Question

1. the perimeter ( p ) (in yards) of a soccer field is represented by the formula ( p = 2l + 2w ), where ( l ) is the length (in yards) and ( w ) is the width (in yards).

a. solve the formula for ( w ).
b. the perimeter of the soccer field is 330 yards. find the width of the field.
c. about what percent of the field is inside the circle?

1. consider the equation ( |4x + 20| = 6x ). without solving, how do you know that ( x = -2 ) is an extraneous solution?
2. you use the equation ( \frac{m}{5} - 26 = 2l - \frac{1}{2}g ) to calculate the amount of money ( m ) in your account at the end of the month, where ( l ) is the number of lawns mowed and ( g ) is the number of gallons of gas used.

a. solve the equation for ( m ).
b. what does 130 represent in your equation from part (a)?
c. how much money is in your account at the end of the month when you mow 7 lawns and use ( 11\frac{1}{2} ) gallons of gas?

1. the speed of light is 11,176,920 miles per minute, and the distance from earth to the sun at a specific time is 92,955,807 miles. about how long does it take for sunlight to reach earth?

Explanation:

Step1: Isolate the term with \(M\)

Given \(\frac{M}{5}-26 = 2\ell-\frac{1}{2}g\), add \(26\) to both sides:
\(\frac{M}{5}=2\ell-\frac{1}{2}g + 26\)

Step2: Solve for \(M\)

Multiply both sides by \(5\):
\(M = 5(2\ell-\frac{1}{2}g + 26)=10\ell-\frac{5}{2}g+130\)

Answer:

\(M = 10\ell-\frac{5}{2}g + 130\)