The ages of the men who signed the United States Declaration of Independence ranged from 26 to 70. A histogram shows the distribution of the signers' ages. Which statement about the signers' ages is true?

Answer:

translation 10 units right and a reflection over the axis

Answer:

factors are any group of number or expressions which, when multiplied, produce another number or expression.

Basic example:  4 can be broken into 2 factors---2 and 2.  2 times 2 = 4

Example using an unknown:

2X + 6 = 2 * (X + 3)

In the given problem, there is no whole-number common factor.  A normal convention would be to factor based on the unknown term----thus 8X is factored into 8 and X.

So:  8X + 7 = 8 ( X + 7/8 )

The following would also be correct:

8X + 7 = 4 ( 2X + 7/4 )

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

each term inside the parenthesis is raised to the exponent outsie, that is

(2xy)³

= 2³ × x³ × y³ ← 2³ = 2 × 2 × 2 = 4 × 2 = 8

= 8x³y³

Therefore , the solution of the given problem of expressions comes out to be  students can develop their factoring abilities and avoid mistakes with practise and instruction.

Estimates that combine joining, disabling, and rather than randomly divide should be produced when variables are shifting. If they got together, they could solve a mental puzzle, provide some data, and instead software. A declaration of truth contains formulas, components, and mathematical processes like combination, subtraction, omission, and grouping. Both phrases and words can be assessed and analysed.

Here,

are some pointers to assist students B and C prevent incorrect factoring in the future:

Regularly practise factoring: Since factoring is a talent that must be honed, students should make sure to factor problems frequently. They will be better able to understand the procedure and spot trends in the expressions they are factoring as a result of this.

Verify the indications again because they are prone to error when factoring. Students should double-check their distribution of the signs and make sure no negative indicators are being left out.

Students should double-check their work by multiplying the factors back together after factoring an equation. They'll be able to correct any errors they may have made thanks to this.

If students need assistance with factoring, they should ask an instructor or tutor for assistance. Although factoring can be a challenging ability to master, students can develop their factoring abilities and avoid mistakes with practise and instruction.

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The result of the operation is -1.594×10⁻²).

To solve the given expression, we start by dividing 3.25×10⁻⁴ by 8.012×10⁻²). This can be done by dividing the coefficients (3.25 ÷ 8.012) and subtracting the exponents (10⁻⁴ ÷ 10⁻²).

The division of the coefficients gives us 0.4047, and subtracting the exponents gives us 10 (-4-(-2)) = 10⁻² = 0.01. Therefore, the division of the two numbers results in 0.4047 × 0.01 = 0.004047.

Next, we subtract 2.000×10⁻² from the result obtained above. This is done by subtracting the coefficients (0.004047 - 2.000) and keeping the same exponent (-2).

Performing the subtraction gives us -1.995953, and the common exponent remains -2. Therefore, the final result is -1.995953 × 10⁻² = -1.594×10⁻².

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Therefore, the length of each of the three remaining sides is 46/3 inches, or approximately 15.33 inches.

Perimeter is a term used in geometry to describe the total length of the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The concept of perimeter is important in many practical applications, such as construction, landscaping, and engineering. For example, when building a fence around a garden, the perimeter of the garden would be the length of the fence needed to enclose it. In engineering, the perimeter of a structure or component can help determine the amount of material needed to build or repair it.

Here,

Let's label the sides of the kite as follows:

Side A: the side with a length of 18 inches

Side B: one of the remaining sides

Side C: the other remaining side

Side D: the remaining side that is opposite to Side A

We are told that the perimeter of the kite is 82 inches. The perimeter is the sum of the lengths of all four sides, so we can write:

Perimeter = Side A + Side B + Side C + Side D

Substituting the values we know, we get:

82 = 18 + Side B + Side C + Side D

We also know that Side B, Side C, and Side D add up to the same length as Side A, since the kite is symmetrical. That is:

Side A = Side B + Side C + Side D

Substituting Side A = 18, we get:

18 = Side B + Side C + Side D

Now we have two equations:

82 = 18 + Side B + Side C + Side D

18 = Side B + Side C + Side D

We can subtract the second equation from the first to eliminate Side B, Side C, and Side D:

82 - 18 = 18 + Side B + Side C + Side D - (Side B + Side C + Side D)

64 = Side A

So the length of each of the three remaining sides is:

Side B = Side C = Side D = (Side A - 18)/3 = (64 - 18)/3 = 46/3

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Answer:

4th option

Step-by-step explanation:

given

sinΘ = \(\frac{5}{13}\) and cosΘ = \(\frac{12}{13}\) , then

( \(\frac{5}{13}\) )² + ( \(\frac{12}{13}\) )²

= \(\frac{25}{169}\) + \(\frac{144}{169}\)

= \(\frac{25+144}{169}\)

= \(\frac{169}{169}\)

= 1

showing sin²Θ + cos²Θ = 1

The equation of straight line of the points is given as y = -x - 2

To solve this problem, we simply need to find the equation of straight line which can be done by finding the slope of the line and then intercept of the line.

In the given points;

The formula of slope of a line is given as

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substituting the values into the equation;

\(m = \frac{3 - (-6)}{-5 - 4} \\m = \frac{9}{-9} \\m = -1\)

The slope of the line is equal to 1.

Let's find the intercept of the line

\(y = mx + c\)

Taking point A;

\(y = mx + c\\-6 = -1(4) + c\\-6 = -4 + c\\c = -2\)

The equation of the line is y = -x - 2

Translation: Find the equation of a straight line from two point A(4, -6) and B(-5, 3).

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a)  The test was designed to have a 5% chance of making a Type I error. b) Reject H0 since p-value < significance level. c) Type I error (false positive) if H0 is true and rejected.

A significance test is used to determine whether there is sufficient evidence to reject a null hypothesis, which is a statement about a population parameter, such as a proportion, mean, or standard deviation. The significance level, often denoted by α, is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. The commonly used significance level is 0.05, which means that the test is designed to have a 5% chance of making a Type I error.

In this scenario, the sample proportion is 0.12 and the p-value is 0.03, which is the probability of observing a sample proportion as extreme as 0.12 or more extreme, assuming that the null hypothesis is true. Since the p-value is less than the significance level, we have strong evidence against the null hypothesis, and we reject it. Therefore, we conclude that the proportion is significantly different from the hypothesized value.

If the null hypothesis is actually true, and we reject it based on the sample data, we have made a Type I error. In other words, we have falsely concluded that there is a difference when there is not. False positive is another name for this mistake. Conversely, a Type II error occurs when we fail to reject the null hypothesis when it is actually false, and this error is also known as a false negative.

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The complete question is:

A significance level of 0.05 is used when conducting a proportion-related significance test. 0.12 is the sample statistic. P-value equals 0.03.

a) What chance of a Type I error was the test designed for, if H0 were true?

b) What judgement would you draw on this test (reject or fail to reject)?

c) What kind of error, if any, was there as a result of this test?

Answer:

y=1/3x -4

Step-by-step explanation:

3y-x=-12

y= 1/3x-4

m=1/3

(gradient is the same since its parallel)

y=mX+c

(2) = 1/3(18) + c

2 = 6 + c

2 - 6 = c

c= -4

(y-intercept)

Therefore: y=1/3x-4

To estimate the area under the graph of f(x) = 20x from x = 0 to x = 4, we can use the concept of numerical integration, specifically the trapezoidal rule.

The trapezoidal rule approximates the area under a curve by dividing the interval into small trapezoids and summing up their areas.

Here's how we can estimate the area using the trapezoidal rule:

Since we don't know the specific value of n, let's assume we divide the interval into 4 subintervals, resulting in Δx = (4 - 0) / 4 = 1.

Now, let's calculate the estimated area using the trapezoidal rule:

Area ≈ [(f(0) + f(1)) * Δx / 2] + [(f(1) + f(2)) * Δx / 2] + [(f(2) + f(3)) * Δx / 2] + [(f(3) + f(4)) * Δx / 2]

Substituting the values of f(x) = 20x:

Area ≈ [(20(0) + 20(1)) * 1 / 2] + [(20(1) + 20(2)) * 1 / 2] + [(20(2) + 20(3)) * 1 / 2] + [(20(3) + 20(4)) * 1 / 2]

= [(0 + 20) * 1 / 2] + [(20 + 40) * 1 / 2] + [(40 + 60) * 1 / 2] + [(60 + 80) * 1 / 2]

= [10] + [30] + [50] + [70]

= 160

Therefore, the estimated area under the graph of f(x) = 20x from x = 0 to x = 4 is approximately 160 square units.

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The correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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The probability of a cash flow between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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Option B's equation y = -1/5x + 1/10 has the same slope as the linear function depicted in the table.

One way to describe a linear function is as an algebraic equation with variables raised to the power .A straight line makes up the graph of a linear equation. Y = mx + b, where x and y are variables and m and b are constants, is one of the most typical examples of a linear function.

For instance, if we have the linear function f(x) = 2x + 3, we may calculate the value of f(4) by changing x to 4 and getting f(4) = 2(4) + 3 = 11.

Calculating the difference between y and x for any two points will allow us to determine the slope of the linear function shown in the table. Let's pick the first and last items from the table:

Slope = (change in y) / (change in x) = (0-1/5) / (1/2 - (-1/2)) = (-1/5) / 1 = -1/5

As a result, the table's linear function has a slope of -1/5.

The next step is to find the linear function whose slope is equal to -1/5. Let's look at the possibilities:

A) y = 1/2x + 1/10, slope = 1/2; B) y = -1/5x + 1/10, slope = -1/5 (correct)

C) y = 1/5x - 1/2, slope = 1/5; D) y = 1/2x - 1/10, slope = 1/2

As a result, option B, y = -1/5x + 1/10, is the linear function with the same slope as the one shown in the table.

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The linear function with the same slope as the one represented by the table is: y = -1/5x + 1/10

So the answer is B) y = -1/5x + 1/10.

A linear function is a mathematical function that has a graph that is a straight line.

It can be represented by the equation y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.

To find the slope of the linear function represented by the given table, we can choose any two points and use the slope formula:

slope = (change in y) / (change in x)

Let's choose the points (-1/2, 1/5) and (1/2, 0):

slope = (0 - 1/5) / (1/2 - (-1/2))

= (-1/5) / 1

= -1/5

So the slope of the linear function is -1/5.

Now we need to find the linear function with the same slope.

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept. We know that the slope is -1/5, so we can eliminate answer choices A and D, which have slopes of 1/2 and 1/2, respectively.

To determine the y-intercept, we can use one of the points from the table. Let's use the point (-1/2, 1/5):

1/5 = (-1/5)(-1/2) + b

Simplifying:

1/5 = 1/10 + b

b = 1/5 - 1/10

b = 1/10

So the y-intercept is 1/10.

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The height of the utility pole casting a shadow 10 ft is 32 feet.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

Given that;

Ratio of height of utility pole and its shadow  = x / 10

Ratio of height of sign post and its shadow  = 8/2.5

Equate to determine the height of the utility pole.

x/10 = 8/2.5

Solve for x

x × 2.5 = 8 × 10

2.5x = 80

x = 80 / 2.5

x = 32 ft

Therefore, the height of the utility pole is 32 ft.

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A) Pansy Meadows Primary Care Clinic's total revenue per month is $10,000. B) The clinic's monthly profit is a loss of $15,000. C)  if the commercial insurance company changes the reimbursement rate to $65, the monthly profit would be $30,000. D) if all commercially insured patients are covered by a capitated contract, the monthly profit would be a loss of $33,000.

To calculate the clinic's total revenue, monthly profit/loss, and the impact of changes in reimbursement rates, we'll use the given information and perform the necessary calculations.

Given:

Number of office visits per month = 1000

Fixed costs = $25,000 per month

Variable costs per office visit = $10

A) Total revenue per month:

Revenue per office visit = $10 (variable cost per visit)

Total revenue per month = Revenue per office visit * Number of office visits per month

Total revenue per month = $10 * 1000

Total revenue per month = $10,000

Therefore, Pansy Meadows Primary Care Clinic's total revenue per month is $10,000.

B) Monthly profit (loss):

Profit (loss) = Total revenue per month - Fixed costs - (Variable costs per office visit * Number of office visits per month)

Profit (loss) = $10,000 - $25,000 - ($10 * 1000)

Profit (loss) = -$15,000

Therefore, the clinic's monthly profit is a loss of $15,000.

C) Impact of changing the commercial insurance reimbursement rate to $65:

To determine the impact on profitability, we need to recalculate the monthly profit using the new reimbursement rate.

New total revenue per month = $65 * 1000 = $65,000

Profit (loss) = New total revenue per month - Fixed costs - (Variable costs per office visit * Number of office visits per month)

Profit (loss) = $65,000 - $25,000 - ($10 * 1000)

Profit (loss) = $30,000

Therefore, if the commercial insurance company changes the reimbursement rate to $65, the monthly profit would be $30,000.

D) Impact of all commercially insured patients being covered by a capitated contract:

i. Monthly revenue:

Revenue per patient per month = $2 (capitated payment per patient)

Monthly revenue = Revenue per patient per month * Number of office visits per month

Monthly revenue = $2 * 1000

Monthly revenue = $2,000

ii. Monthly profit/loss:

Profit (loss) = Monthly revenue - Fixed costs - (Variable costs per office visit * Number of office visits per month)

Profit (loss) = $2,000 - $25,000 - ($10 * 1000)

Profit (loss) = -$33,000

Therefore, if all commercially insured patients are covered by a capitated contract, the monthly profit would be a loss of $33,000.

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Assumptions: For the purpose of this exercise, let's assume that we are analyzing defects in a manufacturing process. We will invent data for five different categories of defects and their corresponding frequencies. the cumulative percentage for each category, we find that the top 20% category of defects is Category A.

a. Based on the invented data, the histogram analysis reveals the following distribution of defects and their frequencies:

Category A: 50 defects

Category B: 30 defects

Category C: 20 defects

Category D: 15 defects

Category E: 10 defects

To identify the top 20% of the category of defects contributing to 80% of the total volume, we calculate the cumulative frequency. Starting with the category with the highest frequency, we add up the frequencies until we reach 80% of the total. In this case, Category A contributes the highest frequency, and its cumulative frequency is 50. The total number of defects is 125 (50 + 30 + 20 + 15 + 10). By calculating the cumulative percentage for each category, we find that the top 20% category of defects is Category A.

b. Performing a Root Cause Analysis for the Top Contributing Factor (Category A) using the 5-Why method or Fishbone diagram helps determine the underlying causes. We identify potential factors such as equipment malfunction, operator error, insufficient training, or process variability. By asking "why" repeatedly, we dig deeper into each cause to uncover the root cause.

c. Based on the analysis, we develop a corrective action plan and preventive action plan. For example:

Corrective Action Plan: Assign qualified technicians to regularly inspect and maintain the equipment, conduct additional training for operators to enhance their skills, and implement process control measures to reduce variability.

Preventive Action Plan: Establish a preventive maintenance schedule for equipment, implement a comprehensive training program for all operators, and conduct regular process audits to identify and address potential issues proactively.

The corrective and preventive action plans should clearly define the tasks, responsibilities, and timelines. The maintenance department may be responsible for equipment maintenance, the training department for operator training, and the quality department for process audits. Regular monitoring and evaluation of the action plans should be conducted to ensure effectiveness and make any necessary adjustments.

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The finite difference approximation for a Neumann boundary condition, \(\left(\frac{df}{dx}\right)\), at node \(n\) (right boundary) to \(O(h^2)\) is given by

\(\left(\frac{df}{dx}\right)_n \approx \frac{f_{n-2} - 4f_{n-1} + 3f_n}{2h}\),

where \(f_{n-2}\), \(f_{n-1}\), and \(f_n\) represent the function values at nodes \(n-2\), \(n-1\), and \(n\) respectively, and \(h\) represents the spacing between the nodes.

To derive this approximation, we start with the Taylor series expansion of \(f_{n-1}\) and \(f_n\) around \(x_n\):

\(f_{n-1} = f_n - hf'_n + \frac{h^2}{2}f''_n - \frac{h^3}{6}f'''_n + \mathcal{O}(h^4)\),

\(f_{n-2} = f_n - 2hf'_n + 2h^2f''_n - \frac{4h^3}{3}f'''_n + \mathcal{O}(h^4)\).

By subtracting \(4f_{n-1}\) and adding \(3f_n\) from the second equation, we eliminate the first-order derivative term and retain the second-order derivative term. Dividing the result by \(2h\) gives us the desired finite difference approximation to \(O(h^2)\).

In conclusion, the finite difference approximation for a Neumann boundary condition, \(\left(\frac{df}{dx}\right)\), at node \(n\) (right boundary) to \(O(h^2)\) is \(\left(\frac{df}{dx}\right)_n \approx \frac{f_{n-2} - 4f_{n-1} + 3f_n}{2h}\). This approximation is obtained by manipulating the Taylor series expansion of \(f_{n-1}\) and \(f_n\) to eliminate the first-order derivative term and retain the second-order derivative term, resulting in a second-order accurate approximation.

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Answer: Answer in picture

Step-by-step explanation:

Math

Answer:

*8

Step-by-step explanation:

6.75*8=54

Answer:

8

Step-by-step explanation:

..…..............…...

Answer:

Length = 6.49 cm

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Since we're already given the area and width and want to find the length, we can first rewrite the area formula in terms of l:

A/w = l

Now, we can plug in 25.311 for A and 3.9 for w to solve for l, the length:

25.311 / 3.9 = l

6.49 cm = l

We can check that 6.49 is the correct length by plugging everything into the regular area formula and checking that we get 25.311:

25.311 = 6.49 * 3.9

25.311 = 25.311

Answer:

\(=6g^2-9g+4\)

Step-by-step explanation:

So we have the expression:

\((3g^2-g)+(3g^2-8g+4)\)

Combine like terms:

\(=(3g^2+3g^2)+(-g-8g)+(4)\)

Add or subtract:

\(=6g^2-9g+4\)

This is the simplest it can get.

And we're done!

The functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.The given differential equation is, y''+4y'+4y=e^t ...(1)

We have to find the solutions of the differential equation. Let's solve the differential equation:(1) => r²+4r+4=0Now, solve the quadratic equation using the quadratic formula: r= (-(4)+√((4)²-4(1)(4))) / 2(1)= -2 (repeated)So, the solution of the corresponding homogeneous equation is:(2) yh= (c₁+c₂t)e^(-2t) ---------------(2)Now, we have to find a particular solution of the non-homogeneous differential equation (1).

Let, yp= Ae^t. Now, yp'= Ae^t, yp''= Ae^t. Substitute yp and its derivatives in the equation (1):yp''+4yp'+4yp= e^tAe^t+4Ae^t+4Ae^t= e^t9Ae^t= e^tA= 1/9Therefore, the particular solution is,(3) yp= e^t/9 ------------(3)

Hence, the general solution of the given differential equation is,(4) y= yh+yp= (c₁+c₂t)e^(-2t) + e^t/9Now, substitute the initial conditions in the general solution to get the constants c₁ and c₂:Let, y(0)=0 and y'(0)=0, then,c₁= -1/9 and c₂= 5/9Finally, the solution of the differential equation y''?4y'+4y=e^t is,(5) y= -(1/9)e^(-2t) + (5/9)te^(-2t) + e^t/9 =(e^(2t)+te^(2t))/9+ e^t ...

(Ans)The options that represent the functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.

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Step-by-step explanation:

Given

\( \frac{x}{4} = \frac{1}{3} \\ cross \: multiply \\ 3x = 4 \\ x = \frac{4}{3} \)

Hope it will help :)

Answer:

1/3×4 = 1, 3

x is 1,3

Step-by-step explanation:

hope this helps!

Answer:

Negative infinity, positive infinity

Step-by-step explanation:

The x values go forever in both ways

Answer:

Negative infinity, positive infinity

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

use 0 and 3 for example:

replace x with 0 give you 2*0=0

add 0 with 3 and you get 3

Answer: The answer is no solution because the x cancels out