algebra
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mparis said:
(400/1000) x 100 = (2/5 or 0.4) x 100=40%
http://www.wolframalpha.com/input/?i=400,000/1,000,000
(150/1000) x 100 = (3/20 or 0.15) x 100=15%
http://www.wolframalpha.com/input/?i=150,000/1,000,000
(50/1000) x 100 = (1/20 or 0.05) x 100=5%
http://www.wolframalpha.com/input/?i=50,000/1,000,000
D
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mparis said:
mparis said:
Here's a method taught in about 7th grade:
part / whole = percent / 100
So....for your first problem, the "part" is 400,000, and the whole is 1,000,000. Let x = the unknown percent.
part / whole = percent / 100
400000/1000000 = x/100
I hope you can solve this proportion.
this is just foiling and solving right?
here's how i did it:
(12x )(-2x^3 2y^2)
=(12x(-2x^3)12x(2y^2))------>i know that (12(-2)=-24) and that (x^1(x^3)=x^4), (12(2)=24) and that (x is multiplied my nothing, y^2 stays the same)
=-24x^4 (24xy^2)
=-48x^4 y^2
http://www.wolframalpha.com/input/?i=(12x+)(-2x^3+2y^2)
here's how i did it:
(12x )(-2x^3 2y^2)
=(12x(-2x^3)12x(2y^2))------>i know that (12(-2)=-24) and that (x^1(x^3)=x^4), (12(2)=24) and that (x is multiplied my nothing, y^2 stays the same)
=-24x^4 (24xy^2)
=-48x^4 y^2
http://www.wolframalpha.com/input/?i=(12x+)(-2x^3+2y^2)
mmm4444bot
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mertz said:
Neither.
This is multiplying two polynomials together, but FOIL is not the right terminology here.
FOIL is a process of multiplying together two binomials; there are no binomials, in this exercise.
This is just two properties, one of operations and one of exponents.
The Commutative Property says that we can multiply factors in any order.
The property for multiplying powers says that we add exponents, if the bases are the same variable.
So, we don't even need the parentheses; although, I'll use them around the negative number, to separate the operations there.
\(\displaystyle 12 \cdot x \cdot (-2) \cdot x^3 \cdot 2 \cdot y^2\)
Rearrange the order of these factors, so that constants are next to constants, and like-base powers are next to each other.
\(\displaystyle 12 \cdot (-2) \cdot 2 \cdot x \cdot x^3 \cdot y^2\)
Now simplify.
12*(-2)*2 = -48
Adding exponents 1 + 3 gives 4.
x^4
Putting it all together: -48 x^4 y^2
Hey gurl, next time, please click the [NewTopic] button to start your own discussion. K?
mmm4444bot
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mertz said:
I suspect that gurl was mildly confused before arriving, so I wouldn't bother over what you might have done to her thinking.
Math nerds generally agree on the following.
The word "distribute" applies when multiplying a sum or difference by some quantity.
A(B + C) = A*B + A*C
But, there are no plus signs or minus signs inside the parentheses in gurl's given expression, so even though gurl needs to multiply factors together (like A times B), there is no "distributing" of the 12 across a sum or difference.
12x * (-2x^3 * 2y^2)
See? No sum or difference of any terms here.
I could also use the associate property to regroup the factors, and start breaking the expression down into more and more factors.
(12x) * (-2x^3) * (2y^2)
(12)(x)(-2)(x^3)(2)(y^2)
(12)(x)(-2)(x)(x)(X)(2)(y)(y)
Each of these three lines is just an expression. The same expression, but factored differently.
If the given expression were to be the following INSTEAD, then we would distribute.
12x * (-2x^3 - 2y^2) = (12x)*(-2x^3) - (12x)*(2y^2)
The verb "to solve" in mathematics generally refers to solving an equation. Equations always contain an equals sign. Gurl's given expression is just that, an "expression".
(When two expressions are separated by an equals sign, then that is an equation; a statement that the two expressions have the same value.)
Gurl simply needs to "multiply the factors together as much as possible". We call that process "to simplify".
Finally, "collecting like-terms" applies only to adding and subtracting. When two factors are multiplied together, like x^2 * x^5, we don't "collect" to get x^7 (unless you want to think of collecting insofar as multiplication is nothing more than repeated addition, but I don't think you want to think that.)
Like-terms always have the same exponents, not just the same base.
3x^2 + 4x^2
These are like-terms, so we can "collect" them by simply adding the multiples of x^2 together. Factor first, if you want to see it explicitly.
x^2 * (3 + 4) = 7x^2
The following are not like-terms.
3x^2 + 4x^5
We cannot simplify this expression at all.
Lastly, you might see the word "expand" in some exercise instructions. Like: "Expand the following".
(4x - 5)(7x + 8)
In math, "to expand" means to multiply out (often using the distributive property shown above).
4x - 5 is a binomial (a polynomial with 2 terms)
7x + 8 is also a binomial.
To expand their product (4x - 5)(7x + 8), we use FOIL (which is basically applying the distributive property twice).
Cheers ~ Mark