Step-By-Step Explanation:
(5 + 7) + 6y
associative
because the brakets' spots changed
12 + 6y
combining
because they combined the same type of terms
6y + 12
commutative
because they changed the spots of the 2 terms
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A.
the radicand is b²-4ac
if it is in form ax²+bx+c
when it is
greater than 0, then 2 real roots
equal to 0, then 1 real root
less than 0, then no real roots
so
a=4
b=-12
c=10
b²-4ac=(-12)²-4(4)(10)=144-160<0
so 0 real roots
B.
using quadratic formula because it is easier
for
ax²+bx+c=0
![x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%2B%2F-%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
so
for 2x²-13x+21
a=2
b=-13
c=21
![x=\frac{-(-13)+/-\sqrt{(-13)^2-4(2)(21)}}{2(2)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-13%29%2B%2F-%5Csqrt%7B%28-13%29%5E2-4%282%29%2821%29%7D%7D%7B2%282%29%7D)
![x=\frac{13+/-\sqrt{169-168}}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B13%2B%2F-%5Csqrt%7B169-168%7D%7D%7B4%7D)
![x=\frac{13+/-\sqrt{1}}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B13%2B%2F-%5Csqrt%7B1%7D%7D%7B4%7D)
![x=\frac{13+/-1}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B13%2B%2F-1%7D%7B4%7D)
x=(13+1)/4 or (13-1)/4
x=14/4 or 12/4
x=7/2 or 3
5r + 8 < 63
5r < 63 - 8
5r < 55
r < 55
{r | r < 11}