Derive this equation
\( \frac{3}{( {x + 1)}^{2} } \)
​

The correct  answer and the correct option is A.

It is given that  DEFG is a parallelogram.

Draw the diagonals DF and EG. Place point H where DF and EG intersect.

In triangle HGD and HEF

∠HGD ≅ ∠HEF                            (Alternate Interior angle)

∠HDG ≅ ∠HFE                      (Alternate Interior angle)

By the definition of a parallelogram, the opposite sides of a parallelogram are congruent.

DG ≅ EF                                      (Opposite sides of parallelogram)

According to ASA postulate, two triangles are congruent if any two angles and their included side are equal in both triangles.

So, by using ASA criterion for congruence we get,

ΔDGH ≅ ΔFEH

Since corresponding sides of congruent triangles are congruent, therefore

GH ≅ EH                      (CPCTC)

DH ≅ FH                     (CPCTC)

Option A is correct.

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The probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

To find the probability that a senior takes the bus to school every day given that he or she has a driver's license, we can use conditional probability.

Let's denote the event that a senior has a driver's license as A and the event that a senior takes the bus to school every day as B. We want to find the probability of event B given event A, denoted as P(B|A).

We are given the following information:

The conditional probability formula states that P(B|A) = P(A ∩ B) / P(A).

Substituting the given values, we have:

P(B|A) = P(A ∩ B) / P(A) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

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The probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

To find the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, we need to use the concept of conditional probability. Conditional probability is the probability of one event happening given that another event has already occurred. In this case, we want to find the probability of taking the bus to school every day, given that the student has a driver’s license.

We can use the formula:

P(A|B) = P(A and B) / P(B)

where P(A|B) is the probability of event A happening given that event B has happened, P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.

In the given problem, 84% of the seniors have driver’s licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver’s licenses and take the bus to school every day. We want to find the probability of taking the bus every day, given that the student has a driver’s license.

Plugging in the values into the formula:

P(Taking the bus every day | Having a driver’s license) = P(Taking the bus every day and Having a driver’s license) / P(Having a driver’s license)

P(Taking the bus every day | Having a driver’s license) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

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- Square matrices are the only matrices that can be invertible.
- If a square matrix has a right inverse, it will also have a left inverse.
- Non-square matrices can have either a right inverse or a left inverse, but not both.

In linear algebra, square matrices are the only matrices that can be invertible. A matrix is invertible if there exists another matrix, called its inverse, such that their product is the identity matrix. This means that if A is a square matrix, there exists another matrix B such that AB = BA = I, where I is the identity matrix.

If a square matrix has a right inverse, it will also have a left inverse. This means that if A is a square matrix and there exists another matrix B such that AB = I, then BA = I as well. In other words, the right inverse and left inverse of A will be the same matrix.

On the other hand, non-square matrices can only have either a right inverse or a left inverse, but not both. This is due to the size mismatch between the matrices when multiplying them in different orders. If a non-square matrix has a right inverse, it means that there exists another matrix B such that AB = I. However, this matrix B cannot be a left inverse of A, because the product BA would result in a size mismatch.

Therefore, square matrices are the only matrices that can be invertible. If a square matrix has a right inverse, it will also have a left inverse. However, non-square matrices can only have either a right inverse or a left inverse, but not both.

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Answer:

-867.8916

Step-by-step explanation:

1 ^3= -1×867.8916

- 867.8916

The correct answer is: 0, -3, and 3. At  0, -3, and 3 of x does fx) x4-18x2 have a critical point where the graph changes from decreasing to increasing.

To find the critical points where the graph of the function f(x) = x^4 - 18x^2 changes from decreasing to increasing, we need to find the values of x where the derivative of the function is equal to zero or does not exist.

Let's find the derivative of f(x) with respect to x:

f'(x) = 4x^3 - 36x

To find the critical points, we set the derivative equal to zero and solve for x:

4x^3 - 36x = 0

Factor out 4x:

4x(x^2 - 9) = 0

Now we have two factors:

1) 4x = 0, which gives x = 0

2) x^2 - 9 = 0, which gives x = ±3

So, the critical points where the graph changes from decreasing to increasing are x = 0, x = -3, and x = 3.

Therefore, the correct answer is: 0, -3, and 3.

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Answer:

C. 30 ÷ 6 = 5

Step-by-step explanation:

A. incorrect

         6 - 5 is not equal to 11, it is equal to 1

B. incorrect

         6 × 30 is not equal to 5, it is equal to 180

C. CORRECT

         30 ÷ 6 is equal to 5

D. incorrect

         11 + 5 is not equal to 6, it is equal to 16

Answer:

C. 2L-1

Step-by-step explanation:

:)

The maximum height reached by the rocket is 122.5 m.

In this question, given parameters:

time (t) = 5.0 seconds

By applying second equation of motion the maximum height of the model rocket would be,

h = v₀t + 1/2 (gt²)

where, v₀ is the initial velocity

g is acceleration due to gravity

(9 = 9.8 m/s²)

Since initial velocity v₀ = 0 we get an equation,

h = 0 + 1/2 (gt²)

h = 1/2 (9.8 x 5²)

h = 122.5 m

Therefore, the maximum height is 122.5 m.

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The probability mass function of X( -3, -1, 1 ,3)  is P(X) 1/8 3/8 3/8 1/8.

A fair coin is flipped 3 times and the random variable X is defined as follows:

   X = 3 times the number of heads - 2 times the number of tails

To find the probability mass function of X, we can list all the possible outcomes and calculate their probabilities.

The Possible outcomes are as shown:

   3 heads (X = 3)

   2 heads, 1 tail (X = 1)

   1 head, 2 tails (X = -1)

   3 tails (X = -3)

And the Probabilities are:

   P(X = 3) = 1/8

   P(X = 1) = 3/8

   P(X = -1) = 3/8

   P(X = -3) = 1/8

Therefore, the probability mass function of X is:

X( -3, -1, 1 ,3)  is  P(X) 1/8 3/8 3/8 1/8

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Answer:

5

Step-by-step explanation:

You first start by finding the acceleration of the problem.

a=f/m

Which this case is 45.

The question is asking " How many times greater must it be than A?"

You then divide

45/9

Your final answer is 5.

The acceleration of Object B should be 5 times the acceleration of Object A in order to make the table true.

We have a table that gives the values of mass, acceleration and force of object A and object B.

We have to find by how many times greater must the acceleration of Object B be than the acceleration of Object A to make the table true.

The formula to calculate the force is -

F = m x a

In the table, for Object B -

Mass = 40 Kg

Force = 1800 N

Substituting the values -

a = \(\frac{F}{m}\) = \(\frac{1800}{40}\) = 45 \(m/s^{2}\)

The acceleration of Object A is 9 \(m/s^{2}\).  On comparing the acceleration of both the objects, we can see that the acceleration of Object B is 5 times the acceleration of Object A.

Hence, the acceleration of Object B should be 5 times the acceleration of Object A in order to make the table true.

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Answer:

=> 7+u = 14; u = 7

Step-by-step explanation:

The sum of 7 and u is 14

=> u + 7 = 14

=> u = 14-7

=> u = 7

Answer:

D- Yes. (3b+3)−(b+a+3)

Step-by-step explanation:

hope this helps<3

Here we have a problem of the subtraction of polynomials, is important to know that the subtraction is really straightforward.

The correct option is: Yes. (3b+3)−(b+a+3)

We will see that yes, two polynomials can be subtracted such that the difference is a binomial (a binomial is a polynomial of 2 terms).

Suppose the polynomials:

\(p(x) = a*x^2 + b*x + c\\q(x) = b*x\)

If we take the difference of these two:

\((a*x^2 + b*x + c) - (b*x) = a*x^2 + c\)

So at the end, we have a binomial.

By looking at the options we can see one really similar to ours, it is:

Yes:

\((3b + 3) - (b + a + 3)\\(3b + 3) - b - a - 3\\3b + 3 - b - a - 3 \\3b - b - a\\2b - a\)

Which is the last option, and we can see that after the subtraction of polynomials we have a binomial.

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Answer:

156

Step-by-step explanation:

1) The formula for finding the sum of interior angles of an n-gon is 180(n-2)

2) Plug in 15 for n

180(15-2)

3) Solve

180(15-2)

180(13)

2340

4) There are 15 angles in a 15-gon

5) Divide sum of interior angles by number of interior angles

2340/15 = 156

6) So, the answer is 156 degrees

Answer:

1200 is ur wsener

Step-by-step explanation:

Answer:

1,200 is the result to the problem

Answer:

True

Step-by-step explanation:

trust me, i remember this question

When two variables vary along with each other but the data points are loosely scattered around the line of best fit, the correlation is weak correlation.

We need to find the type of correlation when two variables vary along with each other but the data points are loosely scattered around the line of best fit.

A scatter plot helps find the relationship between two variables. This relationship is referred to as a correlation. Based on the correlation, scatter plots can be classified as follows.

A weak positive correlation indicates that, although both variables tend to go up in response to one another, the relationship is not very strong. A strong negative correlation, on the other hand, indicates a strong connection between the two variables, but that one goes up whenever the other one goes down.

Therefore, when two variables vary along with each other but the data points are loosely scattered around the line of best fit, the correlation is weak correlation.

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Answer:

Part A: The slope f(x) is greater than slope g(x).

Part B: f(x) has a greater y-intercept.

Step-by-step explanation:

Part A:

The slope of the line is (y2 - y1)/(x2 - x1), so now we have to find the slope f(x).

-1 - (-9) / 0 - (-1) = 8/1 = 8

That would be the slope, and for g(x) it would be 3x-2 = 3.

Which means the slope f(x) is greater than slope g(x).

Part B:

First the y-intercept has to be put on 0.

So, the when function f(x) passes through point (0, -1), then y-intercept is -1.

Now we compare g(x) = 3x-2 with the slope-intercept form and b = -2 is the result. form and b = -2 is the result.

Which means the slope of g(x) is -2. Therefore, f(x) has a greater y-intercept than g(x).

Answer:

A)  Slope of f(x) is 8.  Slope of g(x) is 3

B)  f(x) has the greater y-intercept

Step-by-step explanation:

Part A

To find the slope of function f(x), use the slope formula:

\(\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{7-(-1)}{1-0}=8\)

Therefore, the slope of f(x) is 8.

Linear function

\(y=mx+b\)

where:

Given:

Therefore, the slope of g(x) is 3.

Part B

The y-intercept is when x = 0.  Therefore, from inspection of the table, the y-intercept of f(x) is -1.

The y-intercept of function g(x) is -2.

Therefore, as -1 > -2, function f(x) has the greater y-intercept.

Answer:

Percentage of light that penetrates at 150 m will be 0.94%.

Step-by-step explanation:

By using logarithmic regression calculator,

Equation of the regression line will be,

y = 104.5173 - 20.6711(lnx)

Where x represents the depth of the ocean

And y will represent the penetration of light

Therefore, at the depth of 150 m, penetration of the light will be,

y = 104.5173 - 20.6711[ln(150)]

  = 104.5173 - 103.5753

  = 0.9420

  ≈ 0.94 %

Therefore, percentage of light that penetrates at 150 m will be 0.94%.

Answer:

118.125 lb

Step-by-step explanation:

0=2.25

H=6.5 x O

H=6.5 x 2.25

H=14.625

H+O=2.25+14.625=16.875 per day

16.875x7 days=118.125 lb

The value of l is either 2 or 3, depending on whether the second letter drawn is b or not, respectively.The problem can be solved using the pigeonhole principle. We can draw letters one by one until we have seen any two of a, b, and c, but not all of them.

To minimize the number of letters drawn, we want to draw as few letters as possible before seeing any two of a, b, and c. We can start by assuming that the first letter drawn is a. Then, there are two cases to consider:

Case 1: The second letter drawn is b.

In this case, we have seen both a and b, so we stop drawing letters. The value of l is 2.

Case 2: The second letter drawn is not b (i.e., it is either a or c).

In this case, we need to draw one more letter to ensure that we have seen any two of a, b, and c. If the third letter is the same as the second letter, then we keep drawing letters until we see a different letter. Therefore, the maximum number of letters we need to draw in this case is 3.

Therefore, the value of l is either 2 or 3, depending on whether the second letter drawn is b or not, respectively.

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High level data flow diagrams are used in information system to break down into smaller subsystems. Thus the required answer for the given question is Option E.

The Information system is a sector that helps in gathering analyzing and  keeping an organized way to form a distribution of data. This consists of hardware, software, and various networks that are  generally used by people and organizations to streamline working to achieve the required business goals.

It commonly refers to a computerized system but also at the same time describes a telephone by switching controlling system. In this diagrams are used to represent the flow of data through a particular information system to select subsystems to create a system.

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The answer of the given expression as a common fraction in lowest terms is  437/495  .

In the question ,

it is given that ,

the expression is 0.4overline 8 + overline 0.37 ,

that can be written as \(0.4\overline{8}\) + \(0.\overline{37}\)

On further simplifying the above expression further ,

we get ,

= (48 - 4)/90 + 37/99

= 44/90 + 37/99

taking the LCM of 90 and 99 as 990 and solving further ,

we get ,

= 484/990 + 390/990

= ( 484 + 390 )/990

= 874/990

in lowest form it is = 437/495 .

Therefore , the answer to the expression is  437/495  .

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Answer:

$11654 approx

Step-by-step explanation:

Given data

Principal amount =  22300 dollars

Rate= 10.25%

time= 6 years

The expression for the decrease is given as

A=P(1-r)^t-----------Note the negative sign is because of the decrease

substitute

A= 22300(1-0.1025)^6

A=22300(0.8975)^6

A=22300*0.5226

A=$11653.98

Hence the new value is $11654 approx

Step-by-step explanation:

(a) What percentage of the adults exercise?

₹

(b) What percentage of the adults are vegetarian?

€

(c) What percentage of the adults who are vegetarian exercise? [ (d) Is there evidence that adults who are vegetarian tend to be exercisers more often than average?

Yes, because the percentage found in part (c) is much greater than the percentage found in part (a).

Yes, because the percentage found in part (c) is much greater than the percentage found in part ((b).

No, because the percentage found in part (c) is about the same as the percentage found in part ((a).

No, because the percentage found in part (c) is about the same as the percentage found in part ((b).

Answer:

0.9375

Step-by-step explanation:

I know!

Answer:

1.25 x .75 = 0.9375

Step-by-step explanation:

Answer:

9/7 =a

Step-by-step explanation:

9 / -a + 15 = 8

Subtract 15 from each side

9 / -a + 15 -15 = 8-15

9 / -a = -7

Multiply each side by -a

9/-a * -a = -7 * -a

9 =7a

Divide each side by 7

9/7 = 7a/7

9/7 =a

Answer:

9 / 7 = a

Step-by-step explanation:

9 / - a + 15 = 8

Determined the defined range

9 / ( - a ) + 15 = 8 , a ≠ 0

subtract 15 from each side

9 / - a + 15 - 15 = 8 - 15

calculate the difference

9 / - a = - 7

multiply both side of equation by - a

9 / - a × - a = - 7 × - a

9 = 7 a

divide each side by of equation by 7

9 / 7 = 7 a / 7

9 / 7 = a

Answer:

C = 2p² + 3p - 5

Step-by-step explanation:

Let A & B denote the other two adjacent sides respectively.

Let the third side be denoted by C

Given the following data;

Perimeter of triangle = 6p² - 4p + 9

Length of one side = p² - 2p + 1

Length of one side = 3p² - 5p + 3

The perimeter of a triangle is given by the addition of all its three (3) sides.

Mathematically, the perimeter of a triangle is given by the formula;

P = A + B + C

6p² - 4p + 9 = p² - 2p + 1 + 3p² - 5p + 3 + C

6p² - 4p + 9 = 4p² - 7p + 4 + C

C = 2p² + 3p - 5

Yes, irrational numbers such as π are included in the domain of the function f(x) = 7.

The domain of a function is the set of all possible input values (x) for which the function is defined. In the case of the function f(x) = 7, the output value (y) is always equal to 7, regardless of the input value.

Since every real number, including irrational numbers like π, can be an input value for f(x) = 7, the domain of this function is the set of all real numbers, which includes both rational and irrational numbers. Therefore, π is included in the domain of the function f(x) = 7.

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Answer:

28 ft²

Step-by-step explanation:

area of the desk = (5×4) + (4×2) = 20 + 8 = 28 ft²

Answer:

28

Step-by-step explanation:

5 times 4 = 20

4 times 2= 8

20 plus 8=28