For thanksgiving dinner, Evangelina needs to make 2/7 of a pound of turkey for each of the 35 people he invited if she buys a turkey that weighs 8 pounds, will she have enough?

we get:(x + 2) × x × (x - 1) = 8x³ + x² - 2x - 8 = 0Thus, the equation to model the volume of the compartment is 8x³ + x² - 2x - 8 = 0.

Given that

the compartment must be 2 meters longer than it is wide and its depth must be 1 meter less than its width. Let's assume the width of the compartment to be x meters.

Then, the length of the compartment would be (x + 2) meters as it is 2 meters longer than its width. And the depth of the compartment would be (x - 1) meters as its depth must be 1 meter less than its width.

Now, the volume of the compartment would be given by; V = l × w × d V = (x + 2) × x × (x - 1)As given, the volume of the compartment must be 8 cubic meters.

Hence, we get:(x + 2) × x × (x - 1) = 8x³ + x² - 2x - 8 = 0Thus, the equation to model the volume of the compartment is 8x³ + x² - 2x - 8 = 0.

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To find the amount of the payment that goes towards interest at the 12th payment, you should multiply the balance at the 12th payment by the interest rate which is 8%.

The balance of the loan after 12 payments is $4159.90.

Thus the amount of the payment that goes towards interest at the 12th payment is:

4159.90 × 0.08 = $332.79

The principal amount paid at the 12th payment is the difference between the monthly payment of $187.80 and the amount of interest paid of $332.79.

The principal amount paid at the 12th payment

= $187.80 − $332.79

= −$144.99

The negative answer means that the amount paid is the interest.

To find the balance of the loan after the 35th payment, we will subtract the monthly payment from the balance after the 34th payment.

Therefore, the balance of the loan after the 35th payment is:

380.60 − 187.80 = $192.80

To find the amount of the payment that goes towards interest at the 35th payment, you should multiply the balance at the 35th payment by the interest rate which is 8%.

The balance after the 34th payment is $380.60, so the interest payment at the 35th payment is:

380.60 × 0.08 = $30.44

The principal amount paid at the 35th payment is the difference between the monthly payment of $187.80 and the amount of interest paid of $30.44.

The principal amount paid at the 35th payment

= $187.80 − $30.44

= $157.36

Therefore, the balance of the loan after the 35th payment is:

192.80 − 157.36 = $35.44.

The balance of the loan after the 35th payment is $35.44.

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To find the values of the variables in similar polygons, we need more specific information about the problem.

Similar polygons have corresponding angles that are equal and corresponding sides that are proportional. However, without knowing any specific measurements or relationships between the sides and angles, it is not possible to determine the exact values of the variables. Therefore, we cannot provide a numerical answer without additional information.

In order to solve for the variables in similar polygons, we typically need either the ratio of corresponding side lengths or the measure of at least one angle. With this information, we can set up proportions and solve for the unknown variables. However, since the problem did not provide any measurements or ratios, we cannot proceed with finding specific values for the variables. It is important to have precise information about the relationships between the sides and angles of the polygons in order to calculate the values accurately.

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The probability that they will pick neither the chocolate chip nor the walnut topping is, 0.7

Since, the total of all probabilities is 1.00, or 100%.

Now, In the Venn diagram, we have the probabilities 0.2, 0.4 and 0.1;

these sum to,

0.2+0.4+0.1

= 0.6+0.1

= 0.7.

Therefore, the probability that they will pick neither the chocolate chip nor the walnut topping is,

⇒ 1.00-0.7 = 0.3

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"t" is the independent variable representing the number of minutes since Willie started firing the retro-rocket, while "d" is the dependent variable representing the distance from the surface of Mars

The independent variable "t" represents the number of minutes since Willie started firing the retro-rocket. It is the variable that Willie has control over and chooses to manipulate. By changing the value of "t," Willie can observe how it affects the dependent variable "d," which is the distance from the surface of Mars. The independent variable is typically the input or the cause in a relationship or function.

On the other hand, the dependent variable "d" represents the distance from the surface of Mars. It depends on the value of "t" and is influenced by the independent variable. As Willie changes the number of minutes, the distance "d" changes accordingly. The dependent variable is usually the output or the effect in a relationship or function.

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Answer: 4

Step-by-step explanation:

1 1/3 = 4/3

(4/3)/(1/3)

Basically, 4/1

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The area of a quarter circle with a radius of 18 cm is approximately 254.34 cm² (rounded to the nearest hundredth), using the value of 3.14 for π.

To find the area of a quarter circle, we can use the formula A = (π * r²) / 4, where A represents the area and r is the radius. Plugging in the given radius of 18 cm, we can calculate the area as follows:

A = (3.14 * 18²) / 4

≈ (3.14 * 324) / 4

≈ 1017.36 / 4

≈ 254.34 cm²

Rounding the answer to the nearest hundredth, we find that the area of the quarter circle with a radius of 18 cm is approximately 254.34 cm².

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The selling price of juice that costs a beverage company $0.75 to make with a 35% markup is $1.01.

What is markup?

Markup is the difference between the cost of a product or service and its selling price.

The cost of a product is the amount spent on making or buying the product.

The selling price is the amount for which the product is sold.

Therefore, when a company wants to make a profit, it applies a markup to the cost of the product to determine the selling price.

The markup represents the amount of money a company adds to the cost of a product to make a profit.

Here's how to solve the problem:

A beverage company sells juice in all the major restaurants. It costs the beverage company $0.75 to make each bottle of juice. The company uses a 35% markup. What is the selling price of the juice?

Markup = 35% of the cost

Price = cost + markup

Step 1: Find the markup

Markup = 35% of 0.75

Markup = 0.35 x 0.75

Markup = 0.26

Step 2: Find the selling price

Price = cost + markup

Price = 0.75 + 0.26

Price = 1.01

The selling price of juice that costs a beverage company $0.75 to make with a 35% markup is 1.01.

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Rob has (1/2) * x - $25.75 of his earnings left from this week. This is obtained by subtracting the amount spent on bills and the cost of the video game from his total earnings.

To find out how much of his earnings Rob has left, we need to calculate the portion he spent and subtract it from his total earnings.

Given that Rob spends 1/2 of his earnings on bills, he has 1 - 1/2 = 1/2 of his earnings remaining.

If Rob buys a video game for $25.75, we can subtract this amount from his remaining earnings.

Let's say Rob's total earnings for the week were x dollars.

Amount spent on bills: (1/2) * x

Amount spent on the video game: $25.75

Remaining earnings: x - [(1/2) * x + $25.75]

Simplifying the expression, we have:

Remaining earnings: x - (1/2) * x - $25.75

Remaining earnings: (1/2) * x - $25.75

So, Rob has (1/2) * x - $25.75 of his earnings left from this week.

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Given that y is inversely proportional to the square root of x. When x = 64, y = 4.Therefore, y∝1/√x We need to find the value of x when y = 8.Substitute the given values in the above equation and get:y∝1/√xx1/4= k where k is a constant.

the equation becomes y = k/√x Given that x = 64 and y = 4 ⇒ 4 = k/√64 = k/8⇒ k = 4 × 8 = 32Therefore, the equation becomes y = 32/√x Now, we need to find the value of x when y = 8. Substituting the given value of y in the above equation, we get:8 = 32/√x⇒ √x = 32/8 = 4⇒ x = (4)² = 16Hence, the value of x when y = 8 is 16.

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The composite function that can be used to calculate the final price of Ray's laptop is f(c(p)) = 0.81p.

To determine the composite function that can be used to calculate the final price of Ray's laptop, we need to find the composition of the functions c(p) and f(c).

The function c(p) represents the sale price of the laptop, which is 25% off the original price. It can be expressed as c(p) = 0.75p.

The function f(c) represents the price of the laptop with 8% sales tax. It can be expressed as f(c) = 1.08c.

To find the composite function, we need to substitute c(p) into f(c). So, we have:

f(c(p)) = 1.08 * c(p)

Substituting c(p) = 0.75p:

f(c(p)) = 1.08 * 0.75p

Simplifying:

f(c(p)) = 0.81p

Therefore, the composite function that can be used to calculate the final price of Ray's laptop is f(c(p)) = 0.81p.

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The area is then calculated as (1/2) * base * height, resulting in approximately 39.375 square feet.

To find the area of the actual banner, we need to scale up the dimensions from the drawing to real-world measurements. We are given that 1 inch on the drawing is equivalent to 1.5 feet on the actual banner.

The base of the triangle on the drawing is 5 inches, so the base of the actual triangle will be:

5 inches * 1.5 feet/inch = 7.5 feet

Similarly, the height of the actual triangle will be:

7 inches * 1.5 feet/inch = 10.5 feet

Now that we have the base and height of the actual triangle, we can calculate its area using the formula for the area of a triangle:

Area = (1/2) * base * height

Area = (1/2) * 7.5 feet * 10.5 feet

Area ≈ 39.375 square feet

Therefore, the area of the actual banner will be approximately 39.375 square feet.

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Based on Amadou's measurements, the height of the skyscraper is approximately 97.2 meters.

Amadou measures the angle of elevation from his eye to the top of the skyscraper as 44 degrees. To determine the height of the skyscraper, we can use trigonometry. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

In this case, the opposite side represents the height of the skyscraper, and the adjacent side represents the horizontal distance from Amadou to the base of the skyscraper. We are given that the adjacent side is 164 meters and the angle of elevation is 44 degrees.

Using the tangent function, we can set up the following equation:

tan(44 degrees) = height of skyscraper / 164 meters

To solve for the height of the skyscraper, we rearrange the equation:

height of skyscraper = tan(44 degrees) * 164 meters

Using a scientific calculator or trigonometric table, we find that tan(44 degrees) is approximately 0.9659. Multiplying this value by 164 meters gives us the height of the skyscraper:

height of skyscraper ≈ 0.9659 * 164 meters ≈ 97.2 meters

Therefore, based on Amadou's measurements, the height of the skyscraper is approximately 97.2 meters.

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The length of each side is given as 36 meters. Plugging this value into the formula. The square-shaped land, with each side measuring 36 meters, has an area of 1,296 square meters.

To find the area of a square, we use the formula A = ℓ^2, where A represents the area and ℓ represents the length of one side.

In this case, the length of each side is given as 36 meters. Plugging this value into the formula, we have:

A = 36^2.

Simplifying the equation, we get:

A = 1,296.

Therefore, the area of the square-shaped land is 1,296 square meters. The result is obtained by squaring the length of one side (36 meters) to find the total area within the square.

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we would need a total of 5 buses to accommodate all the students and teachers on the trip.To determine the number of buses needed, we divide the total number of students and teachers by the capacity of each bus, which is 58 people.

238 students + 10 teachers = 248 people

To calculate the number of buses needed, we divide 248 people by 58 people per bus:

248 people ÷ 58 people/bus ≈ 4.276 buses

Since we cannot have a fraction of a bus, we round up to the nearest whole number. Therefore, we would need a total of 5 buses to accommodate all the students and teachers on the trip.

It's important to note that rounding up ensures that there are enough buses to accommodate all the individuals, even if there are some empty seats on each bus.

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1/10 of the baker's total cost for 100 pounds of chocolate sprinkles is 10x dollars.

To find 1/10 of the baker's total cost for 100 pounds of chocolate sprinkles, we need to determine the cost per pound of chocolate sprinkles.

Let's assume the cost per pound of chocolate sprinkles is 'x' dollars.

Since it is mentioned that chocolate sprinkles cost as much per pound as sugar, we can assume that the cost per pound of sugar is also 'x' dollars.

Now, let's calculate the total cost for 100 pounds of chocolate sprinkles:

Total cost = Cost per pound * Number of pounds

Total cost = x * 100

Total cost = 100x dollars

To find 1/10 of the total cost, we multiply the total cost by 1/10:

1/10 of total cost = (1/10) * (100x)

1/10 of total cost = 10x

Therefore, 1/10 of the baker's total cost for 100 pounds of chocolate sprinkles is 10x dollars.

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7,875 lbs.

Old furniture weighs = 1,123 lbs.

Combined weight of furniture and truck = 8,122 lbs.

New items = 876 lbs.

First, subtract the weight of the old furniture from the combined weight:

8,122 lbs - 1,123 lbs. = 6,999 lbs.

Then, add the weight of the new items:

6,999 lbs + 876 lbs. = 7,875 lbs.

The best estimate using compatible numbers is approximately 23.33.

To find the best estimate using compatible numbers for the quotient of -137.56 divided by -6.12, we need to identify compatible numbers that are close to the given values.

Compatible numbers are numbers that are easy to work with mentally and provide a close approximation of the actual values.

Let's consider compatible numbers for -137.56 and -6.12:

For -137.56, we can use -140, which is close to -137.56.

For -6.12, we can use -6, which is close to -6.12.

Now, let's calculate the estimate:

-137.56 ÷ -6.12 ≈ -140 ÷ -6

Dividing -140 by -6, we get:

-137.56 ÷ -6.12 ≈ 23.33

Therefore, the best estimate using compatible numbers is approximately 23.33. By selecting compatible numbers close to the given values and performing the division using those numbers, we can obtain a reasonable estimate of the quotient.

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If the remaining time is greater than or equal to N/P minutes, he will finish in time. Otherwise, he won't be able to finish before the dinner party.

To determine if Noah will finish peeling all the potatoes in time for the dinner party, we need to consider the amount of time he has left and his peeling rate.

Let's assume Noah has N potatoes left to peel and he can peel P potatoes per minute. If he keeps peeling at the same rate, the time required to peel all the remaining potatoes is given by N/P minutes.

If Noah has enough time before the dinner party, meaning the remaining time is greater than or equal to N/P minutes, he will be able to finish peeling all the potatoes.

However, if the remaining time is less than N/P minutes, it means there isn't enough time for Noah to finish peeling all the potatoes before the dinner party.

Therefore, to determine if Noah will finish peeling all the potatoes in time, compare the remaining time with N/P minutes. If the remaining time is greater than or equal to N/P minutes, he will finish in time. Otherwise, he won't be able to finish before the dinner party.

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The correct arrangement is 4.5%, 0.3, and 1/7.

To order the percent, decimal, and fraction from least to greatest, we need to find the appropriate value for each of the blanks using the numbers 0-7 exactly once.

Starting with the percent, we can see that 4.5% is the smallest possible value. Moving to the decimal, 0.3 is the next smallest value. Finally, for the fraction, the only remaining option is 1/7.

Therefore, the correct arrangement from least to greatest is 4.5%, 0.3, and 1/7.

It's important to note that the order may not be unique since there could be other valid combinations using the numbers 0-7. However, based on the given information, 4.5% is the smallest, followed by 0.3, and then 1/7.

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The solution to the system of equations is (x, y) = (2, 1).

Given equations are,1. 1/4x + 1/2y = 5/82. 3/4x - 1/2y = 27/8 - 3/8

Now we will solve these two equations by elimination method:

Multiplying equation 1 by 3 and equation 2 by 2,3/4x + 3/2y = 15/8  -------------- (3)

3/2x - y = 6/8 -------------- (4)

Simplifying equation 3,3/4x + 3/2y = 15/8 -------------- (5)

Multiplying equation 4 by 3,4.5x - 3y = 3 -------------- (6)

Now, we will add equation 5 and equation 6,

3/4x + 3/2y = 15/8 -------------- (5)

4.5x - 3y = 3 -------------- (6)

______________15/4x + 0y = 39/8

Therefore, x = 2.Now, substituting x=2 in equation 4,3/2(2) - y = 6/8-3y = -3/8

Therefore, y = 1.

Hence, the solution to the system of equations is (x, y) = (2, 1).

We are given 2 equations as follows:1/4x + 1/2y = 5/8 ...(i)3/4x - 1/2y = 27/8 - 3/8 ...(ii)

Multiplying equation (i) by 3 and equation (ii) by 2,3/4x + 3/2y = 15/8...(iii)3/2x - y = 6/8 ...(iv)We can write equation (iii) as follows: y = (3/2x - 6/8)/-1 = 3/2x - 6/8Now we substitute this value of y in equation (i)1/4x + 1/2(3/2x - 6/8) = 5/8Simplifying,3/4x - 3/8 = 5/8 => 3/4x = 5/8 + 3/8 => 3/4x = 1 => x = 4/3

Now we substitute this value of x in equation (iv):y = 3/2(4/3) - 6/8 = 2/1 = 2

Therefore, the solution to the system of equations is (x, y) = (4/3, 2).

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There are 32 ounces are in a quart

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

128 ounces in a gallon

Also, we have

4 quart in a gallon

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

128 ounces = 4 quart

Divide both sides by 4

So, we have

32 ounces = 1 quart

Hence, there are 32 ounces are in a quart

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The average speed gives us an indication of how fast the winning car was able to cover the race course on average. The average speed of the winning car in the rally car race was approximately 79.38 miles per hour.

To calculate the average speed of the winning car, we divide the total distance covered (515.97 miles) by the time taken to complete the course (6.5 hours).

Average speed = Total distance / Time taken

Average speed = 515.97 miles / 6.5 hours

Calculating the division, we find that the average speed is approximately 79.38 miles per hour.

The average speed gives us an indication of how fast the winning car was able to cover the race course on average. It is a measure of the car's performance and efficiency over the given time period.

In this case, the winning car had an average speed of 79.38 miles per hour, indicating a relatively fast and efficient performance throughout the race.

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The correct statement is given as follows:

The can of pringles has a z-score close to zero, which means it's more likely to happen.

The z-score formula is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

The z-score for pretzels is given as follows:

Z = (25 - 23)/1.2

Z = 1.67.

The z-score for pringles is given as follows:

Z = (40 - 34)/4

Z = 1.5. -> closer to zero -> more likely to happen.

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Therefore, Janine spends 4/5 of an hour doing these activities.

To determine the fraction of an hour that Janine spends doing the given activities, we need to convert the given times to fractions of an hour. We know that 1 hour is equivalent to 1 whole, which means that half an hour would be equivalent to half of a whole.

Similarly, one-fifth of an hour would be equivalent to 1 ÷ 5, which is 0.2, and one-tenth of an hour would be equivalent to 1 ÷ 10, which is 0.1.

Now, let's add the three times together to find the total time:

1/10 hour making the bed + 1/5 hour getting dressed + 1/2 hour eating breakfast = 1/10 + 2/10 + 5/10= 8/10 (which can be simplified to 4/5).

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The height of a cylinder with a volume of 440 cm³ and a diameter of 4 cm can be found using the formula for the volume of a cylinder and the relationship between the diameter and radius. The simplified expression of (a + 2b)(a^2 - 2ab - 4b^2) is a^3 - 6a^2b - 2ab^2 - 8b^3.

1. We are given the volume of the cylinder as 440 cm³ and the diameter as 4 cm.

2. The formula for the volume of a cylinder is V = πr²h, where V represents the volume, r represents the radius, and h represents the height.

3. To find the height, we need to determine the radius of the cylinder.

4. The diameter is given as 4 cm, and since the radius is half the diameter, the radius would be 2 cm (4 cm ÷ 2).

5. Substituting the known values into the volume formula, we have 440 cm³ = π(2 cm)²h.

6. Simplifying further, we get 440 cm³ = 4π cm²h.

7. Dividing both sides of the equation by 4π cm², we have h = 440 cm³ ÷ (4π cm²).

8. Using a calculator, we can evaluate the right side of the equation to get the numerical value of h.

  h ≈ 440 cm³ ÷ (4 * 3.14 cm²) ≈ 34.91 cm.

9. Therefore, the height of the cylinder with a volume of 440 cm³ and a diameter of 4 cm is approximately 34.91 cm.

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the expression to represent the number of people called at 8:00 using a base and an exponent is B = A x r^n.

In mathematics, the expression to represent the number of people called at 8:00 using a base and an exponent is:

B = A x r^n Where, B = the number of people called at 8:00A = the initial number of people calledr = the common ratio between each consecutive term n = the exponent or number of terms in the sequence.

If you have the first term A, the common ratio r, and the number of terms n, then the formula for the nth term, An is given by the formula:

A[n] = A x r^(n-1) If we know the first term, the common ratio, and the number of terms

, we can calculate the sum of the first n terms of a geometric sequence using the formula:

Sn = (A x (1 - r^n)) / (1 - r)

Thus, the expression to represent the number of people called at 8:00 using a base and an exponent is B = A x r^n.

This formula is based on the principles of geometric sequence, where B represents the total number of people called at 8:00, A is the initial number of people called, r is the common ratio between each consecutive term, and n is the exponent or number of terms in the sequence.

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The sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.

To find the sum of a geometric series, we can use the formula:

S = a * (1 - r^n) / (1 - r)

Where:

S is the sum of the series,

a is the first term of the series,

r is the common ratio,

n is the number of terms in the series.

In this case, the first term (a) is 10, the common ratio (r) is 2, and the number of terms (n) is 12.

Plugging in the values into the formula, we have:

S = 10 * (1 - 2^12) / (1 - 2)

Simplifying further:

S = 10 * (1 - 4096) / (1 - 2)

S = 10 * (-4095) / (-1)

S = 10 * 4095

S = 40,950

Therefore, the sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.

The correct answer is D) 40,950.

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After 10 seconds, the snail is 14 inches away from Diana. Let's assume that Diana is at the origin (0,0) and the snail moves at a constant speed. Let's consider the snail is at point (x, y) and Diana is at the origin (0,0). The snail is moving away from Diana at a constant speed. It moves 2 inches in 4 seconds.

Then the distance traveled by the snail in 1 second is

= 2/4inches

= 0.5 inches.

So, the distance the snail travels from (0,0) in x seconds is 0.5x. After 3 seconds, the snail moves

= 0.5(3)

= 1.5 inches away from Diana, and its distance from her is 9 inches.

So, we have y = 9 + 0.5x. This is the equation for the snail's distance from Diana, y, as a function of time, x.

We can see that the equation y = 9 + 0.5x provides the snail's distance from Diana. Here, y is the distance between Diana and the snail and x is the current time. We can observe that the snail moves at a constant pace of 0.5 inches per second since the coefficient of x is equal to 0.5. The constant term in the equation is 9, which stands for the separation between Diana and the snail at the initial value of x, or 0, the starting point.

Therefore, we can infer that the distance between the snail and Diana, y, as a function of time, x, is represented by the equation y = 9 + 0.5x. The distance between Diana and the snail can be calculated at any time using this equation. The distance between Diana and the snail after 10 seconds, for instance, can be calculated using this equation.

For this,

we substitute x = 10 in the equation and get

y = 9 + 0.5(10)

= 14.

Therefore, after 10 seconds, the snail is 14 inches away from Diana.

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Answer:

Length of ab = 10 units

Step-by-step explanation:

X1 = -2, X2 = -8

Y1 = -4, Y2 = 4

[tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} } \\\sqrt{(-8 -(-2))^{2} + (4-(-4))^{2} } \\\sqrt{(-8+2)^{2} + (4+4)^{2} } \\\sqrt{6^{2} +8^{2}} \\\sqrt{36+64} \\\sqrt{100} \\10[/tex]