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alex41 [277]
3 years ago
10

Lisa and alice leave alice's house at the same time. lisa drives north and alice drives west. lisa's average speed is 9 mph slow

er than alice's. at the end of one hour, they are 65 miles apart. find alice's average speed. (round your answer to the nearest tenth.)
Mathematics
1 answer:
alina1380 [7]3 years ago
8 0

The direction of movement of both are perpendicular to each other

Let us say Alice's speed = x mph

then speed of Lisa = x- 9 mph

The distance traveled by Lisa in 1 hour = 1 times ( x-9 ) = x-9 miles

the distance traveled by Alice in 1 hour = 1 times x = x miles

the distance between them is : the length of the hypotaneous of the triangle with perpendicular sides being x and x-9

That is : ( x^2 + ( x-9)^2 ) ^(1/2) which is given to be equal to 65

x^2 + ( x-9)^2 = ( 65)^2

x^2 + x^2 + 9^2 - 2* 9 x = 4225

2x ^2 - 18x = 4225 - 9^2

2x^2 - 18x = 4144

dividing each term by 2

x^2 - 9x = 2072

x^2 - 9x - 2072 = 0

we plug a= 1 b= -9 c=-2072 in the quadratic formula

x= [-b +/- ( b^2 - 4ac ) ]/ 2a

x= [ 9 +/- ( (-9)^2 - 4 ( 1)( -2072) ] / 2* 1

x= 50.24 miles /hour

Answer : Alice's average speed is 50.24 miles.

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Answer:

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Step-by-step explanation:

Given:

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Therefore, to drain the water tower it will take 36 hours.

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3 years ago
Jennys room is 13 feet long and 12 feet wide, Ruth's room is 14 feet long and 11 feet wide, whose room has the greater area?
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Therefore Jenny's room is bigger.

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9514 1404 393

Answer:

  17.  5

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Step-by-step explanation:

The distance formula is used for the purpose.

  d = √((x2 -x1)² +(y2 -y1)²)

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17. d = √((3-6)² +(1-5)²) = √((-3)² +(-4)²) = √(9+16) = √25 = 5

The distance between the points is 5 units.

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3 years ago
Read 2 more answers
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