Question

1. rectangles the formula ( p = 2 l + 2 w ) represents the perimeter of a rectangle. in this formula,( l ) is the length of the rectangle and ( w ) is the width.

a. solve the formula for ( l ).
b. find the length when the width is 4 meters and the perimeter is 36 meters.

1. baseball the formula ( a = \frac { h } { b } ) can be used to find the batting average ( a ) of a batter who has

( h ) hits in ( b ) times at bat.
a. solve the formula for ( b ).
b. if a batter has a batting average of 0.325 and has 39 hits, how many times has the player
been at bat?

1. shopping thomas went to the store to buy videogames for ( $ 13.50 ) each and controllers. the

total amount thomas spent can be represented by ( c = 13.50 g + p ), where ( c ) is the total cost, ( g ) is
the number of games he bought, and ( p ) is the cost of the controllers. the controllers cost ( $ 55 ) and
thomas spent ( $ 136 ) total.
a. solve the equation for ( g ).
b. find how many games thomas bought.

Explanation:

19. RECTANGLES

a.

Step1: Solve the formula for \( l \)

Given \( P = 2l+2w \), first subtract \( 2w \) from both sides:
\( P - 2w=2l \)
Then divide both sides by 2:
\( l=\frac{P - 2w}{2}\)

Step1: Substitute values into the formula

We know \( P = 36\) meters and \( w = 4\) meters. Use the formula \( l=\frac{P - 2w}{2}\) from part (a).
Substitute \( P = 36\) and \( w = 4\) into the formula: \( l=\frac{36-2\times4}{2}\)

Step2: Simplify the numerator

Calculate \( 2\times4 = 8\), then \( 36-8=28\). So the formula becomes \( l=\frac{28}{2}\)

Step3: Divide

\( \frac{28}{2}=14\)

Step1: Solve the formula for \( b \)

Given \( a=\frac{h}{b}\), multiply both sides by \( b \):
\( ab = h\)
Then divide both sides by \( a \):
\( b=\frac{h}{a}\)

Answer:

\( l=\frac{P - 2w}{2}\)

b.