*Given
3(x+y)=y
y is not equal to zero
*Solution
1. The given equation is 3(x+y) = y and we are tasked to find the ratio between x and y. Distributing 3 to the terms in the parenthesis,
3(x+y) = y
3x + 3y = y
Transposing 3y to the right side OR subtracting 3y from both the left-hand side and the right-hand side of the equation would give
3x = -2y
Dividing both sides of the equation by 3,
x = (-2/3)y
Dividing both sides of the equation by y,
x/y = -2/3
Therefore, the ratio x/y has a value of -2/3 provided that y is not equal to zero.
Answer:
Step-by-step explanation:
The answer to this question is 12+6sqrt3.
This is because of the 30, 60, and 90 degree rule. The rule states that the hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.
Using the rule you now know that DF is 12. Then use the Pythagorean Theorem to find the length of DE. 12^2=144, and 6^2=36. 144-36=108.
The square root of 108 simplified=6sqrt3.
Then you add them together and get 12+6sqrt3.
If you are trying to create a garden of potted plants, you would find out how much soil each pot needs/holds and multiply that by how many pots you plan to use. then you would go to the store for potting soil, which let’s say came in smaller packs and you need to purchase multiple. use multiplication estimation to estimate how many bags you’d need.
I know this is a dumb example...sorry this is one I remember from my fourth grade math teacher ahah
Answer:
The fourth term of the expansion is -220 * x^9 * y^3
Step-by-step explanation:
Question:
Find the fourth term in (x-y)^12
Solution:
Notation: "n choose k", or combination of k objects from n objects,
C(n,k) = n! / ( k! (n-k)! )
For example, C(12,4) = 12! / (4! 8!) = 495
Using the binomial expansion formula
(a+b)^n
= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n
For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is
C(n,3)a^(n-3)b^3
=C(12,3) * x^(12-3) * (-y)^(3)
= 220*x^9*(-y)^3
= -220 * x^9 * y^3
