Making connection(math)?

Question

1.)Describe the ways in which a formula is like an equation.how is a formula diff from an equation?explain?

2.)when is it helpful to use a variable?

3.)Describe some methods for solving an equation,show an example of each method?


plsssssss help me.....i cant figure it out....
i dont knw how to do it!!!!please...thax

Answer 1

If those questions were for someone who is just learning algebra, whoever come up with these question should themselves. I don't even know what subjects those questions are appropriate for, Mathematical Theories at graduate level? Here are the answers I come up with:

1. in math context, formulas are expression consist mostly variables. such as x^2+2y or x^2+2x+3. Equations always have equal signs in the expressions as to' equate', such as y=x^2+2 or x^+2x+1=9.

2. Variables are helpful to express values involving unknowns and when unknowns are turned to variables in equations, the variables can be clearly solved with various algebra techniques.

3. (1) factoring x^2+2x-8=0 (x-2)(x+4)=0
(2) quadratic equation: x^2+2x-8=0 a=1, b=2, c=-8
x =(-b±square root of (b^2-4ac))/2a = ( -2 ± square root of (2^2-4*1*(-8))/2*1 = 2, 6


XR

Answer 2

A formula is basically a set of instructions on how to get one value from another (e.g. multiply by 3, add 5, and then square the result: (3x+5)^2). An equation is when we say that the formula result is a particular value (are that two formulas have equal results). An equation is either true or false for any particular value of the input variables, whereas a formula is not true or false but has a certain value.

It is helpful to use a variable when you have an unknown quantity that needs to be manipulated.

Simple arithmetic: 3x = 9 => x = 9/3 => x = 3
Simplification: (x-3) (x+4) - x(x - 1) = 5 => x^2 - 3x + 4x - 12 - x^2 + x = 5 => 2x = 17 => x = 8 1/2
Factorisation: x^2 - x - 20 = 0 => (x-5) (x+4) = 0 => x = 5 or -4