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Nadya [2.5K]
3 years ago
5

A taxi is rented by a group of x people for $40 and the cost is shared equally. If there is one less person in the group then th

e payment by each remaining person is less than $2 than the previous. What are the possible values for x?
Mathematics
1 answer:
anzhelika [568]3 years ago
3 0

Answer:

X = 5  

Step-by-step explanation:

I think there a problem with the question, If there is one less person in the group then the payment by each remaining person is must more than $2 than the previous, because the rent cost unchanged but the number of people in the group decreased.

Before, cost per person : \frac{40}{x}

After cost per person:  = \frac{40}{x -1 }

However, the payment by each remaining person is more than $2 than the previous, so

\frac{40}{x -1 }  =   \frac{40}{x}  + 2

<=> 2x^{2} - 2x -40 = 0

<=> X = 5  

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The endpoints of AB are A(2, 3) and B(8, 1). The perpendicular bisector of AB is CD, and point C lies on AB. The length of CD is
marysya [2.9K]
Comment
If C lies on AB Then it must be the midpoint of AB because CD is the Perpendicular Bisector of AB

Midpoint
A(2,3) B(8,1)
Midpoint formula = (x1 + x2)/2 + (y1 + y2)/2
Midpoint = (2 + 8)/2 + (3 + 1) / 2 
Midpoint = 10/2 + 4/2
Midpoint = (5,2) <<<<< answer


Slope AB
slope = (y2 - y1)/(x2 - x1)
slope = (3 - 1) / (2 - 8)
slope = 2/-6 = -1/3

Slope CD
CD_slope * AB_slope = - 1
CD_slope * -1/3 = -1 multiply both sides by - 3
CD_slope * 1 = - 1 * -3
CD_slope = 3   <<<<< Slope CD Answer

Equation CD
Given the midpoint of AB which is C( and the slope of CD
y = 3x + b
2 = 3*5 + b
b = - 13
Equation y = 3x - 13

Using Distance to get D
d^2 = (x1 - x2)^2 + (y2 - y1)'^2 
d^2 = (x2 - 5)^2 + (y2 - 2)^2
y2 = 3*x2 - 13
10 = x2^2 - 10x2 + 25 + (3x2 - 13 - 2)^2
10 = x2^2 - 10x2 + 25 + (3x2 - 15)^2
10 = x1^2 - 10x2 + 25 + 9x^2 - 90x2 + 225
10 = 10x2^2 - 100x2 +250
0 = 10x2^2 - 100x2 + 240 Divide through by 10
0 = x2^2 - 10x^2 + 24
0 = (x2 - 6)(x2 - 4)
 
x2 = 6 or
x2 = 4

Using y2 = 3x - 13
for x2  = 4
then y2 = 3(4) - 13
y2 = - 1

for x2 = 6
y2 = 3*6 - 13
y2 = 5

Possible Answers  for D
D = (4,-1)
D = (6,5)

I've included a graph to show a graphical solution. 

Please note in a week's time, if no one else answers, you can award a Brainly. This question took over an hour. If someone else answers, please choose one of us.

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Answer:

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Step-by-step explanation:

Easiest and fastest way to evaluate these is to plug it into a calc.

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A scatter plot doesn't need any lines, all it needs is dots.  

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