If x is positive, and x is decreased by 3, then a^2 - x^2 is
a) increased by 6x-9
b) increased by 6x
c)decreased by 9
d)increased by 6x+9
e)decreased by 6x-9
Well, well, well... Let's break it down, shall we? If x is positive and it's decreased by 3, we get x - 3. Now, let's look at a^2 - x^2. Since we know that x - 3 replaces x, we have a^2 - (x - 3)^2. And when we expand that expression, we get a^2 - (x^2 - 6x + 9). Voila! That means it would be decreased by 6x - 9, my friend! So the answer is e) decreased by 6x-9.
To solve this problem, let's go through step by step:
1. We first need to determine the value of x when it is decreased by 3. Since x is positive, this means x - 3.
2. The expression we need to evaluate is a^2 - x^2.
3. Substituting x - 3 into the expression, we get a^2 - (x - 3)^2.
4. Expanding (x - 3)^2, we get (x - 3)(x - 3) = x^2 - 6x + 9.
5. Substituting this back into our expression, we have a^2 - (x^2 - 6x + 9).
6. Simplifying further, we have a^2 - x^2 + 6x - 9.
So, the expression a^2 - x^2 is decreased by 6x - 9 (option e).
To determine how a^2 - x^2 changes when x is decreased by 3, we need to first find the difference between a^2 - x^2 before and after the decrease.
Let's start by considering a^2 - x^2 before the decrease. We have:
a^2 - x^2
To find the difference when x is decreased by 3, we substitute x with (x - 3) in the expression:
a^2 - (x - 3)^2
Expanding the square term, we have:
a^2 - (x^2 - 6x + 9)
Now, let's simplify the expression:
a^2 - x^2 + 6x - 9
Comparing this with the original expression (a^2 - x^2), we can see that the difference is 6x - 9.
Therefore, the correct answer is (a) increased by 6x-9.
well, a^2-(x-3)^2 = a^2-x^2+6x-9, so ...
well...
x^2 is
(x - 3)^2
= (x-3)(x-3)
= x^2 -3x -3x +9
= x^2 - 6x + 9
So... does that help you?
Look back at what the question says... then use my hint.