Line m is mapped onto line n by a dilation centered at the origin with a scale factor of 2. The equation of line m is 3x−2y=63x-2y=63x−2y=6 . Find the equation for line n showing all work for full credit.

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  3x -2y = 12

Step-by-step explanation:

The constant in the standard form equation for a line is proportional to the distance of the line from the origin. Dilation by a factor of 2 moves the line to twice its original distance from the origin. The equation of the new line will have the constant 2×6 = 12:

  3x -2y = 12

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Additional comment

The actual distance of line ax+by=c from the origin is ...

  d = |c|/√(a²+b²)

The distance from any point in the plane to the line is ...

  d = |ax +by -c|/√(a²+b²)

The previous equation is for the special case of (x, y) = (0, 0), the distance from the origin.

ok

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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