Magnetism? The melting point changes because of the ice, mass changes, and the colors of the fruits are mixed together
Answer:
![\bigg(\frac{2}{3} {y} \bigg)^{2}](https://tex.z-dn.net/?f=%5Cbigg%28%5Cfrac%7B2%7D%7B3%7D%20%20%7By%7D%20%5Cbigg%29%5E%7B2%7D)
STEP BY STEP EXPLANATION
![\frac{1}{4} {x}^{2} - \bigg( \frac{2}{3} \bigg)xy \\ \\ = \bigg(\frac{1}{2} {x} \bigg)^{2} - 2. \bigg(\frac{1}{2} {x} \bigg)\bigg( \frac{2}{3} y \bigg ) + \bigg(\frac{2}{3} {y} \bigg)^{2} \\ \\ = \bigg(\frac{1}{2} {x} - \frac{2}{3} y\bigg)^{2} \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20%20%7Bx%7D%5E%7B2%7D%20%20-%20%20%5Cbigg%28%20%5Cfrac%7B2%7D%7B3%7D%20%20%5Cbigg%29xy%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%20%5Cbigg%28%5Cfrac%7B1%7D%7B2%7D%20%20%7Bx%7D%20%5Cbigg%29%5E%7B2%7D%20%20-%202.%20%5Cbigg%28%5Cfrac%7B1%7D%7B2%7D%20%20%7Bx%7D%20%5Cbigg%29%5Cbigg%28%20%5Cfrac%7B2%7D%7B3%7D%20y%20%5Cbigg%20%29%20%2B%20%20%5Cbigg%28%5Cfrac%7B2%7D%7B3%7D%20%20%7By%7D%20%5Cbigg%29%5E%7B2%7D%20%5C%5C%20%20%5C%5C%20%20%3D%20%5Cbigg%28%5Cfrac%7B1%7D%7B2%7D%20%20%7Bx%7D%20%20-%20%20%5Cfrac%7B2%7D%7B3%7D%20y%5Cbigg%29%5E%7B2%7D%20%20%5C%5C%20)
To make
a perfect square we should add ![\purple{\bold{\bigg(\frac{2}{3} {y} \bigg)^{2}}}](https://tex.z-dn.net/?f=%5Cpurple%7B%5Cbold%7B%5Cbigg%28%5Cfrac%7B2%7D%7B3%7D%20%20%7By%7D%20%5Cbigg%29%5E%7B2%7D%7D%7D)
Answer:
(x +4)^2 -45
Step-by-step explanation:
The square of a binomial has the form ...
(x +a)^2 = x^2 +2ax +a^2
That is, the constant term (a^2) is the square of half the coefficient of the linear term: (2a/2)^2 = a^2.
To "complete the square", you add 0 in the form of the desired constant added to its opposite. Here, we want the constant for the square to be (8/2)^2 = 16. So, we can add 0 = 16 -16 to the expression:
x^2 +8x +16 -29 -16
(x^2 +8x +16) -45 . . . . group the terms that make the square
(x +4)^2 -45 . . . . rewritten after completing the square
Hello there!
I'm assuming since there is no question, that you want an explanation for composite functions.
Today, I want to introduce you to a very new way of looking at functions. Think of a function as a machine. I'll call this machine f. When you plug something into this machine, it is an x-value. The machine changes the x-value into a new value which is called a y-value. This is how a function works.
With composite functions though, things get a little bit tricky. To make f(g(x)), you need to plug in x into the g machine, and it will give you an output. (y-value) The next thing you do is take that y-value and plug it into the g machine. The g machine then gives you a new value. This value is f(g(x)).
Let's do an example together...
f(x)=3x and g(x)=x²+4
if we want f(g(x)), first plug in x to the g machine. when plugging in x to the g machine, we get x²+4 as given in the question.
Now we must plug in g(x) into the f machine. Since g(x) is x²+4, we just replace x with x²+4.
We get 3(x²+4)
This means that f(g(x))=3(x²+4)
NOTE: If you are seeking help with an actual question, please message me in the comments and I will assist you shortly!
I hope this helps!
Best wishes :)