What are the solutions to m2 – 9 = 0?

m2-9=0

Step-by-step explanation:

Two solutions were found :

m = 3

m = -3

Step by step solution :

Step  1  :

Trying to factor as a Difference of Squares :

1.1      Factoring:  m2-9  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3

Check :  m2  is the square of  m1  

Factorization is :      (m + 3)  •  (m - 3)  

Equation at the end of step  1  :

 (m + 3) • (m - 3)  = 0  

Step  2  :

Theory - Roots of a product :

2.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2      Solve  :    m+3 = 0  

Subtract  3  from both sides of the equation :  

                     m = -3

Solving a Single Variable Equation :

2.3      Solve  :    m-3 = 0  

Add  3  to both sides of the equation :  

                     m = 3

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

1696 hundred thousand

step-by-step explanation: