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Valentin [98]
3 years ago
5

Aidan is participating in an 8 mile walk for his favorite charity. The organizers used a coordinate grid to plot the course. The

starting point is at (3,1) and the ending point is at (3,9). At (3,7), there's a water station to make sure the walkers stay hydrated. How far along will Aidan be in the walk when he reaches the water station?
Mathematics
1 answer:
Travka [436]3 years ago
3 0

Answer:

Aidan is 2 miles far from the ending point when he reaches the water station.

Step-by-step explanation:

The locations of the starting point, water station and ending point are (3, 1), (3, 7) and (3, 9), all expressed in miles. First we determine the distances between starting and ending points and between starting point and water station by the Pythagorean Theorem:

From starting point to ending point:

D = \sqrt{(3-3)^{2}+(9-1)^{2}} (Eq. 1)

D = 8\,mi

From starting point to water station:

d = \sqrt{(3-3)^{2}+(7-1)^{2}} (Eq. 2)

d = 6\,mi

The distance between the water station and the ending point is:

s = D-d (Eq. 3)

s = 8\,mi-6\,mi

s = 2\,mi

Hence, Aidan is 2 miles far from the ending point when he reaches the water station.

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5 watermelons 6 cantaloupes cost $54. 4 watermelons and 8 cantaloupes $56. how much is a cantaloupe
GREYUIT [131]

Answer:

A cantaloupe costs $4

Step-by-step explanation:

Watermelons = W

Cantaloupes = C

Write given statements as equations

5W + 6C = 54

4W + 8C = 56

Simplify the second equation

4W + 8C = 56

Subtract 8C from both sides of the equation

4W = 56 - 8C

Divide both sides of the equation by 4

W = 14 - 2C

Substitute into second equation

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5(14 - 2C) + 6C = 54

Multiply 5(14 - 2C)

70 - 10C + 6C = 54

Add -10C + 6C

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Add 4C to both sides of the equation

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Subtract 54 from both sides of the equation

16 = 4C

Divide both sides of the equation by 4

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A cantaloupe costs $4

5W + 6(4) = 54

Multiply 6(4)

5W + 24 = 54

Subtract 24 from both sides of the equation

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A cantaloupe costs $4

A watermelon costs $6

Hope this helps :)

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3 years ago
The graph below shows the distance d you run, in miles, as a function of time t, in minutes, during a 5-mile run. Your friend sa
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The correct answer for this question is this one:

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Step-by-step explanation:

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Step-by-step explanation:

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