triangle DEF is formed by connecting the midpoints of the sides triangle ABC. The lengths of the sides of DEF are shown. what is the length of AB​

The requried length of the AB is given as AB = 16.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
Since triangle DEF is formed by connecting the midpoints of the sides of triangle ABC, the length of the sides of triangle DEF is half the length of the corresponding sides of triangle ABC. That is:

DE = 1/2 AB

EF = 1/2 BC

FD = 1/2 AC

We can use the information about the lengths of the sides of triangle DEF to find the length of AB.

Since DE = 8 and EF = 10, we can use the triangle inequality to find FD:

FD + DE > EF

FD + 8 > 10

FD > 2

Similarly, since EF = 10 and FD = 12, we can use the triangle inequality to find DE:

DE + EF > FD

DE + 10 > 12

DE > 2

Finally, since DE = 8 and FD = 12, we can use the triangle inequality to find EF:

EF + FD > DE

EF + 12 > 8

EF > -4

Since all sides of a triangle must have positive lengths, EF cannot be negative. Therefore, the inequalities we have found imply that:

2 < FD < 12

2 < DE < 8

0 < EF < 10

Since DE = 1/2 AB and EF = 1/2 BC, we can write:

AB = 2DE = 2(8) = 16

BC = 2EF = 2(10) = 20

Therefore, the length of AB is 16.

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Which point is located in Quadrant I? A) (0, -5) B) (0, 0) C) (0, 5) D) (5, 1)












































































































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Because Aaron, age 32, is a smoker, he must pay more for life insurance. Given that Company A charges 20% more for smokers, Company B charges 18% more for smokers, Company C charge 25% more for smokers and Company D charges 15% more for smokers, Aaron decides to buy his $250,000 policy from Company B. Which of the following statements is true? A 5-column table with 3 rows titled Annual Insurance Premiums (per 1,000 dollars of face value) 10 year term. Column 1 is labeled age with entries 30, 31, 32. Column 2 is labeled Company A with entries 1.30, 1.57, 1.86. Column 3 is labeled Company B with entries 1.29, 1.55, 1.86. Column 4 is labeled Company C with entries 1.40, 1.64, 2.07. Column 5 is labeled Company D with entries 1.49, 1.88, 2.25. a. Aaron is paying the smallest premium possible with Company B. b. Aaron is paying $93 more in premiums than he would with Company A. c. Aaron is paying $129 more in premiums than he would with Company C. d. Aaron could have chosen any company because the premiums are all the same.

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If a truck used 25 gallons to travel 375 mies, how many miles would it travel on 4 gallons of gas?​

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The Indian coolies and the ex-slaves, who resented these newcomers flooding into the colonies and driving down wages, were instant rivals. This was convenient for the planters—who were skilled at the game of divide and rule. The planters lumped their workers into two distinct but equally nasty stereotypes: Former slaves were described as lazy, whereas Indians were called meek, docile children. "You may have work and plenty of it for a black man and a coloured man, and they will not do it,” claimed planter W. Alleyne Ireland. He conveniently ignored the fact that the ex-slaves wanted to work their own land, not labor for their former owners. The overseers praised the Indians' meekness but also held them in contempt. The Indian, one overseer claimed, "possesses the low, cringing and abject habit common to his nationality." What evidence do the authors include to support the central idea that Indian workers and formerly enslaved people became rivals? anecdotal evidence that Indian workers and formerly enslaved people were paid wages on different scales empirical evidence that planters ignored the fact that formerly enslaved people wanted to work their own land empirical evidence that planters tried to pit formerly enslaved people against Indian workers to the planters’ advantage logical evidence that Indian workers and formerly enslaved people did not get along with one another because wages went down

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Meg plotted the graph below to show the relationship between the temperature of her city and the number of people at a swimming pool:

Main title on the graph is Swimming Pool Population. Graph shows 0 to 30 on x axis at increments of 5 and 0 to 12 on y axis at increments of 1. The label on the x axis is Temperature in degree C, and the label on the y axis is Number of People at the Pool. Dots are made at the ordered pairs 2.5, 1 and 5, 2 and 7.5, 2 and 7.5, 3 and 7.5, 4 and 10, 5 and 10, 6 and 12.5, 6 and 15, 7 and 15, 8 and 17.5, 5 and 17.5, 7 and 20, 9 and 22.5, 7 and 22.5, 9 and 25, 11 and 27.5, 12.

Part A: In your own words, describe the relationship between the temperature of the city and the number of people at the swimming pool. (5 points)

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Lisa has $7.80 to spend on some tomatoes and a loaf of bread. Tomatoes
cost $1.20 per pound, and a loaf of bread costs $1.80.
The inequality 1.20x + 1.80 s 7.80 models this situation, where x is the
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Solve the inequality. How many pounds of tomatoes can Lisa buy?