Please help me with #1

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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Answer:

I want to say that the answer is 14.

Step-by-step explanation:

f(5) = 3x+1 = 14

the ladder reach 14.13 feet high up the wall.

Anelys leans a 16-foot ladder against a wall so that it forms an angle of 61° with the ground.

We have to calculate how high up the wall does the ladder reach.

Solution

We have to calculate how high up the wall does the ladder reach.

Let's assume that the height of the wall is h, and the distance between the ladder's foot and the wall is d.

The hypotenuse of the right-angled triangle (the ladder) is 16 feet.

The angle formed by the ladder and the wall is 61°.

We know that sine function of an angle is the ratio of the opposite side to the hypotenuse:

Therefore: Now we can calculate the height of the wall:

We get that the ladder reaches 14.13 feet up the wall (rounded to the nearest hundredth of a foot).

So, the answer is 14.13 feet.

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For an electric network with three switches ( two are in series and one in parallel), the probability that the system is working is equal to the 0.644 or 64.4 %.

We have, an electric network has 3 switches aligned as present in above figure. Switches present in upper side in network or in series are switch 1 and switch 2 and switch present in parallel is switch 3. The probability that one out of three is turn on = 60% = 0.60

We have to determine probability that the system is working. System is working when all switches are on. Letvus consider the events,

A = Switch 1 is turn on

B = Switch 2 is turn on

C= Switch 3 is turn on

Now, probability that switch 1 is turn on P( A) = 0.60

Probability that switch 2 is turn on P( B)

= 0.60

Probability that switch 3 is turn on P(C)

= 0.60

We know if two events A and B are independent then, we have P(A∩B) = P(A) × P(B)

Here, Switch 1 and switch 2 are independent so, P( A∩B) =0.60 × 0.60

= 0.36

Probability that the system is working =

[(switch 3 is turn on ) or (switch 1 is turn on and switch 2 is turn on)]

= P( C∪( A∩B))

= P(C) + P(A∩B ) - P ( C∩ (A∩B))

= 0.60 + 0.36 - P(C) × P(A∩B)

= 0.96 - 0.6 × 0.36

= 0.96 - 0.216

= 0.644

Hence, required probability is 0.644.

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Complete question:

the above figure completes the question.

an electric network has 3 switches aligned as shown in figure 1 and the probability that one of them is turned on is 60%, independently of the status of the other switches. what is the probability that the system is working? 8 points per problems

There are total of 152 students in 5th grade, then the number of pencils altogether will be equal to 2,736 pencils.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total number of students in 5th grade = 152

Amount of pencil each student have = 18

Then, the total number of pencils altogether,

= 152 × 18

= 2,736 pencils.

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Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

The general solution of the given second-order linear ordinary differential equation is y = (c1 + c2x)e^(5x) + 22/25, where c1 and c2 are arbitrary constants.

The given differential equation is y'' - 10y' + 25y = 22. To find the general solution, we first need to find the complementary function by solving the associated homogeneous equation, which is y'' - 10y' + 25y = 0.

Assuming a solution of the form y = e^(rx), we substitute it into the homogeneous equation and obtain the characteristic equation r^2 - 10r + 25 = 0. Solving this quadratic equation, we find that r = 5 is a repeated root.

Therefore, the complementary function is of the form y_c = (c1 + c2x)e^(5x), where c1 and c2 are arbitrary constants.

Next, we find a particular solution for the non-homogeneous equation y'' - 10y' + 25y = 22. Since the right-hand side is a constant, we can assume a constant solution y_p = a.

Substituting y_p = a into the differential equation, we find that 25a = 22, which gives a = 22/25.

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Answer:

The answer is 9

Step-by-step explanation:

27^2 =729

729/27^4/3

The domain of the relation is {2, 4}.

And the range of the relation is {-4. 1, 3}

The collection of all conceivable independent values that a function or relation may take is known as its domain.

The graph of the relation is shown in the image.

The table that represents the graph,

x → y

2   1

2   -4

4   3

The domain of the relation is {2, 4}.

And the range of the relation is {-4. 1, 3}

Therefore, the domain and range of the relation are given above.

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Three solutions to the first-order regular perturbation problem f(x) = 2x³ - 4.0012x + 0.002 = 0 can be found by setting ε = 0.001.

(a) The values of f(x) for each root can be determined by substituting the roots into the equation. Let's say the roots are x1, x2, and x3. Then, calculate f(x1), f(x2), and f(x3).

(b) To calculate the solution to second order, we can expand the equation f(x) = 2x³ - 4.0012x + 0.002 as a Taylor series up to second order. The second-order solution will involve the first-order term and additional correction terms.

By including these correction terms, we can improve the accuracy of the solution. The exact calculations for the second-order solution will depend on the specific values of the roots obtained in part (a) and the form of the correction terms in the perturbation series.

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Answer

- A suitable two-dimensional figure that can be used to model this frame is a rectangle.

- Perimeter of the rectangular frame = 203.2 cm

- Area of the rectangular frame = 2476.6 cm²

Explanation

A suitable two-dimensional figure that can be used to model this frame is a rectangle because a rectangle is the figure that has four sides with a pair of two equal sides.

The perimeter of a rectangle is given as

Perimeter = 2 (L + W)

where

L = Length of the rectangle = 61 cm

W = Width of the rectangle = 40.6 cm

Perimeter = 2 (L + W)

= 2 (61 + 40.6)

= 2 (101.6)

= 203.2 cm

The area of a rectangle is given as

Area = L × W

L = Length of the rectangle = 61 cm

W = Width of the rectangle = 40.6 cm

Area = L × W

= 61 × 40.6

= 2476.6 cm²

Hope this Helps!!!

The iron pipe weighs 0.9375 kg.

In arithmetic, a product is the result of multiplication or an expression that identifies elements to be accelerated.

In math, to multiply method to feature the same agencies. when we multiply, the number of factors inside the organization increases. The two factors and the product are parts of a multiplication hassle. inside the multiplication problem, 6 × nine = 54, the numbers 6 and 9 are the elements, even as the variety 54 is the product.

2/5 m = 0.4 m

3/8 kg = 0.375 kg

2/5 m = 3/8 kg

0.4 m = 0.375 kg

Multiplying both sides by 2.5,

1 m = 0.9375 kg

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The correct answer is:

**C) 0.28**

The sum of deviations refers to the sum of the differences between individual data points and the mean of the dataset. In any dataset, the sum of deviations from the mean will always equal 0.

This is because, when calculating the mean, you sum all the data points and then divide by the number of data points. The mean represents the "middle" or "balance" point of the dataset. When you add up the differences between each data point and the mean, the positive and negative deviations will cancel each other out, resulting in a sum of 0.

So, any non-zero value for the sum of deviations is impossible. In this case, 0.28 is the only non-zero value.

Based on the given information, where the Reproducibility result is 5% and the Repeatability result is 50%, it indicates that the majority of the variation in the measurement system is due to the repeatability component rather than the reproducibility component.

Re-examine and possibly revise the handling of the part to be measured: If the interaction between the operator and the part is identified as a significant source of variation, addressing this issue by re-evaluating and improving the part handling process can help reduce repeatability errors.

Investigation into the instrument: Validating the proper functioning and accuracy of the measuring instrument is crucial. An investigation should be conducted to ensure that the instrument is calibrated correctly and operating within acceptable specifications.

More training for the operators: Providing additional training and guidance to the operators can help improve their skills and reduce variations introduced by human factors. This includes ensuring they follow standardized measurement procedures, properly handle the equipment, and interpret the results accurately.

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\(\dfrac{b^{-1}}{ca^{-1}-ac^{-1}}=\dfrac{\frac1b}{\frac ca-\frac ac}\)

Multiply the numerator and denominator by \(ac\):

\(\dfrac{\frac1b}{\frac ca-\frac ac}\cdot\dfrac{ac}{ac}=\dfrac{\frac{ac}b}{c-a}\)

Since \(b=\frac14\), we have \(b^{-1}=\frac1b=4\). So substituting the values of a, b, and c gives us

\(\dfrac{\frac{ac}b}{c-a}=\dfrac{3\cdot5\cdot4}{5-3}=\dfrac{60}2=\boxed{30}\)

Answer:

15/4

Step-by-step explanation:

Substituting, we get the following:

Answer:

cant be solved, when you try to you get

-1+78 = 77

which is

77 = 77

1=1

So cannot be factored

Step-by-step explanation:

Answer:

15x-3y

Step-by-step explanation:

Ok, this question might seem hard but its not! theres only 2 varibles here, x and y. In this problem we add the 2 numbers that are x which gives us 15x and then the -3y gets added to the rephrasment.

The maximum error in the calculated area of the rectangle is approximately 8.7 square centimeters.

To estimate the maximum error in the calculated area of the rectangle, we can use differentials. The formula for the area of a rectangle is A = length * width.

Given:

Length (L) = 52 cm (with a maximum error of 0.1 cm)

Width (W) = 35 cm (with a maximum error of 0.1 cm)

We want to find the maximum error in the calculated area (dA) when the length and width have a maximum error of 0.1 cm.

Using differentials, we have:

dA = (∂A/∂L) * dL + (∂A/∂W) * dW

Let's calculate the partial derivatives (∂A/∂L) and (∂A/∂W):

∂A/∂L = W (since the width is constant when differentiating with respect to L)

∂A/∂W = L (since the length is constant when differentiating with respect to W)

Substituting the values:

∂A/∂L = 35 cm

∂A/∂W = 52 cm

Now we can calculate the maximum error in the calculated area (dA) using the given maximum errors in length (dL) and width (dW):

dA = (35 cm * 0.1 cm) + (52 cm * 0.1 cm)

dA = 3.5 cm + 5.2 cm

dA = 8.7 cm

Therefore, the maximum error in the calculated area of the rectangle is approximately 8.7 square centimeters.

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Solution

The answer is

Absolute Value Function

The given statement is True because If the sample mean is close to the population parameter, it suggests representative sampling regarding the variable of interest, although other factors should be considered too.

When the sample mean closely approximates the population parameter, it indicates that the sample is capturing the central tendency of the population. The mean is a measure of central tendency that reflects the average value of the variable of interest in the population.

If the sample mean is similar to the population mean, it suggests that the sample is a good representation of the population in terms of that particular variable.

However, it is important to note that representativeness is a relative concept. A sample may be considered representative in one sense but not necessarily in all aspects. Other factors, such as the sampling method, sample size, and sampling bias, also influence the representativeness of a sample.

In summary, when the obtained mean of the observations in a research study is close to the population parameter, it provides evidence that the sample is representative of the target population to some degree, indicating that the sample captures the central tendency of the population for the variable under investigation.

However, representativeness should be assessed in consideration of other factors as well.

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Answer:

7centimeters

Step-by-step explanation:

it just is lololololol

Answer:

7

Step-by-step explanation:

The statement that It is sufficient to test an analogy by asking what are its relevant similarities is false.

Analogy refers to the process of comparison of two or more items such that it explains some idea, or classification or familiarity and representativeness. Studying the analogies helps in enhancing, strengthening and reinforcing the skills in areas such as reading comprehension, homophones, deductive reasoning and logic.

Testing an analogy only by relevant similarities will produce partial results which might not be suitable to fully explain the reason. Hence, both relevant similarities and differences are to be considered for more detailed review. Different kind of analogies used to explain the differences or similarities are synonym and antonym, symbol and reference, degree of differences.

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Let x represent the number of students attending the dance.

Band A: Cost = $600

Band B: Cost = $350 + ($1.25 × x)

Let's denote the number of students attending the dance as "x".

For Band A, they charge a flat fee of $600 to play for the evening, so the cost would be constant regardless of the number of students. We can represent this cost as a single equation:

Cost of Band A: $600

For Band B, they charge $350 as a base fee, and an additional $1.25 per student. Since the number of students is denoted as "x", the cost of Band B can be represented as follows:

Cost of Band B = Base fee + (Cost per student * Number of students)

Cost of Band B = $350 + ($1.25 × x)

Now we have a system of equations representing the cost of the two bands:

Cost of Band A: $600

Cost of Band B: $350 + ($1.25 × x)

These equations show the respective costs of Band A and Band B based on the number of students attending the dance. Paula can use these equations to compare the costs and make an informed decision while keeping the ticket price as low as possible to encourage student attendance while covering the expenses.

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Answer:

Z= 82

Step-by-step explanation:

Answer:

I hope this helps!

Answer:

1 → e

2 → f

3 → b

4 → d

5 → a

Step-by-step explanation:

Look for the corresponding sides by paying attention to the angle pairs since the angles do not change when the polygon is scaled.

Answer:

5x + 2

Step-by-step explanation:

X is going to be the "number"

5 times the number

and then add two

Answer:

2 + 5 x n  

Hope this helps