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3 years ago

How far is football field to the park? show your work

Mathematics

1 answer:

nalin [4]3 years ago

6 0

Answer:

10.95 miles

Step-by-step explanation:

$a = Park\ to\ Home\\\\b = Park\ to\ Football\ Field \\\\t_{h} = Park\ to\ Library\\\\t_{h} = \sqrt{a^{2} - 2^{2} } \\\\t_{h} = \sqrt{b^{2} - 10^{2} } \\\\b = \sqrt{12^{2} - a^{2} } \\\\-----------\\\\a^{2} - 2^{2} = 12^{2} - a^{2} - 10^{2} \\\\2a^{2} = 144 - 100 + 4 = 48 \\\\a = \sqrt{24} = 4.9\ miles \\\\-----------\\\\b = \sqrt{144 - 24} = \sqrt{120} = 10.95\ miles$

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#1) We want a line that passes through (1, -3) and is parallel to y = 2-4(x-1). First we simplify our equation using the distributive property:

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Subtract 2x from each side"

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This means the slope is -2; the slopes are the same, so the lines are parallel.

#3) The slope of our given equation is 2. To be perpendicular, the second line must have a slope that is a negative reciprocal (flipped and opposite signs); this makes it -1/2. Using point-slope form,

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#4) The slope of Main Street on the diagram, found by using rise/run, is 2. This means the bike path will also have a slope of 2 in order to be parallel. The park entrance is at (0, 4). This makes the equation y = 2x+4.

#5) Two lines with the same slope are always parallel. They are never perpendicular.

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2 years ago

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How far is football field to the park? *show your work*

How far is football field to the park? show your work