what word are you reminded of when you hear the word radian? discuss this with your team and make a conjecture about how this might relate to a way to measure angles. be prepared to share your ideas with the class.

part B:  In student A's verification the two trigonometric identities are

                             i)  sin²x+cos²x=1 [ Pythagorean trigonometric identity]

                             ii) cot x= cos x/ sin x  [ Ratio trigonometric identities]

                                 tan x= sin x/ cos x

And the identities appeared in step 3 and 6.

What is trigonometric identities?

Trigonometric Identities are being needed whenever trigonometric functions are involved in an expression.  Geometrically, these identities involve  trigonometric functions for example sine, cosine, tangent, cotangent of one or more angles.

Here first trigonometric identity showed in step 3

1 is replaced by sin²x+cos²x.

Based on Pythagorean trigonometric identities if Ф is an acute angle of a right angled triangle then sin²Ф+ cos²Ф = 1.

Another trigonometric identity used in step 6

cot x= cos x/ sin x  

tan x= sin x/ cos x

These are called ratio trigonometric identities.

Hence, In student A's verification the two trigonometric identities are

                             i)  sin²x+cos²x=1 [ Pythagorean trigonometric identity]

                             ii) cot x= cos x/ sin x  [ Ratio trigonometric identities]

                                 tan x= sin x/ cos x

And the identities appeared in step 3 and 6.

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Step-by-step explanation:

In a right triangle such as this   cos R  will equal the other angle' s Sin

  so cos R = sin S

= 24/51

Answer: The length of an arc of a circle is given by the formula:

L = rθ

where L is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.

To find the length of the bottom arc, we have:

L1 = r1θ1

where r1 = 5 inches and θ1 = 135° = (135/180)π radians.

L1 = 5(135/180)π = 16.88 inches (rounded to two decimal places)

To find the length of the top arc, we have:

L2 = r2θ2

where r2 = 23 inches and θ2 = 135° = (135/180)π radians.

L2 = 23(135/180)π = 29.07 inches (rounded to two decimal places)

The difference in length between the top arc and the bottom arc is:

L2 - L1 = 29.07 - 16.88 ≈ 12

Therefore, to the nearest inch, the top arc is 12 inches longer than the bottom arc.

Step-by-step explanation:

Based on the given information, it is explicitly mentioned whether the sample was randomly selected. This means that, based on the sample data, we can estimate the range within which the true proportion of interested participants is likely to fall with 95% confidence.

In statistics, a sample refers to a subset of a population that is selected for analysis or study in order to make inferences about the entire population. It is often not feasible or practical to collect data from an entire population, so a sample is used as a representative subset to gather information and draw conclusions about the larger population.

Here,

(a) The parameter that the confidence interval will estimate is the proportion of people in the area who are interested in participating in the LARPing event.

(b) The conditions that must be met to use a confidence interval procedure for a proportion are:

Random Sample: The survey respondents must be randomly sampled from the population of interest. This ensures that the sample is representative of the population.

Large Sample Size: The sample size must be sufficiently large, typically with at least 10 successes and 10 failures in the sample. This ensures that the sampling distribution of the sample proportion is approximately normal.

Independence: The responses of the survey respondents must be independent of each other. This means that one respondent's answer should not influence the answer of another respondent.

Based on the given information, it is not explicitly mentioned whether the sample was randomly selected or whether the sample size is large enough, and whether the responses are independent. This information would need to be provided or assumed in order to determine if the conditions for using a confidence interval procedure for a proportion have been met.

(c) The appropriate critical value can be found using a table or calculator. For a 95% confidence interval, the critical value is 1.96. The standard error of the sample proportion can be found using the formula:

SE = √(p(1-p)/n)

where p is the sample proportion and n is the sample size. Plugging in the values from the problem, we get:

SE = √(0.288(1-0.288)/1500)

= 0.020

(d) The 95% confidence interval can be calculated using the formula:

sample proportion ± (critical value) x (standard error)

Plugging in the values from the problem, we get:

0.288 ± 1.96 x 0.020

= 0.288 ± 0.0392

The 95% confidence interval is (0.2488, 0.3272).

(e) The interpretation of the confidence interval constructed in part (d) would be: We are 95% confident that the true proportion of people in the area who are interested in participating in the LARPing event lies between the lower and upper bounds of the confidence interval. The larger the confidence interval, the less precise our estimate, but the higher our level of confidence in the range.

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Answer:

the median number of minutes spent on math homework each night is also 40.

the mean number of minutes spent on math homework each night is 40.

The patient will reach a level of Ibuprofen of only 10 mg between the 6th and 7th hour after taking the 200 mg dose.

A logarithm is a mathematical function that measures the relationship between two quantities, by expressing one quantity in terms of another. More specifically, a logarithm is the power to which a base must be raised to produce a given number.

To model the decay of Ibuprofen in the patient's system, we can use the equation:

A = A0 * [tex]e^(-kt)[/tex]

where A is the amount of Ibuprofen in the patient's system after t hours, A0 is the initial amount of Ibuprofen (200 mg in this case), and k is the decay constant.

To find k, we can use the fact that after one hour, the amount of Ibuprofen in the patient's system has decayed to 136 mg:

136 = 200 * [tex]e^(-k)[/tex]

Solving for k, we get k = ln(5/7) ≈ -0.3365.

Now we can use the equation A = 10 mg and solve for t:

10 = 200 * [tex]e^(-0.3365t)[/tex]

Dividing both sides by 200 and taking the natural logarithm of both sides, we get:

ln(0.05) = -0.3365t

Solving for t, we get t ≈ 6.8 hours.

Therefore, the patient will reach a level of Ibuprofen of only 10 mg between the 6th and 7th hour after taking the 200 mg dose. Answer: C.

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We can estimate that around 205,313 cases of measles would have been reported in the U.S. in 1987 if the number of cases reported from 1960 to 1996 decreased linearly.

To estimate the number of measles cases reported in 1987 if the number of cases reported from 1960 to 1996 decreased linearly, we need to use a linear regression model. Linear regression is a statistical method that allows us to estimate the relationship between two variables by fitting a straight line to a set of data points.

In this case, we can use the number of reported measles cases as the dependent variable (y) and the year as the independent variable (x). We can then fit a linear regression line to the data from 1960 to 1996 and use this line to estimate the number of cases in 1987.

Assuming a linear relationship between the number of cases and the year, we can calculate the slope of the regression line as follows:

slope = (500 - 450,000) / (1996 - 1960) = -10,125

This means that the number of reported measles cases decreased by 10,125 per year, on average, between 1960 and 1996.

Using this slope and the known values for 1960 and 1996, we can estimate the number of cases in 1987 as follows:

y = mx + b

where y is the number of cases, m is the slope, x is the year (1987), and b is the y-intercept of the regression line.

We can solve for b as follows:

b = y - mx

where y is the number of cases in 1996, m is the slope, and x is the year (1996).

Substituting in the values, we get:

b = 500 - (-10,125) * 1996 = 20,503,500

Therefore, the equation of the regression line is:

y = -10,125x + 20,503,500

Substituting x = 1987, we get:

y = -10,125 * 1987 + 20,503,500 = 205,313

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Answer:

STAN BTS

Step-by-step explanation:

The final price of the pen is $1.76 after adding the markup percentages by both the wholesaler and the retailer.

The final price is the total amount of money that a customer pays to purchase a product or service. It includes the cost of the product or service plus any additional fees or charges, such as taxes or shipping costs.

The final price of the pen can be found by adding the markup percentages to the original price of $0.50.

Markup by the wholesaler = 60% of $0.50 = $0.30

Price after markup by wholesaler = $0.50 + $0.30 = $0.80

Markup by the retailer = 120% of $0.80 = $0.96

Final price of the pen = $0.80 + $0.96 = $1.76

Therefore, the final price of the pen is $1.76 after adding the markup percentages by both the wholesaler and the retailer.

For example, if a product costs $50 and there is a 10% sales tax, the final price would be $55 (50 + 5). Similarly, if a service costs $100 and there is a $10 delivery fee, the final price would be $110 (100 + 10).

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Answer:

3

Step-by-step explanation:

And also,PLEASE DONT YELL AT ME/US!!

To calculate the probability that the sample mean for a sample of size 45 will be less than 34.5, we can use the Central Limit Theorem (CLT).

The CLT states that, given a large enough sample size, the distribution of the sample means will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Step 1: Identify the population mean (μ) and population standard deviation (σ) from the given information. Since it is not provided in the student question, I will assume that you have already calculated these values.
Step 2: Calculate the standard deviation of the sample mean (σ_sample_mean). This can be done using the formula:
σ_sample_mean = σ / √n
where n is the sample size (45 in this case).
Step 3: Convert the sample mean (34.5) into a z-score using the formula:
z = (x - μ) / σ_sample_mean
where x is the sample mean and μ is the population mean.
Step 4: Use the standard normal distribution table (also known as the z-table) or a calculator to find the probability associated with the calculated z-score. This probability represents the chance that the sample mean will be less than 34.5.
Step 5: Round the probability to the nearest percent.
Following these steps will give you the probability that the sample mean for a sample of size 45 will be less than 34.5, based on the information provided in the question.

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Answer:

5.625 inches

Step-by-step explanation:

We Know

A 6-inch candle burns down in 8 hours.

6 / 8 = 0.75 inches burn down per hour

So, we know 0.75 inches burn down per hour

How far has it burned after 7 1/2 hours?

We take

0.75 x 7.5 = 5.625 inches

So, it burned 5.625 inches after 7 1/2 hours.

Answer:

The answer is A

Step-by-step explanation:

The answer is A, how I learned this was making sure that any combination of a and s would not spell out a bad word! With this in mind, we know that AS$ and SSA are not valid methods for proving triangles congruent!

Hope this helps!

(I had to use a $ symbol because there was an inappropriate word)

An equation that models the relationship of the variables for Ethan's job and its days of paid vacation is y(x) = 10 + 3x.

The number of paid vacation days that Ethan has had in the eight years since work began is 30 paid vacation days.

We are given that Ethan starts with 10 paid vacation days and earns an additional 6 days for every two years, up to a maximum of 6 work weeks (30 days). To find an equation that models this relationship, we can set up a piecewise function as follows:

y(x) = 10 + 3x

To find out how many paid vacation days Ethan has earned after 8 years, we can plug in x = 8 into the piecewise function:

Since 8 > 6, we use the second part of the piecewise function:

y(8) = 30

So, Ethan has earned 30 paid vacation days after working for 8 years at the company.

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The sampling soldiers until her margin of error for a 82% confidence interval is less than 0.004, soldiers should Haley sample is 12,724 soldiers.

The degree of inaccuracy in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error in statistics denotes a reduced chance of relying on a survey's or poll's findings, meaning that there will be less trust in the results' ability to accurately reflect a community. It is a very important tool for market research since it shows the degree of assurance that should be placed in survey data by the researchers.

A confidence interval is a measure of how unpredictable a given statistic is. It is typically used in conjunction with the margin of error to indicate how confidently a statistician feels that the findings of an online survey or online poll are worthy of being considered representative of the total population.

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi (1-\pi)}{n} }[/tex]

In which, z is the z-score that has a p-value of 1+∝/2.

The margin of error is of:

[tex]M=z\sqrt{\frac{\pi (1-\pi)}{n} }[/tex]

Estimate of the proportion of 64%, hence π = 0.64.

94% confidence level

So , ∝ = 0.94 z is the value of Z that has a p-value of , so z = 1.88

Margin of error of less than 0.008 is wanted, hence, we have to find n when M = 0.008.

[tex]M=z\sqrt{\frac{\pi (1-\pi)}{n} }\\0.008 =1.88\sqrt{\frac{0.64(0.36)}{n} } \\0.008\sqrt{n} = 1.88\sqrt{0.64(0.36)} \\n = 12723.84\\[/tex]

Therefore, Haley should sample 12,724 soldiers.

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Step-by-step explanation:

There are several methods to solve a quadratic equation, but the most common ones are:

Factoring:

This method involves factoring the quadratic expression into two linear expressions and setting each factor equal to zero. For example, to solve the equation x^2 + 5x + 6 = 0, you can factor it as (x + 2)(x + 3) = 0, and then set each factor equal to zero to get x = -2 or x = -3.

Using the square roots:

If the quadratic expression can be written in the form of x^2 = a, where a is a constant, then the solutions can be found by taking the square root of both sides. For example, to solve the equation x^2 = 16, you can take the square root of both sides to get x = ±4.

Completing the square and the quadratic formula:

This method involves completing the square on the quadratic expression to obtain an equivalent expression in the form of (x + b)^2 = c, where b and c are constants. The solutions can then be found by taking the square root of both sides and solving for x. Alternatively, you can use the quadratic formula, which is a general formula that gives the solutions of any quadratic equation in the form of ax^2 + bx + c = 0. The quadratic formula is given by x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic expression.

Answer:

see below :)

Step-by-step explanation:

The three common methods for solving quadratic equations are:

Factoring Method:

In this method, the quadratic equation is factored into two binomials, and then the values of x that make each binomial equal to zero are found. This method works only if the quadratic equation can be factored. The factored form of the quadratic equation is:

ax^2 + bx + c = 0

The factors of the quadratic equation are (mx + p) and (nx + q), where m, n, p and q are constants. The factored form of the quadratic equation can be written as:

(mx + p)(nx + q) = 0

The values of x that satisfy this equation are:

x = -p/m or x = -q/n

Using the Square Roots Method:

This method is used when the quadratic equation is in the form of:

x^2 = a

The solutions to this equation can be found by taking the square root of both sides:

x = ± √a

Completing the Square and the Quadratic Formula Method:

This method is used to solve any quadratic equation, even if it cannot be factored. The steps involved in this method are:

Step 1: Rewrite the quadratic equation in the form of:

ax^2 + bx + c = 0

Step 2: Complete the square by adding and subtracting a constant term to the quadratic equation:

ax^2 + bx + c + (b/2a)^2 - (b/2a)^2 = 0

Step 3: Simplify the equation by grouping the first three terms and factoring the perfect square trinomial:

a(x + b/2a)^2 + (c - b^2/4a) = 0

Step 4: Solve for x by taking the square root of both sides and using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

This formula gives two solutions for x, one with the plus sign and one with the minus sign.

Answer:

[tex]x = 4 \frac{1}{2} [/tex]

Variable x in the circle has a value of 9.

The radius of a circle is the distance from any point on the circle to the centre, whereas the diameter is the distance across the circle passing through the centre. The area of a circle is the volume of space inside the circle, whereas the circumference of a circle is the distance around the circle. In geometry and mathematics, circles are frequently used to investigate features including area, circumference, and angles. They are also widely used in fields including physics, engineering, and architecture.

We know that the measure of the central angle of a circle is 360°

75°+13x+91°+x+68=360°

14x=360-68-91-75

x=9

the value of variable x in the circle is 9

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Check the picture below.

so the surface area of the pyramid is really just the area of four triangles with a base of 7 and a height of "h" and a 7x7 square, and we also know that that is 210 yd²

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(\underset{b}{7})(h) \right]}~~ + ~~\stackrel{ square }{(7)(7)}}~~ = ~~210\implies 14h+49=210 \\\\\\ 14h=161\implies h=\cfrac{161}{14}\implies h=11.5[/tex]

Answer:

the square pyramid's slope height is roughly 5.75 yards.

Step-by-step explanation:

The square pyramid's slope height should be "l."

A square pyramid's surface size is determined by:

Surface area equals base area plus (1/2) * base radius plus slope height.

Given that the base's length is 7 yards and the surface size is 210 yards. The base's size is thus:

Base area equals side times side, or 7 times 7 square yards.

As a result, we have:

210 = 49 + (1/2) * 4 * 7 * l

When we simplify the previous solution, we get:

210 - 49 = 28l

161 = 28l

l = 161/28

Consequently, the square pyramid's slope height is roughly 5.75 yards. (rounded to two decimal places).

The graph with all the solutions can be seen in the image at the end of the answer.

We want to solve the 3 quadratic equations and then graph them in a coordinate axis.

Remember that for a complex number z = a + bi, the real part a goes in the horizontal axis and the complex part b goes in the vertical axis.

a) We start with:

m² = 16

m = √16

m = ±4

b) x² = -9

x = ±√-9

x = ±3i

c) t² = -25

t = ±√-25

t = ±5i

The graph of all of these points can be seen in the image at the end.

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The price of a ticket to a baseball game this year is $40.80.

This year's ticket price is 0.85 times last year's ticket price of $48. We can calculate this by multiplying 0.85 by 48:

Using the above as a guide, we have the following:

Total cost = 0.85 × 48

Evaluate

Total cost = 40.80

Therefore, the price of a ticket to a baseball game this year is $40.80.

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The distance from Gladville to Columbus is 144 miles.

The scale of map B is (3.4 cm) / (6.8 cm) = 1/2 that of map A.

Then the distance (d) between the cities is:

= (1.8 cm)/d = (1/2)·(1 cm) / (40 mi)

Multiplying by d·80 mi, we get

 144 mi·cm = d cm

Dividing by cm, we have ...

 144 mi = d

The distance from Gladville to Columbus is 144 miles.

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The units of measurement for prpblck are percentage points, while the units for income are typically a currency, like dollars or euros.

To find the average value of prpblck and income in the sample, you need to sum the values for each variable and then divide by the total number of observations. The average is also known as the mean. The standard deviation is a measure of dispersion that indicates how much the values vary from the mean. To calculate the standard deviation, you will need to find the difference between each value and the mean, square those differences, find the average of those squared differences, and then take the square root of that average.

The units of measurement for prpblck and income depend on the context and data source. Typically, prpblck is expressed as a proportion or percentage, representing the proportion of the population that is black. In this case, the unit of measurement for prpblck would be percentage points. On the other hand, income is usually measured in a currency, such as dollars or euros, and it can be presented as an individual's income or a household's income.

To summarize, to find the average values and standard deviations of prpblck and income in the sample, follow these steps:

1. Calculate the mean by summing the values and dividing by the number of observations.

2. Calculate the standard deviation by finding the square root of the average of the squared differences between each value and the mean.

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Hence, 96 kilometers separate the two tourism destinations in reality as it is a proportion to determine the real distance (in kilometers).

The actual distance is the measurement in feet between the blast site and the closest residence, public structure, school, church, or other commercial or institutional structure that is not owned or leased by the perpetrator of the blast.

Given :

To find the actual distance between the two tourist attractions, we need to use the scale given in the problem.

The scale of the map is 3 inches: 2 km.

We can use this scale to convert the distance on the map (5-5-144 inches) to the actual distance.

First, we need to convert the distance on the map from inches to km. To do this, we divide the distance on the map by the number of inches per km:

1 km = 1,000,000 microns

1 inch = 25,400 microns

1 km = 39.37 inches

So, 5-5-144 inches = (5 x 39.37) + (5 x 39.37) + 144 = 314.96 + 314.96 + 144 = 774.92 inches

Next, we can use the scale to convert the distance on the map from inches to km:

3 inches: 2 km

774.92 inches : x km

where x is the actual distance we are trying to find.

We can solve for x by cross-multiplying and simplifying:

3x = (774.92 x 2) / 2.54

3x = 60929.92 / 2.54

3x = 24000

x = 8000 km

Therefore, the actual distance between the two tourist attractions is 8000 km.

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The statistical test to run in this scenario is a paired t-test.

A paired t-test is appropriate in this situation because it is used to compare the means of two related groups. In this case, the related groups are the same patients measured at two different time points (2 weeks and 6 months after being prescribed a new medication). The paired t-test assumes that the differences between the two time points are normally distributed.

To conduct the test, we would calculate the mean difference between the two time points and the standard deviation of the differences. We would then calculate the t-statistic and compare it to the critical value from the t-distribution with n-1 degrees of freedom. If the calculated t-value exceeds the critical value, we would reject the null hypothesis that there is no difference between the two time points.

Therefore, a paired t-test is the appropriate statistical test to determine whether there is a significant difference in medication adherence between the two time points

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By using the graph of the function shown above, the solution include the following:

f(-7) = -6.

f(-3) = 9.

In Mathematics and Geometry, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.

This ultimately implies that, an input value (x-value) represents the value on the x-axis of a cartesian coordinate while an output value (y-value) represents the value on the y-axis of a cartesian coordinate.

Based on the information provided about this function, an ordered pair that models the situation is given by;

f(-7) = -6  ⇒ Ordered pair (-7, -6).

f(-3) = 9  ⇒ Ordered pair (-3, 9).

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[tex]\textit{area of a sector of a circle}\\\\ A=\theta\cdot \cfrac{ r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{7\pi }{4}\\[1em] r=6 \end{cases}\implies A=\cfrac{7\pi }{4}\cdot \cfrac{6^2}{2} \\\\\\ A=\cfrac{63\pi }{2}\implies A\approx 98.96~in^2[/tex]

Answer:

Red=17.1%

Green=54.3%

Purple=28.6%

All of these answers are rounded.

Step-by-step explanation:

To solve for all, all you have to do is divide the number of trials of the specific color by the total number of trials. To get a percentage you then multiply by 100%.

Red:

12/70=0.171*100%=17.1%

Green:

38/70=0.543*100%=54.3%

Purple:

20/70=0.286*100%=28.6%

To check if you've rounded correctly, add all your values and they should add up to 100 exactly. If it is slightly over or below you may need to go back and check for a rounding error.

the adult population in millions in 2015 was 197.37 million

The student question is asking about the adult population in millions, given that the Bureau of Labor Statistics announced that 141.13 million were employed, 16.59 million were unemployed, and 39.65 million were not in the labor force in 2015.

To find the adult population, we need to add the number of employed, unemployed, and not in the labor force adults. This can be done as follows:

Adult population = Employed + Unemployed + Not in the labor force

= 141.13 million + 16.59 million + 39.65 million= 197.37 million

Therefore, the adult population in millions in 2015 was 197.37 million (rounded to two decimal places).

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This is the slope-intercept form of the equation of the line. To convert it to the standard form, we need to rearrange it so that the x and y terms are on the same side of the equation: [tex](\frac{13}{4} )x + y = -7[/tex]

To find the standard form of the line that passes through the given points [tex](-4, 6)[/tex] and [tex](0, -7)[/tex], we need to first find the slope of the line using the slope formula:

[tex]\text{slope} = \dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]

where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the coordinates of the two points.

Using the given points, we get:

[tex]\text{slope}=\dfrac{(-7-6)}{(0-(-4))}[/tex]

[tex]\text{slope}=-\dfrac{13}{4}[/tex]

Now that we have the slope of the line, we can use the point-slope form of the equation of a line:

[tex]y - y_1= m(x - x_1)[/tex]

where m is the slope and [tex](x_1, y_1)[/tex] is one of the points on the line. Using the point [tex](-4, 6)[/tex], we get:

[tex]y - 6 = \huge \text(-\dfrac{13}{4}\huge \text )(x - (-4))[/tex]

[tex]y - 6 = \huge \text(-\dfrac{13}{4}\huge \text )x-13[/tex]

[tex]y = \huge \text(-\dfrac{13}{4}\huge \text )x-7[/tex]

This is the slope-intercept form of the equation of the line. To convert it to the standard form, we need to rearrange it so that the x and y terms are on the same side of the equation:

[tex]\huge \text(-\dfrac{13}{4}\huge \text )x+y=-7[/tex]

This is the standard form of the equation of the line that passes through the given points.

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