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Answer in explanation

Step-by-step explanation:

Linear Modeling

It's given a situation where a student has two summer jobs and wants to collect $750 to pay for a down payment on a car. He gets paid $25 for each lawn mowed and $15 for each pool cleaned

Let

x = number of lawns mowed

y = number of pools cleaned

He wants to make $750, thus:

25x + 15 y = 750

Dividing by 5, we have the model that represents the linear relationship:

5x  + 3y = 150

The x-intercept can be found by setting y=0:

5x  + 3(0) = 150

5x = 150

Dividing by 5:

x = 150/5 = 30

x = 30

This represents the situation where the student gets his $750 by only mowing 30 lawns, no pools cleaned.

The y-intercept can be found by setting x =0:

5(0)  + 3y = 150

3y = 150

y = 150/3 = 50

y = 50

This represents the situation where the student gets his $750 by only cleaning 50 pools, no lawns mowed.

Starting from the basic equation

5x  + 3y = 150

We can give x some arbitrary value (less than 30) and find the value for y.

For example, for x=12

5*12 + 3y = 150

60 + 3y = 150

3y = 150 - 60 = 90

y = 90/3=30

This solution corresponds to the case where the student gets $750 by mowing 12 lawns and cleaning 30 pools.

For example, for x=21

5*21 + 3y = 150

105 + 3y = 150

3y = 150 - 105 = 45

y = 45/3=15

This solution corresponds to the case where the student gets $750 by mowing 21 lawns and cleaning 15 pools.

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225