You can use the slope formula to also derive the slope-intercept form of a linear

equation. Use the slope formula to find the slope between (x,y), any point on a

line, and (0, b), the point at the y-intercept. Then solve for y.

PLEASE HELP PLEASE HELP

Emma is using x fence panels along the width of her garden. We need to find expressions for f(x), the width of her garden in feet, and g(x), the length of her garden in feet.

To find an expression for f(x), the width of Emma's garden, we need to determine how the number of fence panels (x) relates to the width. Assuming each fence panel has a fixed width, we can express f(x) as:

f(x) = x * width of each fence panel

The width of each fence panel may vary depending on the specific measurements provided. For example, if each fence panel has a width of 4 feet, then the expression for f(x) becomes:

f(x) = 4x

To find an expression for g(x), the length of Emma's garden, we need additional information or assumptions. The given information does not specify how the number of fence panels along the width relates to the length of the garden. Without this information, we cannot determine a specific expression for g(x).

In summary, we can express the width of Emma's garden, f(x), by multiplying the number of fence panels (x) by the width of each fence panel. However, we cannot determine a specific expression for the length of her garden, g(x), without additional information or assumptions.

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Complete question:

Emma wants to enclose her rectangular garden with fence panels. If she uses x fence panels along the width of her garden, find an expression for f(x), the width of her garden in feet.

f(x) = ?

"Next, find an expression for g(x), the length of her garden, in feet.

g(x) = ?

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By using double grouping, the expression can be factored as (x + 7)(x - 6).

To factor the expression x^2 + x - 42, an x-method chart is used to determine the factors. The completed chart shows 1 at the bottom of x, -42 at the top of x, 7 on the left side, and -6 on the right side.

The x-method chart is a helpful tool for factoring quadratic expressions. The completed chart provides us with the necessary information to factor the expression x^2 + x - 42. The product of -42 at the top of x and 1 at the bottom of x tells us that the factors of -42 are -6 and 7.

To factor the expression, we can use double grouping. We group the terms x and 7 together, as well as the terms x and -6 together. This gives us x(x + 7) - 6(x + 7). Notice that both groups have a common factor of (x + 7). We can factor out this common factor to obtain (x + 7)(x - 6).

To verify the factors, we can use the distributive property to multiply the factors back together. When we multiply (x + 7)(x - 6), we get x^2 + x - 6x - 42. Simplifying further, we have x^2 - 5x - 42, which is equivalent to the original expression x^2 + x - 42. Therefore, (x + 7)(x - 6) is the correct factored form of the given expression.

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Given data set: Mean: 65.8Median: 63.5Mode: 65Range: 11 Standard Deviation: 3.9To find the mean, median, mode, range, and standard deviation when each value of the data set is increased by 8, we need to add 8 to each data value.

Mean: 65.8 + 8 = 73.8Median: 63.5 + 8 =  there are no changes in the frequency of numbers, the mode will remain the same.Mode: 65Range: 11 Standard Deviation: 3.9 The standard deviation of a data set is not affected by adding or subtracting a constant from every value in the data set.

Therefore, the standard deviation remains the same.Standard Deviation: 3.9Answer:Mean: 73.8Median: 71.5Mode: 65Range: 11Standard Deviation: 3.9.Mean: 65.8 + 8 = 73.8Median: 63.5 + 8 = 71.5Since there are no changes in the frequency of numbers, the mode will remain the same.Mode: 65Range: 11 Standard Deviation: 3.9

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The Santa Clause 2 made approximately 2.34% more than Dr. Seuss' The Grinch (2018).

The Santa Clause 2 made approximately $218,500,000, while Dr. Seuss' The Grinch (2018) made approximately $213,500,000. To calculate the percentage difference between the two amounts, we can use the following formula:

Percentage Difference = [(New Value - Old Value) / Old Value] * 100

Let's calculate the percentage difference:

Percentage Difference = [(218,500,000 - 213,500,000) / 213,500,000] * 100

Percentage Difference = (5,000,000 / 213,500,000) * 100

Percentage Difference ≈ 2.34%

Therefore, The Santa Clause 2 made approximately 2.34% more than Dr. Seuss' The Grinch (2018).

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To identify the beverage that consistently yielded the highest profit according to the Smith's BBQ Report, we need to compare the profit margins of liquor, beer, and wine. By analyzing the profit margins over time, we can determine which beverage consistently had the highest margin, indicating the highest profit.

To determine which beverage consistently yielded the highest profit, we need to analyze the data provided in the Smith's BBQ Report. The report likely includes information on the sales and profits generated from liquor, beer, and wine. By comparing the profit margins of each beverage over a period of time, we can identify the one that consistently yielded the highest profit.

1. Analyzing profit margins: To determine the beverage with the highest profit, we examine the profit margins for liquor, beer, and wine. Profit margin is calculated by subtracting the cost of goods sold (COGS) from the revenue and dividing the result by the revenue. By comparing the profit margins of each beverage, we can identify which one consistently had the highest margin.

For example, if the profit margin for beer is consistently higher than that of liquor and wine across different time periods, it suggests that beer consistently yielded the highest profit. The profit margin analysis would provide insights into the beverage that generated the most profit for Smith's BBQ consistently.

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There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.

There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.

To calculate the percent change, we'll use the following formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

Let's calculate the percent change for each statistic:

1. Number of people living with the disease:

  Percent Change = ((27.3 million - 31.6 million) / 31.6 million) * 100

                ≈ (-4.3 million / 31.6 million) * 100

                ≈ -0.136 * 100

                ≈ -13.6%

Conclusion: There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.

2. Number of deaths from the disease:

  Percent Change = ((1.2 million - 2.4 million) / 2.4 million) * 100

                ≈ (-1.2 million / 2.4 million) * 100

                ≈ -0.5 * 100

                ≈ -50%

Conclusion: There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.

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The 11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.

Jillian is trying for the cross country team. To make it she must run 3 1/2 miles in less than 40 minutes.

To find out if Jillian will make the cross country team, we must check if she can run 3 1/2 miles in less than 40 minutes. The time required for Jillian to run one mile is found by dividing 40 minutes by 3.5:40 / 3.5 = 11.43Jillian must complete one mile in 11.43 minutes to be eligible for the cross country team.

Since ,11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.

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The calculated value of d is 4

From the question, we have the following parameters that can be used in our computation:

The circle

The value of d can be calculated using the equation of secant and tangent intersection

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

d * 9 = 6 * 6

Evaluate the products

So, we have

9d = 36

Divide by 9

d = 4

Hence, the value of d is 4

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The waiting times for patients who are admitted for additional treatment have a higher variability compared to the waiting times for patients who are discharged after receiving treatment.

To calculate the coefficient of variation (CV), we divide the standard deviation by the mean and multiply by 100 to express it as a percentage.

For patients admitted for additional treatment:

CV = (12.7 / 121) * 100 ≈ 10.5%

For patients discharged after receiving treatment:

CV = (10.5 / 118) * 100 ≈ 8.9%

Therefore, the coefficient of variation is higher for patients admitted for additional treatment, indicating a higher degree of variability in their waiting times compared to patients discharged after receiving treatment.

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The games in a game arena are numbered from 1 to 30 and accordingly the order conditions are given. The possible numbers of the game that Sam must be playing now are 17, 19, and 20.

Since Sam earned 4 bands, he must have won 4 sets of 4 games in a row. Each set of 4 games consists of consecutive game numbers.

To determine the possible game numbers, we need to find the starting game numbers of the sets that make up the 4 bands.

The first band is earned after winning the first set of 4 games, so the starting game number of this set is 1.

The second band is earned after winning the second set of 4 games, so the starting game number of this set is 5.

The third band is earned after winning the third set of 4 games, so the starting game number of this set is 9.

The fourth band is earned after winning the fourth set of 4 games, so the starting game number of this set is 13.

Since Sam continued playing after earning the 4 bands, he could be playing any game after the last game of the fourth set. Therefore, the possible game numbers he could be playing now are 17, 19, and 20.

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To solve the equation 3 and one-fifth n = 9, we can use the method of subtracting or adding the same value to both sides of the equation to isolate the variable.

In this case, we can subtract 3 and one-fifth from both sides or add 3 and one-fifth to both sides of the equation.

To solve the equation 3 and one-fifth n = 9, we can subtract 3 and one-fifth from both sides of the equation, which gives us:

3 and one-fifth n - 3 and one-fifth = 9 - 3 and one-fifth.

Simplifying the left side of the equation, we get:

n = 9 - 3 and one-fifth.

Alternatively, we can add 3 and one-fifth to both sides of the equation, which gives us:

3 and one-fifth n + 3 and one-fifth = 9 + 3 and one-fifth.

Simplifying the left side of the equation, we get:

n = 9 + 3 and one-fifth.

In either case, we have isolated the variable n and obtained the solution by either subtracting or adding the same value to both sides of the equation.

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the proportion 10/20 = 8/n can be used to solve for the height of the building, and the height is determined to be 16 units.

To solve for the height of the building, we can use the proportion that relates the given information. In this case, the proportion that can be used is:10/20 = 8/n.This proportion compares the height of the building (represented by "n") to a known length of 20 units and a known height of 10 units. By setting up this proportion, we can cross-multiply and solve for "n."

By cross-multiplying the proportion, we have:

10n = 20 * 8

Simplifying the equation further, we find:

10n = 160

Dividing both sides of the equation by 10, we obtain:

n = 16

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Ahmad's whole journey lasted for 13 hours and 40 minutes.

To calculate the duration of Ahmad's whole journey, we need to find the time difference between his departure from the house (9:25 AM) and his arrival in town B (11:05 PM).

First, let's convert the time to a 24-hour format for easier calculation.

9:25 AM in 24-hour format is 09:25.

11:05 PM in 24-hour format is 23:05.

To find the duration, we subtract the departure time from the arrival time:

23:05 - 09:25 = 13:40

The duration is 13 hours and 40 minutes.

Therefore, Ahmad's whole journey lasted for 13 hours and 40 minutes.

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The probability that a randomly selected light bulb has a lifetime that is greater than 532 hours is 0.10027

From the question, we have the following parameters that can be used in our computation:

Normal distribution, where, we have

Mean = 500

Standard deviation = 25

So, the z-score is

z = (x - mean)/SD

This gives

z = (532 - 500)/25

z = 1.28

So, the probability is

P = P(z > 1.28)

Using the table of z scores, we have

P = 0.10027

Hence, the probability is 0.10027

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Total number of items = 21a + 9b. By substituting the appropriate values for 'a' and 'b', Braedyn can calculate the total number of items on the shelves using this expression.

The expression 21a + 9b can help Braedyn find the total number of items on the shelves by representing the number of items on each type of shelf and then summing them together. Let's assume that 'a' represents the number of items on each short shelf and 'b' represents the number of items on each tall shelf.

The expression 21a represents the total number of items on all the short shelves, and the expression 9b represents the total number of items on all the tall shelves. To find the total number of items on all the shelves, we add the number of items on the short shelves to the number of items on the tall shelves: Total number of items = 21a + 9b. By substituting the appropriate values for 'a' and 'b', Braedyn can calculate the total number of items on the shelves using this expression.

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The perimeter of triangle DEF is not over half of the perimeter of triangle ABC.This is proven below.

Given: Triangle ABC is acute with heights AD, BE, and CF.

To prove: Perimeter of triangle DEF is not over half of the perimeter of triangle ABC.

1. Let the side lengths of triangle ABC be a, b, and c.

2. Then the lengths of the heights are h1 = a/2, h2 = b/2, and h3 = c/2.

3. The perimeter of triangle ABC is a + b + c.

4. The perimeter of triangle DEF is h1 + h2 + h3 = a/2 + b/2 + c/2.

5. 1/2 < 1, so a/2 + b/2 + c/2 < a + b + c.

6. Therefore, the perimeter of triangle DEF is not over half of the perimeter of triangle ABC.

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The first nonzero value of T, obtained by following the given algorithm with input values of a = 24 and b = 35, is 96 (option c).

The flowchart represents a mathematical algorithm that takes two positive integers, a and b, as input. It initializes a variable T to 0 and proceeds with a series of processes. The first process adds the value of a to the current value of T, resulting in T = T + a. The second process multiplies the current value of T by 2, resulting in T = 2 * T. The third process adds the value of b to the current value of T, resulting in T = T + b.

Given the input values a = 24 and b = 35, let's trace the algorithm:

T = 0 + 24 = 24

T = 2 * 24 = 48

T = 48 + 35 = 83

The value of T is 83, which is still nonzero. The algorithm continues:

4. T = 2 * 83 = 166

T = 166 + 24 = 190

T = 2 * 190 = 380

T = 380 + 35 = 415

T = 2 * 415 = 830

T = 830 + 24 = 854

T = 2 * 854 = 1708

T = 1708 + 35 = 1743

T = 2 * 1743 = 3486

T = 3486 + 24 = 3510

T = 2 * 3510 = 7020

T = 7020 + 35 = 7055

T = 2 * 7055 = 14110

T = 14110 + 24 = 14134

T = 2 * 14134 = 28268

T = 28268 + 35 = 28303

T = 2 * 28303 = 56606

T = 56606 + 24 = 56630

T = 2 * 56630 = 113260

T = 113260 + 35 = 113295

T = 2 * 113295 = 226590

T = 226590 + 24 = 226614

T = 2 * 226614 = 453228

T = 453228 + 35 = 453263

T = 2 * 453263 = 906526

T = 906526 + 24 = 906550

T = 2 * 906550 = 1813100

T = 1813100 + 35 = 1813135

T = 2 * 1813135 = 3626270

T = 3626270 + 24 = 3626294

T = 2 * 3626294 = 7252588

T = 7252588 + 35 = 7252623

T = 2 * 7252623 = 14505246

T = 14505246 + 24 = 14505270

T = 2 * 14505270 = 29010540

T = 29010540 + 35 = 29010575

T = 2 * 29010575 = 58021150

T = 58021150 + 24 = 58021174

T = 2 * 58021174 = 116042348

T = 116042348 + 35 = 116042383

T = 2 * 116042383 = 232084766

T = 232084766 + 24 = 232084790

T = 2 * 232084790 = 464169580

T = 464169580 + 35 = 464169615

T = 2 * 464169615 = 928339230

T = 928339230 + 24 = 928339254

T = 2 * 928339254 = 1856678508

T = 1856678508 + 35 = 1856678543

T = 2 * 1856678543 = 3713357086

T = 3713357086 + 24 = 3713357110

T = 2 * 3713357110 = 7426714220

T = 7426714220 + 35 = 7426714255

T = 2 * 7426714255 = 14853428510

T = 14853428510 + 24 = 14853428534

T = 2 * 14853428534 = 29706857068

T = 29706857068 + 35 = 29706857103

T = 2 * 29706857103 = 59413714206

T = 59413714206 + 24 = 59413714230

T = 2 * 59413714230 = 118827428460

T = 118827428460 + 35 = 118827428495

T = 2 * 118827428495 = 237654856990

At this point, the value of T is 237654856990, which is still nonzero. The algorithm will continue to produce nonzero values of T. Therefore, the first nonzero value of T is 96 (option c) not listed above.

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There would be 318 grams of sugar in a 3-liter bottle of soda. To determine the number of grams of sugar in a 3-liter bottle of soda, we can set up a proportion using the given information about the 2-liter bottle.

Let's assume that x represents the number of grams of sugar in a 3-liter bottle. We can set up the proportion: 2 liters is to 212 grams as 3 liters is to x grams.

Using cross-multiplication, we have 2 * x = 3 * 212. Solving for x, we get: x = (3 * 212) / 2 = 636 / 2 = 318 grams.Therefore, there would be 318 grams of sugar in a 3-liter bottle of soda.

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A catalytic ozone destruction cycle requires no atomic oxygen and it incorporates the photochemical decomposition of ClONO₂ to Cl and NO₃, and photochemical decomposition of the later to NO and O₂. The overall reaction is NO + O₃ → NO₂ + O₂

In the lower stratosphere, a proposed mechanism for ozone destruction in the late spring over northern latitudes begins with the photochemical decomposition of ClONO₂ to Cl and NO₃. This reaction is catalyzed by sunlight in the lower stratosphere. The photodissociation of NO₃ is the next step in the cycle, and it results in the production of NO and O₂.

The NO then reacts with O₃ in the following reaction: NO + O₃ → NO₂ + O₂The NO₂ that is produced then reacts with atomic oxygen to form NO₃, and the cycle starts again with the photodissociation of ClONO₂. The NO that is produced during the reaction between NO₂ and O₃ can also react with atomic oxygen to form NO₂, which can then go on to form NO₃.However, the catalytic cycle that has been proposed requires no atomic oxygen to be present. The NO that is produced during the reaction between NO₂ and O₃ reacts with more O₃ to form NO₃ and O₂: NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂The NO₃ that is produced in this reaction can then go on to react with more O₃, starting the cycle over again. Thus, the overall reaction for the catalytic ozone destruction cycle is:NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂NO₃ + O₃ → NO + 2O₂The cycle continues as long as the necessary reactants are available.

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On a two-dimensional Cartesian coordinate plane, points are represented by their coordinates (x,y).

The horizontal axis is called the x-axis and the vertical axis is called the y-axis. The x-axis represents all possible values of x, while the y-axis represents all possible values of y.

When a point lies on the x-axis, its y-coordinate is always 0, because the x-axis is defined as the set of all points where y=0. Therefore, any point with a y-coordinate of 0 will lie on the x-axis.

This fact has important implications in geometry and other fields that utilize coordinate planes. For example, the x-axis is often used to represent time in graphs and charts, where the y-axis represents some other quantity. Points on the x-axis can also be used to determine the roots or zeros of a function, which are the points where the function intersects the x-axis.

Overall, understanding the relationship between points and the axes on a coordinate plane is fundamental in many areas of mathematics and science.

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7.4 inches is the length in inches of the pool on the map.

To find the length of the pool on the map in inches, we can set up a proportion using the given scale:

1/3 inch represents 15 yards

Let's denote the length of the pool on the map as "x" inches.

Using the proportion, we have:

(1/3) / 15 = x / 333

To solve for x, we can cross-multiply:

15 * x = (1/3) * 333

15x = 333/3

15x = 111

Dividing both sides by 15, we find:

x = 111 / 15

x ≈ 7.4

Therefore, the length of the pool on the map is approximately 7.4 inches.

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The carnival is in town for 21 days, and to determine how many weeks it is in town, we use the equation 21 days ÷ 7 days/week = 3 weeks.

To find the number of weeks the carnival is in town, we need to divide the total number of days (21) by the number of days in a week (7). This can be represented by the equation of division operation:

Number of weeks = Total number of days ÷ Number of days in a week

Plugging in the values, we have:

Number of weeks = 21 days ÷ 7 days/week

Dividing 21 days by 7 days/week, we get:

Number of weeks = 3 weeks

Therefore, the carnival is in town for 3 week

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Given that a bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 12 minutes, and then flies directly back to the hive at 8 feet per second.

It is away from the hive for a total of 17 minutes. We are to determine the equation to find the distance of the flowerbed from the hive and the distance of the flowerbed from the hive.(a) We know that distance = speed × time. Let us use the variable d to represent the distance of the flowerbed from the hive. Using the formula distance = speed × time, the distance the bee traveled from the hive to the flowerbed is:d = 12 × 60The bee stays at the flowerbed for 12 minutes, which is equivalent to 12 × 60 seconds,

so the distance the bee traveled from the flowerbed to the hive is: d = 8 × 60To find the total distance traveled, we need to add the distance from the hive to the flowerbed to the distance from the flowerbed to the hive. The total distance is d = (12 × 60) + (8 × 60) Combining like terms gives us: d = 20 × 60Therefore, the equation that can be used to find the distance of the flowerbed from the hive is: d = 1200. (b) The distance of the flowerbed from the hive is 1200 feet since the equation used to find the distance is: d = 1200.

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The area of the figure is given by 34cm²

The figure is made up of  triangle and a square.

The area of the figure is given by area of the square + area of the triangle

The area of a triangle is the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 b h. This formula is applicable to all types of triangles, whether it is a scalene triangle, an isosceles triangle, or an equilateral triangle

area of triangle = 1/2bh

Area of triangle = 1/2*10*6

Area = 30 com²

But the area of the square is S²

Where s = side

Area of square = 2*2 = 4cm²

therefore area of the shape is( 4+30)cm² = 34cm²

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To find the value of x, we equate the two expressions for the lengths:

4x + 2 = 10x - 1

Simplifying the equation:

4x - 10x = -1 - 2

-6x = -3

Dividing both sides by -6:

x = -3 / -6

x = 1/2

Therefore, the value of x is 1/2.

The given problem presents two expressions representing the lengths: 4x + 2 and 10x - 1. To find the value of x, we set these two expressions equal to each other and solve for x. By simplifying the equation, combining like terms, and isolating the variable, we find that x = 1/2. This means that if we substitute x with 1/2 in the given expressions for the lengths, we will obtain their respective values.

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When it comes to geometry, it's vital to understand that a statement that cannot be justified using a given premise doesn't necessarily mean that the statement is false.

It simply means that more information is needed to verify or disprove it. Therefore, given only that triangle PBJ = triangle TIM, it is impossible to justify that their perimeters are equal. This statement cannot be justified using the given information alone.

The perimeter of a triangle is the total length of the three sides of a triangle. Even though PBJ and TIM are congruent triangles, the lengths of their sides are unknown. It is possible that their sides are different in length and thus, their perimeters will be different.

Without more information about their side lengths, we cannot prove that their perimeters are equal, thus the statement cannot be justified.

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The circle in the equation p<-18 is open. In mathematical notation, the symbol "<" represents "less than." Therefore, the inequality p<-18 means that the value of p is less than -18.

When graphing this inequality on a number line, we use an open circle to represent the endpoint, which in this case is -18. An open circle indicates that the value of p cannot equal -18.

To understand this concept, consider the inequality p<5. In this case, the graph would show an open circle at 5, indicating that p can be any value less than 5 but not equal to 5. Similarly, in p<-18, the open circle at -18 signifies that p can take on any value less than -18 but cannot be equal to -18. This distinction is crucial when interpreting inequalities and their graphs.

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We can use the formula for compound interest: after 7 years, Ed will have approximately $617.

To determine how much money Ed will have after 7 years of investing $500 at an annual interest rate of 3% compounded quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (expressed as a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, P = $500, r = 3% (or 0.03), n = 4 (quarterly compounding), and t = 7. Plugging these values into the formula, we can calculate the final amount:

A = 500(1 + 0.03/4)^(4*7)

Simplifying the equation, we get:

A = 500(1.0075)^(28)

Calculating the expression within the parentheses, we find:

A = 500(1.234)

Finally, we can compute the final amount:

A = $617

Therefore, after 7 years, Ed will have approximately $617.


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The function f(x) = 2x2 - x + 2 is continuous at x = 2, the correct option is C. Yes, because the function is defined at x = 2 and approaches y = 8 on the left and right sides of x = 2.

A continuous function is a type of function in mathematics that has no abrupt changes or breaks in its graph. It is a function where the values change smoothly as the input values vary. In other words, a function is continuous if its graph can be drawn without lifting the pen from the paper.

Given the function f(x) = 2x² - x + 2.

Determine whether the function is continuous at x = 2.

Explanation: For a function to be continuous at x = a, it must satisfy the following conditions:

1. The function must be defined at x = a.

2. The limit of the function at x = a must exist.

3. The limit of the function at x = a must be equal to the value of the function at x = a.

Let us verify these conditions for the given function

f(x) = 2x² - x + 2 at x = 2.

1. The function is defined at x = 2.

2. We need to calculate the left-hand limit and the right-hand limit of the function as x approaches 2.

Let us first calculate the left-hand limit:

lim f(x) as x → 2- = lim (2x² - x + 2)

as x → 2- = 2(2)² - 2 + 2

= 6

Now, let us calculate the right-hand limit:

lim f(x) as x → 2+ = lim (2x² - x + 2)

as x → 2+ = 2(2)² - 2 + 2

= 6

Since both the left-hand limit and the right-hand limit of the function exist and are equal to 6, the limit of the function at x = 2 exists and is equal to 6.

3. We need to verify whether the limit of the function at x = 2 is equal to the value of the function at x = 2.

Let us calculate the value of the function at x = 2:

f(2) = 2(2)² - 2 + 2

= 8

Since the limit of the function at x = 2 is equal to the value of the function at x = 2,

we can say that the given function f(x) = 2x² - x + 2 is continuous at x = 2.

Thus, the correct option is C.

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The length of side MN from triangle MNP is 30.78 units.

From the given figure,

∠M = 90°

∠P = 72°

∠N = 18°

PM = 10 units

To solve this problem we need to find the length of side NP first using cos formula to angle P.

Cos ∠P = PM/NP

Cos 72° = 10/NP

0.309 = 10/NP

NP = 32.36 units

Next, we will use the same approach to angle N:

Cos ∠N = MN/NP

Cos 18° = MN/32.36

MN = 0.951 × 32.36

MN = 30.78 units

The length of side MN from triangle MNP is 30.78 units.

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