Answer:
The runner's unit rate is 0.09 miles/minute.
Step-by-step explanation:
Given:
Distance cover by runner = 8 miles and the time taken = 92 minutes.
Now, to calculate the runner's unit rate.
We put the formula to get the unit rate:
Velocity = distance/time
v = 0.09 miles/minute (approximately)
Therefore, the runner's unit rate is 0.09 miles/minute.
Answers:
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How to get those answers:
Let w be the unknown width in centimeters. This variable is some positive real number. This means w > 0 which will be useful later.
The length is "1 cm less than 3 times its width" and it tells us the length is defined by the expression 3w-1. Whatever w is, we triple it to get 3w and then subtract 1 to get the final length.
Multiply the length and width to get the area 102
length*width = area
(3w-1)*w = 102
3w^2-w = 102
3w^2-w-102 = 0
We could guess and check our way to factoring this, but that's not very efficient. The quadratic formula is the better option. It may seem a bit messy, but it's a more direct path that doesn't involve guessing.
We ignore the second solution (w = -5.667 approximately) because we stated earlier that w > 0. In other words, a negative length does not make sense, so that's why we ignore it.
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If w = 6 cm is the width, then 3w-1 = 3*6-1 = 18-1 = 17 cm is the length.
Note that length*width = 17*6 = 102 which is the proper area we want. This confirms the answers.
Answer:
The earning of Sam is $312.5
Step-by-step explanation:
Given as :
The total earning of John and Sam together = $1200 per week
Let the earning of sam each week = x
So, The earning of John is ( 3 x - $50 )
Now, According to question
John earning + Sam earning = $1200 per week
So, ( 3 x - $50 ) + x = $1200
Or, 4 x - $50 = $1200
Or, 4 x = $1200 + $50
Or, 4 x = $1250
∴ x = = $312.5
And ( 3 x - $50 ) = 3 × $312.5 - $50
So, = $ 887.5
Hence The earning of Sam is $312.5 Answer