36 is, 15 is not
A perfect square is the result you get from squaring a number. 36 is one because 6x6 equals 36
Answer:
This is a rectangular prism
Step-by-step explanation:
As you can see from my attachment, this figure models a rectangular prism when put together :)
Answer:
5
Step-by-step explanation:
Hi,
find the x- and y-intercepts:
10x + 4y = 20
finding x-intercept when y = 0
10x = 20
x = 2 Pt(2,0) the x intercept
finding y-intercept when x = 0
4y = 20
y = 5 Pt(0,5) the y intercept
Answer:
1/2, 3
Step-by-step explanation:
This is a pretty involved problem, so I'm going to start by laying out two facts that our going to help us get there.
- The Fundamental Theorem of Algebra tells us that any polynomial has <em>as many zeroes as its degree</em>. Our function f(x) has a degree of 4, so we'll have 4 zeroes. Also,
- Complex zeroes come in pairs. Specifically, they come in <em>conjugate pairs</em>. If -2i is a zero, 2i must be a zero, too. The "why" is beyond the scope of this response, but this result is called the "complex conjugate root theorem".
In 2., I mentioned that both -2i and 2i must be zeroes of f(x). This means that both
and
are factors of f(x), and furthermore, their product,
, is <em>also</em> a factor. To see what's left after we factor out that product, we can use polynomial long division to find that
![2x^4+5x^3+5x^2+20x-12=(x^2+4)(2x^2+5x-3)](https://tex.z-dn.net/?f=2x%5E4%2B5x%5E3%2B5x%5E2%2B20x-12%3D%28x%5E2%2B4%29%282x%5E2%2B5x-3%29)
I'll go through to steps to factor that second expression below:
![2x^2+5x-3=2x^2+6x-x-3\\=2x(x+3)-(x+3)\\=(2x-1)(x+3)](https://tex.z-dn.net/?f=2x%5E2%2B5x-3%3D2x%5E2%2B6x-x-3%5C%5C%3D2x%28x%2B3%29-%28x%2B3%29%5C%5C%3D%282x-1%29%28x%2B3%29)
Solving both of the expressions when f(x) = 0 gets us our final two zeroes:
![2x-1=0\\2x=1\\x=1/2](https://tex.z-dn.net/?f=2x-1%3D0%5C%5C2x%3D1%5C%5Cx%3D1%2F2)
![x+3=0\\x=-3](https://tex.z-dn.net/?f=x%2B3%3D0%5C%5Cx%3D-3)
So, the remaining zeroes are 1/2 and 3.
Answer:
The last one which you was on is correct.