Answer:
(c) y < x^2 -5x
Step-by-step explanation:
A quadratic inequality is one that involves a quadratic polynomial.
<h3>Identification</h3>
The degree of a polynomial is the value of the largest exponent of the variable. When the degree of a polynomial is 2, we call it a <em>quadratic</em>.
For the following inequalities, the degree of the polynomial in x is shown:
- y < 2x +7 . . . degree 1
- y < x^3 +x^2 . . . degree 3
- y < x^2 -5x . . . degree 2 (quadratic)
<h3>Application</h3>
We see that the degree of the polynomial in x is 2 in ...
y < x^2 -5x
so that is the quadratic inequality you're looking for.
__
<em>Additional comment</em>
When a term involves only one variable, its degree is the exponent of that variable: 5x^3 has degree 3. When a term involves more than one variable, the degree of the term is the sum of the exponents of the variables: 8x^4y3 has degree 4+3=7.
Answer:
Step-by-step explanation:
b.
d.
e.
![\frac{2x^2-10x+12}{x^2-4} *\frac{2+x}{3-x} \\=\frac{2[x^2-5x+6]}{x^2-2^2} *\frac{2+x}{-(-3+x)} \\=\frac{2[x^2-2x-3x+6]}{(x+2)(x-2)} *\frac{x+2}{-(x-3)} \\=\frac{2[x(x-2)-3(x-2)]}{(x+2)(x-2)} *\frac{x+2}{-(x-3)} \\=\frac{2(x-2)(x-3)}{(x+2)(x-2)} *\frac{x+2}{-(x-3)} \\=\frac{2}{-1} \\=-2](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5E2-10x%2B12%7D%7Bx%5E2-4%7D%20%2A%5Cfrac%7B2%2Bx%7D%7B3-x%7D%20%5C%5C%3D%5Cfrac%7B2%5Bx%5E2-5x%2B6%5D%7D%7Bx%5E2-2%5E2%7D%20%2A%5Cfrac%7B2%2Bx%7D%7B-%28-3%2Bx%29%7D%20%5C%5C%3D%5Cfrac%7B2%5Bx%5E2-2x-3x%2B6%5D%7D%7B%28x%2B2%29%28x-2%29%7D%20%2A%5Cfrac%7Bx%2B2%7D%7B-%28x-3%29%7D%20%5C%5C%3D%5Cfrac%7B2%5Bx%28x-2%29-3%28x-2%29%5D%7D%7B%28x%2B2%29%28x-2%29%7D%20%2A%5Cfrac%7Bx%2B2%7D%7B-%28x-3%29%7D%20%5C%5C%3D%5Cfrac%7B2%28x-2%29%28x-3%29%7D%7B%28x%2B2%29%28x-2%29%7D%20%2A%5Cfrac%7Bx%2B2%7D%7B-%28x-3%29%7D%20%5C%5C%3D%5Cfrac%7B2%7D%7B-1%7D%20%5C%5C%3D-2)
k.
If you have a fraction, you can multiply any constant, if you do it on both the top and bottom and get the same answer. For example, multiply 2 on both sides of 1/3 to get 2/6, or 3 times 1/3 to get 3/9. So 2/6 or 3/9 would work.
Answer:
(x+9)(3x+27)
Step-by-step explanation:
3x^2+54x+243 (243×3=729, Product=729, Sum=54) [27+27=54, 27×27=729]
3x^2+27x+27x+243
3x(x+9)+27(x+9)
=(x+9)(3x+27)
