Answer:
25x^2 - 60xy + 36y^2
Step-by-step explanation:
(5x - 6y) ( 5x - 6y)
Use foil to get the result when this is expanded.
F: (first term in each factor): 5x*5x = 25x^2
I: Use the last term first factor multiplied by first term second factor
- 6y * 5x = - 30xy
O:Outside. Use first term first factor and last term second factor
5x * -6y = - 30xy
L: last term in both factors -6y * - 6y = 36y^2
All them together
25x^2 - 30xy - 30xy + 36y^2
and combine
25x^2 - 60xy + 36y^2
First of all, the identity property of multiplication (which is what this is I'm assuming) is that the number 1 multiplied by any other number is that number itself. (An example would be 2 multiplied by 1, which would be two) So in this problem, this rule applies too, since 2/3 multiplied by 1 would be 2/3!
Hope this helped :)
The original functions are: f(n) = 500 and g(n) = [9/10]^(n-1)
A geometric sequence combining them is: An = f(n)*g(n) = 500*[9/10]^(n-1):
Some terms are:
A1= 500
A2 = 500*[9/10]
A3 = 500*[9/10]^2
A4 = 500*[9/10]^3
....
A11 = 500*[9/10]^10 ≈ 174.339
Answer: the third option, An = 500[9/10]^(n-1); A11 = 174.339
Answer:
Step-by-step explanation:
Given a general quadratic formula given as ax²bx+c = 0
To generate the general formula to solve the quadratic equation, we can use the completing the square method as shown;
Step 1:
Bringing c to the other side
ax²+bx = -c
Dividing through by coefficient of x² which is 'a' will give:
x²+(b/a)x = -c/a
- Completing the square at the left hand side of the equation by adding the square of half the coefficient x i.e (b/2a)² and adding it to both sides of the equation we have:
x²+(b/a)x+(b/2a)² = -c/a+(b/2a)²
(x+b/2a)² = -c/a+(b/2a)²
(x+b/2a)² = -c/a + b²/4a²
- Taking the square root of both sides
√(x+b/2a)² = ±√-c/a + b²/√4a²
x+b/2a = ±√(-4ac+b²)/√4a²
x+b/2a =±√b²-4ac/2a
- Taking b/2a to the other side
x = -b/2a±√√b²-4ac/2a
Taking the LCM:
x = {-b±√b²-4ac}/2a
This gives the vertex form with how it is used to Solve a quadratic equation.
To find your constant of variation, you just need to figure out what you multiply the x by in order to get f(x). In other words, what do you multiply the 3 by to get 6? What do you multiply the 7 by to get 14? Another way to think of it is to divide f(x) by the x to get your constant.
