalar value that indicates how challenging it is to alter an object's rotational velocity around a certain rotational axis. The role of mass in linear mechanics is analogous to that of rotational inertia in rotational mechanics. Because it measures moment of inertia as it is rotating, this property is also known as rotational inertia. A measurement of an object's resistance to changes in its angular velocity is called rotational inertia. Imagine turning an item with a specific torque. As the torque is being applied, measure the angular acceleration. The rotational inertia of the item increases as the resultant angular acceleration decreases.

Here,

The major calculations are attached in image.

Moment of Inertia of plate passing through O is I = Ma²/12

and, ly = Mb²/12

by perpendicular axis theorem I2 = Ma²/12+Mb²/12

The distance of edge and the center is d = √(a²+b²)/4

So by parallel axis theorem, IA = Ma²/12+ Mb²/12 + Md² = M(a²+b²)/3

M(a²+b²)/3 is the rotational inertia of the block about a rotating axis passing through one of its corners and perpendicular to its large faces.

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Answer:

The answer to the question is

25 % increase in production rate

Step-by-step explanation:

To solve the question, we note that

Initial number of products = 84 toy robots per day

Present production rate = 105 robots per day

The percentage increase is given by the increase in production rate divided by the original production rate multiplied by 100  

Where increase in production rate = 105 - 84 = 21

Percentage increase = 21/84 ×100 = 25 % increase

Step-by-step explanation:

Reread the underlined sentence on page 4.

What does the figurative language in this

sentence suggest about the narrator?

He feels that people should have used better tools

to help them detect advanced life forms on other

planets.

He sympathizes with people for not apprehending

that there was advanced life on other planets.

He is unable to believe that there could be any

form of life more advanced than humans.

He blames people's exaggerated idea of their

superiority for their failure to imagine life more

advanced than themselves.

Answer:

\(19\%\)

Percentages are evaluated values that say how much of a whole is occupied by that value. For example, if we were to say 75% of a strawberry pie remained, we could also see this as 3/4, or three-fourths.

To solve this particular problem, we will need to divide two values and convert a decimal to a percentage.

First, set up the fraction of economics majors that are freshman students to the total number of freshman students.

\(\displaystyle \frac{1634}{8600}\)

Then, divide the two using a calculator or long division.

\(\displaystyle \frac{19}{100}\)

Finally, to convert this to a decimal, use a calculator.

\(0.19\)

To convert a decimal to a percentage, multiply the decimal by 100.

\(0.19 \times 100 = 19\%\)

The final answer is \(19\%\).

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Answer:

19%

Key Points:

In order to find the percentage of freshman majoring in economics, we must divide the econ major students by the overall size of the freshman class.

\(\frac{1634}{8600}\)

Our next step is to grab a calculator and input 1634 ÷ 8600. You can alternatively use the long division method but a calculator would work best. After calculating, your answer should come out to be 0.19

Now, you need to multiply it by 100 so that you can create a percentage.

0.19 × 100 = 19%

Therefore, 19% of the freshman class are economics majors.

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Answer:

Step-by-step explanation:

The length of the base is 3 feet and the height of the triangle is 6 feet.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

Given that the height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet.

The dimensions of the triangle will be calculated as,

A = (1/2)  x b x h

A = (1/2) x b x ( b + 3 )

54 = ( 1 / 2 ) x ( b² + 3b )

108 =  ( b² + 3b )

( b² + 3b - 108) = 0

( b² + 12b -3b -108 ) = 0

(b - 3 ) ( b+ 12 ) = 0

b = 3 and b = -12 ignore negative value.

The height will be calculated as,

h = b + 3

h = 3 + 3

h = 6 feet

Therefore, the length of the base is 3 feet and the height of the triangle is 6 feet.

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Answer:

Please make me as brain list and i am new in this app

Step-by-step explanation:

a)  (((x3)+((6•(x2))•y))+(12x•(y2)))+23y3

b) x2+y2+z2-2xy+2xz-2yz

=x^2+y^2+z^2-2xy+4-2yz

=x^2+y^2+z^2-2xy+4-2yz

If the building itself will be used as one of the sides of the enclosed area. The maximum area that can be enclosed by the fencing is: 31,250ft².

Let the area be x ft long

Let the width be (500 -x )/2

Hence,

x × (500 - x)/2 = -1/2x² + 250x

When,

x = 250

So,

Maximum area =-1/2 × 250² +250 ×250

Maximum area = -31,250ft + 62,500ft

Maximum area = 31,250ft²

Therefore 31,250ft² is the maximum area.

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0.54

Simplify ——

10

Equation at the end of step

1

:

6 9

—— • ——

10 10

STEP

2

:

3

Simplify —

5

Equation at the end of step

2

:

3 9

— • ——

5 10

STEP

3

:

Final result :

27

—— = 0.54000

50

Answer:

The answers should be...

13. t= -2

14. x= -1

15. x= -1

Step-by-step explanation:

None of the provided statements (A, B, or C) correctly identify the project variance based on the information given in Table 1 alone.

Based on the given information, it is not possible to determine the project variance using Table 1 alone. The project variance represents the overall variability or uncertainty associated with completing the entire project.

Statement A suggests that the project variance is 5.222 because it is the same as the variance of the critical path. However, the critical path is a sequence of activities with the longest total duration, and its variance alone does not provide an accurate measure of the project variance.

The critical path may not include all activities and their associated variances.

Statement B proposes that the project variance is 5.222 because it is the sum of the variances of all activities in the project. While summing the variances of individual activities provides a measure of overall variability, it does not necessarily represent the project variance.

The project variance considers the interdependencies and interactions among activities, which cannot be solely determined by summing individual variances.

Statement C suggests that the project variance is 2.582 because it is the variance of the last activity in the project.

However, the variance of a single activity cannot determine the overall project variance accurately. Other activities and their variances may influence the project's total uncertainty.

Therefore, none of the provided statements (A, B, or C) correctly identify the project variance based on the information given in Table 1 alone.

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Answer:

Step-by-step explanation:

Reflection over any line is a rigid transformation that does not change angles or lengths. Dilation is a transformation that changes lengths by the same scale factor, but has no effect on angles. Dilated figures are similar to the original.

When ΔXYZ is reflected over a vertical line, no lengths or angles are changed. When the reflected triangle is dilated by half, we get ...

  Y'X' = (1/2)YX . . . . . . . makes option 3 false

  X'Z' = (1/2)XZ . . . . . . . makes option 4 true

Since no angles are changed, we have ...

  Angle XZY ≅ Angle Y'Z'X'   (another name for angle X'Z'Y')

  ... makes option 2 true

Of course, the resulting triangle is similar to the original, so ...

  △XYZ ~ △X'Y'Z' . . . . . option 1 is true

Answer: Half the side of NL from the original figure.

Step-by-step explanation:

When it is a scale factor of 1/2 all the sides are halved there fore nl is halved.

In conclusion for a. If the system is homogeneous , every solution is trivial true. b. If there exists a trivial solution, the system is homogeneous false. c. If there exists a nontrivial solution, there is no trivial solution false.

How to solve?

a. If the system is homogeneous, every solution is trivial.

This statement is true. A homogeneous system of linear equations has the form Ax = 0, where A is the coefficient matrix and x is the vector of variables. The trivial solution is always x = 0, which satisfies the equation. Any other solution would require a nonzero x vector, but then Ax would be nonzero, contradicting the fact that it equals zero in a homogeneous system.

b. If there exists a trivial solution, the system is homogeneous.

This statement is false. A system of linear equations can have a trivial solution (i.e., all variables are equal to zero) without being homogeneous. For example, the system

x + y = 0

2x + 2y = 0

has a trivial solution (x = 0, y = 0) but is not homogeneous.

c. If there exists a nontrivial solution, there is no trivial solution.

This statement is false. A homogeneous system of linear equations can have both trivial and nontrivial solutions. For example, the system

x + y = 0

2x + 2y = 0

has both a trivial solution (x = 0, y = 0) and a nontrivial solution (x = 1, y = -1).

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Answer:

Given that MNP is a triangle. Q is the midpoint of MN and R is the midpoint of NP.

The length of QR is 4x -11 and the length of MP is 9x - 29.

We need to determine the measure of MP.

Value of x:

The value of x can be determined using the triangle midsegment theore

Applying the theorem, we have;

Substituting the lengths, we get;

Subtracting both sides by 8x, we have;

Adding both sides of the equation by 29, we get;Thus, the value of x is 7.

Measure of MP:

The measure of MP can be determined by substituting x = 7 in the length of MP.

Thus, we have;

Thus, the measure of MP is 34.

Answer:

Total number in favour:

Probability:

Total number in against:

Probability:

Answer:

------------------------

The two given angles form a linear pair, hence:

The probability that a project with an expected completion time of 15 weeks and a variance of 4 weeks will be completed in 18 weeks is approximately 0.9332 or 93.32%.

To calculate the probability, we need to use the z-score formula and the properties of the normal distribution. The z-score measures the number of standard deviations an observation is from the mean.

First, let's calculate the z-score:

z = (x - μ) / σ

Where:

x = the value we want to find the probability for (in this case, 18 weeks)

μ = the mean or expected completion time (15 weeks)

σ = the standard deviation or square root of variance (2 weeks, since variance is 4 weeks)

Now, let's substitute the values into the formula:

z = (18 - 15) / 2

z = 1.5

Next, we need to find the probability associated with the calculated z-score. We can look up this probability in a standard normal distribution table or use a calculator.

Using the z-score table or calculator, we find that the probability associated with a z-score of 1.5 is approximately 0.9332.

Therefore, the probability that the project will be completed in 18 weeks is approximately 0.9332 or 93.32%.

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Answer:

14 + 2 + 15

Step-by-step explanation:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(2x-y=6\implies -y=-2x+6\implies y=\stackrel{\stackrel{m}{\downarrow }}{2} x-6\leftarrow \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line whose slope is 2 and it passes through (-4 , -6)

\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-4)}) \implies y +6= 2 (x +4) \\\\\\ y+6=2x+8\implies y=2x+2\)