Rewrite the perimeter formula, P = 2l + 2w, to solve for the length, l, and then use this formula to find the length of a rectangle whose width is 7 inches and perimeter is 42 inches.

14 inches

Step-by-step explanation:

In the above question, the perimeter formula is given as:

P = 2L + 2W

We are asked to rewrite the formula to solve for L.

This means to make L the subject of the formula

P = 2L + 2W

2L = P - 2W

Divide both sides by 2

L = P - 2W/2

We are to use the above formula to find the length of a rectangle whose width is 7 inches and perimeter is 42 inches.

P = Perimeter

L = Length

W = Width

L = P - 2W/2

L = 42 - 2(7)/2

L = 42 - 14/2

L = 28/2

L = 14 inches

Therefore, the length of the rectangle = 14 inches

There are different ways to solve a quadratic equation, the main ones that i'm thinking about right now are:
1) factor the equation as a product:
 ex:        x^2+ 4x + 3 =0
             (x+3) (x+1) = 0
              x=-3 and x=-1 are the solutions.
To find (x+p) and (x+q) you have to think that (p+q )have to be equal to the number that is multiplied by x, in my example it was 4 (3+1=4), (p times q) have to be equal to the last number of the quadratic equation, the one that is not multiplied by any x, that in my example is 3 (3 x 1= 3)

2) The other way to solve a quadratic function is by using a formula:
    given: ax^2 +bx +c=0
    x= (-b +/- √(b^2 - 4ac)) / 2a
    
 ex: 3x^2 + 4x -2=0
    x= (-4 +/- √16-4(3)(-2)) / 6= (-4 +/- √16+24)/6= (-4 +/- √40) / 6
now there are 2 possibilities: x= (-4+√40) /6
                                                        and
                                              x= (-4 - √40) / 6
I hope the examples were clear enough also if i did't get very nice numbers. Look closely to the sings + and -, they are very important